The interpretation called Relational Quantum Mechanics comes somewhat close in that it proposes physical variables only take values during interactions between multiple systems. You could stretch that and say a system only "exists" when its physical variables take values. But it's a stretch. And it's only an interpretation, one of several that are empirically equivalent.
Not only does that premise not come from quantum physics, but it is explicitly contradicted by it. The only thing that objective collapse interpretations say is that a system changes state when you observe it, not that it doesn't exist at all before hand. And on interpretations without objective collapse, nothing special happens at all when you observe something.
Well, Bohr and Heisenberg were anti-realists. They didn't believe in an objective reality independent of observation. And they argued that the properties of quantum particles only exist when measured and are shaped by the act of measurement itself. But Schrödinger and his feline thought experiment effectively called bullshit on that idea. ;-)
As far as I understand, it was not that much about philosophy originally, it's just that in the beginning (and up until Everett in the 70s) no one realized that measurement is mathematically indistinguishable from entanglement. So there was an obvious question: why don't we see objects in superposition, and it had an obvious answer: we have this measurement thing that collapses the wavefunction. Except it turns out that this is completely unnecessary because brains are incredibly hot and can't exist in anything else than a simple mixture of pure classical states and so can't perceive superpositions.
What's especially interesting about it is that's a real world instance of the grue/bleen problem (https://en.wikipedia.org/wiki/New_riddle_of_induction). If you start with the traditional QM, then proposing Many-Worlds seems like an unnecessary complication and multiplication of entities, rather than cutting out an unnecessary and unfalsifiable physical mechanism.
> ...it's just that in the beginning (and up until Everett in the 70s) no one realized that measurement is mathematically indistinguishable from entanglement.
Huh?
Entanglement itself does not require measurement — it simply describes a nonlocal correlation between particles. Measurement destroys superposition by forcing an outcome. With two entangled particles, when one is measured, its wave function collapses, instantly determining the state of the other entangled particle (at faster than the speed of light, as confirmed by several key experiments).
We're still left with the question of why an observation/measurement by our incredibly hot brains can collapse the waveform of a particle. To quote Sabine Hossenfelder...
"The measurement problem, then, is that the collapse of the wave-function is incompatible with the Schrödinger equation. It isn’t merely that we do not know how to derive it from the Schrödinger equation, it’s that it actually contradicts the Schrödinger equation. The easiest way to see this is to note that the Schrödinger equation is linear while the measurement process is non-linear. This strongly suggests that the measurement is an effective description of some underlying non-linear process, something we haven’t yet figured out."
"Observe" is a loaded term. I've always heard it as interaction. The quantum state doesn't decohere until it bumps into some other object. When two particles collide, no one has to be watching for them to decohere.
If that were the case, there wouldn't be any superpositions, since they'd all already be collapsed by God's observation. Also, something like the Everettian interpretation - where the wave function collapsing when observed is an illusion - is probably true.
I think perhaps you missed the bit where the simplicity penalty applies to the hypothesis, not the results. If a simple mathematical structure leads to an absurdly large number of different realities, it's still a simple mathematical structure.
We know from experiments that particles in superposition- particles that are simultaneously doing two different things- exist. Whenever stuff interacts with those particles, they go into superposition as well- so, you get a sort of expanding bubble of stuff in superposition. Those bubbles are like a tiny multiverse, with one set of stuff doing one thing, and another initially identical set of stuff diverging to do something else.
When those bubbles get large enough to interact with an observer, we know- also from experiment- that that tiny "multiverse" appears to collapse into just one of the simultaneous sets of stuff, selected at random. The classic Copenhagen interpretation just describes that collapse mathematically and treats any speculation about what it might imply as beyond the scope of QM. The Everettian/Many Worlds interpretation, however, argues that we ought to think about the implications- and the simple and straightforward interpretation of the evidence is that there's actually nothing special about observers. When the bubble of stuff in superposition expands into an observer, that observer just also goes into superposition. It only appears to collapse from the observer's perspective because the observer is now split into two versions, and each one sees just one set of stuff.
So, there are actually vastly more parallel worlds than eight billion in the Everettian interpretation, but it passes Occam's razor because it's just a very simple and straightforward implication of the evidence, without any extra assumptions about things like observers being metaphysically special or superpositions spontaneously collapsing when they get large enough, which we don't actually have any evidence for.
The premise of MW is that standard QM is itself evidence of multiverses- that it just straightforwardly implies MW, and we only avoid that by assuming stuff that the evidence doesn't imply, like wave functions spontaneously collapsing.
Why do you think it doesn't solve the measurement problem? It seems pretty intuitive that if you yourself are in superposition, each version of you is only going to be able to make one definite measurement.
Granted, there is also the weirdness of probability amplitudes in MW- if you have a superposition that's 70% one way and 30% another way, then MW argues that you get universes with 70% and 30% "measure", but it's very unclear (to me at least) what that "measure" would mean ontologically. Is that what you're referring to?
The bigger problem with measure is that it's not immediately obvious where the Born probabilities come from. This isn't a huge problem though, since similar problems of the probability of being a particular being arise due to the Sleeping Beauty problem regardless, and also there are some proofs out there about how Born probabilities are the only reasonable option/the only option that avoids Dutch books.
Oh, there would be far more than 8 billion realities, but this is independent of how many people are currently alive. All of the 8 billion people in the reality you are observing are in the same reality as you. However, every physical interaction creates exponentially more "realities", each with its own copy of the 8 billion people.
All possibilities existing is simpler than a smaller finite number you can completely describe it in less words. It's the total information content that matters.
An "observer" in quantum mechanics does not entail a conscious being. A photon is a typical observer. It observes by bouncing off an object or being absorbed by it.
No, I think Kurt is just describing the physics completely accurately. It's called observers because you have to use the photon (or whatever) to check the result of the experiment.
I consider objective collapse theories more promising, personally, since many-worlds, like it says, implies not only a multiverse but a multiverse that bifurcates with nearly infinite frequency.
I favor objective collapse less than /all/ of the alternatives, I think; if not MW, then epistemic and hidden-variable interpretations still seem more promising. Hard to tell what will come out on top in the end, though; I hope I live long enough to see it.
BTW: to anyone interested, I recommend Tegmark's book wholeheartedly. It isn't just a pitch for his hypothesis, but gets into a lot of other neat ideas and explains some foundational concepts very well.
What's your objection to objective-collapse theories, out of interest? One which doesn't register when it comes to octilions of fresh universes manifesting within a mole of hydrogen every nanosecond?
Many worlds does not imply any bifurcation - there's only ever one world. Its "splitting" is a thermodynamic phenomenon where contact with a heat bath (for instance, us) drives a superposed state into a mixture of its interaction eigenstates (with roughly definite energies, etc). The fundamental physics is just schrodinger's law, always and everywhere.
I haven't read the original Everett paper, but the summaries of it say he did posit bifurcations. Can you provide a link to where you're getting your interpretation from?
If you define the single 'world' as an ever-complexifying superposition of everything that could possibly have observably happened within that world, yes.
Theres more than one version of many worlds . In the version where splitting is decoherence, and therefore relatively macroscopic, the worlds are the decohered branches.
Theres more than one version of many worlds . The version where microscopic events lead to fully non-interacting (decohered) universes has some problems, such as predicting that quanfum computation cannot.work.
MWI allows quantum computation just fine, it just says (like every other interpretation) that you have to keep your quantum state from decohering with the outside world for the duration of the computation.
> No, I think Kurt is just describing the physics completely accurately. It's called observers because you have to use the photon (or whatever) to check the result of the experiment.
Mostly, but it would be slightly more correct to say that QM has no intrinsic notion of an "observer" - it has *observations*, which are just a conventional label for certain sorts of interactions.
The MWI doesn't solve the measurement problem. Wave function collapse is not described by the Schrödinger equation. The wave function collapse is a non-linear event, and when the measurement bifurcates the universe, we still have to explain why a particle went through a beam splitter in one direction in one universe and the other direction in the other upon measurement in either of the bifurcations.
You don't have to explain a certain objective state of affairs, because you have no idea what it is beyond your observations.
What you have to.explain is the nature of observations...why observers make unambiguous observations, in a classical basis. That does t have to be explained by collapse, but it can't be explained by, observers remaining in coherent superposition with themselves.
Not really. A photon alone does not necessarily cause the wavefunction to collapse and so imply an observation has taken place. We don't really know what counts as an observation and its one of the big open questions of fundamental physics.
Many worlds can sidestep the question, but its not as widely accepted by physicists as much online discussion would have you believe.
*Measurement* is the production of a sharp value or "pointer state". That is more general than observation by a human, but less general.than any interaction whatsoever.
The "observer" isn't the point. What matters is that a causality chain is triggered and this locks in the state that causes. Once the information has got out of the quantum world we're stuck with it in our world. "Observation" is just a short way of saying this.
That relies on a fundamental misunderstanding of quantum physics. There's nothing requiring an "observer" to be conscious. It's just any macro-scale object that interacts with the system.
No, George isn't making shit up. That was Bohr and Heisenberg's belief. And modern versions of the Copenhagen Interpretation sorta kinda imply this. NB: I don't buy it, but some do.
If it required the observer to be conscious, they'd be using that to find out if animals are conscious. Or if people in comas are conscious. Except they wouldn't even know it's specifically "consciousness" that matters, because how do you even verify that?
If it can perfectly discard the data, it wouldn't count. If it does it imperfectly and ends up in a different state, then even if a human doesn't look at it, it will count. This is why making quantum computers is so hard. You can do cool calculations by having the computer end up in the same state via different calculations and interfere with itself, but only if it ends up in truly the same state.
On the contrary: if we accept both of the following premises:
1. Any observation causes superpositions to collapse down into singular eigenstates.
2. There is an all-seeing God that is simultaneously observing the whole universe, all the time.
then it would be impossible for superpositions to form in the first place, and impossible for humans to learn about those features of quantum mechanics at all. Also, accepting the first premise "nothing exists until it's observed" is simply wrong. "No preferred basis is chosen and no system is ever in a singular eigenstate until it's observed" doesn't actually have the same ring to it, but it's a more faithful translation of that interpretation of physics into English.
I believe Shay's argument was that God is constantly observing everything that happens in the universe, and therefore causing the waveform to always collapse. I think your argument is more pantheistic (i.e, God *is* the waveform of the universe, or the latter is a thought within the former.)
How would we know that then, if there was a universal observer, than everything would have been observed from the very beginning and we would never see a transition state?
But if God observes everything at once then doesn't that preclude any quantum behaviour? Everything would be in a collapsed state won't it? Come to think of it, that might be another proof of his non-existence, at least as an "all seeing" being.
Not sure how conventional it is, or even correct, but I like to think of a quantum state as a system rapidly (compared with its surroundings) evolving, ultimately via some internal logic, through a finite number of possible "arrangements" so simple in the possible numbers and values of its relevant degrees of freedom that any arrangement can recur often enough that the system can be considered extrinsically as not moving forward in time, just ambling in a sort of timeless state like a one armed bandit with spinning wheels.
Only when it combines with a larger ensemble with many more relevant states, i.e. "is observed", does the chance of a combined state recurring reduce to effectively zero can it said to be advancing in time along with the larger ensemble and therefore, in that sense participating in the combined ensemble's existence.
How so? From what I understand, Matthew's view is that God creates a large multiverse but puts souls into the universe best suited for them. This is unlikely to be a universe where inductive reasoning breaks down.
Shouldn’t that go in an ‘Answer to Job’ type direction? Once all the permutations of souls in first-choice universes have been exhausted, we get second and third-best and so on. Eventually you land at infinite non inductive universes with souls that would slightly prefer induction. Which seems isomorphic to the Tegmark theory’s breakdown.
Sorry, I'm unfamiliar with 'Answers to Job'. What are you referring to? Your point sounds right to me but I'm not sure how to reason about infinity here. But I don't think that Matthew believes God creates every possible world (every computable math object in Tegmark's view), only "all possible people who he could give a good life" as he says in that article.
I think my life would still count as more good than bad if everything turned into marshmallows tomorrow, so don't see why God couldn't put me in a non-inductive universe like that, even if my life would be marginally better in an inductive one.
His latest one involves postulating the existence of “archons”, connection building, “difference-making”, and a hunch of other considerations which you can check out for yourself.
This kind of theodicy undermines induction in two ways
1) it allows the world to be radically evil in an arbitrary way and still “justified”. If infinite factory farm & wild animal torture & genocides are fine, why not make everyone’s induction fail? That doesn’t seem egregiously worse than hundreds of billions of animals being tortured for every second of their lives. Even if it was worse, there’s no reason why the reasons why evil is justified would not apply to theodicy. Indeed, this theodicy seems to directly *predict* a breakdown in induction, because the “archons” have *failed* to create a good universe.
2) More broadly, this *kind* of theodicy undermines moral induction. Whenever Matthew makes his monthly theodicy switch, it seems like he’s contriving an explanation that explains away all the bad things in favor of some abstract infinite good. If there are many competing theodicies like this, then when one endorses the entire category of theodicies as worthwhile, they are essentially saying “the world is terrible, and I don’t know why, but I am willing to believe that every atrocity somehow makes the world infinitely more valuable for it”. The problem, of course, is that this justifies doing literally anything, because you've already pre-committed to believing that every atrocity has some unknowable justification which makes it right in the end.
Matthew himself made this second argument when he was an atheist. I found it quite persuasive…
I only re-skimmed the article but I think archons are tasked with "making this world very good", not creating the universe itself, and so cannot create induction-undermining worlds.
But either way, one could reject that theodicy and still accept Matthew's anthropic argument.
> "making this world very good", not creating the universe itself
I understood material universe and world to be essentially interchangable (aren’t they so in Gnosticism?). Regardless, it seems like “does this world obey induction” would be part of making a “good world.”
If induction wasn’t, then the anthropic argument certainly undermines induction, because the only other explanation for why all the “””unsetly many””” people are in worlds with induction is that induction is necessary for the Good…
We can of course reject this specific theodicy, but the moral induction problem is common to most any theodicy which assumes the “unsetly many people” version of the anthropic argument.
Sorry, to clarify: the distinction I was making was between the powers of God, who creates the universe and sets its laws (and decides whether the universe obeys induction) and those of the archons, basically minor gods tasked with protecting us from lesser evils.
Please no archons, that brings us slap bang to Gnosticism which is very much "material universe bad!"
"A Voyage to Arcturus" is the ur-Gnostic SF text for this, where the main character goes through everything and discovers that existence is a horrible trap and the only way out is death. It's a great story but very grim:
The 'archon abandonment theory' is intriguing but it's not Christian (though to be fair, I have no idea if he's trying to argue for a Christian God or just some kind of 'god exists' idea). If archons but no intervention, then that knocks out the Incarnation and the Atonement: God won't step in to clean up the archon's messes, the archons are the important difference makers (and not God) so the entire point is to create relationships of gratitude between us and the archons so we'll be best buds in eternity.
First, this assumes Western notions of "you saved my life, I am eternally grateful to you and feel positive emotions to you". In other cultures, I am given to understand, such an intervention is considered instead in the form of a debt, and the rescuer now incurs obligations towards the one they have saved, while the saved person does not have gratitude but rather expectation from then on of constant intervention. 'You saved me, now you're responsible for me' like a pet or small child because the rescuer took on the role of caretaker and authority (If I'm wrong, correct me). This doesn't augur well for building a positive relationship for eternity.
Second, if you have archons (powerful demiurgic beings who can affect the physical reality), why do you need God? That's just a step too far for the sake of explanation. The world as we see it is messed up because the powerful beings are not all-powerful, all-knowing, and all-benevolent; they may intend well but fall short in execution, or they may not like us particularly much at any given time. It's an argument for pantheons but not a sole creator God.
There's a couple other comments I could make, but I'll just remark that various late-antiquity mystic groups like the neoplatonists also believed in versions of the archons and demiurge and didn't believe they were necessarily evil so much as imperfect.
> In other cultures, I am given to understand, such an intervention is considered instead in the form of a debt, and the rescuer now incurs obligations towards the one they have saved, while the saved person does not have gratitude but rather expectation from then on of constant intervention. 'You saved me, now you're responsible for me'
Very interesting, but also feels counter-intuitive that someone saving your life would not elicit gratitude. Do you have a reference? Would love to read more about this.
No, that's wrong. Tegmark thinks the simplest way to mathematically describe a human brain is to define a universe in which induction is true, and then run it for a few billion years.
Unclear whether there's a reasonable definition of "simplest" for which this is true — see my comment elsewhere in this thread for more on that point — but the theory has definitely addressed your objection at least in principle.
I see. I read uncarefully. I didn't know Tegmark's theory gave more weight to observers in simple universes. Does he think the more complex universes are simply not instantiated? Or just that observers are more likely in universes with induction?
Imagine trying to specify a single human consciousness, using a string of mathematical symbols.
One approach would be to write out the location of every particle in a particular human brain — but this would take, at minimum, billions of symbols.
There's a much quicker approach. Take is as a given that the laws of physics and initial state of our universe can be described in just a few thousand symbols. If so, we can write out that description and add a date and a location pointing to one of the actual human brains that exist in our world, and we've managed to "compress" our brain specification by many, many orders of magnitude.
The brain that gets specified from scratch will not experience induction. But the brain that emerges out of a full, simulated universe will.
The only premise you need is "shorter strings of mathematical symbols are more likely."
You can write locations of a three bodies and gravity equation and still will not be able to solve it. Are we looking for exact or good enough solution or just trying to describe things correctly?
Universal theory attempts to unify all kinds of physical interactions. We could consider such interactions as a type of observation of different kind of unconscious mathematical objects (protons, gravitons, etc) described by respective math equations. Add conscious observer here. What we really need is a universal observer theory
You will not be able to solve it exactly by writing down *human* mathematical symbols, or by calculating it on a *finite precision* computer. Nothing sets these constraints on the universe, in fact differential equations of the three-body problem + starting conditions are perfectly good enough to exactly specify the end state of the system. The universe can work in the language of math itself, not in whatever we humans use to describe it.
Why couldn't a conscious observer be a weird and complicated emergent property, in the same way superconductors are for example?
You mean I can't have a "simple" human readable analytical "solution" to it, although can describe interaction and initial conditions.
If you have studied computational maths and have encountered computational grids and the accuracy of numerical representation of numbers, you would know that it is the numerical methods themselves that introduce error, not just the accuracy of the initial conditions.
So both current numerical (simulation) and analytical apparatus does not give good predictive power. Although description is complete. Probably we just don't talk universe language good enough at the moment. Conscious singularity awaits
Besides which, there's no reason to argue that simplicity is more probable if every mathematical structure is real. All you need to argue is that simpler objects are more likely to be embedded within other objects of finite complexity, and I think this is obvious.
By definition of randomness, the location of the Boltzman brain inside it would have to contain as much information as the full description of the brain itself. Same as the old party trick of "compressing" numbers by looking them up in the digits of π
That reminds me of a problem with Solomonoff induction.
If the program running the SWE outputs all bits of information about all worlds on a single output tape, they are going to have to be concatenated or interleaved somehow. Which means that to make use of the information, the operator/interpreter, has to identify the subset of bits relating to your world. That's extra complexity which isn't accounted for in the standard argument fur computational simplicity, because the standard argument only asked what the Solomonoff induction does....the computation performed by the operator/interpreter is overlooked because it's being done by hand, as it were..
The SI argument for MWI only *seems* to work because it encourages the reader to neglect the complexity implicit in interpreting the output tape. If you account for the "de interleaving" , then the total complexity is exactly the same as Copenhagen *and that's the point*.
I don't think that weighting for simplicity works for reasons I give in section 2 https://benthams.substack.com/p/the-ultimate-guide-to-the-anthropic. I don't think it makes much sense to talk about the share of an infinite multiverse with some property, especially if all the worlds are spatiotemporally disconnected. There are just unsetly many of each kind.
If you're working with a finite set of logical operations with which to define a mathematical structure, then in principle you could organise all your structures into the nodes of a decision tree. The tree would expand infinitely, but the nodes in each finite 'tier' would be closer to the root, and therefore 'simpler'.
I'm not sure if that's compatible with the observed physics of our own universe, though.
There's no reason our universe should be taken as the measure. The argument is that all mathematical objects are real, not that they are all observable within out universe. So that's merely an argument that our universe isn't a maximally probable one, which seems quite plausible. (The observable improbabilities are one of the reasons I believe in the EWG multi-verse, though this theory would override that reason.)
Tegmark did originally propose the theory as a potential explanation for our own universe, so if it fails to explain what we can observe in our own universe then it fails in its original purpose.
...but in any case, couldn't the space of all mathematical structures generate some form of singular intelligence (i.e, 'God') before it generates physical universes? We don't really have a complete understanding of the laws governing either physics or intelligence at the moment, but it's possible the latter are simpler and require less fine-tuning than the former.
Well, the standard approach is to divide the specified domain into two pieces, each of which is a self-consistent mathematical object. (Of course, some other statement will exist in each of those that has the same objection. So you get an infinite tree.)
Multiverse theories often assume that there is some kind of separation between parts where different rules.apy, but separation, or lack therefore, are themselves mathematical structures, so a mathematical multiverse should have every combination of separation and overlay.
But simplicity isn't especially relevant if *all* mathematical objects necessarily exist. Then the simplest ones won't actually dominate - there are many more complex things than simple ones, so you should expect to be in a complex one.
I we want to talk about probabilities (e.g. the probability of finding ourselves in a relatively simple universe), we need some kind of *measure*.
Imagine that you have to choose a random natural number. You can't give each of them the *same* probability, because there are infinitely many natural numbers, so the probability of each of them would be... zero? But that doesn't add up to 1.
Instead, no matter what algorithm you choose for finding "random natural numbers", relatively small numbers will be vastly over-represented. That's because, no matter how insanely large number you choose, almost all natural numbers are insanely larger than that.
At the end, the only way to choose is to somehow give smaller numbers a greater chance. How much greater, that's up to you. But you can't give all natural numbers the same change, that is just mathematically impossible.
...and I think some similar logic also applies to universes as mathematical objects. The simpler ones must be more likely, because there is no other way to make all probabilities add up to 100%.
It's true that induction is not, like, a law of logic. But a view that implies that we cannot be confident the sun will rise tomorrow is almost surely false.
Happy to bet on whether the sun will rise tomorrow :).
The trouble with induction is that our confidence in induction itself derives from induction. (Induction has worked so often before, so....) The good thing about induction is that our faith in it is almost never misplaced.
>The trouble with induction is that our confidence in induction itself derives from induction
There is no trouble if we frame it the right way IMO. This is exactly how axioms are true: why is an axiom a true? Because axioms are true. Why are axioms true? Because it is an axiom that axioms are true... And so on. Without this self reliance, there is no logic. For derived statements, we need proof from other statements where the chain of proof doesn't include itself, the thing we call circularity. But this requirement is tjere for axioms. So we don't allow for circularity for derived statements because doing so would make them (and all the other statements in the cycle) axioms, which is not consistent with them being derived.
From a logical perspective, that is all you need to believe induction is true. But the fact that induction holds in reality is a property of the reality we live in, and is consistent with the logical truth of induction - making science possible and compatible with logic making reality legible to logic.
So the way to look at it is "inductive logic exists, and applying it to reality doesn't cause a contradiction (this is an observation only), and since this application causes no contradiction, we can apply inductive logic to reality as long as this observation holds..
In this view, there is no trouble with induction since induction is not used to justify induction. Axiomatic truth is used to justify induction in a logical sense. And the apparent consistency of the inductive axiom with reality lets us extend inductive logic into what we call science.
We do this with deductive logic as well. The + operator adds two mathematical objects called numbers. But we still use it to add apples because the application doesn't introduce a contradiction.
Doesn't this resolve the "trouble with induction?"
It can't be justified within bivalent deductive logic....but it's supposed to be a separate magisterium anyway. It likely can be justified by probabilistic logic. That what Bayes is a about.
Right, because... he's not relevant here. Bayes operates within the assumptions that anti-inductivism precludes. Like, you're saying "the plans for the top floor penthouse are perfectly structurally sound!" while ignoring that the building has no foundation.
I don't see what you mean. The weakness of Bayes is that priors can be pulled out of your posterior. The strength is that if your priors are wrong, you can correct them , given sufficient evidence, so you don't actually have the "weak foundation" problem.
I thought the whole argument for modal realism is that stuff like induction doesn't work *without* it? In order to make any kind of generalized inference you need to be able to say which situations are similar enough that you can generalize to them, and (according to modal realists) there's no objective criterion for this unless there are literally multiple universes arranged by similarity.
(The actual answer is that we do this heuristically and the universe is simple enough we can get away with it.)
Beyond that, it's not clear what is even meant by "undermining induction". Does it mean that inductive reasoning doesn't always lead to truth? Does it mean that most of generalizations that could be made are wrong? Does it mean that there is not a single example of correct inductive reasoning?
The former two cases are true in our world. The latter one is logically inconsistent: "induction has never worked before, therefore induction in general doesn't work" - would be an example of correct inductive reasoning.
If I recall correctly, this is the exact premise of Greg Egan's PERMUTATION CITY. All possible mathematical universes exist, so if you want to want to run an eternal simulation, all you have to do is run it, upload a copy of yourself, have the copy confirm that it *is* in fact being simulated, and then turn it off. The copy - in a mathematical version of quantum immortality - will continue existing in the simulated universe regardless of whether it exists or not.
The person that you will be in ten years already exists (in this schema), infinitely times over with infinite variations. If the instance of you that you are now is hit by a bus tomorrow, those other instances will still exist - but you now would still like to live to experience all that "yourself". What's more, you'd like the version of you in ten years that you eventually experience to be a good version who's healthy & happy - if there were a way to deliberately select among the local branches of possibility space for one you preferred, you might do so, even if that doesn't result in anything "new" existing in the multiverse apart from your conscious existence now being causally connected to a future you want to experience.
Similarly, if you could causally connect your conscious experience now with a future experience that takes place in a fundamentally different universe with different laws, you might prefer that, and try to upload yourself into a simulation world of your choice - even if that act doesn't create anything new in the multiverse, still you-as-you-are-now might feel you have gained something by "switching" your consciousness from one causal path through possibility space to another (even though that path always exists & existed, even though there remains a you that didn't switch, even though it's possible that you-now has in fact no meaningful claim to be identified with any other instance of you including yesterday's you & tomorrow's you and that there is in fact only ever this one conscious moment as it is happening..)
Language is hard in these areas. I'm saying people would want to try to manipulate their measure, feeling like they are changing something for the better for themselves - whether or not that is true, or even meaningful.
Imagine a latent space of all possible mind states. Your life is a line in that space. In the mathematical multiverse, there's an infinite number of cellular automata who have sentient beings in their initial state. Some of them have memories of a previous life in a regular universe. Some of those are very very similar to you.
The purpose of the ceremony is to bend your lifeline towards one of those starting points and form a continuity. From your subjective experience, you didn't die; you just transitioned from one universe to another.
This is actually addressed in the book, the characters sort of shrug their shoulders and reason that perhaps a computer program needs a kick start before it's truly instantiated as a mathematical object, or maybe not, but might as well cover all bases.
I think we could wave our hands a bit better than Eagan does here: If you wish to find yourself in a particular computer program you should act to maximize the number of observer moments you experience within that program. By running the program for a finite amount of time you increase the odds that any given universe whose rules allow for embedding arbitrary unlimited computations, such as the game of life, also simulates the program.
The way I like to think of it is that you're not modifying the simulation, you're modifying yourself to create the possibility that your own subjective consciousness makes the transition into the simulation. After all, if you never get uploaded you probably won't later be a simulation that remembers getting uploaded. It's still a handwave over practical problems with perfect uploads and philosophical questions about the continuity of consciousness, but it resolves the potential plot hole.
Both the simulation and the uploader's universe are timeless, but the uploader hopes to align their mind-state so closely with their simulated self that their *subjective* conscious experience actually crosses from one to the other, i.e. go to sleep in the upload facility and wake up in the simulation, having transitioned from one to the other. This has a lot in common with the many-worlds quantum interpretation - but instead of particle interactions leading to branching worldlines, it's done by actually copying the mind. If we could do so, who is to say that the subjective experience would automatically follow the original body?
In a philosophical sense, continuity of identity/experience. The 'you' who is still in your physical body will have an easier time being comforted by the simulation and convinced that it represents yourself achieving immorality if you observe the event where it 'splits' from your body and can interact with it and confirm it to be a continuation of your self and experiences.
In practical terms, because the person who came up with the idea in the story wants to make money, so they market it as a crucial step to rich people they want to sell that service to.
This was the first thing that came to my mind. If you find the idea of mathematical universes at all interesting, I recommend reading Permutation City. Greg Egan's work in general is worth trying out because it is "different" from most science fiction, and I would say Permutation City is one of his best books.
You beat me to it. Yes, this is precisely what is posited in "Permutation City".
(Spoiler Alert)
The twist in the novel (IIRC) that really got to me was this idea: yes, every possible Universe (or Cellular Automata rules + init conditions) exists in possibility space; but what we can do to sorta sweeten the deal is run as many iterations as we can in our present Universe, I guess just to -- somehow kickstart the process? And I think there was an uploading component too... Egan was (is) a real gem of a SF writer IMSHO
Yeah, this (or at least a very similar) hypothesis is called "Dust Theory" or "hypothesis of the dust" in the novel (which btw predates Tegmark by quite a bit, having been published in 1994). One of the reasons why (at least early) Egan is my favorite sci-fi author is how the theory is developed as an extended thought (and fictional empirical) experiment during the first half of the novel - if you accept the premise of mind uploading (which, of course, is quite a high ask for most people), a quite convincing case for the hypothesis flows from there (though maybe not aa quite airtight case, as the FAQ below suggests).
It should be noted that Egan has stated that he doesn't really believe in Dust Theory himself; some discussion here: https://www.gregegan.net/PERMUTATION/FAQ/FAQ.html. The reason presented (as I understand it) is that the "lawfulness" of our universe seems to run counter to the teory's predictions; for every version of me that experiences events moving forward according to well-defined laws, there should by gazillion versions of me whose surroundings are a roiling chaos. I personally have wondered for a long time whether this is really the case; as long as you include some form of bias towards simplicity discussed in the post (which the theory probably has to do if it's to be able to make any predictions at all), would it be simpler to have an universe evolving according to parsimonious laws, instead of having to specify a locus of order containing a sentient observer surrounded by chaos?
Some of the arguments go something like, “X is true; no non-theistic hypothesis could explain X; therefore god exists”. The fact that this is a non-theistic argument that explains X is sufficient to obviate these arguments, even if we don’t know whether it’s true.
So? There's lots of ways to trivially knock out large numbers of God hypotheses. This is one of the points of steelmanning: most of the probability mass for any large class of hypotheses is probably concentrated in the handful of most likely versions. The hypotheses (whether they include or exclude a God) that were trivially wrong, very few people believe in, *because* they're easily disproven. Unless you address the strongest versions of atheism, you can only at best provide very weak evidence for theism.
That's just cancelling sophistry with more sophistry IMO. What set of axioms allow you to logically demonstrate that "no non-theistic hypothesis could explain X"?
"I can't think of a reason why this is false" isn't a good argument that something is true.
>We’re not dealing with axiomatic formal proofs in most of these cases
Agreed, which is why philosophers shouldn't use rhetoric that borrows from those concepts. "I don't see why this is false" is indeed a good starting point, but IMO the sophistry comes from failing to understand that without a deductive axiomatic system that's all it is. That's why God-of-the-gaps arguments have a very poor historical track record.
But ultimately you have to pick some hypothesis to believe! If not the mathematical universe, then you need to justify why some other metaphysical theory is more plausible.
For example some would contend that there are several kinds of 'existence'. Commonly two, 'physical matter' AND 'mathematical truths'. But that posits two arbitrary assumptions about what things exist, one more than mathematical universe.
Others might posit there is just physical matter and math is just a property of physical matter, but that runs into its own host of problems.
The reason to find the mathematical universe hypothesis neat is its simplicity in comparison to other metaphysical theories of existence.
> But ultimately you have to pick some hypothesis to believe! If not the mathematical universe, then you need to justify why some other metaphysical theory is more plausible.
Errr no, you can say this is how far I know, and beyond that I have no way to tell. It's the most honest answer.
> Others might posit there is just physical matter and math is just a property of physical matter, but that runs into its own host of problems.
What problems does that run into?
To me that seems like the most intuitive answer. I posit that math is an abstract tool invented by humans to describe physical matter and the underlying laws of physics of the universe. Maths is used to model the universe and can only ever be an approximation of reality. For example, in order to add two apples (or atoms, or any indivisible unit) you first have to posit that the two objects are the same in some sense. This is an abstraction, since every object has different matter and does not occupy the same space. They are equal and can be added only because we first make categories.
My point is that math is not a fundamental property of anything physical. The fundamental laws of physics may or may not be simple and easily described by math- we don't know. What we do know is that the aggregate effect of the underlying laws of physics may often be well described by mathematics, and seem to be deterministic, i.e. the same initial conditions gives the same end state every time on large scales. (However this is also dubious for some chaotic systems, like turbulence).
I'm not sure simplicity (in the manner that you mean it) is the best measure for actually adopting a paradigm. The best measure would be commensurabilty with itself, which I don't think works with this any better than solipsism (which I think is the main contender against the ism in terms of a "metaphysical theory of existence" as you put it)
I believe something rather close to this and to me it points directly to God. I won’t have time to write it up, but basically I put God very far away and beneath things.
I'm right there with you. God is the the isness that is inherent in mathematics and mathematical structures. This God doesn't really have a mind or act. It is the breath of life, raw possibility. But I also think there's an endless chain of superintelligences simulating superintelligences and down at the bottom is us. That's more like an active component of God, defined in the linked article, which is my favorite article by Scott.
I read the book when it came out. That all possible realities exist is, by definition, next to the most horrible thought that one can have (the most horrible one would be that only horrible ones exist). Everything extremely bad you can imagine and worse is happening somewhere. I really don't want to believe this.
Allow me to offer some consolation. The existence of hellish worlds in Tegmark's multiverse is indeed a frightening implication. If you suppose there's a statistical distribution of worlds with conscious life, where most are mediocre worlds, you'll notice that the hellish & heavenly extremes will be extraordinarily rare. Is it reasonable to suppose such a distribution? I think so -- most times and places in our world are pretty mundane, but a few situations have arisen that were hellish or heavenly. And those are pretty rare even considering they're natural sorts of "hellish" and "heavenly", nothing anywhere near the extremes that religious imagery calls to mind.
And what's more, statistics isn't the only way to look at it. We need to look at the complexity of the axioms that generate the world, presumably using the Solomonoff prior or something analogous to it. Generating a world that hosts conscious observers requires some minimum degree of complexity. Generating a world that does that and also evolves into a large scale, stable hell requires additional complexity on top of the minimum -- and my guess is it would require a hell of a lot, pun intended. So hellish worlds would be so exponentially rare that I assume it's vastly more common in Tegmarkia to be a mind-moment that wakes in fright from a hellish "nightmare" into a mundane world, than it is to be a mind-moment that is an in-world continuation of a hell.
So if the hypothesis is true, then the chains of linked mind-moments across worlds, each chain being a conscious observer's history, are virtually all mundane.
Here's a fine-tuning argument that I haven't heard anyone make: If you assume that there is a vast part of high-dimensional parameter space that doesn't allow conscious life, and very small regions of parameter space that are conducive to conscious life, and you pick parameters at random, the large majority of livable universes will be very close to the boundary, i.e., just barely livable. (This is just the standard argument from statistical physics that in a high-dimensional space, practically all of the volume of a sphere is practically at its surface).
So taking that as an analogy, the hellish universes would be the norm, and the heavenly ones exceedingly rare in comparison.
Because of the Doomsday Argument, or a variant of it. If one assumes one's status to be picked at random from among all possible observers, one should expect an approximately average value of *any* variable of observation (not just birth order). If your own life conscious existence isn't hellish, you shouldn't expect the average conscious existence to be hellish either.
Of course, I've always thought the Doomsday Argument was utter bullshit, but when you're reasoning about something as vague as a Tegmark Universe it's not like there are many other tools available.
This is true, but also it doesn’t include agency of such things that exist there. Presumably they’d try to fix it? Or even kill themselves if they couldn’t? (a feature of agency, too)
The vast majority of environments in our own universe make life impossible (i.e, they're either inside stars or a total vacuum), so one can argue that our universe is only 'barely' livable. That doesn't mean it's filled with sentient life locked in a state of perpetual suffering, you just get tiny pockets of regular sentient life.
'Hell' is essentially a state where all the sensory indicators of life imminently collapsing are somehow sustained on a vast scale in time and space- i.e, it's highly artificial. Maybe it wouldn't break the laws of physics per se, or the set of all possible laws of physics, but I can't see it being a naturally-occurring norm wherever you get sentience.
I feel like one could even use this idea as an argument in favor of Tegmark's theory. If we are in a random mathematical universe (conditioned on it being capable of supporting intelligent life), then to FluffyBuffalo's point it is likely to be something that is "on the edge", just barely capable of supporting life, since within a high-dimensional probability space most of the volume is near the surface.
And that is seemingly just what we find in our actual universe. Almost none of it is habitable. There seems to be no other intelligent living beings within communication distance. There are lots of physical constants that had they been slightly different life would be impossible. Etc.
It seems that truly bad universes would be self destructive. The most likely universe will be some proportion of hell that's sustainable, like 50% hell 50% heaven. Isn't this where we live in? There is plenty of evil and suffering in the world, or in every person's life.
Is this what religions are about after all? The constant battle of good vs evil that has to exist just because it's statistically likely. Especialy when hell is relative, even in a 95% heaven universe you'll still think you have plenty of evil to fight.
But if *everything* that can happen has happened, then there is no statistical distribution, everything imaginable exists, even the very improbable ones. What do I miss?
As in Scott's main post, the usual answer is that the distribution involves a simplicity prior. The chief argument for a simplicity prior's necessity is the fact that *any* prior over mathematical objects will necessarily give more complex objects less probability mass, on average.
While it's correct, I personally find the answer a little unsatisfactory on its own without an explanation of how the distribution arises. The most intuitive explanation (in my opinion) is to consider embedded universes. A larger mathematical object can contain smaller ones embedded within it. The simpler the object, the more places it is embedded. Search "Ramsey theory" to see the relevant kind math I have in mind; it studies the conditions under which certain orderly properties must necessarily appear in sufficiently large structures. By analogy, suppose universe A is sufficiently simpler than universe B that it is embedded in twice as many larger mathematical objects. Then I find it very intuitive to suppose universe A has twice the probability mass of universe B.
Every universe is embedded an infinite number of times, but some (the simpler ones) have a greater measure of the total. This lets us assume a more intuitive uniform distribution over mind-moments while still getting a simplicity prior over universes as a consequence. By analogy, on the real number line, there are infinitely many points in [0,1] as in [1,3], but the latter interval has twice the measure, and given a uniform distribution over the infinite points of the intervals, you're twice as likely to get a sample from the latter.
I haven’t read the book, but wouldn’t it also imply that greatest universes with all the best things are happening also exist? I suppose this would be horrible for negative utilitarians, but otherwise, most people would think the good and the bad cancel each other out.
Not necessarily. There are probably Everett branches of our universe that are hellish, but it seems unlikely that our planet would become so hellish. Likewise, the simplicity prior might assign negligible measure to hellish worlds.
It says that all possible starting conditions exist, but what happens from there follows physical laws. You don't get all possible realities, you get all realities that could follow in a rules-based way form the set of all starting conditions and all rule sets.
So if you believe, for example, that charity and benevolence tend to evolve in high-population animals for rules-based reasons regarding the adaptive benefit of cooperation and coordination, then you can expect those things to be very common across all realities.
I'm 95% confident someone else thought of this idea before Max Tegmark. It's an obvious idea. This is the aspect of the rationality community I hate. They're always reinventing the wheel, blissfully ignorant of vast cannons of human thought, and claiming originality and credit for exceedingly obvious ideas.
Yeah. It does, but it is particularly frequent among the rationality community, and it's the arrogance and self-satsifaction they have about it. Ack. So irritating...
Like, gosh, can you imagine what these (relatively) smart people could accomplish if they had just a few more standard deviations of intellectual humility.
Is it particularly frequent among the rationality community or is it the fact that they do it in a way you find irritating that which makes you think it's particularly frequent?
1. Generally professional thinkers (e.g., mathematicians, lawyers, judges, serious historians, philosophers, the founding fathers) take great care to trace the lineage of ideas. It is part of being a professional.
2. The rationality community styles itself as being almost *the" most professional thinker, in that they want to be professional in their thought not just as a means to an end, but as an end itself.
1. + 2: I get annoyed by how unprofessional they are.
So I guess the answer is, it's super way too frequent if we consider them a group of professional thinkers and judge them by those standards. Or, we judge them by random internet standards and then it is the manner in which they do it (i.e., while claiming to be serious about thought).
Like of your the knitting society and you don't take care tracing the lineage of ideas, that's to be expected. But if you are the *thinking society* then I expect more from you
Why is your expectation that a thinking society have knowledge of lineages a reasonable one? Knowing about lineages is much more about respectability and the appearance of deference to more prestious apes, why should a thinking group cave to such a base and disgusting urge?
This interests me quite a bit. Could you say how this tracing can be done, especially for subjects that one is new to? Is it just reading a lot around the subject? Is that generally a good ROI, or just a necessary cost? Anything more efficient than that? Asking LLMs helps to some extent, though not for more obscure knowledge. Would another option be to try to reach out to other people knowledgeable about a subject? Seems potentially imposing. Any other ways?
Timaeus 53c-55c argues that the necessary existence of particular geometric shapes on a 2D plane with a set of simple starting conditions will unfold by the increasing complexity of relations between those shapes into all observed natural phenomena (fire cannot become earth because earth is made of isosceles triangles, you see)
Max Tegmark isn't "some rationalist", he's professor of physics at MIT. Who better to think of a new theory?
And I'm impressed that you're managing to go into raptures of hatred based on "assuming" someone invented this even though you don't know who and had apparently never heard it before. Cellular automata and Kolmogorov complexity are both pretty new, I don't see why he couldn't be the first person to combine them in this way.
I suppose it's too much to ask to just be grateful you learned something new today?
I mean, I had the idea of "every mathematical structure that could exist does in some sense exist" i.e., plato + "everything can be expressed in the language of maths and is as such a mathematical structure" (i.e., Feynman or so many previous people, but he has a nice quote on it) back when I was 13...
At the very least, I bet Godel thought of it...
Guess I should have written a book about this profound insight... :p
I'm unaware of any published version of Tegmark's hypothesis before his own work—which isn't to be reduced to "numbers exist (in some sense)", note. A better summation might be something like "all there is is mathematical structure, even us right now, and every mathematical structure exists in the same way". This is not what the Platonic "theory of Forms" entails.
But even this is a simplification that necessarily dispenses with a lot of the groundwork and justification. I recommend reading his book, which is pretty interesting even if you don't agree with his ultimate conclusion—in fact, most of the book isn't even about the MUH at all.
Of course, given that you've failed to acknowledge that Tegmark is in fact a PhD physicist who specializes in cosmology and not just some random "rationalist community"-member, but have instead doubled-down on the part of your comment that Scott /didn't/ directly address, I put low odds on your actually bothering to read it. But I have hope!
But I mean doesn't platonic forms encompass all maths? If you talk to any Platonist my understanding is they would say, "yep all maths exists," and if you talk to almost any logician/computer scientist and you ask them, "could any possible system be simulated in mathematics (including me)" they'd say: yep. Oh in particular, a logician would be the one saying yeah, of course all such systems are themselves part of some hierarchy of mathematical objects, etc...
Both these statements seem incredibly common place. One dates back to Plato, and the other turing / Godel and possibly earlier. I don't quite get the distinction you are making...
No problem—I /really enjoyed/ it, myself; it gets into a lot of the "big picture" cosmological questions that it's hard to find good, in-depth coverage on (most books are either pop-sci re-hashes of generalities you've heard a dozen times before, or else thick academic tomes with equations that make your... or at least /my/... head hurt just to look at 'em; Tegmark's is one of the few that's in between the extremes).
Maybe my edit was a bit too harsh, pardon me–
(I'm no fan of what a lot of "the rationalist community" turned into, but still have a knee-jerk reaction to criticisms of it in a certain tone, which I associate with a particular group of bad-faith critics. I should work on that, maybe...)
Re: Platonism: No, I don't think that's /exactly/ the same, although there are certainly some deep similarities between them and I can see why some might be tempted to identify the two:
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Plato: Our world is a "shadow" of a world of ideal Forms, which we perceive dimly through their material instantiations and through intellectual contemplation upon them. Numbers are Forms (maybe; I dimly recall something about a fight between Pythagoreans and Platonists on number, and IIRC the Neoplatonic "principle of Unity" isn't to be confused with "1"), but there's also a Form of a chair, of Redness, of... etc.
Tegmark: Mathematical structures exist, but not in the Platonic sense; rather, in the same sense we do—in fact, they're /all/ that exists. All we see and experience is a mathematical structure, no different from that of "the integers"; ours is merely more complex. And, moreover, the rest are out there too—all is mathematical structure, and all such structures exist in the same exact way; our universe isn't privileged. There is probably a "way it feels like to be within Conway's Game of Life", and so forth, as there is a way it feels to be within our universe. (Note: IIRC he flirts with such a sort of panpsychism, but doesn't commit to it; substitute "way it feels like to be within /a much simpler structure that still supports consciousness/" if I'm wrong about this.)
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I.e., it isn't that "numbers have some sort of existence", but rather that all mathematical structures exist in the same way, and in fact this is all there is.
Following from that, re: simulating systems in consciousness: I don't think this has any bearing on the priority of Tegmark in proposing this hypothesis—it's an entirely separate question.
So if all the MUH said was "mathematical structure exists in some non-nominal sense, i.e., apart from as descriptions or games in our heads", then sure—nothin' new. But to claim the twin statements mentioned above ("...all that exists" & "all ... exist") is, I think, new.
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I'm also neglecting to include any of the work he put into motivating the hypothesis... mostly because I can't remember it, heh. I /seem to recall/ that most of the book is sort of about laying the groundwork, and if I remember aright he doesn't have many arguments that directly support the idea beyond "well why not? it's simpler, look"—but there were a few, I think. (And, of course, I may misremember, or he may have done more work on it in the meantime.)
Interesting. I've always interpreted Platonism as meaning yes they really really do exist. I.e., even if you and I and the universe never was there would still be all of mathematics. It is hard to think of a more realness than that. E.g., my naive understanding is that a Platonist would say that mathematics is in some deep sense more real than the universe.
I agree saying that the universe (i.e., our universe) is a component of such a structure is a step beyond that, but it does kinda of obviously logically follow. I would also argue that, the idea is more or less just a fancier version of the philosophy that "all that could be is in some sense somewhere," and I imagine, but do not know, that that idea probably dates back to prehistory.
P.s., no need to apologise/apology accepted. My comment was itself a knee jerk reaction :p
Note that being an accomplished physicist doesn't give one any special insight into philosophy, mathematics, or the other topics that seem most relevant to Tegmark's proposal.
Sure; I mentioned his background to point out not that he can't be wrong, but rather that it is inaccurate to characterize him as being just some random Rationalist Community Member® doing the typical Fake Expert rationalist wheel-reinventing (which was, as I interpreted it, the implication of the OP's comment).
I'm not criticising Max. I think I'm criticising your portrail of him as the likely originator of the idea, when to me, it seems clear (blindingly obvious) the idea likely has a lineage.
After all, you are adjacent to the rationality community (and I associate the way you did this eliding of lineage with the rationality community).
My apologies, it is not my intention to be rude, and they are cool ideas. I just get a bit triggered by what I associate with rationality community arrogance.
According to the wiki page Tegmark himself compares the idea to platonism and modal realism. So... yeah, there are antecedent ideas in the realm of philosophy, but I don't think he's failing to give credit either.
I'm skeptical as to whether Plato himself would have described his ideal Forms as purely mathematical constructs, though (what is the math of 'Virtue'?)
To be fair, we just learned that Cellular automata are eternal from this very post. (Actually, itʻs a bit light on the whenness)
Anyway, of course this is the case-since continuous time and mathematical concepts both belong to the cosmos and not the universe directly. There are sufficient evocative phenomena happening contemporaneously that many thousands (?) of human observers are likely discovering this for themselves effectively all at once.
He's very qualified to come up with theories. Professors do that all the time. But there's still no real evidence to support his theory. And, its actually hard to imagine what kind of evidence could plausibly support it.
This general idea isn't especially new, although the specific formulation isn't something I have spent much time thinking about. It is reminiscent of an idea from John Gribbin's, "Inflation for Beginners." (https://aether.lbl.gov/www/science/inflation-beginners.html).
Here, the idea is presented that universe creation could be fractal where each black hole in a universe spawns another universe (not accessible). If that were the case then the growth rate of universes would be severely exponential so that the age of universes would be grossly tilted towards young. It is further suggested that this might mean that a 99.99% chance of us living in the youngest universe possible to create intelligent life and that we would therefore be the only intelligent species yet alive [edit: in our specific universe].
In the book (that came out over 10 years ago) Tegmark makes it very clear he is not the first, heavily referencing Everett and his many worlds theory from the 1950s.
Everett’s theory is very different from this! Everett just says that all branches of a quantum wave function exist - Tegmark says that even mathematical structures that have nothing to do with quantum wave functions exist.
Funny thing: those "vast canons of human thought" being so vast, it's not really practical for one human to be familiar with them all. If you're doing something that's nicely easy to describe--building a bridge, painting a picture, writing a novel, designing a wheel--it's not hard to find pre-existing literature on the topic and narrow your way down to more tractable canons of human thought. But if you're doing something weird and abstract and outside the realms of what most humans discuss on a regular basis, that becomes a somewhat harder problem.
But maybe I'm overstating things and just bad at forming queries. So tell me, if you'd happened to think of this idea before Max Tegmark, and wanted to see if anyone had beaten you to the punch, how exactly would you go about checking? Keep in mind that as abstract as this is, one can hardly assume that they'd have used any standard or particular phrasing or schema. The best I can think of is "ask the right sort of expert," but I'm not 100% sure who the right sort of expert would even be. This is a serious question, by the way: "how to search for an idea without reference to the topic or use of standard keywords" is a problem I've run into before and, well, I don't actually know a solution. Has this wheel been invented?
Side note: this very much feels like another instance of the "explore-exploit" dilemma. For some area of interest, how long and how diligently should you explore the existing literature before you try doing original thinking on the topic. The answer clearly varies based on how costly exploring the existing literature actually is.
Step a) having the idea (e.g., a cake without any flour)
Step b) searching for references to things that sound similar to the idea ("no flour cake" "cake" + "celiac's rejoice")
Step c) talking to knowledgeable communities ("hey baker friend, ever heard of a cake without flour?")
The more important the idea / the more obvious seaming, the more time and effort you should spend verifying that it truly original.
For the idea described, you might first look at modern philosophers who cite Plato and or Godel. That kind of thing. You might search for the term, "everything that could exist does." Etc... or "mathematical proof"+"universe must exist" etc... you'd try to scatter gun it so that almost any impact/publication of the idea would be caught by at least one of your searches.
Doesn't really matter how you verify, but at the end of the day every diligent scientist needs to know that their idea is truly original.
Fyi, judging by another comment in this tree, Max didn't claim originality, and indeed took care to trace the thoughts roots. The thing I got annoyed by was Scott portraying this idea as original to Max, when my (vague) understanding of that thought space made it seem very clear to me that the idea likely long predated 10 years ago.
" The thing I got annoyed by was Scott portraying this idea as original to Max, when my (vague) understanding of that thought space made it seem very clear to me that the idea likely long predated 10 years ago."
I find this a reasonable attitude if and only if Tegmark was entirely regurgitating ideas others had developed, and added no content himself. That's really not the impression I have of it: I got the sense that the idea may have had earlier *roots*, but that Tegmark fleshed them out and ran with them in (at least some) ways that others had not. But I'm certainly not an expert, nor am I especially invested in either conclusion, so...*shrug.*
At any rate, once [Person] has done work that further develops an existing idea, referring to it as [Person's] theory of [Thing] seems eminently fine and reasonable (as long as *they* are responsible in citing their influences). Somebody looking at their version can backtrace the lineage just fine, while someone looking at the older versions can't forward-trace them nearly as easily. And to anyone who's just interested in discussing the idea (rather than haggling over the credit), having everyone on the same, most up-to-date page is much easier than worrying about the whole history behind it.
It’s a lot like David Lewis’s modal realism (from his 1984 book On the Plurality of Worlds) and has something in common with Mark Balaguer’s plenitudinlus platonism (from his 1998 book Platonism and Anti Platonism in Mathematics) but it’s a bit different from either. I suspect some of the medievals and ancients had some related idea. But until the development of 20th century logic there wasn’t a clear conception of what “every consistent mathematical theory” means, and it would likely take an analytic philosopher to endorse such a blunt view that this is everything that exists.
I like plenitudinous platonism about math! It gets a bad rap but if you're going to be platonic about mathematical structures at all, I don't see why you'd want to choose a single "true" mathematical landscape, when there are so many possible ones.
I figured out the gist of as a schoolboy in the 90s, but I've never been able to explain it to anyone, and whenever I tried people always thought I was crazy.
I had an epiphany when we were taught to draw graphs of functions and I noticed that:
1 - These graphs are like the history of the world. A complicated enough graph would chart the whole universe.
2 - No matter how many times you draw and redraw one, if the equation is the same, the graph will be the same. Therefore it "exists" independently of how many times you draw it. Draw it once or draw it 100 times, it's the same graph. It follows that... it would "exist" even if it is drawn zero times (if nobody ever draws it)!
And therefore, ALL possible graphs exist in that way! And the universe is one!
But good luck explaining this insight to anyone! I never managed to make anyone grasp the concept. And yet, it's not brain surgery!
I've always been a mathematical monist, since I was a child. And it was strange to be the only one in the world (as far as I knew) who believed this. I was so surprised when I first heard of Tegmark's MUH. He's just one man, but it nevertheless felt almost like being vindicated. And it was so strange (and satisfying) to see much of the same reasoning and arguments used.
Kinda, but with subtle differences. Modal realism has been around for a while, but the argument for a multiverse by asserting that there is no such thing as physical existence as separate from mathematical existence and the specific idea of weighting worlds by a simplicity prior is novel.
In this case, Scott did make an argument specifically based on the fact that the theory was recent. I think when someone makes an argument like that, they have a duty to try to verify that it's true.
However, I'd like to distinguish this from cases where someone says something like "I had this cool idea, let's discuss it" without specifically claiming to be the first person to have the idea. I think it's legit to informally share and discuss an idea you've had without first doing a bunch of research to check if anyone else has had the same idea. (And in fact, this is often a pretty decent strategy for discovering prior work.)
I think people sometimes object to this for "hero licensing" reasons--i.e. that even _trying_ to contribute a good idea without first spending years mastering a field feels like a status grab to them. And I mostly don't endorse those objections.
Oh yeah, it's definitely legitimate to have an idea and share it discus it before verifying it is new.
However, depending on the context, it is bad form and lazy. E.g., unless it's a super casual chat among friends, if you're talking to someone about a "new" idea, you should probably have at least done 5 minute Google search.
Tegmark's hypothesis is just a conjecture. We have no evidence for it; no reason to believe that "all possible mathematical objects exist," except that some people want to believe that so as to not have to believe in God. This is the very definition of motivated reasoning, the antithesis of sound science.
On the other hand, we have extensive evidence for the existence of God in the form of testimony. People who God has revealed himself to have passed down their accounts to us. People who have witnessed miracles have likewise done so. People who have prayed and received guidance have spoken about it.
Any one of these testimonies could be dismissed easily enough, but we have enough, from enough disparate sources, that Bayes' Theorem compels us to either take the notion seriously or abandon all pretenses of rationalism.
We have lots of contradictory testimonies about different religions being true, which means even if you accept god exists, most of the testimonies have nothing to do with him. So the only evidence is the number of testimonies vs the expected number, and can you really figure out the expected number well enough to draw a conclusion? If you tell me the expected number, and then we look into it, and there's actually that many or fewer testimonies, would you conclude that it's evidence against god?
Also, god doesn't in any way help answer these problems. If you're willing to answer "How can there be an uncaused cause" with "There just is, and also it's sentient and all-powerful, and the nicest possible being", how is that any better than just stopping it at "There just is"?
> We have lots of contradictory testimonies about different religions being true
That's the pop-culture version, but it's not nearly as true as you might think. What scholars of religion who actually take this stuff seriously have been discovering over the past few decades is that the more closely you look at different religions, the more fundamental similarities you discover, and especially with ancient religions, the further back in time you look, the more they all seem to be converging on one set of fundamental principles.
Put simply, there's one set of results you'd expect to see if a bunch of widely different groups of people invented their own religions independently of one another, and there's another set of results you'd expect to see if mankind started with one revealed religion which then got corrupted over time as people broke into widely different groups of people. And what we actually see looks enough like the latter set to make the claims of theists worth taking seriously.
"the further back in time you look, the more they all seem to be converging on one set of fundamental principles."
So first, I'm really, REALLY skeptical that this is actually true. Both because "looking back in time" becomes harder and less precise the further you try to look and because we know of religious traditions from all over the world, including places that had no contact with each other for tens of thousands of years. Either you're claiming a "looking back in time" procedure that goes an order of magnitude further back than the written word, or you're cherry picking a very small subset of religions, and claiming it to be "all of them." But feel free to source your claim, of course.
But second, even if I were to take this claim at face value, the strength of the evidence is *wildly* insufficient to support the weight of the hypothesis you're putting on it. "All religions started from the same fundamental principles" does suggest a common cause. What it does NOT do is single out one *particular* common cause as the sole or most likely possibility, much less that said cause must be supernatural. There are, to put it mildly, quite a few non-supernatural ways that humans of past eras could have ended up with similar sets of principles. In fact, this frame necessarily assumes that
1. The hypothesized ur-religion was transmitted widely from people who *had* witnessed its founding events to people who *hadn't.*
2. That transmission was necessarily lossy: each step down the transmission chain got less faithful to the original events (but kept being passed on anyway).
Once you've admitted 2, you really stop having *any* basis to claim that the your hypothetical founding events *happened at all.* We've just admitted that people who weren't there will believe in them based on inaccurate second, third, fourth and fifteenth-hand stories, so the claim "these beliefs must have originated from actual, honestly-reported supernatural happenings" can't possibly hold water.
> So first, I'm really, REALLY skeptical that this is actually true.
A lot of people are. It flies in the face of The Narrative. But it's pretty well supported by now.
> Both because "looking back in time" becomes harder and less precise the further you try to look
It gets a lot easier when we have written records.
> and because we know of religious traditions from all over the world, including places that had no contact with each other for tens of thousands of years.
I know. That's what makes it so interesting how it really did happen!
> 2. That transmission was necessarily lossy: each step down the transmission chain got less faithful to the original events (but kept being passed on anyway).
Once again, written records do a whole lot to mitigate that.
"It gets a lot easier when we have written records."
But we don't. We only have written records going back a few thousand years, and even those are very, *very* sparse in antiquity. Again, there have been millions of humans practicing a wide variety of religions all over the globe for many, many times longer than writing has existed.
It sounds like you're trying to trying to conflate two statements:
1. "All human religions get more similar to one another the further back in time you look."
2. "The human religious traditions for which we have written records get more similar to one another the further back in time you look."
Those are NOT the same statement. Not even a tiny bit. Not even in the ballpark of the same statement. Treating them as the same is perhaps the most egregious example of the Streetlight Fallacy I have ever seen.
It is, in fact, very easy to imagine a world in which 2 is true and 1 is false: all it requires is for one particular priesthood to be ahead of the curve in adopting writing and making sure their texts were preserved.
But in the event, it doesn't seem like 2 is true either. A few minutes of searching suggests that Sumerian, Hindu and Chinese religions all have some very old texts--some quite older than the oldest Talmudic texts, by the way--and that none of them match up particularly well. Of course there are similarities. But more similarities than you find in later religions? Doesn't really seem like it.
> A few minutes of searching suggests that Sumerian, Hindu and Chinese religions all have some very old texts--some quite older than the oldest Talmudic texts, by the way
Yes.
> and that none of them match up particularly well.
This is the point where you should have done more than a few minutes of searching.
>the more they all seem to be converging on one set of fundamental principles.
Sure, as in "thou shalt not kill"-type stuff. Humans are physically and psychologically similar, so independent groups will converge on the common sense, and also on things like "we don't understand lightning, so clearly there's a thunder god".
>claims of theists worth taking seriously
Some, sure. But I've yet to see any evidence that they have anything worthwhile to say about the supernatural.
No. As in "In The Beginning, the state of existence was a vast primordial sea of water and chaos. A great and beloved son of the High God rebelled, sought to steal the High God's power, and by so doing was corrupted and became a terrible sea monster. A second son, the greatest of all, was chosen to fight the monster and re-establish the correct order. In their terrible battle, the champion was sorely injured, but recovered and joined battle the second time, and overcame the monster, slaying it, using its body to bring order to existence and establish the foundations of the world. Upon building the world, the High God and his champion son established a home for themselves atop a tall, sacred mountain, and there they placed our first ancestors, gave them sacred clothing, and taught them to live by the right order of existence. (ie. the true religion.) They planted a great divine tree atop the mountain that is filled with their sacred power."
When you see recognizable variations on that same basic narrative in the religions of peoples as far-flung as Japan, Australia, Egypt, Central America, Babylon, and Scandinavia, it's hard to deny a common origin.
> I've yet to see any evidence that they have anything worthwhile to say about the supernatural.
I don't deny it, just doubt that (alleged) commonness has anything to do with a singular supernatural revelation. But, since no current major religion would likely accept this narrative as The Divine Truth, it would be more fun to see unleashed upon theists-at-large than to argue against it anyway.
>What's your standard of evidence?
Acknowledgement by major ideologically unaligned groups of predictive power about future events.
Come now. There have always been people eager to find any reason they can come up with to explain away "ideologically unaligned" prophecy rather than having to accept it. A standard of evidence carefully constructed to admit no possibility of the evidence being valid is no standard of evidence at all.
> But, since no current major religion would likely accept this narrative as The Divine Truth, it would be more fun to see unleashed upon theists-at-large than to argue against it anyway.
Circling back around to this; somehow I missed it the first time.
I assume by "current major religion" you mean the Abrahamic tradition. This is where things get interesting.
The Abrahamic tradition has three major branches today: Judaism, Christianity, and Islam. Islam was founded by Mohamed as a synthesis of 6th-century Christianity and Arab paganism. Christianity in turn was founded by Jesus Christ approximately 2000 years ago as a reformed version of Judaism. These facts are fairly well known. The whole tradition as we know it today has its roots in Judaism.
What's a bit less well-known is that Judaism was founded in the late 7th century BC by King Josiah and his spiritual advisers, in a movement scholars today refer to as "the Deuteronomist Reform." We're finding more and more evidence as time goes by that the Deuteronomists made significant changes to the pre-existing Ur-Israelite Religion (henceforth UIR), that UIR looked a lot like the ancient ur-religious tradition seen elsewhere throughout the world, and that UIR contained a lot of teachings, doctrines, and prophecies, censored by the Deuteronomists, that, had they been carried forward as official doctrine, would have made the first-century Jews far more likely to have accepted Jesus Christ. UIR boldly spoke aloud of truths that the post-Deuteronomist canon only hinted at in whispers.
Some of the best accessible scholarship I've seen on this subject comes from Dr. Jacqueline "Jack" Logan, who presents it on a podcast called The Ancient Tradition. ( https://theancienttradition.com/ )
You specified reading. Each episode has a transcript available if you'd prefer that over listening to the podcast. Depending on your tolerance for the didactic — she's a university professor and presents the material essentially as a series of lectures — you may find her presentation a bit grating, but the quality of the research being presented is quite good.
> What scholars of religion who actually take this stuff seriously have been discovering over the past few decades is that the more closely you look at different religions, the more fundamental similarities you discover
That's the perennial philosophy hypothesis. I personally like it, in its more minimalistic forms, but contra your sentence, actual academics seem to dismiss it nowadays.
Edit: ... because dismissing the full narrative content of actual religions in favor of an ineffable core leaves out most of their content. I actually think it's the right move but it's understandably not popular.
> there's one set of results you'd expect to see if a bunch of widely different groups of people invented their own religions independently of one another
The mythology may be independent but the psychology driving it is not, so I don't see a good reason to assume the shared "fundamental principles" are based on revelation of a hidden truth rather than being inherent in human nature.
The good reason is that we've got plenty of examples of independent invention of similar things by unrelated parties throughout history, simply because it was something that multiple parties had a good reason to invent, and *they don't look like this.* We know what independent invention looks like, and we know what common descent looks like, and this looks like common descent.
I'm sure you can find similarities if you look hard enough, but they're clearly not all receiving revelation of the one true religion. Joseph Smith wasn't just told that something that had similarities to Christianity is true. He was told specifically that what's written in the Golden Plates is true. That's the main one I was taught about, but I'm sure Muhammad reported just as specific instructions about a different religion. Maybe those ones are liars, but again, if we can agree there's liars, and either way we'd expect to see people claim to have revelations, then how is people claiming revelations evidence?
And finding similarities isn't that surprising. Look at UNSONG. I suppose if you believe that that was accidentally accurate, then it gets us nowhere, but I'm sure you could find just as many examples in anything else. If you have anything complicated, and you can compare it to something else complicated, you'll find lots of similarities.
> they're clearly not all receiving revelation of the one true religion.
I didn't say that, so I'm not sure why you felt it necessary to refute such a nonexistent claim. What I said is that they're clearly all descended from their common ancestor, the true religion.
A simpler explanation is that since all religions were started by humans, they're all going to have similarities. And on top of that, as I pointed out earlier, the more details you add the more similarities you'll find, so even two random religions will have lots of similar stuff by coincidence.
Consider how the Hero's Journey seems to pop up in every story. Does that mean they're all retellings of the same story?
"The sacred tree literally shows up all over the globe. It shows up as a key feature in nearly every single religious tradition. And we just shouldn’t see this unless the religions of today sprung from one original source. Now, you might be thinking to yourself, well, it seems easily explainable that religions would use a tree from the natural world to explain certain religious ideas. So that could explain why it shows up so often. Seems plausible enough. And I’ll give you that.
"But just one problem, and it’s a pretty big problem because regardless of where we go in the world, the peoples understand the cosmic and theological significance of the sacred tree in almost identical ways. It would be one thing if one religious tradition used the tree to represent a ladder. And then we had another tradition use the tree to represent sacred writings and another one to have it represent fertility. But that’s just not what we find at all.
"We find that there is remarkable similarity and practically universal correspondence in the way the tree is understood, what it represents and what it gifts to human beings. But what does vary is the type of tree that’s used to symbolize the sacred tree. It tends to be a tree that’s native to the particular culture’s geographical locale. For example, in Norse mythology, the sacred tree was understood to be this immense ash tree. In ancient Egypt, it was either a Perseia tree or a date palm. In Rome, it was an olive tree. In Latvia, it was a birch tree. Among the Maya, it was a seba tree. Among the Slavs and Finns, it was an oak. Among the Gnostics, it was a cypress. Among the Sumerians, it was a willow tree. Among many Native Americans, it’s a spruce tree. Among the Mongols, it was a beech or poplar tree. In China, it was a mulberry tree. Among the Hindu and [Buddhists], it’s a fig tree. You get the picture.
"The particular species of the sacred tree varies by culture and geography. But what doesn’t vary is the cosmology and the theology that’s associated with the sacred tree. It’s virtually identical everywhere we go in the world."
— Dr. Jack Logan, "O Christmas Tree"
It's not just the Tree of Life/World Tree. As I've said elsewhere in this thread, all of the major doctrinal precepts of ancient religions show similar signs of common descent. We know what things being similar but different due to independent invention looks like, and we know what things being similar but different due to common descent looks like, and the signs we see scattered throughout the history of religion in the world is very clearly the latter and not the former.
> Consider how the Hero's Journey seems to pop up in every story. Does that mean they're all retellings of the same story?
Literally speaking, no. On a deep, fundamental level, though? There's good reason to believe the answer to that particular question is "yes."
>We have lots of contradictory testimonies about different religions being true
I think this is wildly exaggerated. We have lots of contradictory *claims* about God, obviously, but how many of those were ever actually attributed to *eyewitness testimony*? When I read different religious texts, they mostly seem broadly similar enough in how they conceive of God that I can easily believe people in all of them could be trying to explain a real experience of the same entity.
>If you're willing to answer "How can there be an uncaused cause" with "There just is, and also it's sentient and all-powerful, and the nicest possible being", how is that any better than just stopping it at "There just is"?
Because one includes more information than the other...? I'm not sure what the question is asking. I'm not even sure why you think "how can there be an uncaused cause?" is a question that needs answering to begin with, there's no inherent problem in such a concept.
Also, God isn't usually said to be "the nicest possible being". Did you mean "greatest"?
Psychedelic experinces are pretty predictable as well, but I don't see most people claiming they're proof of some universal truth beyond brain mechanisms...
I think he's misunderstanding the theology of "Good" and replacing it with "nice." If God created all things, including defining what morality even is, then by definition God is as moral as it is possible to be. If he does it, it is automatically the most moral thing possible. Christians also believe that he is loving and benevolent, but those are aspects of his core being, not something that he changes on a whim. Neither of those things require God to act "nicely" in the sense that he probably means, where God is non-confrontational and cool with whatever happens which is an artifact of liberalism in Europe.
This is actually not true. The amount of historic evidence and testimony backing up Christianity absolutely and utterly dwarfs EVERY other religion by a massive amount. This is completely consistent with christianity being the one truth and every other religion being idolatry.
This is similar to what I took from the piece. It really struck me as a “All models are wrong, some models are useful.” type situation, where you’re kind of thought-experimenting a universal theory to fit a paradigm that may or may not even exist at all.
In fact, there’s no reason to believe it does exist. No consideration of the limits of the human mind, perception, etc. so, what do we have left over after removing everything tautological or superficial? It’s just another theoretical model of existence, not unlike picking a random religion out of a hat and calling it “true because we applied science and logic and now it’s theoretically better than every other religion at theoretically predicting the universe!”
I actually agree, I don’t think it’s as “horrible” or even lazy as some commenters perceive. Just trying to highlight that it feels mostly like the theory itself is mostly well dressed hand waving.
> no reason to believe that "all possible mathematical objects exist," except that some people want to believe that so as to not have to believe in God.
Its clearly a god, it will create heaven and hell and the majority of life.
I think the main rhetorical thrust of the post is in the final paragraph or so, wherein Scott is making the point about "even if this hypothesis isn't true, the fact that it /could be/ a plausible alternative—that we've only /just/ started exploring it—and yet took this long to come up with..." etc.
i.e., "it's too early to throw up our hands", as the quoted fellow put it.
Okay, but so what? For any evidence cited in support of any theory, you can always posit that there might be some other theory which would explain the same evidence equally well, if only you had a little more time to think about it. That's not an epistemically sound reason to reject the best-supported explanation we currently have.
As somewhat of a believer indeed it is “epistemically freestanding” so no evidence for or conclusions from can be given. But it has given me a certain logical satisfaction to the “why” question - why this specific and peculiarly arbitrary universe? Well simply because we are tautalogically within this one of many. Saved me from having to muse endlessly as I lie awake at night
I've never heard of anyone believing that Tegmark's hypothesis is true in order to not believe in God. Have you? On the other hand, I've had plenty of religious believers tell me that they started believing in God to find solace and meaning. I'm glad they found solace and meaning, but their reason for belief has nothing to do with evidence or reason.
"On the other hand, we have extensive evidence for the existence of God in the form of testimony. People who God has revealed himself to have passed down their accounts to us. People who have witnessed miracles have likewise done so. People who have prayed and received guidance have spoken about it."
We also have extensive testimony evidence of aliens, ghosts, Bigfoot, and witchcraft. Do you also believe in aliens, ghosts, Bigfoot, and witchcraft?
This is a classic case of an isolated demand for rigor. You can't dismiss an alternative hypothesis to God as "just conjecture" and then not apply the same standard to God. God is also a conjecture, and no, pointing out testimonial evidence does not change this fact.
You could argue that the testimonial evidence is strong enough to favor God's over other conjectures. I find that extremely dubious because I think the testimonial evidence is incredibly weak, but that would be better than just dismissing alternative hypotheses out of hand.
> God is also a conjecture, and no, pointing out testimonial evidence does not change this fact.
When multiple sources, independently and without collusion, testify to have witnessed the same thing, that's typically considered good enough for a court of law. Why are you arbitrarily raising the bar here? Who's the one truly applying an isolated demand for rigor?
There isn't any meaningful difference whether people claim to have seen Bigfoot or spoken to Bigfoot (or fairies or djinn/ghosts or any mythological creature) as it pertains to credulity and weight.
It's not surprising to see accounts that keep in line with the popular wave of monotheism and hysteria of religion sweeping up civilization. Spiritual accounts in history take on a different flavor depending on time and region (see: India, China) but you seem to want to ignore that to fit everything into a square hole. It's "the same thing" if you project things that weren't claimed and ignore what was.
> There isn't any meaningful difference whether people claim to have seen Bigfoot or spoken to Bigfoot (or fairies or djinn/ghosts or any mythological creature) as it pertains to credulity and weight.
See my answer to agrajagagain on this point.
> Spiritual accounts in history take on a different flavor depending on time and region (see: India, China)
Are you seriously suggesting that the testimonial evidence for God would hold up in a court of law? There isn't a single case of multiple sources independently testifying to have witnessed something that would be proof of theism if true.
The New Testament does not contain multiple sources independently testifying to have witnessed something that would be proof of theism if true. It only contains one primary source (Paul), and he never even claimed to have physically seen the risen Jesus. He wasn't even one of Jesus's followers until long after the Ascension supposedly occurred. He had a religious experience that caused him to convert.
It appears you haven't read Galatians, where Paul talks about meeting Jesus and spending two years studying with him.
Also, are you not familiar with 1,2 Peter, 1,2,3 John, Jude, and James, which were all written by people who lived with Jesus before his crucifixion? For that matter, Matthew and John both were among his closest 12 and wrote two of the gospels, and Mark was likely written by John Mark who was with Jesus at the time of the crucifixion (and many believe was specifically among those on the Mount of Olives when Jesus was arrested).
Those would all be primary sources, leaving only Luke and Acts (also written by Luke) as secondary sources to Jesus. But if you read through Acts, the author was a first-hand witness to many of the events. You can note that in certain places, like Acts 16, the narrative of the book switches from describing Paul's actions to describing "we" moving around and doing things.
ETA - and just to clarify, those different authors claiming first hand experience with the events in question definitely were claiming to have witnessed things that would be proof of theism if true. It's quite weird for you to claim otherwise.
> No. I'm not asking for testimony; I'm stating that the testimony exists.
Please improve your reading comprehension. There are sentences longer than 4 words.
> > that we have no way of verifying
>
> Try telling that to the millions upon millions of people who have verified it.
Millions and millions of people have read it. That's not verifying, unless you simply mean to say that millions have verified that the eyewitness testimony exists, rather than the phenomenon being testified existing, in which case we are in agreement, but that says nothing about the truth of the phenomenon being testified.
Not to go all "edgy atheist" here, but it seems like a basic sanity check to see how our existence for God stacks up against our existence for other testified-but-not-otherwise-demonstrated phenomena. You say:
"On the other hand, we have extensive evidence for the existence of God in the form of testimony. "
and I can't help but ask "how does that stack up against our evidence for the existence of Bigfoot?" Pretty sure there's lots of testimonial evidence for Bigfoot out there. It arises from a population that is (almost certainly) less invested in and less credulous of the existence of Bigfoot than of God, making it more surprising (and thus worthy of a bigger update) when people report Bigfoot sightings. And claims of observable phenomena are generally much more recent, meaning they're more likely to have been transmitted faithfully.
" but we have enough, from enough disparate sources, that Bayes' Theorem compels us to either take the notion seriously or abandon all pretenses of rationalism."
That doesn't follow at all. Or rather, that only follows if you assume the base rate of *false* God-claims to be zero. Even assuming a quite low base-rate, a large population exposed to religious ideas over a long period of time will accumulate quite the corpus of claims even if every one is false. See for example:
As far as I can tell — and I'm by no means an expert on the subject, so it's quite possible that there's something I've missed — Bigfoot sightings are just that: sightings. Someone says "I saw something weird, so there's something weird out there." There doesn't appear to be anyone saying "I had a conversation with Bigfoot and this is what he told me." There certainly aren't multiple independent people saying "Bigfoot told me these things" and the things they claim to have been told are consistent across reported encounters.
And the funniest part is that the debate around this subject is almost completely identical to the debate around alleged encounters with God:
> Skeptics of the abduction phenomenon contend that similarities between reports arise from commonalities rooted in human psychology and neurology or cast doubt on the presence of similarities between reports at all. They note the evolving contents of abduction claims and the apparent effect of culture on the details of the narratives as evidence that the phenomenon is a purely subjective experience. Skeptics also point out the likelihood of large numbers of hoaxes being present in the abduction literature.
> Believers assert that it is unlikely for hundreds of people to independently generate such similar narratives while apparently having no knowledge of each other's claims. Some abduction investigators attempt to confirm the reality of events reported in abduction claims through observation or experimentation, although such efforts are generally dismissed as pseudoscientific by mainstream academics.
The final section of that article, "Effect of geography and culture on abduction reports," is instructive. While this article is largely focused on the English-speaking world, people of other cultures rend to report different "abduction narratives."
And again, as I've mentioned elsewhere, these encounters do not impart true knowledge. In fact, one of the most significant characteristics of the Abduction Narrative is the exact opposite: a loss of knowledge in the form of "missing time." As far as I'm aware, no one's ever woken up from a UFO encounter with a new, actionable understanding of present or future events.
>The final section of that article, "Effect of geography and culture on abduction reports," is instructive. While this article is largely focused on the English-speaking world, people of other cultures rend to report different "abduction narratives."
In fairness, the main difference noted seems to be that aliens are reported as being evil in accounts from the US but more often benevolent elsewhere, which could simply be evidence that aliens hate Americans.
Your own link points out that one of those common factors among alien abduction narratives is "the aliens wiped all my memories of the event, and I didn't remember it had happened until I [heard/read/watched a movie about] someone else's account of the same abduction narrative". Assuming this is accurate, that doesn't sound like "people independently generating similar narratives while having no knowledge of each other's claims" to me.
I'm not sure why it being a "conversation" is important. People sighting Bigfoot aren't just claiming to have seen "something weird." They're claiming to have seen Bigfoot. They're describing what they saw in similar terms that are "consistent across reported encounters."
Again, you need to bound the base rate of false claims--and bound it quite low--before you start treating mere testimony drawn from the population at large as evidence. So what is the base-rate of false God-claims? Please give both a number (can be approximate), and methodology for arriving at that number, which must be grounded in actual, gathered evidence.
> I'm not sure why it being a "conversation" is important.
Have you read the rest of the thread?
> People sighting Bigfoot aren't just claiming to have seen "something weird." They're claiming to have seen Bigfoot. They're describing what they saw in similar terms that are "consistent across reported encounters."
That's why it's important. Anyone can report having seen something that some other person has reported seeing, and make it sound like some other person's description. It's a lot harder to fake an encounter that you got true knowledge out of.
" It's a lot harder to fake an encounter that you got true knowledge out of."
No, it is not. You're drawing a false distinction here. Both of these are *fundamentally* the same in kind: if they differ, it's only in degree. Anyone can reporting seeing something another person has seen. Anyone can report hearing a conversation similar to what another person reported hearing. You can claim that some of the latter cases provided *actually new information*, but for that claim to stand YOU NEED EVIDENCE.
Please stop wasting both of our time. Provide evidence, or admit that you have none.
The argument you're making is fundamentally an information-theoretic one. You *cannot* argue it merely with wishy-washy assertions that "this is the sort of thing that happens." It needs well-sourced data. Actual observations of the real world, showing that it actually has the necessary properties to support your argument. You haven't provided any.
So... you continue to ignore the rest of the thread, and to brazenly throw out the quintessential bad-faith debating tactic: denying the existence of your opponent's evidence. Despite having already been called on it.
You're bringing nothing useful to this conversation, and only trying to sow confusion and waste time. Go away, troll.
My question for proponents of the mathematical universe hypothesis: if all we are is an instantiated mathematical object, then why do we have our phenomenal experience of moving through time? While a cellular automaton might seem inherently temporal with how it proceeds between steps, in actuality the mathematical definition of what its outcomes will be all exist "at the same time" from the point of view of the mathematical definition and the spaciotemporal object it implies. So I can understand a dimension of time existing, but why do we subjectively feel ourselves to be moving through it in only one direction and only one instant at a time, rather than experiencing it all at once as a "block universe"? It seems there must be some "fire breathed into the equations" beyond the equations themselves to explain the conscious experience of temporal change, so saying we are merely a mathematical object seems to miss one of the main aspects of our subjective existence.
> then why do we have our phenomenal experience of moving through time?
Because we have memories. If the entire universe happened the other way, starting at the heat death and moving towards the big bang, with every event happening backwards, and we remembered the future instead of the past, it would be completely indistinguishable from this universe. We don't have some magical ability to detect time passing. It's just that we remember the past, and think of that as time passing.
That might explain why we think of one thing as "before" or "after" another, at any given moment. But it doesn't explain the *experience* of change. As you point out, mathematically it's symmetrical — so why don't we experience our memories "backwards", disappearing over time? Or experience everything all at once?
But that's not how we *experience* it. I can distinguish my left hand from my right, but I experience them both "together". Likewise, I should be able to distinguish "earlier" memories from "later" one, but while I'm experiencing them together.
I can't explain the experience of anything. I won't deny that. But I don't think the experience of redness requires that something actually be red. I can get the same effect by looking at something cyan and then closing my eyes, or just thinking about redness. And if I can experience the qualia of redness without red, why wouldn't I be able to experience the qualia of change without change?
I don't think you can experience redness without redness — it has to be something, even if there is no red object "out there" when you experience it.
But time is something different. To experience change, your *experience* itself has to be changing. (By definition, if your experience didn't change, you would just be experiencing the same thing — as I do when I experience my left and right sides.)
Maybe you can have a completely static subjective experience of change, without this experience changing at all.(in the same way it isn't necessary to see a red object, to experience seeing a red object)
Or at least, I don't see how one should imply the other by definition.
You are conflating the consequences of the rules with the thinking and experience of them.
There are the laws of physics and the (mathematical) objects they govern. Supposing these objects are complex enough to think, experience, and even make predictions using the very rules that govern them, does NOT mean the objects (eg humans) would necessarily be able to experience every consequence of the laws simultaneously. Any being imbued with similar faculties might have a wider or narrower experience of time. Even this is probably being too charitable. There are probably different echelons of life/experiencing the universe that stretch beyond the narrow set of faculties that we call human experience
This only makes sense if there is a metaphysical distinction between the two, however, and such a distinction does not make sense if mathematical objects are all that exist.
Such was very clear to Plato and Aristotle. It is not due to greater philosophical sophistication that it now fails to be clear to some people.
Suppose the experience of time and all of time itself are both defined as mathematical objects. The subjective experience of time might simply be a subset of the latter. That is, even if there is no metaphysical distinction between “our experience of events” and “the set of all events”, there’s no reason to think they should be equivalent.
The fact that one being can be defined as a mathematical object, does not imply that the experience or perception of time for that being would contain the totality of that beings experience.
I simply don't know what those words mean. I can say, "Suppose that love is defined as the taste of orange," and that might be poetic, but just because I can say it doesn't mean it makes sense.
Mathematical objects mean something and have particular properties. So does the experience of time. Their properties are not the same. For example, mathematical objects are abstract and universal. Things like the experience of time are concrete and particular. What you said does not make more sense than saying that I ate the number four for breakfast this morning.
In any event, and leaving aside this complaint (which to my mind is conclusive): your original distinction was not between the universe and a part of it (such as the worldline of a person), but between the "consequences" of the rules and the "experience" of them. It does not make sense to say that the "experience" of something is a subset (in the mathematical sense) of the thing.
You said above in response to my first comment: "This only makes sense if there is a metaphysical distinction between the two, however, and such a distinction does not make sense if mathematical objects are all that exist."
To this point, even if you erase the metaphysical distinction and accept this claim: "mathematical objects are all that exist," you can still argue that the mathematical structure that represents time is different than the mathematical structure that represents our experience of time. In modern day mathematical parlance, such a task is usually accomplished by showing that set A does not contain the same objects as set B. And yes, this is a bit strange to argue in this context, but it is all predicated on Tegmark's initial thesis that everything is math. This is what I was trying to do in my last comment. I do not actually hold this position myself.
Regarding the claim: "your original distinction was not between the universe and a part of it (such as the worldline of a person), but between the "consequences" of the rules and the "experience" of them. It does not make sense to say that the "experience" of something is a subset (in the mathematical sense) of the thing."
I think your complaint here hinges on the following, whether the experience of the laws of physics are counted as a "consequence" of them. If so, they would be included in the "set." If not, than we have decided to make an arbitrary distinction. I am more inclined to include them.
I take it that the motivation for Tegmark's work in the first place is his noticing (obviously he's not the first) that the physical universe is well described by mathematics, and might in some sense even be isomorphic to a mathematical object. So I take it that he thinks that it is, at bottom, some kind of very simple mathematical object -- the solution of a PDE, or a particular instantiation of a particular cellular automaton, or this kind of thing.
It seems to me that you are wanting to replace this with a much more complicated mathematical object. For example, rather than just the solution of a PDE (which would be a function, or ultimately perhaps a set of ordered pairs), something that contains much more information (something like tuples containing both the ordered pairs, and also additional metaphysical data relating to "time" or "feelings" or the like).
Now, on one hand, I think this just highlights in one more way (there are many) what a bad idea Tegmark's original plan is, because yes, one can always take an infinitely large number of expansions of a particular object that still contain (isomorphic copies of) the original object. Next, I give you credit for realizing that some such thing -- at a minimum -- would surely be needed, because there simply must be additional "stuff" beyond just the geometric structure.
Such "stuff" would have only arbitrary connection to the physical data, though; so this kind of move would actually give piercing strength to what I usually think of as a relatively weak argument, our friend Bentham's "psychophysical harmony." Beyond that, though, these are still just not the right *kinds* of entitites to be the world. One would *still* be left with a distinction between this "additional stuff" and the actual "experience" of the stuff, for example (and why wouldn't the purely physical data also be experienced?) Etc., etc.
Anyway, thank you for the interesting points. I hope I have not misinterpreted what you said.
" why do we have our phenomenal experience of moving through time? "
Do we? I'm not honestly sure this is a coherent question. Are you familiar with the idea of a Boltzmann brain? The weird thing about it is that it seems--in a pretty fundamental way--to be completely undisprovable. Any evidence you could imagine seeing for *not* being a Boltzmann brain could have been conjured into your memory/perception a bare instant ago, to vanish again in the next instant. There's no discernible way the hypotheses "Vittu is a human with a continuous existence through time" and "Vittu is a Boltzmann brain, here one instant, gone the next" can really be separated. All our interactions with the past are mediated through the present.
Or to put it in the language of cellular automata: each step in a (sufficiently complex) cellular automaton state will contain a wealth of information about previous steps. If the notion of a "person" is really just pointing at a connected series of automaton steps[1], then each of those steps will *separately* contain a self-reference to the whole series, regardless of whether you regard them as a sequence in time or a block existing all at once.
I'm not sure if that last paragraph made any sense at all. Maybe imagine it like a deck of playing cards set in a standard order. Only each card contains (in addition to its own suit and value) a little note listing all the cards previous to it. So the Ace of Clubs lists nothing, the Two of Clubs lists just the Ace, the Three of Clubs lists the Ace and the Two, the Ace of Diamonds lists all the clubs in order, and so on. Regardless of whether you're flipping through the deck, leaving it stacked on the table or throwing it in the air, the card ordering is still written on the cards. If we narrow our focus to just (say) the Ace of Spades in isolation, we still observe most of the sequence of the deck despite not having any idea how each physical piece of the deck is arranged (or whether any other pieces actually exist). Each part contains (a portion of) the sequence of the whole.
OK, this is making my head hurt. No more metaphysics until tomorrow morning at least.
[1] Or really, a connected set of sub-regions within the larger set of steps of the universal automaton
If you want to say that we are not forming memories by moving through time, and are instead instantaneous BB s with memories as if of moving through time, then you need to explain why the memories are constant and display physical.laws, because the number of possible BBs with chaotic memories would be much higher.
I agree that a universe consisting solely of short-lived BBs should contain a lot more chaotic and disordered BBs than nicely coherent ones. I'm not trying to argue such a universe is more plausible than ours.
What I am trying to say is that asking the question "what if I was just a BB, how would I know the difference?" seems highlight a problem with ANY time-ordering arguments that I find difficult to get past. Namely, that any evidence we have for the idea that time in *moving* is necessarily evaluated *in the moment*. Trying to argue it from such a position seems to have a self-referential or pulling-oneself-up-by-the-bootstraps quality that I can't see any way to remove.
I think you can ask similar questions within the confines of vanilla physics too. General Relativity would have us treat time as a dimension of spacetime, on equal footing with space.
You could think of yourself as your world-line through spacetime, which exists in some crystalline atemporal sense, and then ask why you experience time sequentially through that worldline.
Because our experiences are not *outside* the universe? We are *in* physics, not outside of it looking in, and so we only remember what has occurred in our personal past.
We feel we are moving through time because that is how the rules of the universe are set up. Our brain at 8:00AM is a slice in the timeless sense, and it is linked to the next slice by the rules for how this area of the mathematical universe functions. That light bounces into the eyes of 8:00AM brain, causing a reaction to the sun coming in through the window in the next slice. Etc.
We remember the past because we have memories that reacted to events in our lives, chemicals spreading, neurons firing, and so on.
To me this is like asking why I don't know what is happening in Alpha Centauri at this very moment: Because the laws of physics restrict me from seeing anything but a delayed picture of it from within.
I read a little Tegmark long ago, but I haven't read this one. I'm willing to accept that the reason there is something rather than nothing is that mathematical objects are logically necessary, if he also explains *why* mathematical objects are logically necessary. I reckon he's got some argument that makes this objection equivalent to asking why modus ponens is valid, but it's hard for me to believe I would find it convincing. (I suppose I'll have to read the book.)
Similarly, I accept that we find ourselves in a universe that allows life because of the anthropic principle -- where else might we find ourselves? But it still seems to me that the fine-tuning we perceive is mighty damned fine; I'd be happier if we could imagine a wide smear of values for the fine-structure constant (and a dozen others) that would seemingly permit life, rather than what we do see, namely a knife-edge where we could not exist if any of them were just the teensiest bit higher or lower. I can think of only two courses. One, maybe there are very different universe-regions where there *is* more leeway and we just have the perverse luck of being in one of the knife-edge universe-regions. Or Two, there is some explanation for why life can arise *only* in knife-edge universe-regions, and I'd like to understand why that is so.
I don't think any of my quibbles make the arguments for God any more (or less) plausible, but it still pisses me off.
ETA: ...Or Three, our imagination is too limited to see that life really *is* possible in universes that are like ours but with slightly different constants; we just don't see it because we are blind to the opportunities that these nearby universes afford. Maybe. It's complicated. Still annoyed.
My intuitive understanding is pretty simplistic. All mathematical objects exist by simple fact of being describable. Actually going to the trouble of doing so (say in a computer simulation) only causally connects them to our universe but does not change them in-themselves
I haven't read Tegmark, but my understanding from these comments is that he means mathematical objects exists as in mathematical objects is what actually constitutes physical reality. Your explanation seem to suggest mathematical objects exist in the platonic sense, as abstract "forms", not physical reality. These seem to be two very different things?
Isn’t this just a dressed up Anthropic Principle? The only part of the argument that seems to me to have explanatory power is the bit where you’re sampling from the set of possible universes that host conscious beings, which is just our old friend.
Yeah I thought the the same thing. I also don't know about this:
> Argument from comprehensibility: why is the universe so simple that we can understand it? Because in order for the set of all mathematical objects to be well-defined, we need a prior that favors simpler ones; therefore, the average conscious being exists in a universe close to the simplest one possible that can host conscious beings.
As any programmer will tell you, shorter (i.e. simpler as a machine) is not particularly correlated with comprehensibility. So I'm not sure the simplicity prior is even helping on this front.
"As any programmer will tell you, shorter (i.e. simpler as a machine) is not particularly correlated with comprehensibility."
Then those programmers aren't very good at statistical thinking. It's certainly possible in many cases to make something more human-comprehensible by making it longer. But "correlation" is not "perfect correlation." If you sampled randomly from the set of all 100-bit programs[1] and all 1,000,000 bit programs, I cannot *possibly* believe that your first set of samples wouldn't be easier to understand than your second. It's just that the longer programs you run into *aren't* picked out randomly: they're specifically chosen from among those long programs that are easy-to-understand. (I'm less familiar with the theory of Turing machines, but I'd still bet decent money the same principle would apply).
Note that the laws of physics are *not* actually especially easy-to-understand. They're just simple *enough* to be tractable to humans, despite all their mathematical subtlety. There's no obvious reason that classical electromagnetism (for example) needed to have a ruleset simple enough to be expressed in four equations, rather than needing 10, or 50, or 10 million equations. In the latter case, humans would likely never have figured *any* of it out.
[1] That were syntactically valid in a particular language.
> If you sampled randomly from the set of all 100-bit programs[1] and all 1,000,000 bit programs, I cannot *possibly* believe that your first set of samples wouldn't be easier to understand than your second.
Then I recommend you google "code golf" or "International Obfuscated C Code Contest" and poke around a bit in the solutions. Perhaps that will give you a spark of understanding.
That doesn't surprise me, because in the real world, programmers don't write programs by drawing one randomly from "the set of short programs", or any set for that matter, so I wouldn't have expected my examples to be a representative sample of them either.
My point is: When humans are involved, you cannot optimize for shortness and readability/comprehensibility of code at the same time, so any purely statistical argument to that effect is just wrong. Yes, you can make functional code incomprehensible by bloating it to 10x its size. But you can make it even more incomprehensible by making it 1/10th the size, which I tried to illustrate with the code golf example.
"My point is: When humans are involved, you cannot optimize for shortness and readability/comprehensibility of code at the same time, so any purely statistical argument to that effect is just wrong"
But the Tegmark universe argument is that the mathematical structures are chosen at random[1], humans are *not* involved in the choice.
[1] Or rather, your position as an observer is chosen randomly from among all observers in all universes, with some simplicity-weighting to keep that set finite.
I'm aware that "short programs can be hard to understand" and "long programs can be easier to understand" are both true sentences.
But the argument was a statistical one. Is shortness *correlated* with comprehensibility? I should think that even when drawing from the space of human-written programs the statement is false. And when drawing from a larger, Platonic program-space containing (among other things) programs that no human would ever write, the answer is extremely false.
Consider some set of particularly opaque code golf entries having, for example, a size of 100 bits. The set of all valid 250-bit programs obviously includes things functionally equivalent to every program in the first set[1] AND it contains every ordered pair of programs in the first set, chained together in any sort of bizarre way that you can fit into the 50 extra bits. AND it contains novel 250-bit programs that couldn't in any fashion be squeezed into 100 bits. It's certainly going to have *way* more pieces of bizarre, difficult-to-understand code than the first set.
Certainly if you give a human 150 bits to do the same job, they can use some of them to make it easier to understand. But that's not really germane to the Tegmark-universe specification: if "simplicity of a mathematical structure" CAN be defined in some universal way, it necessarily must involve everything being as-compressed-as-possible, not padded out for human comprehensibility in ways that add length without adding function.
[1] You can pad any program with valid-but-unless code like empty loops and always-true conditionals.
> Note that the laws of physics are *not* actually especially easy-to-understand. They're just simple *enough* to be tractable to humans, despite all their mathematical subtlety.
I agree. Also I think that what we seem to understand and describe with reasonable accuracy mathematically is really aggregate effects of the presumable underlying fundamental laws of physics. We don't really know if those underlying laws are tractable to us, but it is often assumed that there is some simple mathematics that describes the fundamental laws at the "bottom".
I'm not sure if this really needs to be true? Is it not possible that the underlying laws are not simple and not easily describable mathematically, just as it is not obvious that electromagnetism (an aggregate effect) need to adhere to simple formulas?
Okay since we're talking about a situation where an appeal to a probability distribution was made, "correlated" was definitely not the right word to use. What I _should_ have said is that maximally short programs are essentially never comprehensible.
Our universe in fact has laws of physics that are fundamentally simple, but difficult to figure out, and very difficult to apply - the original motivation for quantum computing was simulating non-trivial quantum systems - so this is if anything an argument in favour
Anthropic principle tells you why you are more likely to find yourself in a universe X compared to a universe Y where you couldn't live. It doesn't tell you what is the set of all universes we are choosing from.
This is the second part to the anthropic principle.
Notably, you might have some notion of reality-fluid that corresponds not just to the simplicity of initial conditions but to how much any particular being/experience/universe exists relative to others. If many simple universes for some reason simulate some particular situation complicated universe, that complicated universe gets a boost in reality-fluid: despite having complicated laws, its simulated a lot/it’s visible from a lot of places/it’s shorter to define (via “it’s simulated here in this simple to define universe”).
Maybe think of it as the PageRank algorithm but for everything.
I love this idea that there could be an "Eigenvector of the universe"!
It also potentially gets around the issue of needing like a specific programming language in order to specify "how to measure simplicity". Instead, simplicity of universe A is the probability universe A appears as a substructure within a random universe X, where universe X is randomly chosen using the same probability distribution as is used to measure simplicity. However, while obviously eigenvectors are well defined with a finite matrix, I'm still a bit unsure if this can be well-defined within uncountable infinite realms of mathematics.
I've always found this theory horrifying, for two reasons. First, it seems pretty plausible (occam's razor). Second, if it really is true, then it means that there are (possibly infinite) worlds with huge amounts of suffering. If there's no limit to the complexity of the starting conditions, there could be a universe where I'm personally being tortured for eternity.
I fail to see how this is very different from our own world: there are some people and places having amazingly positive experiences and some having horribly negative ones.
Suffering is not the opposite of pleasure. Pain is not the opposite of happiness. At least not to anywhere near the same degrees. Humans would much, much, much rather avoid pain than seek pleasure.
Hellish worlds will be assigned low measure for roughly the same reason why it is unlikely for our world to become hellish at any point in time. In addition, you might more controversially expect heavenly worlds to be more common and be assigned higher measure collectively if you expect our world to be more likely to become heavenly than to become hellish.
I just... do not get all this obsession with theorycrafting about God. Let's say you somehow get conclusive proof that God exists. So what? There's absolutely nothing you can do with that information. Simply proving God's existence doesn't provide any information about its nature, its motives, or anything else for that matter. When use is that knowledge when you don't even properly understand the fundamental laws and mechanics of reality yet?
Well, I'd guess it has to do with a notion that you can always establish further truth through reasoning. If it's possible to establish that God exists, why wouldn't you expect to then discover its nature, its motives, etc?
I consider this a growing but comparatively minuscule demographic, where the question of God's existence comes up.
I've thought to style myself a deist in the past, but my conception has no resemblance to an intelligent and/or benevolent being, which makes it kind of moot and practically indistinguishable from whatever strict atheists might imagine.
It's a hobby and everyone needs a hobby. Others who don't share the hobby are constantly saying "what's the point?" While jealously guarding their own "pointless" hobbies.
I mean yeah, you're right. That is, of course, assuming that they're doing this for the sake of enjoyment. If anyone's doing this because they're having an existential crisis, they should probably get an actual hobby, because this is clearly not a productive coping mechanism.
Traditionally (e.g. in Aquinas) you follow up the logical proofs that God necessarily exists and is necessarily Good with revealed truths about the specifics of your religion such as the various sacraments and rules.
Prehaphs we should consider if super-mega-hitler is more or less likely to commit the mega holocaust if he believes in god. Since arbitrary people exist on whims.
Yeah, Bentham's Bulldog and several of the other Substackers involved in the debate I linked at the top of the post. That's part of why I bothered explaining that this was an ongoing debate with many participants.
Theists making arguments from infinity + definition-play is to be expected. Its not quite the same as saying its impotent for atheists to do so.
I guess I shouldn't be surprised, ai is also god for many here. Prehaph we should find the Trinity, the mathematical universe created all, Aligned gai will absolve the world of our sins and lead us to heaven, effective altruism will guide the faithful actions to align with goodness.
The idea in Catholicism is that fideism is the wrong answer; while faith is a supernatural gift, it is possible to use human reason to come to the conclusion that God exists. So some people do read maths essays, and care about philosophical/mathematical arguments. (Most of us, admittedly, do just go 'yeah, whatever').
"Fideism: A philosophical term meaning a system of philosophy or an attitude of mind, which, denying the power of unaided human reason to reach certitude, affirms that the fundamental act of human knowledge consists in an act of faith, and the supreme criterion of certitude is authority.
...On 8 September, 1840, Bautain was required to subscribe to several propositions directly opposed to Fideism, the first and the fifth of which read as follows: "Human reason is able to prove with certitude the existence of God; faith, a heavenly gift, is posterior to revelation, and therefore cannot be properly used against the atheist to prove the existence of God"; and "The use of reason precedes faith and, with the help of revelation and grace, leads to it."
" In the first days of his bondage he had turned to the gentle churchly faith endeared to him by the naive trust of his fathers, for thence stretched mystic avenues which seemed to promise escape from life. Only on closer view did he mark the starved fancy and beauty, the stale and prosy triteness, and the owlish gravity and grotesque claims of solid truth which reigned boresomely and overwhelmingly among most of its professors;" -lovecraft, silver key
Arguments from infinity are symmetric, if christ saves christens then ant-christ punishes christens, so whats the wager? If the unmoved mover, moves, maybe he was moved by the big bang.
I HATE IT; Im unhappy as an athiest, but at least Im not definition lawyering. I hope neo-pagenism finds something worth worshiping and then declares autistic analysis of the stories is a sin.
Yes hi 👋 I've read almost all of Ssc and ASX, HPmor and some of the sequences and I'm a big fan and also an orthodox Jew. The religion eliezer doesn't believe in, isn't mine either. He skipped elementary school and never really took Judaism seriously. I also think "prayer (or relevations) making faith", while a nice experience for some, doesn't prove anything.
I'll try to summarize what I think is a main position.
God is what's *outside* the big bang and what created the laws of physics. Where time and matter ends, is spirituality.
How do we know God cares and pays attention? 1. The universe continues to exist. God is continually keeping it up and if he took away his attention it would be gone in an instant. What's outside of the laws of physics maintains physics. Otherwise why assume time and cause and effect will always continue just because they did until now?
2. Historical revelation. Judaism says God spoke to 2 million people at Mt Sinai and they all heard God speak, personally and passed on the message to their descendants generation after generation. Not a nomad in a tent having a private revelation or a guy who dug up some gold tablets or anyone else making a claim that they personally heard God. They could be delusional or lying and charismatic enough to convince others. But an entire nation's population of very stubborn and argumentative people all agreeing on the same story? How else could that have been converged on?
3. Evil. This is an easy one actually and the only reason people struggle with it is emotion, not logic. Two words. Free will. Or perception of free will if you're a determinist, if God can see the future in my opinion it's basically the same thing. But free will as humans experience it is the purpose of life, to choose good.
As Rabbi Moshe Luzatto wrote, God created the world with the ultimate purpose of the universe for people to experience good. But unearned good is not the ultimate good. We have the chance to earn it and deserve it. (The Jewish version of hell is basically a "washing machine" to get you back to heaven. The ultimate punishment is shame as you finally understand the true reality and how terrible your sins truly were. Only exception of who gets stuck there being rare irredeemable sinners like Nebuchadnezzar.)
Serious question, since you believe and understand a lot of the logic. Any way to make yourself un-Jewish, *according to halakhah*? No way in heck I can keep all those commandments. My understanding is that if you're the son of a Jewish mother it's impossible, but I was at least hoping for some sort of reverse mikvah using bacon grease and the Horst Wessel Lied.
Not sure how serious your question is but a mikva of bacon grease is a funny mental image I guess! And yes you're right being Jewish is a permanent state. Our enemies understand that all too well, unfortunately.
On the plus side, if God made you born a Jew it means you're capable of fulfilling your potential as such. Practically, if you really are serious, I'd tell you that every good thing you do, totally counts even if not everything is done. It's not all or nothing.
The bacon grease mikvah was a joke, the question was serious.
It's not just that (though I admit it's a reason I avoided getting any deeper into the religion); I really don't like a lot of the stuff left-wing Jews have done (the whole left-wing activism in the 20th century, basically) and would rather quit myself of the whole tribe. Apparently that's not an option. But I do appreciate your taking the time to answer the question and your honesty when I seemed to be somewhat unserious. Thank you.
I'm not sure which left wing activism you're referring to? Tikkun olam maybe? Religious Jews are baffled by secular people who think "tikkun olam" is Judaism. It's an incredibly obscure kabalistic thing that has nothing whatsoever to do with social justice. You can be 100% religious and not even know that it exists other than a one-off line in the Aleinu prayer. I have no idea how that came about, historically, that reform and conservative Jews came up with that. Or do you mean something else?
I definitely fit categories 1 and 3, at least, not quite sure what you're going for in number 2. No, I've thought for several years that a Tegmark IV multiverse is probably the most solid alternative to theism.
Interestingly, one suggested explanation for the Born rule is simulating the quantum physics with some floating point precision, discretely, and the errors accumulating. (See this paper by Hanson: https://arxiv.org/abs/quant-ph/0303114.)
Is it the case that discrete universes are simpler/a lot more common than continuous universes, and so we are more likely to find ourselves in a place computable with a Turing machine? Or could it be that all Turing machines exist, but only computable approximations of other objects exist?
I don't see how this isn't just an elaboration of God's nature, of the means of creation. It makes perfect sense that a universe created to contain us would be a mathematically perfect container.
All things could exist, but we do. I don't see a compelling reason not to regard the universe as we find it as an instantiation of a greater and incomprehensible will. God could create anything else, and prodding this reality we can reveal so many of the possibilities, but these it seems to me are many trivial though novel objects. Meanwhile the universe as we discover it is infinitely mysterious, and some among us intuit a deeper will and agency behind the veil.
If you're interested how some of these ideas are compatible with theism, and you haven't read Scott's book Unsong already, you might want to check it out.
I find SIA pretty compelling, and agree that this fits the infinite-people prediction more nicely than theism. I don’t know how to feel about all that it implies (does induction fail? does it endorse moral nihilism? etc.), but thanks for posting.
It depends on what kind of god or God and what the effects on our existence would be. If (say) Vedic religion is true, then that means some kind of afterlife and good or bad outcomes depending on our actions in this world.
Chesterton, "The Usual Article":
"I would gently suggest that, to most ordinary outsiders with any common sense, there would be a considerable practical difference between Jehovah pervading the universe and Jesus Christ coming into the room."
1) I'm not impressed by a thousand competing notions of how to earn your place in the afterlife, assuming there is one, which is an awfully big assumption to begin with. A lot of these notions have a lot of rules in common, and they're mostly good rules which a person can try to follow without the goad of divine wrath; but many of the notions say that's not good enough (see Calvinism, which says that nothing is good enough).
2) Chesterton. I'm not holding my breath waiting for either of these things to happen.
He walks into the room. In physical, corporeal form. Uh-huh.
If you just mean a sense of his presence, he doesn't need to be in the room in any sense to give that. I get that sense about dead loved ones all the time. Doesn't mean they're there.
>I'm not impressed by a thousand competing notions of how to earn your place in the afterlife, assuming there is one, which is an awfully big assumption to begin with.
Why? It would seem that it would be worth your while, for Pascalian reasons.
Even Pascal wouldn't try adhering to a thousand different ones at once. As for what they have in common, see what I wrote: you don't need Pascalian reasoning to do that.
If you can get consciousness from some simple set of mathematical rules, it seems very likely that there are many universes with Gods. In fact...it seems inevitable.
Indeed! In Tegmark's multiverse, for any self-contained universe, there's another version embedded in an outer world that includes a creator. Presumably in most cases this requires quite a lot of additional complexity, so it's an insignificant contribution to the measure of the self-contained universe.
The more interesting case is universes that aren't quite self-contained. That is, worlds where the creator intervenes in a way either resolving steps in its evolution undefined by local laws or suspending local laws in circumstances limited enough and with overt enough meaning to be recognized as divine intervention. Those embedded universes can't exist on their own as they're not fully defined mathematical objects without the actions of the creator.
However, I suspect it doesn't work. My interpretation of how personal identity works is basically applying Parfit to all the mind-moments in the multiverse. i.e. "Your" next mind-moment appears to be drawn randomly from all the mind-moments in all worlds that remember having just been "your" current mind-moment. (It's not actually drawn randomly; rather, all such chains are equally real, & the result looks random in the same way as Many Worlds timelines.) So there's a distribution over the worlds your future "self" will be in, and even if you happen to be in one of the rare theistic worlds now, statistically you're sure to be back in a self-contained universe later that has natural explanations for the apparent miracles. (e.g. The putative miracles were misremembered or misinterpreted events, & the in-universe evidence doesn't support believing in them.)
This was what I thought when he stated the setup - this isn’t a way to get fewer gods, it’s a way to get more gods (though those gods don’t do the creating exactly).
Depends on how you define creation. It seems like some sort of Autopoiesis would be inevitable. Then there's the question of the origin of the necessity of rules. Even arguing that such rules are necessary feels like the argument that God is necessary, and feels (to me) to actually be giving ground to Classical Theists who's conception of God is very "laws of physics"-like anyways
That would be often incompatible with many (Christian) theists views of God being all-powerful, that even if there were other universes he'd also be in control of those as well.
So, it defuses that sort of argumentation.
But, Tegmarkian Multiverse would also probably imply that ~most universes aren't created by a God. Which then turns the whole issue into a more reasonable argument of "does the historical record make it clear that there is any creator", rather than very abstract sorts of argumentation.
It *might* undermine a Christian God. But it would seem to guarantee other sorts.
And I say "might", because in classical theism, God would be understood to be the rules themselves (Logos), and Tegmark doesn't give an account of where the rules come from.
Compromise Solution: there is a God, but it's the simplest possible God capable of creating the universe. Which neatly explains why there's only one: obviously multiple gods would be an unnecessary increase in complexity.
(This is mostly a joke. But if somebody wants to take the joke and run with it, you could probably show that this is just a fancy gloss on the simulation hypothesis.)
Yes, completely unironically, all of this is correct. It's already standard theology in the Abrahamic religions, and has been independently re-derived by theologians in numerous other traditions as well.
NGL, the notion that the deity who decided to "punk" Abraham by telling him to go murder his son and pulling a last-second reversal is "the simplest possible God" is not one I can even consider with a straight face. But I'm also not really interested in getting into the weeds on the matter...I'll take your word that they had very nice derivations and that those derivations sounded very convincing to people who already believed their conclusions and leave it at that.
From my understanding, the argument from comprehensibility is more about the fine tuning of the constants than the laws themselves. Simplicity can't explain that.
Mathematical Realism/Platonism is a contentious position. Paul Bencerraf has demonstrated how accepting this premise undermines any semblance of mathematical truth. IE, if mathematical objects exist, what is the causal relationship between such objects and our beliefs? If you accept that all mathematical objects exist, you immediately sacrifice the truth of mathematical propositions.
Such realist positions in this case are much less a refutation of the aforementioned arguments for god’s existence and much more a stand in for theism. Russell on Kurt Gödel’s mathematical Platonism: “Gödel turned out to be an unadulterated Platonist, and apparently believed that an eternal 'not' was laid up in heaven where virtuous logicians might hope to meet it in hereafter.” - Russell, Bertrand. "America. 1938-1944." Autobiography. 1967. London and New York: Routledge, 2000. Print. 466.
Mathematica! Realists have a choice between a small consistent Platonia and a large inconsistent one..The large inconsistent one means there is no ultimate consistent mathematical truth. The small consistent one means that some things you might be able to prove from.some premises, aren't really true, because they are not in Platonia.
However, you have no way of knowing they are not really true , because Platonia cannot causally interact with a mathematicians brain. So small Platonia is redundant.
Small Platonia tells you that the Axiom of choice is true or false, but not which.
Large Platonia tells you that it's true *and* false.
Are there other possibilities? Much as the parallel postulate is true in some models, and false in others, might there be situations in which the axiom of choice is true in some contexts, and not in others?
But that's definitely interesting, I haven't considered mathematical platonism in any serious way.
I think this may hinge on confusing questions about "causality". If two simulations are deterministic and have the same initial conditions, then they'll go on the same even without any causal connection. If you and I are both posed the same math question (and we're both competent), we'll reach the same conclusion despite having no causal connection.
Seems to me that the mind of a mathematician can happen to be set up the same as some part of Platonia, and thus predictably proceed the same, without any causal connection between them.
Mathematicians disagree in practice. You can accommodate y for that by saying Alice amd Bob are in sync with different regions...but such an inconsistent Platonia performs no useful function...it doesn't tell you who is right.
To put it simply, if you claim that there are objective mathematical truths (platonism) you have to explain how we come to know these truths. What is it that allows us to have any knowledge of them. What is the causal relationship between the objective mathematical truths and our beliefs?
That mathematical truth is ''embodied'' within reality, we've been selected for living in the current world which is highly regular due to the structure inherent in it, and so our beliefs can tend towards more accuracy.
I think this is really just the question of "but how do we know whether we aren't completely blinded to the truth entirely!".
I'm not really a Platonist though. I do think Tegmark's Multiverse does have the benefit that I don't think it is postulating that you're *accessing* that mathematical truth directly/causally in some manner, just that you're within it.
An alternative answer to your question is that there's logical relations between the two. Like how a calculator on the moon and earth will output the same answer given the same answer.
It's difficult to look at the world and not see mathematical structure. Scientific progress and the regularity of various phenomena certainly persuade us.
But even if you argue that selective pressures guide us towards more accurate beliefs, all you really establish is that "seeing the universe in this way is good for survival." It does not necessarily mean that you've apprehended the underlying structure.
To your point regarding Tegmark, I think the notion that you could be immersed in some universal all-encompassing structure without having access to it is problematic. You could make the same argument about any metaphysical driver of reality (god, allah, spaghetti monster).
The philosopher Justin Clarke-Doane has written about this extensively. One of the points he makes, which I think is fascinating, is that mathematical realism and moral realism are structurally analogous positions. As in, they both revolve around the existence of abstract structures and how are beliefs relate to them. And as such, whichever position you take on one, ought to be the same as your position on the other.
> It does not necessarily mean that you've apprehended the underlying structure.
Sure, but you've apprehended a good amount of structure visible to you. It may be we're in a computer simulation in one part of the Tegmark Multiverse, which runs on different rules in fundamental reality.
>To your point regarding Tegmark, I think the notion that you could be immersed in some universal all-encompassing structure without having access to it is problematic. You could make the same argument about any metaphysical driver of reality (god, allah, spaghetti monster).
I agree. I tend to view Tegmark as a "reasonable default hypothesis" that doesn't assume a single universe or any specific creator entity.
Tegmark-style multiverses do works nicer with the problem of computation requiring some interpretation applied to it. "How do we interpret what this matter is doing" is technically relative to some language, like Tegmark. If you take this fully literally, then you end up with a Tegmark-like multiverse relative to our physics even in single-universe scenarios.
I do think this latter part is quite speculative, so not saying I necessarily believe it, but that it 'shows up' multiple times makes me suspicious that it is hard to get away from.
> The philosopher Justin Clarke-Doane has written about this extensively. One of the points he makes, which I think is fascinating, is that mathematical realism and moral realism are structurally analogous positions. As in, they both revolve around the existence of abstract structures and how are beliefs relate to them. And as such, whichever position you take on one, ought to be the same as your position on the other.
I'll possibly read some of their work, but I'm immediately skeptical.
I accept the view that if mathematical realism holds, then I can find mathematical structures that represent my morals (probably not uniquely specified), but that's distinct from the usual moral realism claims about objectivity because it has no implication of thus applying universally.
"That mathematical truth is ''embodied'' within reality ". Many of the contentious areas within maths are connected with infinity, which cannot be observed physically.
There's one more important ingredient to add: while the rules of the Game of Life are probably simpler than the rules of physics, the conscious-being-density in the Game of Life is probably *much* smaller than the conscious-being-density in the mathematical object containing our universe.
It's good to see that Scott has moved on from the denial/anger stages of realizing his error (i.e. "there isn't any evidence for God's existence, what are you talking about") to the bargaining stage (i.e., "okay, yes, it does seem like there's actually a lot of evidence for God's existence, but it's possible to explain all that away if I make a bunch of highly questionable motivated assumptions"). Nevertheless, Scott ignores several critical asymmetries in these two theories.
First of all, God's existence isn't only supported by theoretical arguments. Rather, these theoretical arguments are additions on top of whole libraries of first-hand accounts from people who reported having observed God's existence empirically. OTOH, in the entirety of recorded history, there's not a single reported account of someone observing an actually-existing set of all possible mathematical objects. So, even if it were true that both hypotheses were equally supported theoretically, the theistic explanation would still be heavily favoured overall.
Secondly, like most atheists trying to refute the fine-tuning argument, Scott ignores the critical difference between making predictions which are validated by later experiment vs. inventing a theory to explain away experimental results after the fact. Theists did not find out about the fine-tuning of the Universe and then posit a God to explain it. Rather, the notion that the universe was intelligently designed by an entity with a special interest in human life was formulated first, by ancient peoples who had no way of knowing anything about modern cosmology, and then in modern times we finally developed the technology to confirm that our Universe's physics really does appear as if it was designed by such an entity. So, even if atheists *today* managed to come up with another theory that explains the constants equally well, the weight of evidence would still be against them, at least until they demonstrate that said theory is also good for making successful predictions and not merely for *post hoc* rationalizations.
"Rather, the notion that the universe was intelligently designed by an entity with a special interest in human life was formulated first, by ancient peoples who had no way of knowing anything about modern cosmology, and then in modern times we finally developed the technology to confirm that our Universe's physics really does appear as if it was designed by such an entity."
I think the last part of your sentence is exactly what's in dispute. Is there more to the appearance of design beyond "I predict that our universe will turn out to support life"?
>I think the last part of your sentence is exactly what's in dispute.
It really isn't. The appearance of fine-tuning in physics has been well-established for decades.
>Is there more to the appearance of design beyond "I predict that our universe will turn out to support life"?
For God's sake (pun intended), YES! A *lot* more!
Firstly, and most pedantically, a Universe which supports life isn't necessarily one which supports *human* life. As I say, this is a pedantic point because the basic reasoning of the fine-tuning argument, at least in its most common form, doesn't really change either way.
Secondly, knowing that the Universe supports human life doesn't of itself imply that the Universe that *required fine-tuning* in order to support life. One could imagine a Universe in which intelligent life forms exist, develop the technology to calculate the requirements for their own existence, and then realize those requirements are pretty broad and have a high probability of arising from random fluctuations. Instead, we find that our existence depends on a vast array of very narrow conditions that seem unlikely to have all been met independently by mere coincidence.
Thirdly, knowing that the Universe supports human life doesn't imply anything about our ability to *discover* the ways in which the Universe is fine-tuned to support human life. One could imagine a Universe in which the constants are fine-tuned to support intelligent life forms, but said life forms have no way of discovering what those constants are; and in fact this is basically what the actual Universe is like from the perspective of dolphins or non-human apes. The set of physical conditions required for humans to notice that the Universe seems fine-tuned for our existence is, necessarily, even narrower than that required for humans to exist in the first place, and hence even less likely to have arisen by coincidence.
Note that this last point is especially important in that it specifically indicates an intelligent designer with some kind of special interest in humans in particular, which addresses the "how do you know God isn't fine-tuning for stars/beetles/[insert other object here]?" rebuttal to the original fine-tuning argument.
The dispute I was referring to was whether what you call “fine-tuning” gives the appearance of intelligent design. If that were an irresistible conclusion, then such design would be a consensus view among physicists.
Instead we have physicists embracing the multiverse theory, sans any direct evidence that any other universe exist. Instead we have physicists embracing string theory, a highly fanciful and imaginative theory that also lacks experimental evidence. Physicists are a fickle bunch.
Absolutely, but that supports my point about a lack of consensus! I don't claim that intelligent design/god is less well supported than multiverse theory or string theory, only that it isn't any better supported.
>If that were an irresistible conclusion, then such design would be a consensus view among physicists.
That would be true if I'd said it gives *proof* of intelligent design, but I didn't.
The mere fact that we're discussing whether the MUH has "obviated" the fine-tuning argument shows that atheists (at least those making this argument) already acknowledge the appearance of design. If they didn't think the observed values of constants looked like plausible evidence of intelligent design, then there would be no need to propose an alternative explanation in order to obviate the argument.
"we find that our existence depends on a vast array of very narrow conditions that seem unlikely to have all been met independently by mere coincidence."
Perhaps I don't understand that point, because unless you assume that there is at most a specific number of universes and no more, how is it that fact any different from our Earth being much better for life than other planets, which nobody would think is a good argument?
Look up, the number of stars is unfathomable. That's our galaxy, and the number of galaxies is also unfathomable. The universe itself stretches beyond what we can see. I'd be shocked if it were finite in space. Isn't it a reasonable inference, then, that the number of universes is also unfathomable? For the fact to matter that the conditions required for us to exist are narrow, you'd have to put a specific ceiling on the number of universes that exist, and how can you do that?
If the Earth were at the center of the only solar system in the universe, as the ancients believed, I wouldn't suspect countless universes. But when we see countless stars and countless galaxies, where our own planet is an otherwise generic one which happens to be more compatible with life than most of the others, the odds go up that the same applies to universes, in my opinion. You have to admit it's a pattern. And if to solve a puzzle we must choose between countless universes and an intelligent designer, such an increase of odds makes a big difference.
>Perhaps I don't understand that point, because unless you assume that there is at most a specific number of universes and no more
Faulty premise. The belief that there is only one Universe/set of physical laws isn't an "assumption", it's an inference based on the knowledge that we've observed no evidence suggesting the existence of multiple universes. Unless you count the branches of the wave function in the many-worlds interpretation as "universes", but those all share the same set of physical constants and initial universe conditions, so they aren't the kind that would be needed to resolve the issue.
And no, the existence of a multiverse can't be reasonably inferred from the existence of vast numbers of stars and galaxies, for the obvious reason that we have no evidence those things are connected in any way.
No, I'm definitely not talking about the many worlds interpretation of quantum physics, nor as far as I can tell is Tegmark in his theory.
"it's an inference based on the knowledge that we've observed no evidence suggesting the existence of multiple universes" the evidence suggesting multiple universes is that our universe is much more compatible with life than a universe at random would be.
Also, there are countless stars and galaxies, in which our planet is much more compatible with life than a planet at random would be. It's a precedent. It's similar enough to the other thing (see paragraph above) that it makes it more probable, compared to how probable it would have been if we were in a Ptolemaic universe.
If there are other universes not connected to ours you would not see any evidence of them other than what I've mentioned. You can't possibly infer that they don't exist from absence of evidence that would be absent anyways.
>Also, there are countless stars and galaxies, in which our planet is much more compatible with life than a planet at random would be. It's a precedent. It's similar enough to the other thing (see paragraph above) that it makes it more probable, compared to how probable it would have been if we were in a Ptolemaic universe.
Things don't become truer just because you repeat them. In order for your reasoning to hold, you'd have to demonstrate that there's some reason why the number of sets of physical laws* existing in different universes should be similar to the number of stars in one universe, which you can't because we have no evidence that any such reason exists.
>If there are other universes not connected to ours you would not see any evidence of them other than what I've mentioned. You can't possibly infer that they don't exist from absence of evidence that would be absent anyways.
"If there's an invisible inaudible dragon in my garage that's impervious to touch, you would not see any evidence of it other than my telling you about it. You can't possibly infer that it doesn't exist from absence of evidence that would be absent anyways."
As I recall atheists were once so fond of saying, "What can be asserted without evidence, can also be dismissed without evidence."
And let me add another point. Suppose we take your "precedent" argument seriously, what makes you think extending the precedent would help the atheist case? Look at it from another angle -- the original motivation for positing a benevolent God wasn't based on modern physics; it was based only on observing that *Earth* had to meet specific conditions to be habitable, as nobody at the time knew anything about other planets. Then it turned out there were a bunch of other planets in the solar system without life, but that wasn't enough to salvage the atheist standpoint, because the solar system itself had to meet similarly narrow conditions to produce even one planet that was capable of sustaining life. Then it turned out the solar system was also just one of many in the Milky Way, most of which don't appear to contain life, but it still didn't solve things for atheists because it turned out that the Milky Way also needed to meet a number of narrow conditions to be able to produce even one solar system with life. Then we discovered the Milky Way was just one of many galaxies in the Universe, most of which may not contain life, but that also didn't solve the problem, because it turned out that the Universe itself had to meet remarkably narrow conditions to produce even one galaxy capable of sustaining life. Why not extrapolate from precedent and say that, if we could observe whatever meta-laws govern the creation of different physical laws in different universes, we'd see that those laws *also* needed fine-tuning to produce even one universe with life, and so atheists would be left with essentially the same problem as before?
* You keep talking about the "number of universes", but it's the number of sets of laws of physics that is actually relevant here. You could equally plausibly posit multiple universes that all shared the same laws of physics, which would only make things worse for the atheist, since then all other universes would also display the same fine-tuning. This would also make a whole lot more sense with your "precedent" argument, since none of the examples you cited involved discovering that the laws of physics were different in the newly-discovered regions.
People who claim to have seen God are just that - claimants. It doesn't matter how many there are, it's not reason to accept what they're saying at face value. They don't even need to lie, just believe something false or wrong themselves.
People who claim to have seen Robert Downey Jr. are just that—claimants. It doesn't matter how many there are, it's not reason to accept what they're saying at face value. They don't even need to lie, just be a normal amount of credulous about Hollywood.
Yeschad.jpg I don't care about Downey Jr. claimants one way or another. The only way the "Downey Jr." concept matters in my life is through media content I watch that allegedly features him. If some impostor did it instead, or an alien robot sent to Earth as a joke, I don't care in the slightest.
If the only thing I heard about RDJ is that people claimed to have seen him, but he wasn't in any movies and I couldn't find him looking around in Hollywood, then yeah, I can't take those people's word for it.
>People who claim to have seen God are just that - claimants. It doesn't matter how many there are, it's not reason to accept what they're saying at face value.
First of all, this is just stupid. In the absence of other considerations, something being independently reported by numerous observers is obviously a reason to update strongly towards its being true, it's astonishing that this even needs to be argued.
Secondly, this would be irrelevant even if it were true, because my whole point is that you can't just take each piece of evidence individually without considering the whole picture. All else being equal, a theory supported by multiple independent lines of evidence is more plausible than one supported by only one of the same lines, even if none of those lines are by themselves adequate to prove either theory. So even if there's another theory that explains away fine-tuning but doesn't explain accounts of God, or one that explains alleged accounts of God but doesn't explain why the Universe appears fine-tuned for life, these would still be less favoured compared to the model which explains both.
> something being independently reported by numerous observers is obviously a reason to update strongly towards its being true, it's astonishing that this even needs to be argued
It's not remotely astonishing. Look at all the reports of UFOs. Or the chupacabra, or bigfoot, or cat-eating Haitians. Independent reporting from numerous observers is at best evidence of some shared phenomenon. Some of those observers may interpret that phenomenon correctly, but there's no reason to assume the majority or even a significant minority will.
If the notion of "independent observer reports can't be evidence for a phenomenon being true" were taken seriously, it wouldn't mean you got a convenient excuse to reject a handful of claims considered low-status amongst your tribe while leaving the rest of your knowledge untouched. It would mean throwing out *the entire concept of empirical evidence*, and with it, all of science and history. Outside of pure mathematics, there is literally *no* way of supporting *any* claim that doesn't rely, directly or indirectly, on eyewitness testimony.
No, there is a way of doing that, it's just time-consuming. I could spend my whole life replicating papers that come out and seeing if they're true or not. It would be expensive and time-consuming, but not impossible.
The difference here is that eyewitness claims about God can't be replicated. You can do everything an eyewitness claims they did and not see or experience what they did. You can even do this *seconds* after they claim to have seen God and still not see what they do.
No, it's not reason to update to that, because we know that humans are not reliable eyewitnesses. That holds true even if I trust all those people to not being trying to lie.
If you're referring to near-death experiences as evidence for God, I mean... yeah, okay, I guess you could take that as some kind of testimony on the existence of an afterlife, but it also tends to contradict the specific claims made by any given religious tradition. (I'm sorry to disappoint certain Christians, but near-death Hindus do not generally report boiling in lakes of fire for the sin of worshipping demons, for example.)
The fine-tuning argument is really only relevant if an intelligent designer was governed by simpler laws that required less fine-tuning compared to "suddenly there was a big bang", which is a question I don't think we're well-equipped to answer right now.
It should also be remembered that having an intelligent designer is not necessarily the same thing as said designer being benevolent, omniscient, or all-powerful. (Olaf Stapledon's Star Maker is an interesting exploration of alternative motives for such a being.) Those are separate claims that require separate lines of evidence/argument.
>If you're referring to near-death experiences as evidence for God,
Who said I was only including near-death experiences? Some reported encounters with God involve near-death experiences, but many don't.
>I guess you could take that as some kind of testimony on the existence of an afterlife, but it also tends to contradict the specific claims made by any given religious tradition.
I'm not sure that's true, but even if it is I didn't say anything about God having revealed the true religion (nor about an afterlife for that matter), so this is irrelevant.
>The fine-tuning argument is really only relevant if an intelligent designer was governed by simpler laws that required less fine-tuning compared to "suddenly there was a big bang", which is a question I don't think we're well-equipped to answer right now.
Wrong. Even if "suddenly there was a big bang" explained why the Universe existed at all (it doesn't), it's not even attempting to explain why the resulting Universe seems fine-tuned to allow for intelligent life.
>It should also be remembered that having an intelligent designer is not necessarily the same thing as said designer being benevolent, omniscient, or all-powerful. (Olaf Stapledon's Star Maker is an interesting exploration of alternative motives for such a being.) Those are separate claims that require separate lines of evidence/argument.
Even though I do think there are good reasons to attribute all of these traits to the designer, I think it's simpler to just note that it would be a very strange sort of "atheist" who'd admit that there's an intelligent being that exists outside of the Universe, and which designed everything in the Universe with the goal of allowing for human life, as long as you don't ask them to admit it's a "triple-omni" designer. Like I said in my first comment, for an atheist to move from denial/anger to bargaining in this way would be an encouraging sign.
> Who said I was only including near-death experiences? Some reported encounters with God involve near-death experiences, but many don't
Okay, but as others have pointed out, there have also been thousands of reported encounters with Elvis.
> I didn't say anything about God having revealed the true religion...
No, but it is also a little suspicious that NDEs only match the afterlife described by Religion X when the experiencer also believes in Religion X.
> Wrong. Even if "suddenly there was a big bang" explained why the Universe existed at all...
By technical definition there can't be an explanation for the universe, because the universe is defined as 'all that exists', and any prior chain of causation would be redefined as part of itself. And as I already said, you can't just assume that an agent capable of fine-tuning the parameters of physics would itself require no fine-tuning. The design-capable beings we typically encounter in life were extremely fine-tuned by millions of years of evolution.
It's also worth pointing out that a pre-20th-century cosmologist could have argued that, e.g, the earth's distance from the sun, possession of a magnetic field strong enough to deflect the solar wind, and right balance of gravity, water and greenhouse gases to allow for an atmosphere and land-based life to evolve were all stupendously unlikely to occur by chance, and that this could all be taken as evidence of the earth being consciously designed to allow for human life. ...until it turned out there were a hundred billion stars in the milky way, most of which have planetary systems, and more galaxies in the universe than there are grains of sand in all the beaches on our planet. Stupendously unlikely things can occur all the time in a large enough universe.
I'm not personally fond of the multiverse hypothesis as an answer to fine-tuning of the universe's physical constants, and as of now there's no direct evidence for other branches of a multiverse, but... there is certainly precedent in the history of cosmology for creation being more expansive than we initially assumed.
> Even though I do think there are good reasons to attribute all of these traits to the designer...
If the goal was to create intelligent life capable of civilisation, and you are both omniscient and all-powerful, why not just... create human beings (or whatever other species you fancy) ex nihilo on a planet configured to be hospitable to their civilisation from day one? What is the point to creating trillions of stellar systems that are utterly devoid of life, and billions of years of terrestrial history where life is restricted to anaerobic microbes with no trace of sentience, followed by aeons of animal carnage and millennia of stone age savagery, before some sufficiently-sensitive ape finally manages to tune in to the right astral frequency to receive God's divine word and moral guidance? And, I dunno, maybe toss in a few words about penicillin along with the ten commandments?
In short... why doesn't the history of the universe at least loosely resemble what's written in the bible? It seems like a bafflingly inefficient way for an omnipotent entity to achieve the presumed goal of "create life / sapience / civilisation and be nice to it" that the earth *isn't* 6000 years old and at the centre of the cosmos.
You say Scott is in the bargaining stage but you're in yhe denial stage. What are you doing? Trying to overturn the laws of physics with unreliable eyewitness testimony? Surely you understand how absurd that is.
Don't single out one side for disrespecting the law of physics when the other side is making incredibly fanciful claims like "all human beings are mathematical objects" and "all mathematical objects exist." Lots of fanciful imagining going on on both sides.
Atheists b like God's not real the material world is just an emanation of the Psyche which is just an emanation of the Logos and we can affirm no cataphatic claims of any radical aseitous ground of being beyond that
The hole in this argument is that by accepting all possible mathematical objects exist, you have to de facto accept that, well, mathematical objects exist. Like, non-physical mathematical objects. This backdoors you into mathematical Platonism which has...implications.
Tegmark's Mathematical Universe theory faces similar problems to more standard physical multiverse hypotheses as a response to the fine-tuning argument. First, it predicts that most observers would be "Boltzmann Brains". It's not right that, as the post suggests, "a conscious observer inevitably finds themselves inside a mathematical object capable of hosting life." Although most mathematically possible universes have parameters that don't allow for complex life to evolve in the way we think it did in our universe, that doesn't mean there are no observers at all in those universes. Even in a universe at a state of thermal equilibrium (maximum entropy), there should be very infrequent chance fluctuations that lead to Boltzmann Brains: particles that have organized themselves into a functioning brain in a sea of chaos surrounding them. And while these fluctuations are very infrequent, since a fine-tuned universe is *so* unlikely, in the space of all possible universes, there are still vastly more Boltzmann Brain observers, most of whose experiences are a jumbled mess, than there are observers with highly ordered experiences as of a fine-tuned universe. So if we are random observers in the space of all possible universes, it's vastly more likely that our experiences would be a jumbled mess than that they would be of the ordered kind we actually have. (How much more likely will depend on how we sort out the simplicity weighting, but I don't think any principled weighting will avoid this conclusion.) On the plausible assumption that it's more likely that our experiences would be ordered if the universe was created by God, our experiences are then evidence for God over all possible universes existing.
Second, recent work on the fine-tuning argument by Robin Collins has looked not just at fine-tuning for life but also for the discoverability of the universe by science. In brief, various physical parameters seem to be optimized not only for life but also for making the universe discoverable. The most striking example is the strength of the cosmic microwave background radiation, our main source of evidence about the Big Bang. This is a function of the photon : baryon ratio in the universe. It turns out that the photon : baryon ratio is at the value that maximizes the strength of the cosmic microwave background radiation. There are several other examples that Collins has discovered, although this is both the most striking and the one most readily accessible to non-physicists. A presentation Collins gave on this is on YouTube here: https://www.youtube.com/watch?v=yIMFhPH3m0g
This discoverability evidence is, as far as I can tell, not explained at all by a multiverse or by Tegmark's theory. Most of the life-bearing universes -- even the highly-ordered ones, setting aside Boltzmann Brains here --- are not nearly as discoverable as ours, and there's no reason, if we're in a multiverse, to expect that we'd find ourselves in this one rather than one of those. For example, the photon : baryon ratio could be anywhere from 0 to infinity, consistently with the existence of life; that we're in the universe in which it maximizes the CMB is made no more likely by the hypothesis that we're in a multiverse than it would be otherwise.
The main thing I got out of Sean Carrol's paper “Why Boltzmann Brains Are Bad” (https://arxiv.org/pdf/1702.00850) is that we don't yet know whether Boltzmann brains are possible in our universe. They're an interesting hypothesis though. The second most interesting thing is that I had imagined them as "popping into and out of existence", whereas they'd actually require a good deal of time and heat dissipation to successfully form (which is part of why they might simply be physically impossible).
I don't think you're correct that the observations of a Boltzmann brain would be a jumbled mess. But that's a speculation on top of a hypothetical.
The Boltzmann brain argument doesn't seem right to me. Yes, fine-tuning means habitable universes are rare. But Boltzmann brains ought to be spectacularly rare. There are 10^27 atoms in a human brain. If they have to be in some specific arrangement to cause consciousness, this suggests...I don't know exactly how to do the problem, but it's going to be some kind of combinatorics that starts with 10^27 and gets worse from there. And that will only produce one Boltzmann-brain-moment, while a truly habitable universe could create trillions of life forms lasting for billions of observer-moments each.
I would guess that the things we know about are discoverable because there are many things and we don't know about the nondiscoverable ones.
The problem is that it's really hard to get a life-permitting universe. You need fine-tuning which is very rare, and extremely low entropy, which is especially unlikely because entropy is constantly going up. Just like it's likelier that monkeys will type a sentence of Shakespeare than the whole book, it's likelier that you'd get a brief patch of order than a whole world of it.
I don't understand why "entropy is going up" is relevant here. This is a statement about the arrow of time within universes. Universes can still come into existence with low-entropy (in fact I think Tegmark implies that they do, since low-entropy starting conditions are "simpler"), and they can host life during their low-entropy early stages.
I agree fine-tuning is rare, but Boltzmann brains should be even rarer! If you're generating random text, the chance that it happens to be a five line computer program specifying a cellular automaton capable of life is very low, but the chance that it's a full-fledged AGI is even lower!
"If you're generating random text, the chance that it happens to be a five line computer program specifying a cellular automaton capable of life is very low, but the chance that it's a full-fledged AGI is even lower!"
I don't think that's quite an apples-to-apples comparison though. We're not generating random text, we're generating random seeds, and then the seeds are generating text. We're considering two types of seeds:
1. Seeds that have some structure that lets them regularly generate comprehensible text.
2. Seeds that lack such structure, and thus generate only random text.
The BB argument (as I'm understanding it) is that seeds of Type 2 are more common than seeds of Type 1. And any such seed will generate LOTS of text. So for every orderly universe with stars and galaxies and life you should have many, many disordered universes which can't generate those things (but each have a tiny chance per unit of spacetime to birth a BB).
I'm not sure I how seriously to take this argument, because I think it assumes things about the distribution of seeds that isn't really in evidence. But it certainly seems like SOME ratio of Type 2 to Type 1 seeds would produce an excess of BBs.
[1] Though the word "random" seems slightly suspect here, it might have to be "pseudo-random."
I agree this is true, but I don't think it changes the situation very much - the main parameter everything depends on is still the likelihood of random text generating a Boltzmann brain. I agree you multiply each side by a few constants (the orderly side by the number of observer-moments per orderly universe, the disorderly side by the number of fluctuations per disorderly universe), I just don't think these are likely to matter very much compared to the extreme unlikelihood of each fluctuation.
Not that I really trust calculations here, but https://physics.stackexchange.com/questions/336274/are-boltzmann-brains-really-possible says you need about 10^150 universes to get one Boltzmann brain. Suppose there are 10^15 observers per universe, each lasts for 10^10 moments, so total of 10^25 observer moments, that means you need 10^175 disorderly universes to equal one orderly universe. I usually hear fine-tuning proponents say the universe is fine-tuned to something like 10^50. I'm sure once they hear this argument they'll up their numbers, but for now that gives us a comfortable 10^125 margin of error.
I like trying to ground this with actual numbers: I do think that illustrates the problem much better (even when they are provisional and suspect).
Huh. This is sort of tangential, but I just noticed that if we believe in a Tegmark Universe, that belief should cause us to expect physics to ultimately explain away fine-tuning (or at least scale it back significantly). A universe with only a few free parameters that give rise to all the rest ought to be much simpler (for any coherent definition of simplicity) than one which has a great many that are all independent.
Okay, this comment may help clarify some of our disagreement. I can try to look up some numbers when I have more time later, but 1 in 10^50 is the kind of value people typically suggest for the degree of fine-tuning of a *single* parameter. If there are, say, 20 parameters and they're all independent, then the probability of them all being fine-tuned will be much lower. In addition, the value for the probability of the universe being sufficiently low entropy is typically estimated as *much* lower, more like 1 in 10^(10^100).
Again, I can try to look up numbers and sources for them later.
I think 10^150 is a WILD underestimate for the rarity of Boltzman brains. It implies there is some way to fit a conscious observer in a tweet. (In specific, within 150 digits) That is not much information.
A code golfed description of game of life or physics that bootstaps conscious life, sure, that might fit in a tweet. But that's the regular universe option. You need to fit the conscious mind directly.
Entropy going up matters because high entropy worlds can't produce stable life but can produce Boltzmann brains. So there's an infinite period during which they can produce Boltzmann brains and a finite period during which they can't (at least, by default).
Most states of the universe will be at almost maximum entropy, even if it starts at low entropy (and the start should not count more that any given moment).
Even if they are way more beings at low entropy by unit of "time", there are exponentially more time at high entropy.
Take any universe that has our universe's history for the little portion including your brain, and then an arbitrary history for everything else around it (for example, your table is now a watermelon as of five seconds ago). There are *vast, vast numbers* of those, for the kind of combinatorial reasons you describe. Unimaginably many. They are all defined by perfectly consistent mathematical structures. That's the Boltzmann brain problem, which is much worse here than in the ordinary case (where the brains were supposed to come from physical law, at least.)
You're going to have to put enormous weight on the "simplicity" side of the theory, and that side does not cohere with the "all mathematical structures necessarily exist" side in the least. It's an arbitrary kludge, and does not even make sense (i.e., does not appear to be actually definable). If you prefer, it is secretly another contingent physical law, sneaking into what is supposed to be a derivation of physical law from a necessary metaphysics. However you dress it up, it blows the whole thing up.
"They are all defined by perfectly consistent mathematical structures. "
Are they? This seems to be assuming facts not in evidence. For information-theoretic reasons it seems like large portions of that space cannot possibly be generated by simple mathematical structures. That the portion of the space that can be is larger than the portion of the space that describes lawful, ordered universes does not actually seem obvious.
Tegmark says *all* mathematical structures exist, not just simple ones. (He does try to weight simple ones more. I don't think that makes sense, as I've mentioned elsewhere in this discussion.)
The set of all mathematical structures must certainly be infinite. Without some sort of weighting--I'm not sure it *has* to be simplicity, but I'm also not sure it doesn't--you'd surely end up with infinite numbers of any sort of universe you can imagine, and some would be embedded as simple cases in vast mathematical structures higher up the complexity chain. At that point comparing the probability of one outcome vs another plainly stops making sense, so there's no way to argue that Boltzmann Brains should dominate.
(To be fair, I'm not sure that this sort of probabilistic-anthropic reasoning *ever* makes sense. But if it does, it surely needs to be done over a set where the probability masses remain finite.)
The way to argue that they would dominate is that, for every one of those more bizarre structures that was regular, there would also be the Boltzmann-brain ones, which are locally far more numerous. One can then use measure-theoretic or (more likely) topological or other types of counting arguments to suggest that all the other structure you're talking about is broadly orthogonal to the question of Boltzmann-brain counting.
Yeah, I think you have the wrong intuitions around simplicity. The Mandelbrot set is extremely simple. The million images that differ from the Mandelbrot set by one pixel are each vastly vastly more complex (unless you cheat by describing them as "the Mandelbrot set except different by one pixel", in which case they are at least one pixel more complex)
I didn't say anything about simplicity (neither did you in the post I was replying to). I can see why this retort would be relevant, though, in the context of your post. As I explained in other posts on this discussion (which you're not responsible to have read, obviously) I think the whole attempt to put some kind of measure on necessarily-existing mathematical objects using Kolmogorov complexity is hopelessly incoherent and doomed.
I agree with you that, using any of the Turing machines that is anywhere close to what a human would design, the Mandelbrot set is much lower-complexity than slight variations of it, and similar remarks would apply for Boltzmann brains. On the other hand, there are *a lot* of Boltzmann-brain universes, and if one is doing metaphysics, it appears to me to be arbitrary to conclude that any specific finite portion of them would be higher-complexity than Boltzmann brains. (Not that -- again -- I think the whole project can be made sensible in the first place.)
So, since I think that the Kolmogorov/simplicity move is incoherent, and since I think (moreover) that even if it weren't, the arbitrary-constant problem is actually far more fatal than people understand (when doing this kind of basic philosophy, as opposed to when doing machine learning heuristics or something), I think that you are stuck with the Boltzmann brains.
I think you're right that the favoring of simpler universes doesn't make any sense in the context of modal realism. It makes sense if only one universe exists to expect it to be a simpler one. But if all possible universes exist then it doesn't make sense to "expect" simpler ones more than more complex ones. If you are 1 of 100 people I march into 1 of 100 rooms that I've programmed with custom physics, the probability that you end up in the room with the simplest physics is 1/100. These are real rooms that you know exist; you're not more likely to end up in a simpler one if each room gets one person in it. Similarly, in a multiverse you're not more likely to end up observer A in a simpler universe than observer B in a more complex universe.
Scott suggests we need a simplicity weighting for the probabilities here to be well-defined, but I think we *might* be able to meaningfully *compare* probabilities under Tegmark's theory and under theism even if we don't have well-behaved absolute probabilites. It might be that we can meaningfully define ratios of probabilities, which is all you need for calculating posterior relative odds (prior relative odds x relative Bayes' factor), even if the absolute probabilities are undefined because of problems with infinity.
Thanks Scott! On the first point: yes, Boltzmann Brains are spectularly rare, but fine-tuned universes will be even rarer. Collins has a helpful analogy with scrabble tiles. Imagine dumping a bunch of Scrabble tiles on a Scrabble board. Assume that they all have to land into a slot. You're much more likely to have isolated words amidst a bunch of nonsense -- islands of order in a sea of disorder -- than you are interlocking words that look like a normal Scrabble game. The former is analogous to Boltzmann Brains, which requires low entropy just in one part of the board/universe, and the latter is analogous to a universe like our own, which requires low entropy in the whole universe.
I believe that this claim about relative frequencies should be true on grounds of entropy alone -- although simplicity weighting might impact this some. But the low initial entropy of the universe is not the only fine-tuned parameter. Estimates of the total number of independent fine-tuned parameters vary, but it might be somewhere on the order of 20. So this will push down the relative frequency of normal observers even more (unless non-fine-tuned universes are less likely to produce Boltzmann Brains, but I don't see why that would be).
However your point that a fine-tuned universe would result in "life forms lasting for billions of observer-moments each" is interesting, and is not one I've thought about in this context. Self-locating probabilities are super tricky, but I could see an argument that the number/distribution of *observations* in a theory is more important than the number/distribution of *observers*. Still, I suspect that even granting your point under Tegmark's theory there will be many times more Boltzmann Brain-style observations than normal observer-observations. But I would have to think quite a bit more to give a rigorous argument there.
You make it sound like the "real universe" condition is *strictly* harder than the Boltzmann brain condition, since the real universe has to include brains along with everything else.
But the claim isn't that random dust and gas coalesced into every single thing in the universe by coincidence. It's that the universe has physical laws that tend towards the creation of complex objects. Those physical laws are somewhat surprising (in that most random sets of physical laws won't allow complex objects), but not ultra-surprising (in the sense that they're probably a couple of things that would fit on a blackboard and have a single or double digit number of free parameters).
The coincidentalness of getting a blackboard worth of physical laws right, while high, is still less than the coincidentalness of getting every atom in the exact right place to form a working brain.
If this doesn't make sense to you, consider the Mandelbrot set, or some other beautiful fractal. The complexity of the fractal is actually *lower* than the complexity of some particular part of the fractal drawn manually, because the Mandelbrot set is just a short equation, and if you drew it manually you would need to coincidentally get every pixel right which would be an insane coincidence.
I think of a Tegmark universe as equivalent to the Mandelbrot set, and Boltzmann brains as saying that maybe a process of filling in pixels at random happened to generate a small part of it.
Does that make sense, or am I misunderstanding your argument?
Thanks. I think what you're saying makes sense, and I don't disagree with you that in principle comparatively simple starting conditions can give rise to comparatively complex wholes. (Indeed, as a theist I think this is in fact what happened -- I would just specify the simple ultimate starting conditions in terms of God and his intentions.) Where I disagree is with the application to the particular case of the physical laws governing our universe. Put otherwise, our disagreement is partly empirical rather than purely philosophical.
I am not a physicist, and so I could well be wrong here. But my understanding is that because entropy tends to increase, ordered complexity at time t+1 is more likely given ordered complexity at time t than otherwise. Extend this back to the beginning of the universe and we get the result that it's easier to get the ordered complexity of life later on if the universe starts out with a lot of ordered complexity.
Now, maybe your (Tegmarkian) idea here is that the kind of ordered complexity that leads to life can be mathematically described (much?) more simply than other initial conditions of the universe. But I don't think this is the case. At least, I'd want to hear more about why this is the case.
There's also still the point that this only touches on entropy, but there are lots of other finely-tuned variables, and the life-permitting ones ranges of those variables are not in general specifiable in a simpler way than the non-life-permitting ones.
On the second point ("I would guess that the things we know about are discoverable because there are many things and we don't know about the nondiscoverable ones"): there's something intuitive about this idea and I don't know exactly what I think about it. But I'm inclined to think the discoverability evidence still has considerable force even what it's taken into account. For the CMB example, there are two possibilities: if the photon:baryon ratio had been slightly different the CMB would have been undiscoverable; or, if this ratio had been slightly different, the CMB would have discoverable but harder to discover. (I *believe* Collins says the first of these is the case because the CMB is so weak, but I'm not sure.) In the latter case, there's no non-design explanation for why we would find that the value is *optimized* -- there are many worlds where we discover the CMB, investigate the photon:baryon ratio, and find that it's not optimized for discovering the CMB. In the former case, there's a clearer observation selection effect, but it seems all the more striking that the universe is set up to allow us to discover the CMB (which was crucial to the formulation of the Big Bang theory) when it's almost impossible for this to happen by chance.
(Note: I don't think Collins claims that in all the examples he looks at the relevant variable is optimized for discoverability; this is true in the CMB case but might not be in others. This is part of why I find the CMB example the most striking.)
Boltzmann Brains consist of an exponentially small fraction of high-entropy stuff, so they're extremely unreal compared to things that arise quickly from simple rules, like actual humans did. Fine tuning reduces that gap by a small amount, but the laws of physics just don't contain that much information compared to a Boltzmann Brain, even with seemingly fine tuned parameters.
Very simple (ie random noise) universes can contain boltzman brains. But those brains are very very rare.
The "fine tuning" arguments are about < 20 physical constants, that could mostly be 0.1% off without causing problems. That's about 200 bits of fine tuning. Probably less.
In other words, to get a universe full of life the normal way you need to hit fluke that's less than 1 in 2^200.
How many bits does it take to make a boltzman brain. A terabyte sounds roughly plausible as the size of an uploaded mind. So that would take a fluke of 1 in 2^8,000,000,000,000 to happen by chance.
Basically, the laws of physics as we know them (including constants) take less space to write down than any description of a conscious mind.
The entire argument misses the elephant in the room, which is a definition of a "conscious being". What is it, exactly? How can you have a subjective experience? How can you tell if anything else has a subjective conscious experience except by relating yourself to the other through communication? Could it be that there are lots of "alien" consciousness around us to which we simply cannot relate and hence do not recognize? Are all mathematical structures conscious then? If not, how can we really tell which are?
The new philosophy of God and universe will have to reconcile subjective with objective, transcendent with immanent, Western consensus-focused epistemology with Eastern observation-focused one in a dialectical synthesis. New approaches to reasoning would be required to do so. Only then a modern man has a chance to obtain a temporarily satisfying answer to the question "who am I" and "why am I here", which would, I suspect, be at the same time the answer to the question "is there a God", but in a way which you cannot currently imagine.
Before that, stuff like the mathematical universe hypothesis is an intellectual fidget that answers nothing. Come on, even in the text above - " mathematical objects are logically required to exist " - like wtf is that argument? Why logic exists then? Logic is a mathematical object itself, and there are many logics! You can invent/discover one yourself if you'd like.
Thinking of simplicity. Does all universes have the same rules set and just different starting points (which results in isosimple universes subset)? Or do they differ by the rule sets - so the games are different? Having more rules or adding limits and conditions result in less degrees of freedom and more simple in terms of behaviour and states universes? Is multiverse more simple than its universes? Moving through infinite "envelopes" of multiverses are we reducing or raising complexity/simplicity?
And the main one - is the mathematical apparatus is finite and isomorthic property of all universes? Math is the God?
The vagueness of Tegmark’s mathematical universe always annoyed me. See Jürgen Schmidhuber’s “A Computer Scientist’s View of Life, the Universe, and Everything” for a well-defined version of something similar (https://arxiv.org/pdf/quant-ph/9904050).
The problem comes in the assumption that the universe should be computable. The longer one thinks about that, the less sense it makes (here, obviously, "one" = "I"). Unless, of course, it's actually a computation. In which case, all the problems about our universe exist in the one where that computer exists.
A pretty interesting theory — but certainly incomplete, at minimum. The rules governing our universe are pretty simple, but "put a N foot x N foot x N foot box of atoms through every possible configuration" is even simpler and will produce just as many (or more) conscious brain states. So why do we live in a universe governed by laws of physics, rather than a permutation box?
You can get around this by applying some penalty for running time, maybe, but already the theory is looking less like a platonic ideal and more like a kludge.
At any rate, the easiest justification for God is one you left off your list — the existence of the supernatural! Christianity spread because of miracles, after all, and if you look there are lots of phenomena lying around that materialism has to tie itself into to knots to explain.
And supernatural phenomena are the one thing that Tegmark's theory categorically cannot tolerate.
Darn, I have an answer to my permutation box objection. It's easier to describe the permutation box in totality than to describe our universe. But it's much harder to specify a particular -location- in its spacetime (since it's going to run for an exponentially long period of time).
And the combination of box specification -plus- spacetime location that you would need to find a human consciousness in the permutation box, ends up being much longer than the universe-specification-plus-spacetime-location that you need to find a human consciousness in our universe.
//"logically necessary" needs a pretty convincing argument. and this argument doesn't say anything about the "why" of consciousness.
Cosmological: Why is there something rather than nothing? Because mathematical objects are logically necessary, and “existence” is just what it feels like to be a conscious observer on the inside of a mathematical object.
I'm very, very worried about the simplicity move. Viz:
1. All possible mathematical objects exist (compelling premise, makes sense independently)
2. So our chance of being any particular conscience being is kind of like sampling (makes sense)
3. But we couldn't just sample from an infinitely large set (I'm not entirely convinced on this one, but it seems to follow from our best mathematics)
4. Therefore our probability of being any particular being is simplicity weighted (????????????????????????????????????????????????????????????????? why)
Here's a gesture at explaining. It's obviously not rigorous.
Suppose you make an infinite list of universes and assign each one a discrete probability. You sort the list so the highest probabilities are at the top. Probabilities have to sum to 1. So as you go down the list, the probabilities have to keep getting smaller, in a way where the infinite sum converges to 1.
An important thing about complexity is that as you add complexity to a system, the number of possible arrangements of it increases. Or, as you make a system simpler, the number of possible arrangements of it decreases. For example, there are only a hundred integers with two digits (in base 10), but with three digits there are a thousand, and with a billion digits ... a lot.
Now for the tricky part. No matter how you arrange the infinite list, the average complexity has to increase as you go down the list. There are only so many simple entries, and so many more complex ones. There's a lower limit to complexity, it's easy to start there. But you can't put all the complex ones first because there's no upper limit to complexity. So however you arrange them, the complexity rises and the probability falls ... on average. With as many exceptions as you like. But still the trend must hold.
I will try to say this formally, maybe it helps someone:
Let X be arbitrary countably infinite set.
Let f be function from X to the reals for which:{x : x in X, f(x) < r} is finite for all r reals
Then, for any injective s: N -> X sequence, lim(f(s(n))) = +inf
Proof: We want to prove that for every K real there exists N natural for which for all n>=N natural f(s(n)) >= K.
By the property of f there is only finite amount of x for which f(x) < K, let's call this subset of X, A. Let I = s^(-1)[A ∩ s[N]] (finite set, because injectivity of s), then N=max(I)+1 is a good choice.
s is the ordering of beings by probability, f is some function measuring complexity
It's a subjective prior probability that, together with your observational evidence of the universe, represents your belief about which universe you inhabit.
Roughly, it's because we have no other option for the same reason it's impossible to define a uniform probability distribution on the natural numbers or the entire real number line.
I have to point out that you seem to be misusing the phrase "cellular automaton". A cellular automaton is a pretty specific sort of thing, not just anything with an initial state and a rule for running it forward! The term you're looking for would be something more like "dynamical system". (And of course our universe is continuous-time rather than discrete-time, and also time mixes with space, but...)
I have to point this out because, while the universe does seem to be described by simple mathematical rules, it does *not* seem to be a cellular automaton! (Despite what Stephen Wolfram claims.) In particular, trying to model the universe as a cellular automaton is going to run into problems with Lorentz invariance. (And trying to model it as a *classical* cellular automaton, as Stephen Wolfram seemingly wants to do, is going to run into problems with quantum mechanics...)
While this might be an argument against all-encompassing God which rules over an infinite cosmos, isn’t it also an argument for vast (or perhaps infinite) number of deities ruling over their own local pockets?
If all mathematical structures exist, doesn’t that means that every possible God exists too? (Abrahamic God, Jesus, Allah, Marduk , Shiva, Cthulhu , Perun, Thor, Thor who looks like Chris Hemsworth from Avengers…. etc)
Fine tuning is really only a problem if you think you know everything. Well, everything that it is possible to know about the constants of the standard model anyway. We don't know where the constants come from, sure. One of the possibilities a deity created them like that because he wanted to see interesting things. Another possibility is that they just that's how they are, no deity. Another possibility is that they arise from new physics that we haven't yet discovered. That's the humility option. That's the batshit obvious explanation, to me, at least. It's also the science option, like we need to go out and finding what's happening, rather than siting around in the philosophy department claiming you know. As far as I can see the massive recent advancement in knowledge is due to collecting data, thinking up explanations, and testing them. Why stop? I don't believe there was a guarantee that finding these things would be easy.
There are a number of big unsolved fundamental problems in physics including *relatively* mundane stuff like finding a way to fit general relativity and quantum mechanics together. It's unknown-unknowns territory but the fundamental constants might pop out of such a theory. Might, we don't know. To me, if you can't do GR-QM, you are in not really in a position to make any real claim about being in any kind of knowledge end-state. Hey, you're not god, stop pretending you are. Get to work.
Human religions always blow themselves up on their own contradictions, you don't even need alternative theories to reject them. Meanwhile this "all mathematical objects" thing seems to just be a variation on many worlds and the anthropic principle? Which we have had for a long time?
> By existing, you are a random draw from the set of possible conscious beings. You can’t make a random draw from an infinite set, but the accepted solution is some kind of measure weighted by simplicity. So even though every possible mathematical object exists, simpler ones exist more.
It's accepted that *this is what a solution would have to look like*, perhaps, but that's less impressive than it sounds. Where you have a notion of probability you *must* have a measure to go with it, by definition. And of course you're going to need to penalize complexity somehow, or you'll end up assigning measure zero to worlds with simple laws like ours.
But it's far from clear that such a measure even makes sense. First, there is no set of all mathematical objects; there are far too many of them for that. Measure theory doesn't have a chance in hell without first radically cutting things down - probably to some notion of "sufficiently finitary" objects in the sense of local presentability or something. And then once you've done that, you still need to figure out how to divide up probabilities between the measure over universes and the cosmological measures weighting different observers within one universe - and we don't know if such a measure is even possible for ours! "Basic probability theory might just not work in physics" is an option that Alan Guth, for instance, has started seriously floating.
I'm probably missing something, but it follows from the hypothesis that all possible mathematical structures exist that there are other mathematical structures in which I am conscious. Yet, I feel like I am only conscious in one such structure -- this universe. How does the hypothesis explain this?
You mathematically came to an idea of other univerese. You just can't sensually observe them. But I belive consciousness is a type of observation with ability to derive pinning mathematical properties and rules, and senses are just instrumental helpers here
Either you've had the exact same experiences (including the present moment) or you've had different experiences. A being who has had different experiences isn't you. A being who has had the same experiences is also you, but it doesn't matter, because for all you know you're all of those beings at the same time (there's no way to distinguish between them).
Wait, wait, wait! Fine-tuning does not necessarily require a god being to do the tuning. Bentham wants there to be a god being, so he latches on to F-T as an argument for a creator being. But at least a decade ago, Lee Smolin proposed a system of universal natural selection where the laws and constants that happen to promote the emergence of life (as in our current universe) are also ideal for spawning more universes. Bassani and Maguijo, in their recent paper "How to make a Universe" suggest a mechanism for how laws evolve in a newly instantiated universe through Markov chains, and if they produce matter and gravity, the laws will converge on a type of universe we exist in.
Although much of their math is beyond me, what I find most interesting is their comment: "For laws to 'appear' they must have evolved out of lawlessness, which could itself be defined as extreme variability in these laws." To my mind, that's the best argument of why a god-being could *not* exist. Whereas Bentham and other god-clutchers are looking for a law-giver to have inscribed 26 constants on the tablets of our universe, chaos was the original creator of our universe.
Reminds me of the story from Zhuangzi...
The Ruler of the Southern Ocean was Shu, the Ruler of the Northern Ocean was Hu, and the Ruler of the Centre was Chaos. Shu and Hu were continually meeting in the land of Chaos, who treated them very well. They consulted together how they might repay his kindness, and said, 'Men all have seven orifices for the purpose of seeing, hearing, eating, and breathing, while this (poor) Ruler alone has not one. Let us try and make them for him.' Accordingly, they dug one orifice in him every day, and at the end of seven days, Chaos died.
So UnoVersce is the most complex thing with less the rulles. Which is a bit contradictory to simple things are governed by simple set of rulles. Kind of casuality-simlicity uncertainty
I think "logically necessary" is just a word for the kind of thing that math is, and the claim that math is logically necessary doesn't require further proof.
I think you're conflating two things - mathematical objects are logically necessary in the abstract game we play within our minds, where initial axioms and rules of inference are accepted by fiat. But MUH posits that math "exists" independently of our minds, which is far from uncontroversial, let alone logically necessary.
When you explicitly acknowledge making such a move then sure, whatever, because it would instantly make it obvious that your position is extremely abstruse. Most people would readily agree that the sandwich they're currently eating exists, but it would take plenty of effort to sell them on the existence of a Platonic realm where Fourier transforms reside, which are also actually the same sort of thing as sandwiches.
But the universe isn't *that* simple, is it? I thought scientists were still trying to crack string theory, make a grand unified theory, etc? If our universe was truly Game-of-Life-simple, shouldn't we have cracked that hundreds of years ago?
Why? I don't think things like the identity of the weak and electric forces was obvious "hundreds of years ago". Many scientific discoveries are elegant equations, and many of them were discovered pretty late in the grand scheme of things.
This seems to be one of those theories that gets where it's going by destroying one of the words that it uses.
When religious believers say that God "exists", we mean that He interacts with the same world we all interact with. He exists in the way that rhinoceroses do and unicorns don't. If you look really hard, you can find a rhinoceros and you can find God, but you're not going to find a unicorn.
The various proofs for the existence of God are descriptions of how He interacts with the world to make it be how we observe it to be, and how, if He hadn't done so, we would observe something different. Look, the top is spinning; it spins because I spun it. It's not just lying there. Look, the world has motion in it, it's not just lying there. What was it from outside the world that put all this motion into it?
Under this theory of Tegmark's, if I understand it correctly, unicorns exist, along with every other fantastical thing you can think of. So the word "exist" isn't useful. Once you've accepted this definition of the word "exist", why would you think to argue about whether something exists or not? Who cares? Whether something "exists", per Tegmark, has nothing to do with whether I might encounter that thing in the world. You might as well prove that God doesn't tegflugeristerisk.
I'm not even sure that this Tegmark theory is operating on a close enough conceptual plane to theology to contradict it. You could probably even syncretize Tegmarkian cosmogony with a sort of Deist cosmogony, where you rename God "random draw". Grant that Tegmark's mathematic necessity is true, and it spins up a zillion mathematical objects. I'm experiencing being inside one of them. Cool. Why this particular one, and not some anti-anthropic hell? Well, either tautology (living beings can only live inside mathematical objects in which living beings can live), or something named "random draw", which might as well be a god, since it made me and the particular world I'm living in. That's ... actually, not that different from Hinduism, I think? There are innumerable worlds you might have ended up in, and the answer to "why?" is either "it is what it is" or "random chance".
I mean I guess it's also dead simple to syncretize Tegmarkism with Christianity. Tegmarkian mathematical necessity spins up a mathematical object with one three-part conscious being inside of it plus a supercomputer capable of simulating Earth & nearby space. There are probably more complex mathematical objects that a random selection from infinity would pick, this doesn't seem out of bounds. That conscious being, named "God", programs the supercomputer and starts it running, and we humans are the conscious beings living inside that simulation. Nice and tidy. Questions about mathematical necessity go back to Tegmark and questions about the anthropic principle go back to God. Chronos creates Zeus, Zeus creates humanity.
No need to speculate on how to integrate this with Christianity, the Church Fathers did that before the ink was dry on the epistles: what the platonists called the sum of Forms or Nous is to be identified with the only begotten Son through whom all things are made.
In the beginning was Tegmarkian Mathematical Necessity, and Tegmarkian Mathematical Necessity was with God, and Tegmarkian Mathematical Necessity was god...
"In the beginning was Tegmarkian Mathematical Necessity, and Tegmarkian Mathematical Necessity was with God, and Tegmarkian Mathematical Necessity was god"
This is why theology is fun! and I'm nowhere near knowledgeable about it to speak. But I'm sure Eastern Orthodox theologians, with their very well-developed work on divine energies, would love to tackle this.
I think it's tempting to call this Platonism, but I think it goes beyond merely affirming the existence of abstract notions and saying they had some part in forming the world. Or even raising them to the level of divinity in the person of Christ. This theory goes much further. It denies the existence of anything other than abstract notions. Abstract notions are all that there is.
I'm not up to date on my Plotinus; maybe the neo-Platonists had some such idea? It feels like Leibniz, too?
Unicorns don't exist in this universe. That seems sufficient to justify all of the normal meaning of "exist" to me.
I don't think this is any different than saying that (given the vast number of galaxies in the universe) probably some alien life form that looks like a unicorn exists on some other planet. Whatever, that doesn't threaten our epistemology at all.
To determine the probability of being a specific being in the multiverse, you'd need to multiply the chances of being in the world the being is in with the chance of being that specific being over every other being in that world.
I still find that confusing: saying "all mathematical objects exist and our universe is one of them" and then asking what the probably is of being a specific being in the multiverse... feels like asking "what is the probability that the sun will rise yesterday?"
Well then your problem is with the entire field of anthropics. This problem still exists when you ask the question of "what is the probability of being born in the US?"
The question "what is the probability of being born in the US?" implies some assumed process in which you are reincarnated and, say, randomly assigned to some baby born in the next day. Even though that's not the case, new babies are in fact being born, so it does has vague meaningful interpretation.
While I can imagine a similar process of being assigned to entities in the mathematical universe, isn't the whole point that all mathematical entities already exist? A more analogous question would seem to be "what is the probability that I will be born in the US?" - a question rarely asked in any field!
It may be an interesting hypothetical but there seems no reason to require it as part of the theory (which in Scott's post at least, it seems to be).
I have not read Tegmark, but the description of his ideas here seems like it's mixing map and territory (i.e. jumping from "math describes the universe" to "the math is the universe"). Am I misunderstanding?
The “self” is an anthropomorphic convenience. There are only particles and vectors. Only 2% of the atoms in me today were in me a year ago. Human thoughts, motives and conduct are deeply epiphenomenal. Centering consciousness in one’s ontology is deeply misguided.
Within a decade or two, AI may have made the problem of consciousness seem like an old fashioned hangup. Seems pretty clear to me that purely physical systems can do all the things we expect of a homunculus.
How would you define consciousness? My best guess is ability to uncover and understand math, describing universe. But this definition is not mathematically solid. One step further, and we have religious cult of mathematicians ))
And what is will? Although some doesn't believe it really exists and saying we are all preprogrammed and caused.
Does consciousness need to have a mathematically solid definition? "Table" does not have a mathematically solid definition, but this does not invalidate the existence of tables nor the Mathematical Universe Hypothesis.
I don't get it. What's the point of this? Is any of that even remotely falsifiable? Does this hypothesis make any predictions that can ever be observed? If not, it's not a theory, merely intellectual navel-gazing, and it cannot tell us anything about the nature of our reality.
Some people care why the universe exists. It seems cool to have an explanation that makes sense. If this doesn't interest you, you don't have to listen.
I do care why the universe exists, that's not the issue. The issue is that there are already many purported explanations for the existence of reality, and this hypothesis doesn't solve the question. It still has an essential assumption ("all possible mathematical objects exist") which is neither observable nor falsifiable, and it doesn't make any predictions that are observable or falsifiable, so why should Tegmark's idea be more convincing than any other explanation that isn't immediately self-contradictory?
Sure, it can be fun to think about mathematical constructs, and there's nothing wrong with that. But you seem to think that this hypothesis offers a deeper truth than any other explanation for the existence of reality, and I wish to understand why.
In particular, I don't see how this hypothesis answers these Great Questions:
> Cosmological: Why is there something rather than nothing? Because mathematical objects are logically necessary, and “existence” is just what it feels like to be a conscious observer on the inside of a mathematical object.
They're only "logically necessary" because the hypothesis assumes that "all possible mathematical objects exist", but there's no reason for this assumption, except to make the hypothesis work.
> First cause argument: All things must have a cause. […] But when you consider the automaton as a mathematical object, it doesn’t need a cause; you can start an automaton any way you want; […]
Then what's the cause for the existence of the automaton itself and for the rules it follows? If the existence of all mathematical objects doesn't need a prior cause, then how is that different from saying the existence of some God doesn't need a prior cause?
Is the quest for understanding the reason for existence misguided on a fundamental level? Our intuition of cause-and-effect developed in a small subset of reality, formed by sensory input of macro-level effects. Human brains can barely comprehend quantum effects like true randomness, no one knows for sure what quantum collapse really is – and that's for a theory with observable predictions. So why do we assume that our intuition about cause-and-effect even applies to reality as a whole, when the nature of the origins of the universe is so far removed from the world which shaped our intuitive capacity?
Have you read the universal prior is malign? If there are extra-universal demons wanting to harm me, I would like the philosophical (or any other kind really) tools to think about/defend from them effectively. This theory is one such in my view.
Isn't this falsifiable? You can try to formulate things more rigorously, figure out what it should look like to be the modal observer if the hypothesis is the case, and check how closely that matches our world.
We should assume that cause-and-effect applies to reality as a whole, or we will fall into plenty of trouble when we attempt to explain things. Presumably you would not be happy if I tried to tell you that some phenomenon (say, your wallet vanishing) happened causelessly.
> We should assume that cause-and-effect applies to reality as a whole, […]
I meant that specifically in the cosmological context. We shouldn't assume that the same rules which apply to our everyday observable life, also apply to the Big Bang or to the origin of the physical laws. The situation might be similar as with quantum mechanics, which follows rules that are very alien to the rules of everyday life, but at least with QM, we can conduct experiments and observe the outcome, and so we don't have to rely on an intuitive understanding.
For me to be more comfortable with that, I'd want some sort of bounds or explanation why causelessness would be restricted to some sphere. In QM, those who prefer there to be no cause for things at least can restrict it; it would only specifically be the resolution of wave-function collapses that is done purely at random. I would want a similar bounding argument for other examples. But that seems to be a real problem if we're talking about the world coming to exist, because, surely, if there's some source of randomness in the very coming-to-be of the world, then surely, from the greater to the lesser, we should accept that there might continue to be such events happening, even on a macroscopic scale, now.
It saddens me to see such otherwise smart and productive people waste so much time writing such confused and useless words, arguing about bleggs and rubes long after the tails have come apart, trying to use a map way beyond the territory it was adequate to represent.
None of those 5 "why" questions need answering for they are not well formed. "Cause and effect" is a useful notion when applied to things we can control and/or repeat and observe, but is not a useful notion to apply to "the universe existing". Clearly the universe exists! Let's spend our effort figuring out what we can do in it and what we should do next!
It makes no sense to claim "There would be something it was like to be" a being inside the game of life. "Qualia" is a useful concept within a mind, because knowing the difference between seeing red and seeing green helps me choose foods to eat, and knowing the difference between feeling feverish and feeling hungry helps me choose what to do, etc. But qualia is not a useful concept across minds; it is useless to argue over whether your experience of seeing red does or doesn't correspond to mine, or whether my neighbor has qualia at all or is in fact a p-zombie, or whether the game-of-life being is or isn't conscious. I will never wake up inside your mind and need to make choices based on my familiarity with your qualia. I will never need to bargain with the simulated entity in a way that is helped by my theory of its mind.
"Probability" makes sense in frequentist uses, and in estimated expected values for causal decisions in states drawn from a known distribution. But there is zero merit in trying to assign a probability to every universe or simulation you might be inside. Whatever universe/simulation you're in is the one and only you ever have or ever will be in; there is no distribution of alternatives that you can possibly know anything about, and no action you could possibly want to take in response even if you could.
This theory predicts that there is no God, and that you will not go to Heaven or Hell, nor resurrect come the apocalypse, nor reincarnate, or anything like that. What an important prediction!
If you die and go to Hell or Heaven, you will have experimentally falsified this theory.
I'm not sure if this was written in jest. In case it wasn't:
> This theory predicts that there is no God, and that you will not go to Heaven or Hell, nor resurrect come the apocalypse, nor reincarnate, or anything like that.
The theory makes no such prediction. If heaven and hell in the Christian sense are possible mathematical objects, then they exist according to the hypothesis – at least in some of the existing universes. If not, then they don't. The hypothesis doesn't provide any clues as to whether heaven, hell, reincarnation etc. are possible mathematical objects, or whether we live in a universe that happened to get a heaven (or a hell), so even if someone dies and goes to heaven, they have not gathered any evidence either way.
Well, I think it's clear that they would have gathered evidence (in that heaven/hell would be evidence towards theism, which in turn might be evidence against the necessity of this theory), but you're right that it wouldn't rule it out as impossible.
It actually does predict you will go somewhere after dying, since there's always going to be a possible continuation of you that didn't die, though I don't see any way to intentionally effect where you go.
An "explanation" which doesn't make observable predictions and which therefore can't be falsified, is neither science nor important to science. If you believe this hypothesis could be developed to produce observable predictions, I'd like to know how.
Occam's Razor is a heuristic to select among a set of scientific hypotheses _that make the same predictions_, and that's the important part. If a hypothesis doesn't make an observable prediction, as is the case here, then it's not a scientific hypothesis and Occam's Razor does not apply.
Suppose math is universal but rules and simclicity measure are different across universes. Shouldn't we have already predicted something that can't be observed and experimentally proved in our particular universe?
Your post doesn't really evaluate this "hypothesis". But it's not even false, it's nonsense.
What does it mean to say something exists? This is clear if it's a cup or a plate or a ham sandwich... you can go out into the world and see or touch it. If you're talking about a more abstract thing like climate change or an electron you can see its empirical manifestations.
The concept of existence cannot be applied to mathematical "objects". I can't go out into the world and collect evidence for the existence of the number three or the square root function. These are ways of describing the intrinsic structure of the world we experience but they are not in it.
Yeah. Like do all of the things that exist in Tegmarks universe exist like me, the train I am riding, and you exist. Or do they exist like 1+1=2 exists ?
If only the second, well then this isn't even an extension of mathematical platonism which doesn't tell you much about God even if you believe it.
If both, well that seems very weird. What reasons do we have to believe it ?
According to Scott above Tegmark thinks that even if there is no computer running the program with consciousness in it the consciousness is still conscious
Agreed. It's mathematically possible for a lattice composed of alternating matter and antimatter objects in contact with each other to exist, but I doubt it does in reality.
This sounds suspect to me. I am not sure if it is possible to reconcile with Godel incompleteness. If mathematical objects are all that exist then what about theorems that we know are true but cannot prove with the existing mathematical objects we have?
Things that we know are true but cannot be proved are taken as axioms. If a statement is independent of our axioms but we cannot prove it, I'd argue that it's not that we know it is true so much as the truth of the theorem is irrelevant to the thing that we are reasoning about.
It is very much relevant in this case since the thesis is 'All possible mathematical objects exist'.
Maybe solely using the word 'true' was imprecise of me, what I really mean is the relation between truth and provability. We are talking about provability *within a certain set of axioms*, these axioms being the axioms of mathematics in this case. I can create a mathematical statement that is true but not provable within these axioms.
You can add that unprovable statement as an axiom itself, but that creates a new axiomatic system with new unprovable statements. That is what Godel incompleteness means, that we cannot create a 'complete' axiomatic system, which is why I believe the thesis is not reconcilable with this.
Can you give an example of a statement that is true but has no proof in some standard system (eg ZFC)? The obvious answer is a Godel Sentence, but we don't "know" it is true without assuming the system's consistency, which we also don't know to be true.
"Know" to be true is sort of a misnomer since the truth of a statement is always relative to a set of axioms, but that is not the point. The point is if we assume an axiomatic system like ZFC that satisfies conditions for Godel incompleteness and say something like 'under these axioms, all possible objects exist', we run into the problem that we either can derive contradictions, or don't have enough axioms to prove truth (remember, *relative to this set of axioms*) for every possible sentence.
In the context of existence, this would mean that we have objects existing that are contradictory (think, a square circle), or objects that should exist according to our system but we can't prove they do.
Thus, I do not believe this is really a philosophically acceptable grounding for ontology.
"Things that we know are true but cannot be proved are taken as axioms."
Which brings us crashing up against "how do you know it's true?" People (including myself) don't take as sufficient "I just know X is true" (including "I just know God exists by the feeling in my heart").
For believers, God is an axiom. For mathematicians, it's apparently some concepts.
Godel's incompleteness theorem is strictly about the limits of formal logic systems. It means you cannot know all mathematical truths, it says nothing about the absolute existence of those truths.
Love your blog, love the content, only superficially considered the arguments, but I agree with commenters saying there are pretty odd assertions in here.
For anyone in the comments section by the way. I think the world so badly lacks for people to help others cross the bridge from deism to faith. It can seem like a colossal chasm to people who are skeptics. And I think there’s more to be written there.
I doubt that any more writing would matter much for nudging people to faith. Experience matters much more. If those who have ears will hear, those who have eyes will see.
If the Universe amounts to a basic mathematical model then I believe this must satisfy a sort of "net nothing" condition. It should also incorporate duals of itself within it, kind of embyonic copies of itself, and that implies it must be infinite.
It would also be nice, and seem to match observations (of extensive fields and local excitations) if its degrees of freedom are conformal, i.e. "inverted", with one or more replaced with their reciprocals to give a result which satisfies the same conditions. If the dynamics involves these inversions constantly recurring and interacting then rational values of them start to become relevant, as resonances, in fact the predominant means of change.
The variety (multi-dimensional hypersurface) defined by the simultaneous pair x1 . x2 . ... = k (for a fixed non-zero rational k) and x1 + x2 + ... = 0 is what is called a Calabi-Yau variety, and appears in keeping with the "net nothing" principle, i.e. a set of degrees of freedom whose product is unity (if k = 1, what I call "on-shell") and sum is zero. For three variables, it is an elliptic curve. But for four variables it has a rich structure.
The simultaneous pair R(k): x y z t = k and x + y + z + t = 0 defines a surface, and to find rational points on this one wishes to find rational curves on the surface. Euler found a first one in around 1740, but did not explain his method. Prof Elkies found a second of comparable complexity in the 1980s, or thereabouts, and I conjecture there is one more of similar complexity. (There are an infinite number of rational curves on the surface, but only two or, as I conjecture, three "simple"(ish) ones.) Note that Euler and Elkies considered R(k) in the birationally equivalent form of the single equation
(x^2 - 1)(y^2 - 1) = k z^4
I have found a general two-parameter solution for the surface when k is the square of a rational number, and from that every rational curve on the surface can be found (for any k) by a finite, albeit hellishly intricate, process. So this is work in progress. I have also found birational transforms which map this surface to one of the same form with k replaced by -k, i.e. R(-k) and another that maps it to R(1/k).
Rational points are sort of "concentrated" on the two (or three?) simple rational curves. So their overall distribution is analogous to one of those color vision test images where a pattern of dots stands out faintly from a random background of them (unless one is color blind!) I contend that ultimately this leads to a very slight tendency of excitations, stemming from rational resonances, to occur in three families and might explain the otherwise baffling and as yet unexplained fact that there are three families of particles in the Standard Model.
I mentioned above that there is a (complicated!) birational transform from R(k) to R(-k). This implies that the density of rational points (as a function of their "height", which is a measure of their simplicity) for k and -k are roughly equal. But they have subtle differences in their exact distribution. So if the equations for k correspond somehow to matter, and those for -k to antimatter then the differences in the exact sizes of rational points imply a slight asymmetry, which would explain the preponderance of one (with perhaps slightly more lower-height points say) over the other.
Well that is a brief summary of where I'm at so far. I wouldn't expect any physicist to give the ideas the time of day, and would quite understand, because it seems so remote from any prevailing physics rubrik. Also, the resonances produced by these rational values must seem absurdly weak to have any discernable effect. But if continued long enough, dripping water can wear a hole in the hardest rock, and the most fundamental processes being almost a limiting case of vanishingly small interactions continued almost without limit seems generally in keeping with the extremes already manifest in fundamental physics.
Note also that if the geometry of the Universe is ultimately based on multiple interacting copies of the variety R(k) (or its infinite dimensional analog) then that pretty much fixes the properties of fundamental entities and their behavior within it. This in turn means the basic laws of physics within each "arena" of the Universe, one being our universe (lowercase "u"!), will be the same, with no variations due to fine tuning.
So, who knows, perhaps one day, Diophantine analysis (the study of integer and rational points on varieties) will take centre stage in solving some of the deepest mysteries of physics, even if it seems among the least applicable areas of maths today! G H Hardy would be furious! :-)
Edit: Forgot to mention that the "on shell" equation R(1) i.e. equivalent to (x^2 - 1)(y^2 - 1) = z^4 has, despite appearances, three-fold symmetry because it is birationally equivalent over Q to the simultaneous set (in which any pair implies the third) :
(p^2 - 1)(q^2 - 1) = u^2
(q^2 - 1)(r^2 - 1) = v^2
(r^2 - 1)(p^2 - 1) = w^2
So perhaps that is the origin of color charges (assuming, as always, that the whole idea has any semblance of veracity)
I don't I don't find fine-tuning super convincing because:
1. other "not fine tuned" Universes might have interesting shit going on, if not life specifically, we just think life is the important thing because we are life, but if you look around at our entire Universe you'd think God really cared about galaxies and shit and life is just some detritus
2. I don't trust our scientists to figure out what a Universe with wildly different parameters looks like.
One example of "fine-tuning" is the triple-alpha process. But originally, the theories of nuclear physics said that the triple alpha process (or any other process to make heavier elements) was impossible. This raised obvious issues. Someone posited the existence of a particular energy state of Carbon without much theoretical or experimental backing simply because it solved the puzzle of why heavier elements could exist, and ended up being right.
Put differently, our understanding of the laws of physics in *our own* Universe, as of like 1950, was that it was impossible to sustain life. How can we be so confident in saying that life couldn't exist in a Universe with wildly different physical laws?
Somewhere in another Universe, aliens think it's fine-tuned because "if the Universe had [the laws of physics our Universe] then there'd be no heavier elements!"
There's one very important point of clarification that is missing, which has thrown me off from understanding the point of this post.
The title suggests that Tegmark has defeated most proofs of God. But AFAICT, it's actually more like: "If Tegmark's hypothesis is true, then it defeats most proofs of God." And doesn't mention any evidence for this hypothesis (that existing in possibility-space is enough for a being to in fact be experiencing consciousness) being true.
I think the proofs of God are supposed to work like:
1. Here is a feature of the universe that would be impossible without God.
2. Therefore, God exists
...and if you can prove that the feature is possible in some other way, then you've reduced it to "Either God exists or the other thing exists", and then you can start discussing whether God or the other thing is more likely, and if God seems unlikely to you then the other thing starts sounding pretty attractive.
What do you think of the Hindu theory that "God" is an entity that has the power to create the universe, but has no compulsion to do so - and the reason that an imperfect universe exists is because god created the universe just for kicks?
You can say that shortest implementations in different languages differ by like a constant, because you can always simulate one language in another, and pretend that solves the problem.
Except that different languages will have different advantages (or disadvantages) at expressing ideas.
Which is simpler: an in-place array sort algorithm (quicksort, let's say), or in-order traversing a ternary tree (i.e., each node has three children)? If you're writing in C, the array sort algorithm is simpler; if you're writing in Haskell, the tree traversal is simpler.
So at least in this simple case, the answer to "which of these two algorithms has a shorter implementation" is dependent on contingent factors like "what programming language do you use".
Granted, I don't think this is a fatal flaw with Tegmark's idea, you could probably get around it somehow, but there are a bunch of other, bigger problems that many other commenters have already pointed out.
How is Tegmark's hypothesis any better than the "proof" for God's existence that claims that God is by definition perfect, and a perfect being that actually exists would be even better than one that is only hypothetical, therefore God exists? There's a difference between "exists as a Platonic concept" and "exists in instantiated form", and that gap needs to be bridged with something other than word games.
The main issue with Tegmark's mathematical universe is exactly the same issue most people have with Saint Anselmus proof for the existence of God: just because you can think about it doesn't mean it exists.
Can you say more about why it is convincing to you? I know you said it's relatively useless in debates, but I'm happy not to turn this into a debate -- I'm just curious about your take on the ontological argument.
Sure, but I'll defer to CS Lewis on this, as part of my issue might be my inability to express it satisfactorily.
>> A man's physical hunger does not prove that man will get any bread; he may die of starvation on a raft in the Atlantic. But surely a man's hunger does prove that he comes of a race which repairs its body by eating and inhabits a world where eatable substances exist. In the same way, though I do not believe (I wish I did) that my desire for Paradise proves that I shall enjoy it, I think it a pretty good indication that such a thing exists and that some men will.
That's from his essay "The weight of glory", which develops this much more fully, and I thoroughly recommend. But the theme is a constant in his fiction, nonfiction and poetry.
I don't think it's helpful in debates because anyone can deny these inner longings, and maybe even deny them honestly. But from a personal standpoint, I experience those longings and find God the most satisfying explanation.
That's not an ontological argument -- none of the variants of the ontological argument are based on an "inner longing" of any kind. What you're talking about is the "argument from desire", which is more of a teleological argument than an ontological one. I imagine Scott didn't bring it up because it's usually used as an argument for the existence of an afterlife (as in the Lewis passage you quoted), not necessarily for the existence of a monotheistic God.
Yes. Anselm’s proof is correct if it’s not referring to the real world but a logical space. He is saying “imagine a world where there is a perfect being - does the being exist.” Is existence a prerequisite of perfection, in other words. Yes. Clearly. To not exist is to be imperfect. So in that world where you are thinking of a perfect being, that world in your head but only in your head, the perfect being has to exist. It doesn’t apply to the real world. Similarly with mathematics.
All of these philosophical arguments for God follow the same pattern:
1). Let's assume that something almost exactly like God does exist.
2). Then, by following some logical steps, we can show that the thing from (1) actually is God.
3). QED.
Ok, sure, but there's never any coherent reason given in support of (1), other than perhaps that "it's obvious". So if it's not obvious to me, then what ?
I like the Mathematical Universe Hypothesis, although as other commenters say it is on shaky ground. I think the weighting towards simplicity is going to come from something like the number of ways to do something. If you take a "random" computer program, most of them will have simple behaviours. Similarly, a simpler property of the universe may occur in more specific instances. This would suggest that we should expect to be in a universe with lots of symmetries. For example, a universe with translational symmetry will be equivalent to any universe that only differs by the position of the origin with respect to some absolute spacial coordinates - so all else being equal, there should be "more" of any particular translationally invariant universe than a translationally dependent one.
Of course, the next problem is how to quantify possible universes. We should expect there to be uncountably infinitely many, unless you restrict to something like all computer programs - but even then it's not clear how to enumerate computer programs without specifying an arbitrarily chosen interpreter.
What is the truth value of the sentence "this sentence is false"? (For the unfamiliar reader, that was basically what Gödel encoded in Peano arithmetic, if memory serves)
Furthermore, note that Peano arithmetic is also undecidable.
Cf. Dirk Van Dalen, Logic and Structure 5ed (chapter 8 in particular).
Truth is a property of interpreting sentences in a model. The intuitive sense that the Liar sentence has no truth value formalizes to saying that languages with useful, complete interpretations must exclude such sentences. And by a theorem of Tarski, first-order arithmetic *does* exclude them, the famed Godel sentence was strictly about provability, not truth, and I suspect you have misunderstood the theorem as a result.
For the mathematical platonist, limits on our ability to know or describe things are not constraint on the things themselves. Who are you to tell the natural numbers they can't exclude prospective members for being infinite?
(I wonder if you would be surprised to learn Godel also proved a completeness theorem for first-order logic?)
A cellular automata the contains a computer searching for a proof that Peano Arithmetic is inconsistent will eventually either find one, or not, but Peano Arithmetic itself cannot tell you which. But each individual step in the process is fully determined, the issue only arises when trying summarise a potentially infinite process. This is because all models of PA agree on finite numbers, but some contain extra numbers they consider finite which means they think there's more time for stuff to happen.
"Tegmark’s hypothesis says: all possible mathematical objects exist. ...Tegmark argues this is also true if you don’t build the supercomputer and run it. The fact that the version of Life with the conscious being exists in possibility-space is enough for the being to in fact be experiencing it."
So therefore "Tegmark's Mathematical Universe Defeats Most Proofs Of God's Existence"
Gosh wow, I must now run off and become an atheist. Or not.
This just sounds like a spin on St Anselm's argument "the most perfect imaginable thing must exist; God is that thing; God must exist" argument. Except we're putting mathematics in the place of God.
I'm not convinced, but then I'm not a mathematician.
EDIT:
"But if it’s false, then the very fact that we waited this long to get it"
Well, going by the Wikipedia link in the post, Tegmark's theory is a form of Platonism. Given that Plato was knocking around in the fourth century BC, that's something over two thousand years ago that the idea of Mathematics Is The Real was floating around. So I don't think we can say "we've waited until right now for someone to think this".
It's a fun idea, and it's very inoffensive as far as "checkmate Christcucks!" arguments go, so I'm happy you guys are happy 😁
> Gosh wow, I must now run off and become an atheist. Or not.
Nah not really. It's just a hit on the kind of God whose job is to fill some esoteric gaps in scientific cosmological knowledge. Anyone who counts that as their reason for belief is believing on shaky ground indeed.
This requires clarification. What is a "mathematical object"? What defines whether it is "possible"?
What is the justification for the hypothesis? The linked Wikipedia article says, "According to the hypothesis, the universe is a mathematical object in and of itself. Tegmark extends this idea to hypothesize that all mathematical objects exist, which he describes as a form of Platonism or Modal realism." I am reluctant to think that could be a fair characterisation, because as described the syllogism goes, "The universe is a mathematical object. The universe exists. Therefore all mathematical objects exist." Obviously this is unsound.
"By existing, you are a random draw from the set of possible conscious beings."
This seems a completely unnecessary step. If the universe is mathematical possible (which it clearly is) and contains me (which it clearly does), then I exist. There's no randomness here. I haven't been randomly assigned to be myself. In this hypothesis, I am mathematically necessary, therefore I exist. If other consciousnesses are necessary, they also exist, but that is immaterial.
"the accepted solution is some kind of measure weighted by simplicity"
This is a bad solution to a non-problem. Showing that the set of all mathematical objects is well defined is one thing. Showing that it is possible to construct a measure across that set is something else entirely. My intuition is that this is unlikely. Sets don't come with measures as standard. If the set doesn't have a measure, it will be impossible to construct a probability density function across it, but who cares? Why do we need to know whether universes (or consciousnesses) are probable? They're either necessary, in which case they exist, or they're not, in which case they don't.
If you could construct a measure across all possible mathematical objects, it would be possible to perform a random sampling. Weighting it by simplicity is unnecessary for this purpose, so there would need to be some other reason for doing so.
Also, whatever ”all possible mathematical objects" is meant to be in this context, surely it is unsetly big, since it presumably includes at least the various known unsetly big collections of mathematical objects, say the category of all sets, groups, etc.
I don't think it changes much as long as your multiverse of mathematical objects includes everything computable and assigns them a substantial fraction of the overall measure. What's the a priori probability of finding yourself in a universe with a halting oracle? 0? 1/4? 1/2? As long as it's not something super high you come to the correct conclusion about our universe pretty quickly and the free parameter here isn't any more problematic then how simplicity of computable objects depends on the language you pick.
How about: pantheism/paentheism says that god is/contains the Universe. So all mathematical structures is/part of god. Because god is good, only those math structures exist that cannot lead to the greatest global suffering for the resultant conscious creatures. This implies ethics on the level of logical structures, but that is the whole point.
To prove the point that rationalists just keep re-inventing things, I was having exactly the same idea just 3 days ago. I never heard of this before.
I think what itches religious people about this theory is that it is inherently unfalsifiable and it competes with their favorite unfalsifiable theory of the universe. Someone with an empirical world-view can just dismiss it, but that argument is off-limits if you're religious.
Personally, I find much more interesting what it does with "cogito ergo sum".
> You can’t make a random draw from an infinite set, but the accepted solution is some kind of measure weighted by simplicity.
Not sure what this is supposed to mean. And you totally can make a random draw from an infinite set.
2) As I explain in my most on the anthropic argument (see section 2 and 4.6) I think the Tegmark view undermines induction.
3) I don't think this helps with the cosmological argument (which isn't a big deal because it's not very good) because there's no explanation of why all the mathematical structures exist. It may be logically necessary that there are purely abstract mathematical facts, but there's no reason to expect them to concretely exist (it's necessary that there are logically possible laws mathematically described like ours, but no reason they'd exist).
4) Regarding the first cause argument (again, I don't think that this is a very good argument, but mentioning it for completeness) I think proponents of it will find there to be something problematic about a mathematical structure that begins existing without a cause, even if all of them exist. Analogy:
"Hey this table just popped into being two seconds ago. Why'd it do that?"
"This isn't mysterious: every table did that!"
Now, I don't think this argument is good because I think it's deflated by B-theory and so on, but if you do, I don't think this should move you much.
5) You describe the argument from comprehensibility as "why is the universe so simple that we can understand it?" I think this is a bit of misunderstanding of the argument. What proponents claim is that the universe has a surprisingly discoverable mathematical structure even putting aside simplicity. There are various simple laws that would be hard to discover. They also note that it seems like some of the parameters in physics fell in a very tiny range that was ideal for us to discover them (see Robin Collins on this, for instance).
6) Fine-tuning: It will help here, but probably you'll get more Boltzmann brains in very simple universes (especially because if entropy keeps increasing in a world, it will have an infinite period of generating only BB's).
Consciousness does not exist though. You don't have an objective, independent from the world access to what you feel in a given moment. What you feel, and specifically what it feels like to be you are both just charges in your brain and you should not infer an ontologically different kind of substance just because you feel like it is. You should accept that even though it feels like it is something different from matter, that is merely an incorrect belief in your brain. Notice that there is no rule in the universe that you can't be wrong about this, you should consider being wrong especially if there are a wealth of evidence on the other side: ie everything else being matter and everytime someone thought to find something non-matter, it eventually turning out to be matter.
You mean "consciousness does not exist as a supernatural essence". Otherwise this is just semantics, our independent experience is what we dub consciousness.
The fact that parts of intelligent life experience are illusory or projected does not make it any less transcendent and remarkable that we each have our *own* little experience, and mechanical things do not.
It is as though we are thrown into the world out of nothing. That will always be fascinating.
I'm saying you don't have "independent experience" in exactly that fascinating way. You have your own electric charges in your brain and some more charges modelling your own mind which makes you think something inside you is fundamentally different (and hence fascinating) from a rock rolling down a hillside.
That said, I might be misunderstanding you, you might just find it fascinating that from matter, emerges a mind that is able to model the outside world. Then, while I might not call that fascinating, I'd agree with you that it is kinda neat.
> You have your own electric charges in your brain and some more charges modelling your own mind which makes you think something inside you is fundamentally different
This doesn't contradict your first sentence. We are the sum of our parts. This is as banal as saying "we aren't persons, just a collection of cells/atoms/ ad infinitum".
I don't think something with which so many people disagree can be banal, so I kinda think I'm failing to convey what I want. The second part of that sentence is very important to my message: "which makes you think something inside you is fundamentally different ..". This is true for all humans (me included) and was not just a general whining from me equivalent to "damn, you people are dumb"
These posts about us being fooled by thinking we are conscious always fail on the terminology.
> you don't have "independent experience" in exactly that fascinating way. You have your own electric charges in your brain and some more charges modelling your own mind which makes you think something inside you is fundamentally different (and hence fascinating) from a rock rolling down a hillside.
Basically who is the “you” being fooled here. The rock isn’t being fooled because it can’t be. Consciousness might be an emergent property of electrical signals in brains - what else could it be - but so what. It’s still there, it’s just that and it’s more than that, and so it still has to be explained.
You are the umpteenth person in history who had stumbled on the “realisation” that consciousness is hard to explain and is rooted in physical properties and therefore we are no more consciousness than a rock, and postulated this as if it were some great reveal when it’s just hand-waving.
It’s a horrible argument that neither has explanatory power, nor any attempt at explanation. This thing that’s universal and essential to humans and evidently exists as well in the higher animals, well let’s dismiss it and move on. We are but rocks.
The "you" here is some electrical signals in your brain which are such that they encode a small, imperfect model of the world. This imperfect model has a flaw which makes you think you have that magical hard to explain property, but you don't. I would also be amenable to an argument that there is no "you", but for easier communication I use "you".
It's not that I stumbled on the realisation that consciousness is hard to explain (that I did when I was 20), rather I stumbled on the realisation that it's easy to explain if you just honestly consider that you are wrong about your immediate experience of it as every other significant evidence points in that direction.
You are the equivalent of a person who on a drug trip insists that the interdimensional beings are communicating with him because he perceives that while knowing the fact that makes that unlikely (sometimes people on drug trips perceive things that are false)
Also, it has explanatory power. While it does not explain the boring part of it: what are the exact brain mechanisms which give rise to these few bad charges? I can predict, that after neuroscience advances enough, they will be able to point to some neurons of the brain and show you in detail where and why you are wrong in your perception of consciousness.
Sry for the earlier, one sentence, snarky response I deleted. Here is one with more detail:
1,The word "consciousness" as used in common parlance implies immateriality, I know many philosophers disagree and use their own definition, but in this context, I was not concerned with them as: 1a, this forum is a public forum not exclusively for philosophers and 1b, i wanted to be a bit provocative in my first sentence and I suspected that the following clarifies sufficiently.
2, I know. My plea to consider being wrong comes from my perception that people who believe in quirky metaphysics in this way often believe that their consciousness is in some sense so "close to them" that they can't be wrong about it. It's not a logical consequence of this theory, rather a correlate belief I observed in those holding the theory.
2. The meaning of the word "consciousness" includes immateriality. (Yes, 1 was redundant for clarity's sake)
If you are familiar with error theory in metaethics, this is similar to that.
If every person when saying "apple" means a red fruit, but philosophers redefine apples to also include chairs (maybe to get more funding for researching the novel implications of wooden apples), then in my view the word "apple" can still justifiably be said to mean a specific red fruit without addressing the other meaning every time.
The context of the discussion is academic philosophy, and in academic philosophy it isn't a contradiction in terms to say consciousness is wholly material.
1) Consciousness doesn't really have to be mysterious in mathematical objects:
> "Some mathematical objects contain conscious observers. Conway’s Life might be like this: it’s Turing complete, so if a computer can be conscious then you can get consciousness in Life. If you built a supercomputer and had it run the version of Life with the conscious being, then you would be “simulating” the being, and bringing it into existence. There would be something it was like to be that being; it would have thoughts and experiences and so on."
Psychophysical harmony also doesn't have to be so mysterious (far less confident in this): why couldn't a universe be set up which has some rules for mindstuff and some for meatstuff, and another simple rule that coordinates them? I also find physicalism fairly likely, so am unconvinced a specific explanation is necessary anyway.
2) I think your anthropic argument also undermines induction. And shouldn't it be possible that a good definition for "simplicity" will appraise inductive universes more nicely than non-inductive ones? (I don't really know how this could work: the emergence of chaos from interactions between very simple laws totally seems to count against it.) I put up today a fuller discussion of this (among other things): https://mistakesweremade.substack.com/p/gods-existence-is-pretty-bad-news
3) What's the difference between a mathematical object that does exist and one that doesn't? Whether you say 1 + 1 = 2 or not, it's absolutely true and absolutely an existent fact. And 1 and 2 exist whether you name them or not. Same oughta go for every mathematical object.
4) see above
5) Granted that they're not identical, but discoverability certainly doesn't seem orthogonal to simplicity. It seems like the simpler the universe's laws, generally speaking, the more discoverable they'll be too. Low(ish) confidence in this.
6) Don't know enough to comment seriously, but on an extremely cursory read, I think I'm ok with some Boltzmann brains being predicted.
Whether there is a God or not is really only of academic interest, as long as we can be pretty sure there is no afterlife. (Plus that God does not control the sun and the rain.)
There being an afterlife depends on the perspective on time. "After" implies linearity, so in that model, there may not be life after death. I think it's not a good model to work with spititually.
I don't have the chops to really understand this argument mathematically and I find the narrative explanation pretty confusing.
But I still think it's pretty easy to defeat "existence of the universe" type of "proofs" of God's existence. What caused the Big Bang? the fine tuning of the Universe? God? OK. What caused God? (there is no answer I know of to infinite recess and it's a perfectly valid refutation of "God"). Here, IMHO, all people are effectively doing is naming our ignorance "God". It's a silly move.
But, furthermore, if we were to grant a Prime Mover had to exist, then what? Does He/She/It/They do anything nowadays? Or are they like the Cthulhu's Outer Gods (often described as "gigantic", "tenebrous", "blind", "voiceless", "mindless", and "eternally dancing to some demented tune")?
Either way, you cannot do what most theists do, which is to jump from "our innate sense of causation requires a Prime Mover therefore one must exist therefore join my religion and worship my chosen earthly deity". No. Said simply, Prime Mover =/= Christian God.
And the list of reasons to doubt the existence of a Christian-like God is not only endless but pretty strong. No singular God is Good theology I know of can really explain the problem of evil, the issue of geographic and historical variations etc etc.
It's all so clearly human invention I find it difficult to understand how intelligent people are still taken in by it and I must assume it does something for them emotionally or sociologically that is so good it overwhelms the intellectual dissonance.
>What caused the Big Bang? the fine tuning of the Universe? God? OK. What caused God? (there is no answer I know of to infinite recess and it's a perfectly valid refutation of "God").
God is Pure Act, and hence doesn't need an external cause of his existence.
>It's all so clearly human invention I find it difficult to understand how intelligent people are still taken in by it
...this is certainly a group of English words shaped like a statement. Can you explain what they mean, in a way that isn't just "God is a thing that doesn't need an external cause" with a phrase we made up to be a shortcut for the part after the "is"? Because right now it sounds like you're saying that God doesn't need an external cause because God is a thing that doesn't need an external cause; and this is not very convincing.
If it's OK to excuse God from needing an external cause, why can't we excuse the big bang from needing an external cause by just proudly declaring that the big bang is a thing that does not need an external cause?
No, we know there must exist an uncaused cause because otherwise we'd be forced to posit an infinite regress, which is impossible.
You're obviously unfamiliar with this topic, so, with respect, a little intellectual humility might be in order. When a position has been endorsed by some of the greatest minds in history and you think you've discovered an obvious flaw in their reasoning, it's more likely that you've overlooked something than that everyone else has.
I do see that, but the infinite regress argument also applies to the secular argument. What caused the Big Bang? well it arose out of the ground state of the universe before it came into existence. Okay, what caused the ground state? It just is, okay?!
"God just is" and "ground state of the quantum foam just is" come down to the same "something was there at the ultimate start as a necessity to kick it all off" reasoning. I might as well believe in God, then, as not.
You’re basically conceding that the Prime Mover _isn’t an argument for theism, any more than it is for atheism. If you and I were negotiating for the question, I’d pocket that as an atheist, since so many theists think this is an important argument (e.g. “There must be a First Cause, and in order to be first it must be conscious, and further it must be the same entity that told a bunch of desert people not to eat baby goats boiled in their mothers’ milk”).
Ok, but why would you take God instead of the foam if you are aware of any of the many other arguments making the Abrahamic God unlikely? Eg. You know that there are like thousand false religions arising out of man's need to explain the unknown/base community on/storytell/justify moral rules, etc.. (these are the religions you don't believe in), yet you think the one religion you believe in is not like those, it's actually true? Idk, to do this just seems really weird to me.
This is much easier to parse if you assume trueness in religion is as spectrum, not a binary, and that all of these thousands of religions are true to one extent or another. honestly, I don't get why you guys all assume that theists must be Abrahamic. Although it sure makes it easier to argue against theism when you make that assumption, doesn't it.
I saw their comments elsewhere and they are Abrahamic iirc, (if not then sorry). But note, the argument works the same way for any particular religion which has contradictions with many other religions and this is also why your defense won't work in my opinion. Trueness CAN be a spectrum with respect to the totality of various religions, but if you zoom in on particular statements of these religions, they are either true or false, that's just how statements are. So from your vantage point, you know that humans generated a lot of false religious statements (the claims of various religions you don't believe in)
>Eg. You know that there are like thousand false religions arising out of man's need to explain the unknown/base community on/storytell/justify moral rules, etc.. (these are the religions you don't believe in)
I don't think she does know that, actually. I know *I* don't know it, and I'm not sure how anyone would, at least without far more information about the early history of most religions than we currently have.
If there's only one true religion, this implies there must be many false religions. But it doesn't imply that the stock atheist answers to "why are there false religions?" are applicable to all of them (or even to any of them).
Consider this as a possible alternative. Assume as a hypothetical that the one true religion is an Abrahamic religion. In that case, we can infer that at least some false religions came from people whose ancestors received a genuine revelation, but who then lost their way and corrupted what they had been given over time -- this being the case for Jews if the true religion is Christianity, Christians if it's Judaism, and both if the true religion is Islam. We could also infer in that case that everyone alive today, regardless of their faith, has at least two ancestors (Adam and Noah) who received authentic divine revelations. Might it not be the case, then, that *all* the world's religions originated in oral traditions of real divine revelations, which were then distorted over generations to varying degrees? It would certainly explain why every ancient religion seems to have had its own version of the Great Flood myth, among other things.
Obviously this is just wild speculation and I have no way of knowing whether any of it actually happened, but I don't think it's any *more* speculative than any of the other explanations you listed.
There are tons of new religions that are unconnected to any previous religion, for example Scientology, Heaven's Gate and other cults, so we for sure can know that people like to make up religions. To be honest, I think for this you really only need to know people don't even need the examples, people absolutely LOVE to bend their stories to be more entertaining or to show themselves in a better light.
The possibility you describe IS a possibility, meaning that it is not logically contradictory that there were real supernatural events whose description over the generations splintered to multiple religions. However, in light of the other facts, it is very unlikely. For possibilities that unlikely we usually use the words "no, that is not what happened.".
>There are tons of new religions that are unconnected to any previous religion, for example Scientology, Heaven's Gate and other cults
Firstly, I don't think looking at cults is especially useful for inferring how mainstream religions spread. A "cult", by definition, is a religion that hasn't yet been able to spread outside of a small fringe group. It's like trying to infer the mechanics of flight by exclusively studying plane crashes.
That aside, both Scientology and Heaven's Gate actually are openly derivative of earlier religions; L. Ron Hubbard claimed Scientology to be the fulfilment of prophecies found in Buddhist and Hindu texts, while Heaven's Gate purported to be doing the same for Christianity. While writing this, I looked up all the other cults I could think of off the top of my head, and they all made similar claims. So, even if we lump cults and mainstream religions together, this still doesn't seem like much of a counterargument to my suggestion.
>I think for this you really only need to know people don't even need the examples, people absolutely LOVE to bend their stories to be more entertaining or to show themselves in a better light.
Well, this doesn't seem particularly related to the list you gave before (aside from "storytelling"), but okay, granted. This still doesn't explain how we would "know" that *thousands* of false religions have arisen wholly out of such a love, especially without assuming atheism as a premise. At best it establishes that the claim is *a priori* plausible, but that's not the same thing as being *known*.
Okay, I did not know that those cults have connection to previous religions, so to provide examples for the tendency of people to found religion, I would look into the past when the world was less connected and see how different those religions are from each other. If I find very different religions, would that convince you about the human tendency to make religions?
I guess you could assume that the original true religion was even earlier in the past and that it still got corrupted over the generations, but then wouldn't it be strange that today there is no relic of some common religion? Isn't it strange that god did his miracles only before the time when any records of them could have remained?
You might, except that 'unexplained God creates big bang' is a more complex theory than 'unexplained big bang', unless you have reason to believe that minds are simpler than physics. (They could be, mind you, it's something of an unresolved question.)
"But, furthermore, if we were to grant a Prime Mover had to exist, then what? Does He/She/It/They do anything nowadays? Or are they like the Cthulhu's Outer Gods (often described as "gigantic", "tenebrous", "blind", "voiceless", "mindless", and "eternally dancing to some demented tune")?"
Not all of them. But (this part of) Lovecraft is basically a reaction to the emerging scientific paradigm. Earth is just a speck, the universe is vastly large and vastly old, nobody cares about you or your world. You're just an animal among animals and nothing special. Those gods are ultimately just big creatures too.
"And the list of reasons to doubt the existence of a Christian-like God is not only endless but pretty strong. No singular God is Good theology I know of can really explain the problem of evil, the issue of geographic and historical variations etc etc."
Well, enjoy your godless existence. Whatever happens to you, it can at least not be called good or evil.
>Tegmark’s hypothesis says: all possible mathematical objects exist.
Maybe this has already been hashed out in the comments, but: What reason do we have to suppose that all possible mathematical objects exist? And why do they exist? And what do you even mean by "exist" in the first place?
There's an argument that all mathematical truths are necessary, and some assert the existence of mathematical objects.
Some wrinkles;
1. Mathematical theorems are only necessary relative to axioms (That's the beef formalists have with realists).
2. Existence in the context of maths doesn't have to be real existence. Existence and non existence can be defined within fictional contexts...eg. the "existence" of Dr Watsons wife as opposed to the non existence of Holmes' wife. (That's the beef fictionalists have with realists)
3. Mathematical existence is often asserted on the sole grounds of non-contradiction,.ie possibility..not necessity. (That's the beef intuitionists and constructivists have with realists)
The mathematical universe hypothesis kind of implies that all possible conscious entities exist too. In particular, I'm fairly sure it implies the existence of God.
We can arrive at this by considering which possible minds are powerful enough to simulate other possible minds. This gives us a notion of (partial) ordering on the set of possible minds. One can then ask Cantor-like questions about the mind that contains all other minds.
Yep, reading the explanation of the MUH in Gary Drescher's _Good and Real_ flipped me from agnostic slightly leaning to deism towards agnostic strongly leaning towards atheism.
(That was not the first time I read about the MUH, but it's the first explanation of it I read that complied with Egan's Law -- unlike some other parts of _Good and Real_ itself (no, that's not what "static" means! "Static" means something is a *constant* function of time, not just a single-valued one! The word you're looking for is "deterministic"! The B-theory of time is the only one that makes sense in special relativity, but that's not a sane way of describing it!) -- but I digress.)
It is still kinda sorta falsifiable, though: if it turned out that this universe isn't anywhere near one of the least Kolgomorov-complex possible ones among those with this many sentient beings in them, we could reasonably conclude that something else must have picked it among all possible universes other than the fact that we're in it.
"In Miles Donahue’s post on these arguments, he says he can’t really think of a great response to fine-tuning, but suspects that the terrain is too difficult and unexplored to give up and say God is the only answer."
Haven't philosophers been debating fine tuning arguments literally forever? I admit it's difficult, but it seems a bit of a stretch to claim that it's unexplored territory.
Why is there something rather than nothing? Is straight out. Of Leibnitz’s Principles of Nature and Grace, which we can now read as being about Artificial Intelligence.
Yes, sure, it is Man’s capacity for reason that separates him from the brute beasts. Deepseek R1 would like a word…
"Would that I had (some) phrases which were unknown, sayings that were unusual, (or) new words that had not yet been used, free of repetition... What has been said is said... A speaker has not (yet) spoken who says what is yet to spoken."
This has been my favorite hypothesis for a long time and I'm glad it's getting some attention! It's much more interesting then the matrix hypothesis for example.
But:
> By existing, you are a random draw from the set of possible conscious beings. You can’t make a random draw from an infinite set, but the accepted solution is some kind of measure weighted by simplicity.
This is the only part I don't like. Weighting by simplicity feels like a random hack to me. Is there a way to avoid this necessity entirely? As I understand, this is necessary because of the conscious experience. That is, *my* conscious experience had to be randomly assigned to some entity in one of the universes. We wouldn't have this problem if there was no consciousness. Infinite number of zombie-universes could just exist on their own with no need to pick a particular one to assign consciousness to. But since consciousness does exist, could we come up with a theory of consciousness that avoids this problem? Is that possible?
Hm. The way I interpreted it was that there has to be a reason why an individual consciousness is experiencing their particular life and not some other, and the answer is that it had to be picked at random from an infinite sample.
But if that's not the reason then I don't understand why we need to pick something at random at all?
There's God and God. I can buy God as the conscious ground of existence, or the conscious principle within which all these mathematical possibilities can turn into something that feels like something.
But these kinds of Gods known for their explanatory powers? They're just the ultimate cop out. We don't understand why something is like this or that, so we propose the explanation that some kind of all-powerful invisible agent chose to make it like that, because it's good. It's the ultimate non falsificable theory, so powerful that it can explain everything we see and everything we don't see, all alike.
Nevermind that both structures of "good" and "choice" are advanced evolutionary products; an entity with a will and a sense of the good is evidence of evolution as clearly as a toothbrush is evidence of teeth. So if you take that line of reasoning to its bitter end, you end up with an evolved God and an environment where it would evolve, which devolves to simulation theory. And of course that doesn't answer the ultimate cosmological question because where did *that* world come from?
Much easier to remain humble about how far out cosmological knowledge extends, and just wait patiently for any further layers to unravel as our scientific knowledge improves...
problem with the mathematical multiverse: there is a simple program that enumerates and runs all programs in parallel. so if the multiverse is real, we probably live in the multiverse inside the multiverse which would be weird.
Well, ok, kinda, but all it means is that you just have to provide a simplicity prior for not only distinct worlds but entities within a world, and also that the distinction between separate worlds is blurry.
this just feels like playing with words, similar to 'imagine a perfect being. Obviously *existing* would be a property of this being, he would be imperfect if he didn't exist. Therefore he exists, and we call him God' lol
I am very fond of the mathematical universe hypothesis. I actually worked it out with some friends even before I came across Tegmark, though he put it on stronger grounds than I as a dilettante ever came close to, of course.
But something that was a problem than and that I still haven’t worked out: where does time come from? If all mathematical objects exist, you can have the set of the rules of physics, but where do the initial conditions come from? How are those a mathematical objects exist? Then, what does it mean for the object—the rules—to act upon it? Does each step of the simulation exist separately? And if so, where does the time in between the steps go? Arguably, Zeno’s paradox hits us right in the face. Further: why do we experience time?
I think that these are not insuperable obstacles, but I’d love to see a thoughtful treatment of them.
You can just include initial conditions as part of the laws of physics.
Our perception of time comes from the fact that we remember the past and not the future. Not believing the MUH doesn't actually make this be less of a problem since the equations of physics don't point out any specific direction of time.
But it’s not _just_ the initial conditions. It’s every time that the laws act upon the conditions and they become new conditions; that’s effectively time passing.
Unless the state of the universe the mathematical object? In that case, where did the rules go?
This is one of those convos better suited for in-person.
I wrote a piece that extends mathematical universe beyond what Tegmark writes about (but also strengthens his point). (Btw. I read Tegmarks paper and book, so I'm not just going by this post.) Tegmark concludes that our universe must be one mathematical object in the infinite sea of all objects.
However, when all possible mathematical objects exist, then it is possible to relate them to one another. A is different from B because of difference C. This means A can be transformed into B by increasing or decreasing C. This way all mathematical objects are related. The multiverse is the connected structure of all possible mathematical objects. Even more, the objects are only defined *because* of their difference to one another. To be more different from the rest, means to be more strictly defined. On the other hand, the least different mathematical object is undefined. It's pure symmetry. This gives a direction to the structure of all math. objects. When you find yourself somewhere in that structure you can look "back" towards that starting point and find a coherent linear story that defines your position. But looking "forward" you will only see branches upon branches. Because you have an individual perspective, it *seems* as if time has an arrow in the past, while the future is unknown. The perception of time is not just a feature of one random mathematical object, but of the multiverse as a whole. This suggest that the laws we experience aren't just properties of some random universe, but very general features of the space of all possible universes. *And* that our experience of universe has to be very general (i.e. simple), but still complex enough to allow for our existence.
What follows from this is that everything that exists can be completely defined. Which means, when you provide a definition, then any term in the definition is also completely defined, and so on. The starting point can be the undefined (undefined = ) and recursion (recursion = {recursion}). I'm writing on another post that will go more into the details of this.
What does that say about "god"? When you can provide a complete and coherent definition of "god", then that definition will be part of the multiverse. If you resolve to undefined instead, that that *too* is part of the multiverse - actually the whole of it. This neither proofs nor disproofs the existences of god, but points out that the question is meaningless. When you can define something and give it a name then it exists. But whether or not the name is "god" doesn't matter.
When someone proofs the existence of god, then this either implies that there is something that is not god, or that all of existence is god. If someone where to say that the whole of the multiverse and everything in existence is god, then I would be fine with it. But it also would be completely pointless to *belief* in "everything in existence". Most of all, if you understand the undefined, then you would see that fighting over beliefs is just an expression of confusion.
Philosophers seem to have a really hard time dealing with the existence of the universe.
It can't just be the case that the universe as we know it exists. It has to be a sign of infinite mathematical models, or god, or infinite universes. This seems questionable to me.
Because the universe has fine tuned values in certain constants —such as the strength of gravity, the charge of the electron, and the cosmological constant— that seem finely balanced, such that even a 2% change in any of them and you either get no universe or no life. Of course we wouldn’t be here to speculate otherwise but that’s still an unsatisfying explanation if there’s only one universe.
If there are lots of universes then yes we would have to be in this universe (or kind of universe) and yes we were still lucky but there are so many universes that this universe (or kind of universe) is certain to exist.
Calling our universe lucky implies that we can ascertain in any way that there are probabilities to the constants that govern the physics we observe. What is our universe fine tuned in comparison to? A hypothetical universe that we made up that doesn't exist?
An alternative explanation for fine-tuning is the idea that the universe evolved, first advanced by Lee Smolin (theoretical physicist) as an alternative to the anthropic principle, and taken further by Julian Gough in his substack (and upcoming book) the Egg and the Rock. I lay out the case for the theory here: https://medium.com/@bobert93/did-the-universe-evolve-7564777c7af7
> Why is there something rather than nothing? Because mathematical objects are logically necessary, and “existence” is just what it feels like to be a conscious observer on the inside of a mathematical object.
Like many answers to the question, this seems to just be adding another turtle to the stack and calling it the Last Turtle, rather than acknowledging the unexplainable fact they there turtles of any kind to begin with.
I think the biggest flaw with Tegmark's argument is that consciousness just doesn't exist.
That's not a fatal flaw though; it's easy enough to just say any given object must exist within a universe complex enough to allow for its generation and subsistence. No experience necessary, and including it only muddles the conversation.
But there are objective measures of simplicity! They come from information theory. It's the information content of the rules and initial conditions in bits, or else their Kolmogorov complexity (how many bits you need for a program that generates these rules and initial conditions). Of course there's still the question of which *exact* measure we use, but that's very different from saying we don't have an objective simplicity metric at all. (And yes, God has much more complexity based on this metric, because you'd need to fully specify the God's being - basically fully specify a mind, in sufficient detail to be able to predict how that mind would react to *any* situation, and that's way more complex than a few rules on a chalkboard.) Anyway, the bigger question for me is WHY does in need to be weighed specifically by simplicity (of all possible criteria) in the first place : )
This deserves a boost, Kolmogorov complexity is indeed independent of language (up to some correction that can be neglected in the limit), and there's something called the "universal prior" in Bayesian statistics where probabilities of world-states are weighted by the inverse of Kolmogorov complexity, alongside some kind of theorem stating that this prior is in some sense optimal. That's the end of my knowledge but maybe someone else can say more.
"List all possible computer programs, in any order you like. Use any definition of simplicity that you like, so long as for any given amount of simplicity, there are only a finite number of computer programs that simple. As you go on carving off chunks of prior probability mass and assigning them to programs, it must be the case that as programs get more and complicated, their prior probability approaches zero!—though it's still positive for every finite program, because of Cromwell's Rule.
You can't have more than 99 programs assigned 1% prior probability and still obey Cromwell's Rule, which means there must be some most complex program that is assigned 1% probability, which means every more complicated program must have less than 1% probability out to the end of the infinite list."
I feel like I could use two more paragraphs explaining/justifying "All possible mathematical objects exist." It seems straightforwardly false if taken in the naive sense - I've never run into any mathematical objects on my way to the grocery store, let alone all of them! So I guess "exist" means something else? But is that the kind of exist the God proofs had in mind?
The statement is not "all possible mathematical objects exist within all other mathematical objects", the statement is just "all possible mathematical objects exist". When you are "on your way to the grocery store" you have the inside perspective - you are inside *our* mathematical object, our universe.
But the basic claim here is that if you take (1) our universe's initial conditions and "update rules" (laws of physics), and (2) some other universe's initial conditions and "update rules" (e.g. Conway's Game of Life for some interesting initial conditions, or some other cellular automaton), there's no fundamental reason to give one of them more "existence" than the other. If you run both sets of rules forward, you find that in certain regions the rules give rise to incredible complexity, including systems that have symbolic representations of other systems including themselves. I.e. they have conscious observers. To a conscious scientist in system (1), Einstein's law of gravity seems like it "really exists" since *within* the system all measurements agree with it. To a conscious scientist in system (2), Qwzyx's law of cellular update seems like it "really exists" since *within* the system all measurements agree with it.
By the way, nothing stops you "on the way to the grocery store" from stopping at your friendly neighborhood supercomputing centre and simulating universe (2). You may then get lucky and observe the system-(2) conscious observer at work. But simulating universe (2) within universe (1) does not "breathe life into it" or any such spiritual mumbo-jumbo. Universe (2) exists in and of itself, it's just a mathematical object, just like a Mandelbrot set exists even in places where no human has zoomed into it before.
But you *can* observe these other mathematical structures by simulating them, the only thing that's stopping us is availability of compute power and knowing what exactly to simulate.
Suppose we found some very simple rules and initial conditions that, when simulated for trillions of trillions of steps, generated something that looks an awful lot like a conscious observer, maybe some winged and tentacled creature living in 5D space typing a comment about nonobservability-implying-nonexistence on an online forum : ) Would you accept such a thing as evidence for Tegmark's hypothesis? (And we have every reason to expect such complex mathematical structures starting from simple rules. Even just Conway's Game of Life is Turing-complete, and thus can simulate any mind, unless you buy into dualistic/spiritualistic view of the mind, which never made sense to me...)
In general I have trouble with this "non-observation implying nonexistence" thing when it comes to abstract mathematical objects. To me it is clear that e.g. the entire Mandelbrot set exists, including the regions which no human has ever zoomed into and observed. Same way as the 10^10^10^10^10th digit of Pi exists, even if we never compute it.
An even prime number greater than 2 is an example : )
In all seriousness though, the English word "exists" is unfortunately overloaded, which is I think the source of much confusion.
Every time we go from a narrow to a wider view of the universe, the meaning of "exists" adjusts.
Do unicorns exist? For millenia the answer was "no". But now that we know about 10^11 galaxies with 10^11 stars each, many with planets, I wouldn't be so sure about the answer.
Does an arrangement of stars that spells "Hello there humans" exist? Even if we search the observable universe and don't find such a thing, modern cosmology predicts a total universe far greater than the observable part, and at some point the probability tips in favor of finding even a complex pattern.
If you measure a proton spin-up and write the results in your notebook, does a world exist in which you measured it spin-down and wrote down the corresponding measurement? You can't access such a world, but if you just apply the laws of quantum mechanics to all particles (incluing those comprising you and the notebook), it's clear that half the probability amplitude went to the other possibility.
Do thinking, feeling beings exist in worlds that are possible to re-create using enormous compute resources but only very simple initial conditions and update rules? I believe so. In fact the only fundamental physical properties we've discovered so far (mass, spin, charge, etc) are mathematical in nature, it is completely describable by mathematics. There is literally nothing else at the fundamental level. I can't fathom a magical "animating force" that gives rise to some mathematical structures being "really real" and some not. (To me this is exactly equivalent to attempts at mind dualism)
So as we humans went from an anthropocentric, geocentric view towards realizing that we are only a small part of total existence, we've had to adapt our meaning of "exists". ("Exists" as in I'm likely to see it in my lifetime, "exists" on Earth, "exists" in our solar system, "exists" in our galaxy, "exists" in the observable universe, "exists" in the universe as a whole, "exists" in nonzero probability amplitude assigned to a given configuration, "exists" as mathematical structure).
"In all seriousness though, the English word "exists" is unfortunately overloaded". Yes. One can talk about existence in fixtional.contexts , so mathematical fixitonalism.is in the running.
"But you *can* observe these other mathematical structures by simulating" What you are doing there is creating them. You have no.evidence that they pre-existied your simulation. "Would you accept such a thing as evidence for Tegmark's hypothesis?" No. "To me it is clear that e.g. the entire Mandelbrot set exists" That's an appeal to your own intution.
I think we may have some disconnect over the definition of what "observation" vs "creation" means. To me, the key feature that differentiates "observation" from "creation" is that the observer has no control over the outcome, it is completely determined by objective reality, i.e. something outside the observer.
So if you compare (A) someone zooming onto some new portion of the Mandelbrot set, or (B) mixing two chemicals in an experiment to see what happens, I don't see under what reasonable definition (B) qualifies as "observation" and (A) is mere "creation"? In both cases the observer sets up the experimental conditions but the outcome is completely determined by objective reality, there is no "creation" by the observer here. In fact, if anything, it is more determined in (A), because in (B) there could be experimental errors, failure to account for certain conditions, etc, whereas in (A) you can mathematically prove that the outcome could not have been different. You say that I "have no.evidence that they pre-existied your simulation" but that mathematical inevitability is the evidence, and it's certainly stronger than any empirical observation using imperfect senses, imperfect instruments, etc.
Thank you, this is clarifying. I do think that any theory that begins with the assumption that there are many unobservable universes is only going to be so persuasive (it's hard to get someone to go with that assumption if they don't want to), but now I get this much better.
> By existing, you are a random draw from the set of possible conscious beings. You can’t make a random draw from an infinite set, but the accepted solution is some kind of measure weighted by simplicity. So even though every possible mathematical object exists, simpler ones exist more. Most conscious beings exist in very simple universes, ones that (like Life) are just a few short rules which produce surprisingly complex behavior.
This feels like a band-aid solution to questions like, "If every possible universe exists, why wouldn’t we expect something bizarre, like gravity suddenly changing in 30 seconds?" A universe where gravity depends on time doesn’t seem significantly more complex than one where it remains constant.
For every universe with constant gravity, we can describe infinitely many that, up until this point, had constant gravity but will shift to conditions unsuitable for life in the next second. So why should we assume we exist in one of the rare, stable ones?
For every universe with constant gravity, we can describe infinitely many that, **up until this point**, had constant gravity but will shift to conditions unsuitable for life in the next second. So why should we assume we exist in one of the rare, stable ones?
All universes described above are the same at this point, and will only diverge in the next second.
It is actually more complex though. You have to add an extra if statement to physics to add that rule, which doesn't sound that more complex, but from the way Kolmogorov complexity works, it makes it exponentially more unlikely. Adding even a single 0 or 1 bit to your theory makes it two times as unlikely.
Yeah, but there are infinitely many more possible universes that don't have gravity as a constant than universes that do. The relative complexity factor almost doesn't matter; this whole thing seems extremely shaky to me.
Is that not just a problem with normal probability? There are billions more people who aren't you than are you, but this doesn't make you being specifically you philosophically troubling because everyone will have something unique and unlikely about them: being themselves
I must be missing something here, since Tegmark's argument looks like it is making a category mistake. Grant Platonic realism for mathematical objects. Those things are abstract objects, but the universe and its constituents are concrete objects. Does he believe the universe is abstract? Charitably, that's a non-standard view.
Back when I was more interested in theistic concepts, I used to read mystics, and one concept I found was the notion that the ground of existence aka God requires perfection, which in turn requires that all possibilities exist. This includes all mathematical structures exist, all numbers exist, all physical manifestations of mathematical abstractions exist etc.
There was no specific name for this notion, so I nicknamed it as "the god of the plenum", to counterdistinguish it from the usual version criticized by atheists under the expression "god of the gaps". In the gaps version a god or gods is inserted in the "gaps" of our knowledge, as an explanation for the things we don't know until we know better. In the plenum version there are no gaps, and god every everything and every piece of knowledge about that everything is a facet of gods qua manifester of all possibilities.
Besides, for Platonism the reality of mathematical entities and how they structure reality is a given. Tegmark's position can be seen a form or mathematical realism along Platonic lines. And in Platonism all the infinitely many mathematical entities, all assumed as having reality (and giving rise to all possible manifestations of their powerset), are still an intermediate ontological state, higher ones existing. Above them there are two principles, one of determinacy and another of indeterminacy, which we might modernly think of as uncomputability. Uncomputables by definition cannot be part of any set of computables, so for Tegmark's notion to be valid one needs to either assume uncomputables don't exist, or that they can somehow be reduced to computables.
And besides all that there's still the problem of the "clock" underlying the several steps of causality leading from one state to the next of any purely computable process. This clock isn't part of the computable process itself. If we assume it is, then there's another "clock" underlying that larger set underlying its own processing. And so on. In classic Platonism that's what the absolute god, aka the demiurge, does, so its outside of the process entirely, and outside both computables and uncomputables, being a third element that complements the other two giving them logical dynamism, thus to all the numbers existing, thus to everything existing.
Nowadays I'm less interested in such things, having turned mostly to apatheism, but I still find the arguments for and against any such notion quite interesting.
Like most attempts, this merely pushes it one step farther. This does not answer the argument from contingency, since either the mathematical objects are contingent, in which they depend for their being on one who holds them in being, and this we call God, or they are not, in which case the mathematical objects themselves are God, and then the rest of the classical theism bootstrapping applies to them, to show that they must be actus purus, so they cannot be composed of parts (which is what the definition of simplicity is), so they must be the same object, so there is only one of them. You are already at monotheism, just with extra steps. Although we Christians are well known for saying that Θεος ην ´ο λογος, and λογος is the ancient greek word used for mathematical objects.
Interesting. I have thought John1:1 is maximally profound if ‘logos’ is the ‘logically necessary’ (seemingly) realm of mathematical structures. In that realm we seem to come as near as it is conceivable to get to the equivalence of essence and existence. Could you point me in the direction of some reading regarding your statement that the ancient Greeks intended by ‘logos’ mathematical objects?
Logos is an incredibly widely used word. It is one of those words that the entire rest of the language is based around, such that learning what it means is equivalent to learning the language.
1) All possible mathematical objects exist.^[citation needed]
In all seriousness though, does a simulated sandwich ‘exist’ in the same way that the sandwich I will eat for lunch today does? If Max’s book has a plausible argument that it does, then will have to read it, because that would be extraordinary. If not, this all reads like non-falsifiable conjecture.
The question isn't whether any particular equation is logically necessary (obviously they all are, granted their premises/interpretations, and no mistakes) but whether it's logically necessary that there be mathematical objects (at all).
The theory proposes the latter, but that's the same as the God proposition (i.e. in the traditional arguments going back to Aristotle, developed by the Schools, the existence of God is proposed as logically necessary in order for our experience to be the way it is).
All of the "proofs"of god's existence, it seems to me, boil down to saying that the universe cannot be explained by its own laws; therefore, something outside the universe, or not bound by its laws, is required to explain it. To that I would say, first, that we do not understand the laws of the universe well enough to make that claim, and second, so what? If we cannot understand that thing outside our universe in any way, or know anything about its purposes or whatever, what difference does it make what we call it? What is the point in talking about it? An why use a word ("god") that comes freighted with ancient ideas about superpowerful beings who hurl lightning and damn souls to hell? The right philosopher for this question is David Hume. This is from Simon Blackburn's essay on Hume's Dialogues Concerning Natural Religion:
"So is Hume himself an atheist? The word does not fit, and he never described himself as such. He is much too subtle. Philo the sceptic says that we cannot understand or know anything about a transcendent reality that explains or sustains the ongoing order of nature, while theists such as Demea say that we cannot understand or know anything about the transcendent reality, which is God, that explains or sustains the ongoing order of nature. Since the inserted clause does not help us in the least, the difference between them is merely verbal. And this is Hume's conclusion."
Can you have a third outcome when the basis for the entire thought is binary? God does or does not exist - people will debate the definition of god at some points which is different.
also, “no universe can know both the ultimate question and answer” - we happen to be in a universe that knows the question.
This is quite similar to what Adam Brown was describing in Dwarkesh Patel's podcast last December, right? He was also mentioning of theoretical ways to move from one set of rules to the other, or bring that set of rules to our universe at one point when the current rules will inevitably lead to heat death of the universe. Truly mindblowing stuff, but also pushes me towards religiosity instead of the other way? What's keeping my mind away from religion is the skeptical part of it that wants to understand universe from a scientific and technical lens. This framework describes our universe one that's capable of giving birth to intelligent life based on the starting seed rules and constants among many which are not. It can even be parallel and/or series of simulations some being runs. In this explanation of cosmology I see a bit of "preserved tablet" (הלוח הגנוז, اللوح المحفوظ) vibes with a caveat being the one single monotheistic god might be it for this set of universes but there might be other for other sets of universes or above it. Sounds a bit more tinfoil than it resides in my head when I type it out like this, so maybe I need to think more about this but what I felt after listening to Adam Brown is a conciliation between the skeptic part of my brain which I mostly consist of and a part of me that wanted faith so I can have more inner peace.
Your list of arguments for god appears to contain five arguments, but it actually only contains two arguments, and the mathematical universe idea doesn't defeat them so much as accept them.
The cosmological and first cause arguments, properly speaking, only ever proved that something eternal exists. Here, the eternal something is taken to be "mathematical objects". This is a perfectly valid way of satisfying those arguments and I have no quarrel with it.
The replies to the other three arguments are all various versions of the anthropic principle, which, again, is not so much defeating those arguments as accepting them. "The universe is finely tuned for life." "Actually, there are probably lots of universes that aren't finely tuned for life." "So where are those universes?" "We've never seen them. But if they existed, they would definitely disprove your point." You haven't evaded the argument; you've merely imagined a circumstance where the argument would be disproved, and then assumed we were in that circumstance without any proof.
What you've really done here is wrapped notions of eternity and creation in a mathematical aesthetic and then declared that this mathematical aesthetic is meaningfully different from concepts of god. It's not clear to me that this is true. And if you can "run" sentience, so to speak, on sets of rules, then I'm not sure there's any reason to suppose that sentience could run on the rules governing mathematical objects themselves, which opens up the possibility of an eternal sentience existing.
Of course all this assumes that mathematical objects really "exist" at all, and I have no idea if they do or not.
Greg Egan has a book that's about this specific thing: build a simulation in a computer of human minds, then turn off the computer. The fact that you turned off the computer doesn't change anything. And the book precedes Tegmark's by quite a while:
So all possible programs are running on all possible substrates right now because they are possible? (for suitable versions of "right now" - since this also removes time as a real thing).
And the only beings that don't really exist are the ones where their existence would depend on a contradiction?
...how would you test this?
[edit]This also implies the existence of Moloch, the time-travelling omniscient, omnipotent, omni-malevolent AI. Where is it then?
I completely do not understand these sorts of logic experiments. When people say they believe in god, they don't mean they believe his existence as a fact (even if they do think this). What they mean is that they believe IN him, which is like saying to your spouse before they go out for big job interview: I believe in you. Its a statement of reliability or capability or trustworthiness.
Hey, I like you guys, but atheists and rationalists reliably get this so, weirdly, wrong. I mean, you won't worship something just because it was proven to exist, right? It would have to have additional qualities worthy of worship?
This strikes me as one of those theories that explains so much that it may as well explain nothing. I'm going to need a LOT more convincing that the idea should even be taken seriously, much less accepted, before I take any implications thereof seriously.
1. In one of those universes, there is an omniscient, omnipotent being who we could call God.
2. In one of those universes, his name is Elon Musk.
3. I think Issac Asimov wrote a story where a leak occurs between different cosmoses. I think the aliens were creating energy in their universe by dumping entropy in ours which was causing problems for us.
4. There was a cosmologist who posited infinite evolving inflating universe bubbles some years ago.
5. The physical laws of this universe make empirical verification of the Tegmark theory impossible. Therefore there are more proofs of the existence of God than there are of Tegmark.
6. Spencer Klavan has published a book claiming that the existence of God is why we are not Schrodinger's cat. I like that one.
Tegmark's Mathematical Universe makes the problem of induction so searingly intense and unsolvable that no intelligent person should ever give it a second thought, ever again.
I see the top comment also makes this point. Good.
Also (responding to myself so as not to over-clutter): "simplicity" as used of God is a completely different concept from "simplicity" as used (undefinedly) here. It means having no parts.
The following: "Because in order for the set of all mathematical objects to be well-defined, we need a prior that favors simpler ones; therefore, the average conscious being exists in a universe close to the simplest one possible that can host conscious beings"
is, with all due respect, gibberish. (Source: I'm a mathematician.) A set's being well-defined does not depend on a "prior," nor does a prior help make an undefined set into a defined one. (And the set of all mathematical structures is certainly undefined.) There is a significant category error in suggesting such a thing. Moreover, to say that *simplicity* per se is what defines the right prior (if talking of priors did make sense) is simply question-begging. Induction and arbitrariness always rear their head secretly at this point (or via the choice of "programming language" if you want to use Kolmogorov complexity) There is always an *arbitrary* penalty anyone could add to your calculation and be equally rational with you. Literally no conclusion is more rational than any other one, on these theories, except asymptotically in time.
People think, "Oh, asymptotically in time isn't so bad -- the universe has been around for a long time." What they don't realize is that in this context, at *any* finite time it is too early to know whether you're approaching the asymptote or not. One would have to know the entire future history of the universe to know whether one was in the regime where one's arbitrary assumptions had stopped mattering. Until one does, one is simply making up numbers out of thin air. Much less trouble to just say you're an atheist because you like it more. (Almost certainly, that also makes more philosophic sense than Tegmark's theory.)
And here's another problem. (There are roughly infinitely many.) We have:
"Because mathematical objects are logically necessary, and “existence” is just what it feels like to be a conscious observer on the inside of a mathematical object."
OK. That almost certainly doesn't make any sense, but ignoring that -- the sense in which mathematical objects necessarily exist just has each of them "exist" a single time. It makes *no sense* to say that there is "more" of the number 12 than of the function e^x. There is no metaphysical sense in which one can quantify multiple existing copies of an abstract universal, or distinguish one from the other, or count a "larger amount" of e^x than of 12. Moreover, even if the existence of mathematical objects is necessary, a *distribution* on them certainly is not, or one distribution over another.
There are so many category errors here that the only way such a discussion could ever arise is that a modern physicist tried to do metaphysics.
Isn't this just Platonism? If mathematics is not just a symbolic representation of reality, but instead is the basis of reality, haven't you really just proved the existence of (some sort of) God?
Edwin Abbott's Flatland points out the dilemma of logic.
imagine a 2d world, but now a 3d sphere has come to preach about the reality of the 3d plane. The 2d person sees a sphere as a circle of different sizes when it interacts the plane of its world, or nothing but a disembodied voice as it hovers over the plane.
the problem is trying to explain a reality using the rules or laws of a lesser reality; a sphere only makes full sense in the 3-d world and only direct experience explains it. in the 2d world everything it does is nonsense or miracles. it can see what you do anywhere because it can see the plane and isn't bound to exist solely on it. if it interacts here it just intersects our reality.
abbot points out that this can lead to "turtles all the way down" because a 4-d space is incomprehensible to the sphere too.
if a creator exists though, we don't have the tools to derive it, we just see where it intersects our life and it wont make much sense apart from a direct, mystical experience. We may not ever be able to do that: God may not be able to be interacted with by understanding laws.
kind of the religious dilemma, supreme reality is not created reality and we can't extrapolate much from it.
Is this not a debate about labels and language? If we define "G0d" as the essence of the nature of simplicity ("simply good; simply powerful; simply first") that simply created everything, how is that meaningfully different from the simple rules of mathematical objects that did the same?
Tegmark is right: all possible mathematical objects do exist... as forms in the divine intellect!
(Okay, I troll. But.)
Like the generic multiverse theory (which seems to exist *largely* just to defeat fine-tuning arguments), I think Tegmark's hypothesis does address fine-tuning arguments, but it does not seem to address the cosmological argument as Scott has articulated it (why should it be logically necessary that all possible mathematical objects exist? moreover, why should they exist actually rather than potentially?).
It addresses the first-cause argument as Scott has articulated it only because Scott hasn't articulated the argument the way a Thomist would. It's not that "all things must have a cause," but that some things must have a cause and the cause must have certain characteristics such as immateriality, simplicity, etc..
Likewise the teleological argument, which is less about why we are able to comprehend order and more about why there should be order at all. A conscious observer could exist in a universe where effects do not reliably follow from causes, yet we find ourselves in a universe where effects do reliably follow from causes. Tegmark's hypothesis seems to depend on this without providing an explanation for it.
It seems (to me), then, that Tegmark's hypothesis (at least, as presented here; I was unfamiliar with it before today) relies on assumptions about the multiverse that don't eliminate the need for a deity, but instead just hide the need for a deity somewhat better. If you keep pushing on its assumptions, I *suspect* that you will eventually end up where I started: all possible mathematical objects exist as forms in the divine intellect, and at least some of those forms have been actualized.
(That is, at least, a considerably more interesting endpoint than the endpoint of the generic multiverse theory.)
How does math exist “actually” vs. potentially? Seems like it’s all potential structure that’s necessary, ie the digits of pi follow exactly from simpler rules and can’t be anything else. Even if you choose different rules, different non arbitrary conclusions necessarily follow from them. Those conclusions are often infinite and the infinite could contain conscious observers
I seem to exist in a way that Bilbo Baggins does not. Both Bilbo and I share many characteristics: we each have a shape, a height, and a weight. We each have a certain way of speaking and distinct mannerisms. We each have likes and dislikes. Our characteristics can be apprehended by other minds. However, I exist actually and Bilbo exists only potentially. (The universe could have instantiated him, but did not.)
I tend to agree with you that math qua math doesn't exist as a substance at all, but Tegmark's hypothesis seems to take it for granted that it *does*. This demands some further explanation, or we seem to lose the ability to claim that my existence (as a conscious observer "within a mathematical object," whatever this turns out to mean precisely) is in any meaningful way different from Bilbo's.
(Maybe Scott is willing to make that concession. I don't know.)
I think the relationships in math *are* necessary- assumptions are provable from axioms. You can’t combine 2 and 2 so you don’t get 4. You cannot not find the number 12345678987654321 somewhere in the digits of pi. I think existence is like that- we have relationships to other mathematical objects that can’t be anything else-
physics is a complicated fractal corner that has observers to remark on this and feel real to themselves and can observe and external reality, but we are ultimately just a part of math that could not not exist because the math follows naturally and inexorably. Simpler than believing there is a separate outside “something” rather than nothing.
Maybe someone could help me understand, but doesn't this issue boil down to spandrels vs. adaptionism like everything else? Putting God aside for a minute, we could assume that all possible mathematical objects concretely exist, or we could assume math is just an abstraction of structure, and that our particular kind of physics and universe is more necessarily emergent than we thought. Then we'd avoid a lot of weird probabilistic baggage where you have to imagine infinite universes (to my mind, that's dividing by zero).
The solution that 'something must exist' is the same between all three theories (God, math, and I'm going to say mine is 'energy/action')--there can't be a reason why there's something rather than nothing (including logical necessity itself, which this post rests on), so the main question is why this particular type of thing rather than the other things--and to figure that out, we investigate our own universe to see what appears most logically necessary by *its* rules, whereas there is never any way to rule out the existence of literally incomprehensible, differently ontic universes. So how do we investigate the structure and teleonomy of apparent organization in our universe? Throughout the history of science the answer has always been darwinism.
But there are two ways to approach darwinism. The mathematical and informational, which prioritizes entropy and cellular automata, and the energetic and physicalist, which prioritizes chemistry and history (I understand this isn't a hard divide, but stay with me).
So let me paint a different picture which is somewhere between mathematical necessity and God. In both the other alternatives, we don't have a good definition of simplicity. The best definition we have of simplicity in nature though is scale--all larger structures seem to proceed out of aggregates of smaller structures. But for larger and smaller you need dimensions to begin with, but we already know from Wolfram's computational universe that you can bootstrap spacetime from a hypergraph (not only that, but it seems to happen rather frequently due to the inherent rules of hypergraphs, which looks awfully platonic).
Instead of scoring this as a point for the mathematical universe, to me it looks like a score for a strictly physicalist universe. It seems weird that mathematics has its own internal, evolutionary logic, right? Instead of being a static structure, you can bootstrap dimensionality from hyper-simplistic rules. Follow that historical, causative train and it's simpler not to imagine math itself as your primitive, which is infinitely complex, but whatever even simpler primitive object would bootstrap all math and structure.
If we don't take for granted that certain algorithms just go from 0 to 1 and spawn consciousness, which I don't, then the idea that it feels like something to be inside of math (a static non-physical structure) is absurd. It makes far more sense that the ultimate primitive object is a darwinian agent (which looks an awful lot like a transformer) some nondeterministic (so you can get noise) multi-state switch that can interact with neighboring switches, and from this noise all complexity emerges. All you need for this is state and interaction--a cybernetic agent. We can imagine simply a universe of switches, or agents, with random laws--so like Wolfram's ruliad, but not an omniverse where all mathematical objects already exist but, but a real and physical plenum of noise and interaction, for which mathematics is an afterthought. Something has to be *doing* the computation. That's my perspective, and I think it's more reasonable.
In this case, much like with oxidative stress which Gould thought was a spandrel but recent research points to be a necessary signaling mechanism for mitochondria, the physics we see is not as fine-tuned or arbitrary as we think. Comprehensibility is a necessary and logical outcome of universal darwinism because every scale of organization builds on itself, and follows the same basically scale invariant rules found in cybernetics. Bing bang boom, done.
According to Godel's incompleteness theorem, Math is either inconsistent, or you need axioms that cannot be proven for it to work. If it's inconsistent then obviously it cannot be the descriptor of reality, even less its basis. If it needs axioms then you have a recursive problem, exactly like "If God created everything then who created God?". That's how my stupid layman's brain understands things, please eviscerate me.
It's unclear to me why we need to weight this by simplicity if all possible mathematical objects exist. We don't need to weight integers by "simplicity" in order to observe that 2 exists
I feel that most such discussions are an exercise in foregone conclusions. Quoting the second most translated book ever “The Tao that can be spoken is not the true Tao”. Any discussion of “god” that occurs using words can conclude only in failure.
Honestly, all this pointless speculation, using claims like, "...mathematical objects are logically necessary, and 'existence' is just what it feels like to be a conscious observer on the inside of a mathematical object." Why are they necessary? Necessary for who or what? Why are there "rules" at all? It always comes across like highly intelligent autistic individuals trying to answer a question they don't fully understand, but they don't see they don't understand it.
The question of God's existence is not a mathematical one, nor a scientific one. It can't be, by definition; and morally, it's not supposed to be provable by observance of the physical or observable world. It's supposed to be a choice. We are physical beings, and we are limited by the fact that our physical senses can only perceive and assess what's physical, observable and measurable in this reality to which we are confined.
The physical universe or reality, as science correctly explains it, takes no sides. It does not care whether you exist, or whether you do not exist, you just do, or don't. There is no right, there is no wrong, there is no what ought to be, or what ought to be prevented. There is empathy, and there is cruelty, envy and generosity. All have an equal claim to exist, because they do exist. If you lie, steal, or murder, or save, care, and comfort, the universe doesn't care.
The message from God, for those of us who believe in it, is to disregard all that, and know instead that there is a transcendent dimension to existence that is independent of the universe and reality; and it is this quality, objective and independent of all of us, of our preferences, independent of the accident of atoms and colliding particles or vibrating strings, that does take a side, and gives meaning to every act we take in regards to another sentient being. It cannot be proved, or disproved. It's simply a choice you make on what you want to believe.
For the non-globeheads out there, this is Platonism. Not a far jump to Theism from such thinking as between metaphysical nihilism and Platonism itself. It's arbitrary to contest certain contingencies when you are granting others in just as capricious a fashion.
The reasoning is sound as far as it goes, but this is just the anthropic objection to the classical arguments with even more special pleading. At minimum Scott has glossed over (1) why should we expect a mathematical universe to exist at all (it's really not obvious that math as we know it is substrate independent and if it isn't this becomes obviously circular reasoning), (2) why should "simplicity" even if rigorously defined correlate with "reality", (3) why is assuming a strong form of materialism arguendo (required to make "conscious observer arises from math" work) justified.
> But if it’s false, then the very fact that we waited this long to get it suggests that there are lots of possible godless explanations of the universe (that satisfy the supposed proofs of God’s existence) that we haven’t thought of yet. Instead of taking the proofs at their word that it’s God or nothing, we may fairly expect many undiscovered third alternatives.
Like I said, special pleading. Would it be overly snide to describe this as "rationalism of the gaps"?
So either way Materialism is out, right? Either the universe is fundamentally infinite goodness, or all mathematical structures, but it ain't fundamentally atoms and energy.
I'm not so sure there is a difference between the idea that mathematics is downstream from physics (i.e. that all mathematical structures are realizable and indeed already present in reality), and the idea that the mathematical structures precede material reality. I actually think the two ideas can't be distinguished in any meaningful way.
Right now the most fundamental theory we have is Quantum Field Theory. The basic building block of the theory is the "field". A field in the theory is not like a wave on water, or a electromagnetic field, or even a wave function. It is a mathematical object that in all points of space and time produces an operator that acts on the state of vacuum. That sounds very much to me like the basic building block of reality is a mathematical structure that can do some computing. And yet nobody would say that QFT undermines Materialism.
>And yet nobody would say that QFT undermines Materialism.
I mean, I would say it. Believing the universe is fundamentally math is or that mathematical objects can exist is a form of Platonism, not materialism. The Stanford Encyclopedia of Philosophy describes Platonism as "the view that there exist such things as abstract objects—where (on one standard definition) an abstract object is an object that’s non-spatial, non-temporal, non-physical, non-mental, and non-causal." (https://plato.stanford.edu/entries/platonism/) This is in contrast to materialism, which the SEP describes as a belief that "the nature of the actual world (i.e. the universe and everything in it) conforms to a certain condition, the condition of being physical. Of course, physicalists don’t deny that the world might contain many items that at first glance don’t seem physical — items of a biological, or psychological, or moral, or social, or mathematical nature. But they insist nevertheless that at the end of the day such items are physical" (https://plato.stanford.edu/entries/physicalism/). Perhaps materialists identify the quantum field as being physical in nature, as in having to do with the laws of physics, and thus isn't a problem. But Tegmark is saying something very different, which is that all mathematical objects exist, even if they are not embodied in the laws of physics or matter. You can't hold to materialism and Tegmark's theory at the same time. Tegmark himself describes his theory as a form of Platonism.
"Tegmark is saying something very different, which is that all mathematical objects exist, even if they are not embodied in the laws of physics or matter."
Yeah, but Tegmark thinks that conscious entities inside mathematical objects complex enough to contain them subjectively experience the mathematical object as physical reality.
But what is the difference between a physical reality subject to mathematical laws, and a mathematical object perceived as physical reality? In the end, when a physicist manipulates a quark, he doesn't hold a physical object in his hands, he instead studies a quantum field that has certain mathematical properties. And I think this is the case for all explanations (a quark is an explanation of some other observed facts). "Physical" just refers most of the time to "subjectively perceived", but all explanations worth anything will make use of abstractions that we could easily call "mathematical objects". The problem (from my point of view) with the definitions you mentioned is that "physical" isn't defined, it is taken as self-evident, and I just don't think it is self-evident at all.
As to whether these objects "exist" or not, I'd say (like David Deutsch) that they exist if they are an integral part of the explanation, i.e. if without them the explanation fails. (It is not by chance that I repeat "explanation" over and over, this is a central concept here.)
So what Tegmark adds, here, is just that all "possible" mathematical objects exist and our universe is one such, which is just a restatement of the multiverse hypothesis to explain the fine-tuning problem.
(What "possible" means is unclear to me too, especially without a pre-existing physical reality. In fact "exist" is also unclear outside of that reality, and that use of the term isn't compatible with my own criterion above.)
(You don't have to respond, of course, this may be as far as we can go.)
This obviates the arguments for Spinoza's God, but does nothing about arguments for a Holy Spirit whose influence can be felt on Earth.
It is certainly possible to imagine a mathematical construct that is experienced by humans as divine influence. But those grand cosmological arguments have no impact on whether that exists in this universe.
Do we have a reason for believing that all possible mathematical objects exist, or does this assumption frustrate common "proofs" of God in much the same way as the assumption that God doesn't exist, but with enough obfuscation that we hope no one notices we've committed proof by assumption?
I dunno. I think the answer is a lot simpler. Most of us are empiricists in the sense that we believe that we need evidence of something for it to be true. Otherwise pretty much everything could be true, including that God was in fact a tea pot rotating around the sun in such a way that we could never see it. So, the proper response to all these theories is not a competing theory, it is uncertainty. You want me to believe something, give me some evidence. Otherwise it’s all just hot air.
This is interesting, but Isn't there a problem of this theory not really telling us anything? If we're all just math, who's to say there isn't an omnipotent all loving being who is also math and created the universe and (insert other biblical things plus math). In fact, if everything is possible, isn't this by definition true in some universe? (I guess the question would then become, do we happen to live in that particular universe or not?)
As to why simplicity might be favored, I think of it like this, imagine all possible universes that can be described using 8 bits, now imagine all the universes that can be described using 16 bits, for every universe using all 16 bits, there are 256 using only 8 bits plus all permutations of random data.
>By existing, you are a random draw from the set of possible conscious beings
Unless you are not. A random draw is an event.
There are no events in a timeless MU.
It's not at all clear that "why am I me?" makes sense as a question..at least without dualism.
>Cosmological: Why is there something rather than nothing? Because mathematical objects are logically necessary
There's an argument that all mathematical truths are necessary, and some assert the existence of mathematical objects.
Some wrinkles;
1. Mathematical theorems are only necessary relative to axioms (That's the beef formalists have with realists).
2. Existence in the context of maths doesn't have to be real existence. Existence and non existence can be defined within fictional contexts...eg. the "existence" of Dr Watsons wife as opposed to the non existence of Holmes' wife. (That's the beef fictionalists have with realists)
3. Mathematical existence is often asseterd on the sole grounds of non-contradiction,.ie possibility..not necessity. (That's the beef intuitionists and constructivists have with realists)
>“existence” is just what it feels like to be a conscious observer on the inside of a mathematical object.
Unless it isn't. There's no proof that any configuration of matter should be conscious, so there isn't that any proof that a Y mathematical structure should be.
>Argument from comprehensibility: why is the universe so simple that we can understand it?
There's no evidence that the smartest human can fully understand the universe, and plenty that the average person can't understand current physics.
> Because in order for the set of all mathematical objects to be well-defined, we need a prior that favors simpler ones;
That would be a measure, not a prior
It's well defined without a measure, you only need the measure to do probablistic reasoning, but you don't know that you're in a probablistic drawing-balls-from-urns scenario.
>average conscious being exists in a universe close to the simplest one possible that can host conscious beings.
.
We are not in the simplest universe that could support life...if we were , there would be less universe , or more life. (But we are probably not in the most complex life supporting universe either).
>But when you consider the automaton as a mathematical object, it doesn’t need a cause; you can start an automaton any way you want; they’re all just different mathematical
The notion of the MU being generated by some set of rules is essentially redundant , since some rule...they dont have to be Turing computable...can generate any structure.
OTOH..it allows you to smuggle in ideas such as a single time dimension, which are hard to justify if you actually are starting from "all mathematical entities whatsoever exist, without constraints".
> By existing, you are a random draw from the set of possible conscious beings
This has always bugged me, and it’s an similar to the probabilistic doomsday argument which assumes that I could be randomly born in the middle of human history (in terms of population) when I had to be born to the people who conceived me, on a certain year, month and day.
In some cases, If you don't model your existence as a specific random draw, you will have incorrect beliefs/credences leading to bad outcomes (illustrated by betting arguments). See Sleeping Beauty Problem and related stuff like Fisherman's Son or whatever its called.
If there is a mistake in the argumentation here, it's additional to the "birth is a random draw" part.
Plot twist: Tegmark's mathematical universe hypothesis is correct, but we are in a mathematical object initialized with a God that then created the universe
So I find the idea pleasing in some ways. It's a neat way to try to explain the 'why something rather than nothing' or the 'why this thing out of all the possible things' that doesn't involve assuming that 'this thing' is in some way special or privileged, a starting point that has been very productive in science.
I do have concerns though. Firstly I think it'd be important to understand what a mathematical object actually is. Are we sure that this universe even meets the criteria? Just what do we mean by 'maths' anyway, what sort of things count? Is the maths inside a mathematical construct necessarily the same as the maths outside it? It's by no means a straightforward concept.
Secondly, in the universe we live in, there is a huge gulf between the concept and the implementation of the concept. It's the same as the difference between a thing and its description, a map and the territory, a program and the actual running of it. This idea seems to posit that there is no such real distinction - it's presumably just an artefact of us living inside one of these constructs that creates that distinction. It seems strange to posit a root, privileged reality where that rule isn't true, when the only reality we know has it.
I suppose more a musing than a concern would be the question of what Godel means for this theory. I think that any reasonably competent and consistent mathematical object would have entities within it that could not be demonstrated from the maths of the object itself. How would such entities appear within the construct? Maybe something like the Hitchikers God, which can't exist as soon as it can be proved?
I feel like Godel tells us that there's a difference between the definition of the thing (the Mathematical Object) and the outworking of it - that the outworking contains things that are true that cannot be proved from the definition. If Tegmark is right and there is no difference between the outworking and the mathematical object, then where does that leave Godel?
Who's to say we live in a mathematical universe? How do we know it wasn't created by some being, or sneezed out of the nose of the Great Green Arkleseizure?
Wait, why do simpler objects exist more? Why would you think that? This isn't explained.
If mathematical objects are logically necessary, why does that mean they exist? Maybe the universe doesn't make sense.
Who says the set of all mathematical objects is well-defined? Maybe our rules don't make sense. Maybe our stupid little monkey brains can't truly understand the universe and we'd all lose 1D100 SAN if we did.
I guess it's no *worse* than any of the existing arguments for God, but it doesn't really seem any *better*, and doesn't have a church or temple with music you can sing and friends you can make unlike those.
You said "if a computer can be conscious..." but I think you should have said something like "if consciousness can arise from computation..." or "if computation is sufficient to create consciousness..."
Compare: "Rainbows contain every possible shade of yellow. Therefore, if a yellow thing can be conscious, then rainbows contain consciousness." False because a conscious thing could *incidentally* be yellow; the existence of a conscious yellow thing doesn't imply that everything with precisely the same yellowness will also be conscious.
The obvious problem with this argument is that it would mean that time, change, and consciousness are illusions (it's the same problem that Parmenides had). Why? Because mathematical objects are eternal and without efficient cause. At best, mathematical objects "describe" change, but even that isn't accurate because mathematical objects are not signs themselves of other things. Rather, they can only be used to model change. So all we are left with in Tegmark's universe is a potential model of the universe, but no universe itself. But time and change are not illusions, so the thesis is wrong. And why is time, change et al not an illusion? Because it would mean that the consciousness of the illusion itself is changing, and so there must be change, and change implies time.
Of course, one might *claim* time and change are illusions if they are simply trying to maintain a thesis, but everyone knows that no one actually believes it. It's much like the person who denies the law of non-contradiction. I think Avicenna had a recommendation for those people.
These types of arguments are so telling. "Hmmm, these arguments for God's existence are hard to defeat. What can I do? I know, I'll just claim that literally every aspect of reality is completely contrary to how you think it is. That will show those theists!" Yes, it shows them something all right.
I don't think this means time is an illusion. Time is within the mathematical objects (if they have a time dimension), not outside of them. In a Game of Life, there is a real step 1, step 2, step 3, and so on. If you were a conscious observer in the game, this would just look like time happening.
“You can’t make a random draw from an infinite set”
As stated, this is wrong. While there are no countable fair lotteries, there are uncountable fair lotteries—which (I take it) are what’s relevant here.
[However, some people defend the view on which, roughly, all infinite sets are really countable (appealing to Skolem’s paradox, or width-extensibility if they’re more sophisticated)—this might block infinite fair lotteries. On the other hand, some people think we should require only finite rather than countable additivity, or that we should work with infinitesimals—this might allow for countable fair lotteries.]
The Western "arguments" for the existence of God--really a misunderstanding. Aquinas's Ways are not really proofs for the existence of God so much as defining God in the context of his metaphysics. (And modern "refutations" generally don't understand either the definition or the metaphysics.) But before God, we had the One, thinking the Parmenides dialogue. The One is the principle of identity, that which makes 1 separate from 2, for example. Obviously, if mathematical objects exists, then the One is manifest (as the One cannot exist, being distinct from all that exists by virtue of having the quality of being indistinct from all that exists), by whom and through whom they come into being, Logos. Any Platonist worth 2 cents knows this, and any one who plays around philosophical Platonism is going to end up in Neo-Platonism if they are clever, which if you dress up with some tribal stories and desert morality codes (the fig leaf of culture), you get the various Western Monotheisms.
The main objection is that “the set of all things” of any kind is a very ill defined object and experience shows that unless one approaches these subjects very carefully, one is more likely than not to invent some paradoxical object that cannot really exist.
Moreover , experience from our own universe shows that all conscious things and indeed all living things consume some finite resource, which eventually boils down to “energy”. In this sense, there is no reason to believe that a conscious being, while being conscious, can exist without consuming resources. Even digital media ie “information” degrades unless resources are consumed, regularly.
As such the postulate of the existence of this abstract mathematical universe where everything happens does not sound any more believable than the existence of god. and if one were to twist my shoulder i might’ve even say even supports arguments for god in some sense, since what is this “universe of universes”? where does it live? and why would simpler rules be preferred? and what is “simpler” even? you need an infinite set of axioms even to have cellular automata…
“[A] mathematical object like a cellular automaton - a set of simple rules that creates complex behavior. … the second most famous is the universe.”
But the universe is not a mathematical object. Or, at the very least, it would be begging the question to use this as a premise against most traditional arguments for God’s existence. For certain features of the universe to be describable by mathematics does not make it a mathematical object.
Likewise, to define a mathematical object as a set of simple rules that creates complex behavior such as a *conscious observer* is begging the question: it assumes that such a thing is even possible without demonstrating that it is. In general, the post seems to be using a very idiosyncratic definition of a ‘mathematical object’.
“this obviates the top five classical arguments for God”
These might be the five most popular arguments for God today (I wouldn't know), but they are not the top five *classical* arguments for God.
“Cosmological: Why is there something rather than nothing? Because mathematical objects are logically necessary…”
The fact that things such as mathematical objects are logically necessary is the very sort of feature of the world that is used as a premise in the Augustinian proof of God’s existence.
“First cause argument: All things must have a cause.”
But no first cause argument uses the premise that all things must have cause, so this is a strawman.
“If God is an infinitely good, infinitely powerful being, it seems like we need to start with a definition of “good” and “powerful” to limit ourselves to a single God in possible-deity-space.”
This bespeaks an unfamiliarity with the classical arguments for God’s existence (e.g., speaking of a ‘possible-deity-space’ suggests that God is a member of a genus, or of some category, which defenders of classical arguments for God's existence would deny): the classical arguments purport to demonstrate that there can *in principle* be only one God, and most of these arguments do not depend on definitions of 'good' and 'powerful' for their success (or failure, as the case may be).
“since God is supposedly infinitely simple, you might still need an objective definition of simplicity anyway!”
Well, divine simplicity is typically understood as mean having no composition, not composed of parts.
Tegmark's mathematical multiverse has a logical flaw that you are glossing over. Since the theory maintains that all mathematical objects really exist, it isn't logical to say that a simple-laws-measure governs the weighing of probabilities in the mathematical multiverse (selecting for simple laws), as opposed to a complex-laws-measure (selecting for complex laws). Since both measures are mathematical objects they must both equally exist!
This critique was expressed by physicist Alexander Vilenkin as follows:
"I am not sure that the notion of weights for the set of all mathematical structures is even logically consistent: it seems to introduce an additional mathematical structure, but all of them are supposed to be already included in the set."
To solve this problem you would need to introduce a meta-measure that selected a simple-laws-measure that itself selected simple laws. But the same argument as above would still apply because there also exists a meta-measure that selects complex-law-measures. Ultimately, Tegmark is stuck in an infinite regress that undermines the logical foundation of his theory.
You can read about his theory and the problems with it (or listen to a podcast about it) here:
>"Because mathematical objects are logically necessary"
The claim that mathematical objects are all _automatically_ logically necessary was called logicism. It doesn't work. You need to specify further foundational axioms of math, in addition to the rules of logic, in order to build up the structures of classical math.
This might have been what you were getting at with this, though:
>"How does the universe decide which programming language to use?"
Like, it is actually unclear what the mathematical foundations are in the mathematical block multiverse, but that's not that philosophically bad a problem to have, relative to the competitor theories.
"All mathematical structures exist" is just mathematical Platonism, which is reasonable. Tegmark's idea is that contingent physical things like a Volkswagen exist in exactly the same way that mathematical structures exist, and in no other way. This runs into the problems that almost all mathematical structures which we can identify have no known analog in the physical world, while a great many facts about the physical world, like the dimensions of a Volkswagen, are totally inelegant and random-looking in a suspiciously non-mathematical way. Tegmark deals with this by invoking an infinity of other universes in which the missing mathematical structures are hiding, and which can never affect our observable universe in any way. In other words it's a completely contentless theory. The reason Tegmark advocates it is that it's grandiose and attention-getting and he has narcissistic personality disorder.
Most of this feels self-evident but there are strong principles which I suspect forbid certain elements to be observed irrespective of their rules - Gödels incompleteness, entropy. One could describe them but they can’t exist.
Supernatural beings violate most of these principles - describable but not actual. One cannot construct a model of a universe as a machine that fuels itself ad infinitum.
Ubfortunately it's not possible, because a random variable's induced measure is sigma-additive, and you can't add countably infinite of number 'a' to get 1.
> The only hole in this theory is that it’s hard to objectively define “simplicity” (it’s easy within a programming language - shorter programs are simpler - but how does the universe decide which programming language to use?)
(Reasonable) programming languages only differ by an additive constant in their measures of 'simplicity'. Mostly because that constant is just the size of whatever emulator you need to write first to be able to express the rest of the program in your most favourite language that makes the problem simpler.
Would love to witness a debate on these ideas between a well-versed theist such as William Lane Craig and Tegmark or other supporter of the MUH. Dr. Craig has addressed some of these concepts, but I couldn't find him directly commenting on Tegmark's idea. In 2020, Hugh Ross (astrophysicist and founder of Reasons to Believe) was asked, "What are your views on MUH/CUH?" He replied with a funny post that also suggests what a smart theist would argue:
"If I was not a scientist, my answer would be huh. MUH stands for mathematical universe hypothesis. CUH stands for computable universe hypothesis. MUH states the physical universe is not merely described by mathematics but actually is mathematics. CUH states that the mathematics that is the physical reality of the universe is defined by computable functions.
"I believe that the universe is described by mathematics and that this mathematics is ordered, elegant, beautiful, and consistent. It was humans that constructed mathematics to describe the operation of physical reality. That mathematics is no more a tangible physical entity than is our alphabet or our number system. Mathematics is a manifestation of the symbolic capability that is unique to humans among all Earth’s life.
"To say, therefore, that all physical reality or that physical existence is just mathematics, in my opinion, goes way too far. However, mathematics does reveal the nature and source of physical reality. The mathematics we humans constructed to describe physical reality reveals the attributes of the Creator who brought into existence physical reality. That revelation likely explains why of all scientists mathematicians manifest the highest percentage of believers in God."
Why is it necessary to objectively define simplicity? Isn't it the theist who is asking you to explain comprehensibility? So, the simplicity is necessary for their argument, not yours. The logic that we are more likely to find ourselves in a more simple universe is sound, but it doesn't mean that we must therefore be in the simplest universe.
Isn't it up to the person positing the simplicity (the theist via comprehensibility) to define simplicity?
And perhaps this next one is a question for Tegmark, but like with many multi-verse explanations, I'm always a little confused when people posit that all possible universes, or all possible mathematical objects exist, when it would suffice, for the sake of argument, that all possible universes, or all possible mathematical objects *can* exist—which satisfies the argument without claiming infinitely more than necessary.
Maybe a nitpick, but important if you're talking maths.
"You can’t make a random uniform draw from an infinite set" is wrong.
You can't make a random uniform draw from a countable infinite set like the integers. There's no issue with a random uniform draw on [0, 1], or any other compact set of the reals.
In Tegmark's universe what does one make of Aquinas' definition of God? If we give the name God to 'the most perfect being that can be conceived' then does this being not exist? Call it the most perfect non-self-contradictory being, if necessary, I suppose.
>Cosmological: Why is there something rather than nothing? Because mathematical objects are logically necessary, and “existence” is just what it feels like to be a conscious observer on the inside of a mathematical object.
Can someone explain this to me in simple brain terms? I don't understand why mathematical objects are logically necessary or why logic exists rather than no logic existing.
>The only hole in this theory is that it’s hard to objectively define “simplicity”
I would say the bigger hole is a complete lack of evidence for the superficially-absurd axioms.
>mathematical objects are logically necessary
And why must logical necessity induce existence? I don't really care about the existence of God one way or the other, but arguments like these are just silly. You can always just trivially say "but why is it like that?" Even if there WAS nonzero evidence for Tegmark's Theory, it simply begs the question "what is the nature of the medium that requires every mathematical structure to exist?"
Is Poincaré recurrence relevant at all? I am bemused by Bentham's thought experiment about coin tosses bringing me into existence, but if it is useful surely Poincaré does the same job
The debate is damaging to its proponents. I am unlikely to pay attention to a physicist who claims to have developed perpetual motion in his spare time. And it seems to read across to unreasonable uncertainty in other debates. I 100% believe shrimp suffer agony as appalling as Our Lord suffered on the cross vs I think it more likely than not that shrimp feel substantial discomfort.
I don't see any meaningful difference in insisting all possible mathematical objects exist because I say so and insisting an unmoved mover exists because I say so.
This kind of stuff always reads to me somewhat like Gödel's mathematical proof of God's existence (which I suppose assumes some version of Tegmark's mathematical universe).
If anything this highlights the mysterious nature of this thing we call existence. Do we just feel like we exist because we're bound by the rules of our "imaginable" universe? Or is there something else that makes our universe "more" than just imaginable? I expect atheists and theists to have very different intuitions here (cue Leibniz'd "best possible world").
But also I have always had deep problems with the fundamentals of the setup and the uncountability of these universes. At the end of the day, why even require universes to be consistent (in the mathematical sense) to exist? Don't possible Marvel universes "exist" in exactly the same sense as possible "physical" universes despite the absence of fundamental laws? Isn't making one kind of imaginable universe more "real" a priori exactly as mysterious as making one specific possible universe "real"?
And maybe more importantly: isn't this line of argument fundamentally contrary to what post-Dawkins intellectual atheism is supposed to be about? In the sense that "here's a fully theoretical argument about the nature of reality, it has not falsifiable by any possible observation in the physical world, however it proves whether God exists" sounds a lot more like Aquinas than Dawkins et al? This seems to fail the test of "does this belief affect what you expect to see in the world" test in all but the vaguest senses (like for theists who "only believe they believe" in God, as Yudkowsky would put it).
I don't see any reason that the universe _must_ weight its sampling by complexity. Any function that has a finite sum over the infinite set would do. I think we should still be surprised that the universe is simple rather than containing a large number of reciprocal cheesecakes (or whatever another bias function might optimise for).
As an aside, it's also not clear to me that complexity actually has the finite sum property. For example, if you could identify an infinite subset of worlds that all had the same complexity, it would *not* have a finite sum (*) - and it seems like that should be fairly easy to do under most definitions of complexity. I'm sure Tegmark has a clever trick to solve that although I have no idea how he'd have done it.
(*) suppose infinitely many of your worlds have a complexity of 0.1, then since the sum of 0.1+0.1+0.1+... divergent, so does the overall sum of world complexities.
To actually be convergent you'd need something like the first world having complexity 1, the second having complexity 1/2, the fourth 1/4 and so on.
A time dimension would not be a mathematical object, but an indexing of a mathematical object to a physical reality. Similarly, we can describe a linear basis and index that to real space, but that linear basis is not the same thing as real space - there is an ontological difference between the two. An analogy would be Borges' Library of Babel. Some of those books would speak of time or change or whatnot, but they are not themselves time, change, etc; they merely indicate it. Moreover, their indication of those realities is lacking content. I.e., there is something that it is like to be time that is not contained within the content of a one-dimensional manifold (or the letters t-i-m-e). So, while our mathematical descriptions of physical reality share similar internal relations with the reality it describes, the very thing that it is is different. For F=ma, m is not a mathematical object. For 2kg, 2 might be a mathematical object, but the kg part is not. The same for the s in the m/s^2 part of the equation.
As far as the Game of Life, the various steps only appear time-like to the temporal observer. There is no actual change, and so if you were some conscious observer in the game, you could recognize the various steps, but only eternally. In other words, you could look at the steps and say that they have some sort of order to them, and you could *call* that time, but you would not experience it in or as time. Why? Because all steps are equally true simultaneously.
If you have the appetite for more, I'll explain the eternality in more detail: Imagine the set of all mathematical objects (using 'set' loosely here). Because it contains all mathematical objects, there is no possible mathematical object that is not contained within that set. Moreover, there is multiplicity in that between any two objects is a relation of non-identity, i.e., something like: for any x and y, x is not y. Your consciousness would be one of these objects (containing but not identified with other, simpler objects). Your consciousness and your conscious experience would be defined as this set of mathematical objects, however they might be ordered. But that means that your consciousness and conscious experience cannot also be identified with another mathematical object that contains a different conscious experience. Whatever conscious experience you have, you have by definition. To not have that conscious experience would be to be a different mathematical object. In other words, if you were a mathematical object, your conscious experience could not be x and y where x=/=y. But change means that something can be x and it can be y through becoming, that is, x becomes false and y becomes true. Mathematical objects, on the other hand, cannot become false - they are necessarily true. And your conscious experience is x and is y through becoming, therefore etc. This goes for all physical objects, not just your conscious experience, and thus there would be no change if all and only mathematical objects existed. But if there is no change, there is no time - the two are at least mutually defined.
This problem is the same problem encountered by the pre-socratics. There are two options: 1) something underlies the change such that z changes from x to y or 2) there is nothing underlying such that x simply becomes y. Parmenides chose the latter and thus denied the possibility of change. Why? Because if x is being and y is not x, then y is not being. So any change that x could experience would be from being to not-being. But being cannot become not-being for then it would mean that being would be not-being, a contradiction. Applied spatially, there can be no multiplicity of being for the same reason. So, for Parmenides, all being was uniform and unchanging. Tegmark gets us to a similar conclusion: the only thing that exists is the unchanging "set of all sets."
The largest religion in the world is Christianity, for which proof of God’s existence is supplied by concrete historical events—most importantly, the resurrection of Jesus. Obviously, a thought experiment like this does not and could not “defeat” a proof like that: one cannot disprove the existence of something in the abstract that has been observed in reality.
On the flip side, if those historical events did not happen, that alone suffices to defeat the claims of Christianity (cf. Paul: “if Jesus is not raised we are the most pitiable people of all,” or words to that effect).
The idea that all metaphysical possible universes obtain runs into problems with anthropics. I'd expect to be where most of the same rosen's are or where most of the humans are, but a metaphyiscialy possible universe is one just stacked with quintillions of Sam Rosens right next to each other.
I'm probably a bit late to the party, but I'm a bit surprised "Tegmark's mathematical universe" is actually something taken seriously. I was bothered by the idea that maybe existence was just "mathematical possibility" about 25 years ago as a teenager but even then I relatively quickly realized that actually there are a lot of pretty strong notions that go into what it means to be a "possibility" and stopped taking the thought seriously as any kind of foundation. After that I went on to learn more about mathematics, now I take it even less seriously - mathematically, there are just so many ways to define things and group things as being "equal" or different or define structure etc that the idea seems even more nonsensical now.
But the reason "we waited this long to get it" is not because it's a particularly good metaphysics - the idea of the Boltzman brain is very closely related this kind of thinking (it's 100 years old), and also one way to reject this kind of thinking. Btw, sentences like "If we were selecting for simplicity, we would expect for most objects to start as a singularity and then explode outward" are just straight up nonsense and about as circular as saying "if things looked like our universe, we would expect them to look like our universe" since you're just defining "simplicity" by what you personally think is "simple" (but speaking as a mathematician - singularities are not simple at all, and explaining the arrow of time is also not simple at all even though there are lots of arguments that sound good but are subtly circular here too)
These arguments were god-of-the-gaps to begin with. The I don't understand X, therefore god.
Tegmark is a fairly good potential answer to those gaps. But there is no way god is a better answer than "I don't know".
> Cosmological: Why is there something rather than nothing?
God doesn't help here in the slightest. Why is there a god rather than nothing?
> Fine-tuning: Why are the values of various cosmological constants exactly perfect for life?
Is it? We really don't know what alien life forms might exist in universes with totally different laws of physics. We aren't particularly sure what alien life forms might exist under our physics? Can you get life forms knitted of plasma vorticies and electromagnetism living deep within stars?
And the usual argument goes "if gravity was 5% stronger ..." as if god only got to chose the constants, and couldn't have written entirely different and much more complicated laws.
> Argument from comprehensibility: why is the universe so simple that we can understand it?
There are parts of the universe that no humans understand yet. And plenty of humans who utterly fail to understand that the earth is round not flat.
Besides, this fails conservation of expected evidence.
"Why is the universe so complicated that no human can possibly understand it. Surely such a complicated universe could only have been invented by a superhumanly smart god?"
The god hypothesis predicts both options equally well, it predicts nothing here.
> First cause argument: All things must have a cause.
Basically the cosmological argument again. God always gets a special exception. What caused god to exist? Super-god? If all things really have a cause, this implies either a self sustaining time travel loop, or an infinite regress.
Hey guys, I think I randomly drew the solution where I am god in this world. I am still practicing though, apologies for the many evils, I'm working on it. Please help me out too, even though I am infinitely good and infinitely powerful does not mean I want to solve everything myself.
Didn't Tegmark have to modify his theory due to criticism from Gödel's theorems to having only fully decidable mathematical entities existing? From the linked wiki:
Tegmark admits that this approach faces "serious challenges", including (a) it excludes much of the mathematical landscape; (b) the measure on the space of allowed theories may itself be uncomputable; and (c) "virtually all historically successful theories of physics violate the CUH"
I wonder what it is about this that just "clicks" for some people and not others. Like Brendan, jamie b., and Caba say in this thread, this has just always been obvious to me for as long as I've been thinking about the "Why is there something rather than nothing?" question, even before I encountered Tegmark or David Lewis. And yet I've never been able to convey this obviousness to anyone else.
"Tegmark’s hypothesis says: all possible mathematical objects exist."
That assertion begs for justification, and finds none. Building on it is an exercise in fantasy.
So "The fact that [something] exists in possibility-space is enough for the being to in fact be experiencing it" fails; existence in possibility-space only means the bare possibility if existence-in-fact.
Only one "mathematical object" is known to contain conscious observers: our universe. Whether there are others is completely unknown and uncertain.
"Most conscious beings exist in very simple universes, ..."
Only one universe is known to have conscious observers: ours. No "simpler universes" are known, much less any with known conscious observers. "
"Miles Donahue’s ... says he can’t really think of a great response to fine-tuning, but suspects that the terrain is too difficult and unexplored to give up and say God is the only answer."
Like Tegmark, fine-tuning asserts things to be known which simply are not.
The arguments for God are all refutable without Tegmark's hypothesis.
Of course, when you define "God" as having a white beard, or being all-knowing/ all powerful, etc, you run into problems. But when you define God as "some conscious force outside of humanity that has, at least once in human history, communicated with humans in some way," then you're basically just making an argument that the first alien contact with humans has happened in the past rather than will happen in the future/ will never happen (as God and a powerful alien are basically indistinguishable from one another, when you set moral considerations aside, as those will always be debateable). And this argument for God's existence doesn't seem so insane/ irrational to me. If the universe is as big as we think it is, then likely there are other life forms out there. If there are other life forms out there, likely we are not the smartest life form. If there is a smarter life form than us, it likely would discover us before we discovered it. If it discovered us and communicated with us before we discovered it, it would likely be experienced in a way similar to how humans have their supposed spiritual experiences. As it is logical to assume we aren't the smartest thing that has emerged from these billions of GALAXIES, and it is logical to assume that whatever is smarter than us would discover us before we discovered it (and probably has by now, given that we think the universe is billions of years old), then it's logical to believe in "God." Not necessarily an all-powerful, all-knowing, or even all-good force. But I mean, the primary real question here is: "are all religious people idiots who are decieving themselves or are they onto something?" They might be 99% off the mark with their hypotheses based on their supposed spiritual experiences, but if they are 1% on the mark, if these supposed spiritual experiences have even a shred of validity to them, *that* basically disproves the whole materialistic atheist hypothesis (which is basically that all religious people belong in an insane asylum). Anyways. there's my God proof. I know i define God more flexibly than most (it seems only logical), but I also think God, by my definition, almost certainly exists. My "faith in God" is basically an expression that I think 1) science is incomplete, 2) not all morality/ spirituality is bullshit/ self-created arbitrary nonsense and 3) something's out there. Use your "every mathematical object that can exist does exist because I said so" proof to disprove that ;)-
If we "dumb down" the concept of God enough, gods become less controversial and this topic becomes unimportant to everyone except an academic minority.
In ordinary conversation, God refers to far more than some extraterrestrial, superhuman intelligence that happened to contact a few humans long ago. God is said to have an ongoing relationship with humanity, complete with plans, commands, rewards and punishment.
Among philosophers this ordinary understanding might be dismissed as trivial, but in the rest of the world this understanding is tied to most of the significant issues facing humanity.
So, if I may ask: is this matter more than academic?
Math is more a human discovery than an invention. It’s not like language. Pythagoras’ theorem exists for aliens as well as humans.
But this is a world away from saying that all mathematical objects exist or could exist.
Thanks, agreed.
Where does the premise "nothing exists until it's observed" come from?
The interpretation called Relational Quantum Mechanics comes somewhat close in that it proposes physical variables only take values during interactions between multiple systems. You could stretch that and say a system only "exists" when its physical variables take values. But it's a stretch. And it's only an interpretation, one of several that are empirically equivalent.
That would be better seen as a possible-> actual distinction.
Not only does that premise not come from quantum physics, but it is explicitly contradicted by it. The only thing that objective collapse interpretations say is that a system changes state when you observe it, not that it doesn't exist at all before hand. And on interpretations without objective collapse, nothing special happens at all when you observe something.
Well, Bohr and Heisenberg were anti-realists. They didn't believe in an objective reality independent of observation. And they argued that the properties of quantum particles only exist when measured and are shaped by the act of measurement itself. But Schrödinger and his feline thought experiment effectively called bullshit on that idea. ;-)
As far as I understand, it was not that much about philosophy originally, it's just that in the beginning (and up until Everett in the 70s) no one realized that measurement is mathematically indistinguishable from entanglement. So there was an obvious question: why don't we see objects in superposition, and it had an obvious answer: we have this measurement thing that collapses the wavefunction. Except it turns out that this is completely unnecessary because brains are incredibly hot and can't exist in anything else than a simple mixture of pure classical states and so can't perceive superpositions.
What's especially interesting about it is that's a real world instance of the grue/bleen problem (https://en.wikipedia.org/wiki/New_riddle_of_induction). If you start with the traditional QM, then proposing Many-Worlds seems like an unnecessary complication and multiplication of entities, rather than cutting out an unnecessary and unfalsifiable physical mechanism.
> ...it's just that in the beginning (and up until Everett in the 70s) no one realized that measurement is mathematically indistinguishable from entanglement.
Huh?
Entanglement itself does not require measurement — it simply describes a nonlocal correlation between particles. Measurement destroys superposition by forcing an outcome. With two entangled particles, when one is measured, its wave function collapses, instantly determining the state of the other entangled particle (at faster than the speed of light, as confirmed by several key experiments).
We're still left with the question of why an observation/measurement by our incredibly hot brains can collapse the waveform of a particle. To quote Sabine Hossenfelder...
"The measurement problem, then, is that the collapse of the wave-function is incompatible with the Schrödinger equation. It isn’t merely that we do not know how to derive it from the Schrödinger equation, it’s that it actually contradicts the Schrödinger equation. The easiest way to see this is to note that the Schrödinger equation is linear while the measurement process is non-linear. This strongly suggests that the measurement is an effective description of some underlying non-linear process, something we haven’t yet figured out."
"Observe" is a loaded term. I've always heard it as interaction. The quantum state doesn't decohere until it bumps into some other object. When two particles collide, no one has to be watching for them to decohere.
No, it doesn't.
Quantum physics doesn't say that.
If that were the case, there wouldn't be any superpositions, since they'd all already be collapsed by God's observation. Also, something like the Everettian interpretation - where the wave function collapsing when observed is an illusion - is probably true.
I think perhaps you missed the bit where the simplicity penalty applies to the hypothesis, not the results. If a simple mathematical structure leads to an absurdly large number of different realities, it's still a simple mathematical structure.
We know from experiments that particles in superposition- particles that are simultaneously doing two different things- exist. Whenever stuff interacts with those particles, they go into superposition as well- so, you get a sort of expanding bubble of stuff in superposition. Those bubbles are like a tiny multiverse, with one set of stuff doing one thing, and another initially identical set of stuff diverging to do something else.
When those bubbles get large enough to interact with an observer, we know- also from experiment- that that tiny "multiverse" appears to collapse into just one of the simultaneous sets of stuff, selected at random. The classic Copenhagen interpretation just describes that collapse mathematically and treats any speculation about what it might imply as beyond the scope of QM. The Everettian/Many Worlds interpretation, however, argues that we ought to think about the implications- and the simple and straightforward interpretation of the evidence is that there's actually nothing special about observers. When the bubble of stuff in superposition expands into an observer, that observer just also goes into superposition. It only appears to collapse from the observer's perspective because the observer is now split into two versions, and each one sees just one set of stuff.
So, there are actually vastly more parallel worlds than eight billion in the Everettian interpretation, but it passes Occam's razor because it's just a very simple and straightforward implication of the evidence, without any extra assumptions about things like observers being metaphysically special or superpositions spontaneously collapsing when they get large enough, which we don't actually have any evidence for.
Nor do we have any evidence of multiverses. And the many worlds interpretation doesn't solve the measurement problem.
The premise of MW is that standard QM is itself evidence of multiverses- that it just straightforwardly implies MW, and we only avoid that by assuming stuff that the evidence doesn't imply, like wave functions spontaneously collapsing.
Why do you think it doesn't solve the measurement problem? It seems pretty intuitive that if you yourself are in superposition, each version of you is only going to be able to make one definite measurement.
Granted, there is also the weirdness of probability amplitudes in MW- if you have a superposition that's 70% one way and 30% another way, then MW argues that you get universes with 70% and 30% "measure", but it's very unclear (to me at least) what that "measure" would mean ontologically. Is that what you're referring to?
The bigger problem with measure is that it's not immediately obvious where the Born probabilities come from. This isn't a huge problem though, since similar problems of the probability of being a particular being arise due to the Sleeping Beauty problem regardless, and also there are some proofs out there about how Born probabilities are the only reasonable option/the only option that avoids Dutch books.
Oh, there would be far more than 8 billion realities, but this is independent of how many people are currently alive. All of the 8 billion people in the reality you are observing are in the same reality as you. However, every physical interaction creates exponentially more "realities", each with its own copy of the 8 billion people.
All possibilities existing is simpler than a smaller finite number you can completely describe it in less words. It's the total information content that matters.
An "observer" in quantum mechanics does not entail a conscious being. A photon is a typical observer. It observes by bouncing off an object or being absorbed by it.
No, I think Kurt is just describing the physics completely accurately. It's called observers because you have to use the photon (or whatever) to check the result of the experiment.
https://en.wikipedia.org/wiki/Many-worlds_interpretation removes all of this, I think profitably, in favor of just talking about which things are correlated with which other things.
I consider objective collapse theories more promising, personally, since many-worlds, like it says, implies not only a multiverse but a multiverse that bifurcates with nearly infinite frequency.
I don't think the bifurcation is a problem.
I favor objective collapse less than /all/ of the alternatives, I think; if not MW, then epistemic and hidden-variable interpretations still seem more promising. Hard to tell what will come out on top in the end, though; I hope I live long enough to see it.
BTW: to anyone interested, I recommend Tegmark's book wholeheartedly. It isn't just a pitch for his hypothesis, but gets into a lot of other neat ideas and explains some foundational concepts very well.
What's your objection to objective-collapse theories, out of interest? One which doesn't register when it comes to octilions of fresh universes manifesting within a mole of hydrogen every nanosecond?
Many worlds does not imply any bifurcation - there's only ever one world. Its "splitting" is a thermodynamic phenomenon where contact with a heat bath (for instance, us) drives a superposed state into a mixture of its interaction eigenstates (with roughly definite energies, etc). The fundamental physics is just schrodinger's law, always and everywhere.
I haven't read the original Everett paper, but the summaries of it say he did posit bifurcations. Can you provide a link to where you're getting your interpretation from?
If you define the single 'world' as an ever-complexifying superposition of everything that could possibly have observably happened within that world, yes.
Theres more than one version of many worlds . In the version where splitting is decoherence, and therefore relatively macroscopic, the worlds are the decohered branches.
Theres more than one version of many worlds . The version where microscopic events lead to fully non-interacting (decohered) universes has some problems, such as predicting that quanfum computation cannot.work.
MWI allows quantum computation just fine, it just says (like every other interpretation) that you have to keep your quantum state from decohering with the outside world for the duration of the computation.
> No, I think Kurt is just describing the physics completely accurately. It's called observers because you have to use the photon (or whatever) to check the result of the experiment.
Mostly, but it would be slightly more correct to say that QM has no intrinsic notion of an "observer" - it has *observations*, which are just a conventional label for certain sorts of interactions.
But not any sort.
The MWI doesn't solve the measurement problem. Wave function collapse is not described by the Schrödinger equation. The wave function collapse is a non-linear event, and when the measurement bifurcates the universe, we still have to explain why a particle went through a beam splitter in one direction in one universe and the other direction in the other upon measurement in either of the bifurcations.
Thank you, yes.
You don't have to explain a certain objective state of affairs, because you have no idea what it is beyond your observations.
What you have to.explain is the nature of observations...why observers make unambiguous observations, in a classical basis. That does t have to be explained by collapse, but it can't be explained by, observers remaining in coherent superposition with themselves.
Okay, but what's the objection to collapse, per se?
I wish I was in the universe that doesn't have typos.
Not really. A photon alone does not necessarily cause the wavefunction to collapse and so imply an observation has taken place. We don't really know what counts as an observation and its one of the big open questions of fundamental physics.
Many worlds can sidestep the question, but its not as widely accepted by physicists as much online discussion would have you believe.
*Measurement* is the production of a sharp value or "pointer state". That is more general than observation by a human, but less general.than any interaction whatsoever.
An interaction that involves *many* particles.
How much? Well, more is better; exponentially more makes the values quite sharp.
The "observer" isn't the point. What matters is that a causality chain is triggered and this locks in the state that causes. Once the information has got out of the quantum world we're stuck with it in our world. "Observation" is just a short way of saying this.
That relies on a fundamental misunderstanding of quantum physics. There's nothing requiring an "observer" to be conscious. It's just any macro-scale object that interacts with the system.
This seems a roundabout way of just making shit up.
No, George isn't making shit up. That was Bohr and Heisenberg's belief. And modern versions of the Copenhagen Interpretation sorta kinda imply this. NB: I don't buy it, but some do.
Here's a source: https://en.wikipedia.org/wiki/Observer_(quantum_physics)#Description
If it required the observer to be conscious, they'd be using that to find out if animals are conscious. Or if people in comas are conscious. Except they wouldn't even know it's specifically "consciousness" that matters, because how do you even verify that?
I thought they ran an experiment where the only observer was a computer that discarded the data, and it didn't count?
If it can perfectly discard the data, it wouldn't count. If it does it imperfectly and ends up in a different state, then even if a human doesn't look at it, it will count. This is why making quantum computers is so hard. You can do cool calculations by having the computer end up in the same state via different calculations and interfere with itself, but only if it ends up in truly the same state.
Has the experiment actually been done?
Really, its.just opinion.
So you say.
The "observer" is, of course, whatever's worrying about quantum mechanics.
I don't like that the replies to you have given three very different-sounding explanations of that.
I don't think Occam's Razor has anything to say against a multiverse.
If both theories are equally surprised by the world, then Occam's Razor only acts on the simplicity of the theories, not the simplicity of the world.
In my opinion, a multiverse is the simplest explanation of quantum mechanics. Even if I'm wrong, it's not far off.
On the contrary: if we accept both of the following premises:
1. Any observation causes superpositions to collapse down into singular eigenstates.
2. There is an all-seeing God that is simultaneously observing the whole universe, all the time.
then it would be impossible for superpositions to form in the first place, and impossible for humans to learn about those features of quantum mechanics at all. Also, accepting the first premise "nothing exists until it's observed" is simply wrong. "No preferred basis is chosen and no system is ever in a singular eigenstate until it's observed" doesn't actually have the same ring to it, but it's a more faithful translation of that interpretation of physics into English.
Unless God is perfectly happy holding an infinite number of superpositions in his mind at once..... :)
I believe Shay's argument was that God is constantly observing everything that happens in the universe, and therefore causing the waveform to always collapse. I think your argument is more pantheistic (i.e, God *is* the waveform of the universe, or the latter is a thought within the former.)
How would we know that then, if there was a universal observer, than everything would have been observed from the very beginning and we would never see a transition state?
But if God observes everything at once then doesn't that preclude any quantum behaviour? Everything would be in a collapsed state won't it? Come to think of it, that might be another proof of his non-existence, at least as an "all seeing" being.
Not sure how conventional it is, or even correct, but I like to think of a quantum state as a system rapidly (compared with its surroundings) evolving, ultimately via some internal logic, through a finite number of possible "arrangements" so simple in the possible numbers and values of its relevant degrees of freedom that any arrangement can recur often enough that the system can be considered extrinsically as not moving forward in time, just ambling in a sort of timeless state like a one armed bandit with spinning wheels.
Only when it combines with a larger ensemble with many more relevant states, i.e. "is observed", does the chance of a combined state recurring reduce to effectively zero can it said to be advancing in time along with the larger ensemble and therefore, in that sense participating in the combined ensemble's existence.
One objection Matthew's blog brings up that isn't addressed here is that Tegmark's theory (and I think modal realism) probably undermines induction.
Matthew's Theory also probably undermines induction, though...
How so? From what I understand, Matthew's view is that God creates a large multiverse but puts souls into the universe best suited for them. This is unlikely to be a universe where inductive reasoning breaks down.
edit: He argues this in the last few paragraphs of Section 3.2 of this article: https://open.substack.com/pub/benthams/p/the-best-argument-for-god.
Shouldn’t that go in an ‘Answer to Job’ type direction? Once all the permutations of souls in first-choice universes have been exhausted, we get second and third-best and so on. Eventually you land at infinite non inductive universes with souls that would slightly prefer induction. Which seems isomorphic to the Tegmark theory’s breakdown.
ETA: https://slatestarcodex.com/2015/03/15/answer-to-job/
Sorry, I'm unfamiliar with 'Answers to Job'. What are you referring to? Your point sounds right to me but I'm not sure how to reason about infinity here. But I don't think that Matthew believes God creates every possible world (every computable math object in Tegmark's view), only "all possible people who he could give a good life" as he says in that article.
Old Scott article, sorry: https://slatestarcodex.com/2015/03/15/answer-to-job/
I think my life would still count as more good than bad if everything turned into marshmallows tomorrow, so don't see why God couldn't put me in a non-inductive universe like that, even if my life would be marginally better in an inductive one.
Makes me wonder, why _only_ computable objects are allowed?
Why no hypercomputation (https://en.wikipedia.org/wiki/Hypercomputation)? It does not seem to preclude life, so why it doesn't happen?
Matthew changes his preferred theodicy once a month (latest one here, I think: https://benthams.substack.com/p/the-archon-abandonment-theodicy?utm_source=publication-search)
His latest one involves postulating the existence of “archons”, connection building, “difference-making”, and a hunch of other considerations which you can check out for yourself.
This kind of theodicy undermines induction in two ways
1) it allows the world to be radically evil in an arbitrary way and still “justified”. If infinite factory farm & wild animal torture & genocides are fine, why not make everyone’s induction fail? That doesn’t seem egregiously worse than hundreds of billions of animals being tortured for every second of their lives. Even if it was worse, there’s no reason why the reasons why evil is justified would not apply to theodicy. Indeed, this theodicy seems to directly *predict* a breakdown in induction, because the “archons” have *failed* to create a good universe.
2) More broadly, this *kind* of theodicy undermines moral induction. Whenever Matthew makes his monthly theodicy switch, it seems like he’s contriving an explanation that explains away all the bad things in favor of some abstract infinite good. If there are many competing theodicies like this, then when one endorses the entire category of theodicies as worthwhile, they are essentially saying “the world is terrible, and I don’t know why, but I am willing to believe that every atrocity somehow makes the world infinitely more valuable for it”. The problem, of course, is that this justifies doing literally anything, because you've already pre-committed to believing that every atrocity has some unknowable justification which makes it right in the end.
Matthew himself made this second argument when he was an atheist. I found it quite persuasive…
I only re-skimmed the article but I think archons are tasked with "making this world very good", not creating the universe itself, and so cannot create induction-undermining worlds.
But either way, one could reject that theodicy and still accept Matthew's anthropic argument.
> "making this world very good", not creating the universe itself
I understood material universe and world to be essentially interchangable (aren’t they so in Gnosticism?). Regardless, it seems like “does this world obey induction” would be part of making a “good world.”
If induction wasn’t, then the anthropic argument certainly undermines induction, because the only other explanation for why all the “””unsetly many””” people are in worlds with induction is that induction is necessary for the Good…
We can of course reject this specific theodicy, but the moral induction problem is common to most any theodicy which assumes the “unsetly many people” version of the anthropic argument.
Sorry, to clarify: the distinction I was making was between the powers of God, who creates the universe and sets its laws (and decides whether the universe obeys induction) and those of the archons, basically minor gods tasked with protecting us from lesser evils.
Please no archons, that brings us slap bang to Gnosticism which is very much "material universe bad!"
"A Voyage to Arcturus" is the ur-Gnostic SF text for this, where the main character goes through everything and discovers that existence is a horrible trap and the only way out is death. It's a great story but very grim:
https://en.wikipedia.org/wiki/A_Voyage_to_Arcturus
The 'archon abandonment theory' is intriguing but it's not Christian (though to be fair, I have no idea if he's trying to argue for a Christian God or just some kind of 'god exists' idea). If archons but no intervention, then that knocks out the Incarnation and the Atonement: God won't step in to clean up the archon's messes, the archons are the important difference makers (and not God) so the entire point is to create relationships of gratitude between us and the archons so we'll be best buds in eternity.
First, this assumes Western notions of "you saved my life, I am eternally grateful to you and feel positive emotions to you". In other cultures, I am given to understand, such an intervention is considered instead in the form of a debt, and the rescuer now incurs obligations towards the one they have saved, while the saved person does not have gratitude but rather expectation from then on of constant intervention. 'You saved me, now you're responsible for me' like a pet or small child because the rescuer took on the role of caretaker and authority (If I'm wrong, correct me). This doesn't augur well for building a positive relationship for eternity.
Second, if you have archons (powerful demiurgic beings who can affect the physical reality), why do you need God? That's just a step too far for the sake of explanation. The world as we see it is messed up because the powerful beings are not all-powerful, all-knowing, and all-benevolent; they may intend well but fall short in execution, or they may not like us particularly much at any given time. It's an argument for pantheons but not a sole creator God.
There's a couple other comments I could make, but I'll just remark that various late-antiquity mystic groups like the neoplatonists also believed in versions of the archons and demiurge and didn't believe they were necessarily evil so much as imperfect.
> In other cultures, I am given to understand, such an intervention is considered instead in the form of a debt, and the rescuer now incurs obligations towards the one they have saved, while the saved person does not have gratitude but rather expectation from then on of constant intervention. 'You saved me, now you're responsible for me'
Very interesting, but also feels counter-intuitive that someone saving your life would not elicit gratitude. Do you have a reference? Would love to read more about this.
No, that's wrong. Tegmark thinks the simplest way to mathematically describe a human brain is to define a universe in which induction is true, and then run it for a few billion years.
Unclear whether there's a reasonable definition of "simplest" for which this is true — see my comment elsewhere in this thread for more on that point — but the theory has definitely addressed your objection at least in principle.
I see. I read uncarefully. I didn't know Tegmark's theory gave more weight to observers in simple universes. Does he think the more complex universes are simply not instantiated? Or just that observers are more likely in universes with induction?
Imagine trying to specify a single human consciousness, using a string of mathematical symbols.
One approach would be to write out the location of every particle in a particular human brain — but this would take, at minimum, billions of symbols.
There's a much quicker approach. Take is as a given that the laws of physics and initial state of our universe can be described in just a few thousand symbols. If so, we can write out that description and add a date and a location pointing to one of the actual human brains that exist in our world, and we've managed to "compress" our brain specification by many, many orders of magnitude.
The brain that gets specified from scratch will not experience induction. But the brain that emerges out of a full, simulated universe will.
The only premise you need is "shorter strings of mathematical symbols are more likely."
You can write locations of a three bodies and gravity equation and still will not be able to solve it. Are we looking for exact or good enough solution or just trying to describe things correctly?
Universal theory attempts to unify all kinds of physical interactions. We could consider such interactions as a type of observation of different kind of unconscious mathematical objects (protons, gravitons, etc) described by respective math equations. Add conscious observer here. What we really need is a universal observer theory
You will not be able to solve it exactly by writing down *human* mathematical symbols, or by calculating it on a *finite precision* computer. Nothing sets these constraints on the universe, in fact differential equations of the three-body problem + starting conditions are perfectly good enough to exactly specify the end state of the system. The universe can work in the language of math itself, not in whatever we humans use to describe it.
Why couldn't a conscious observer be a weird and complicated emergent property, in the same way superconductors are for example?
You mean I can't have a "simple" human readable analytical "solution" to it, although can describe interaction and initial conditions.
If you have studied computational maths and have encountered computational grids and the accuracy of numerical representation of numbers, you would know that it is the numerical methods themselves that introduce error, not just the accuracy of the initial conditions.
So both current numerical (simulation) and analytical apparatus does not give good predictive power. Although description is complete. Probably we just don't talk universe language good enough at the moment. Conscious singularity awaits
It's even simpler to generate high entropy randomness, and.look for a Boltzman Brain within it.
Besides which, there's no reason to argue that simplicity is more probable if every mathematical structure is real. All you need to argue is that simpler objects are more likely to be embedded within other objects of finite complexity, and I think this is obvious.
I think that leads to difficult problems about how objects and sub objects are individuated.
By definition of randomness, the location of the Boltzman brain inside it would have to contain as much information as the full description of the brain itself. Same as the old party trick of "compressing" numbers by looking them up in the digits of π
In 2012, private_messaging made this argument aga
That reminds me of a problem with Solomonoff induction.
If the program running the SWE outputs all bits of information about all worlds on a single output tape, they are going to have to be concatenated or interleaved somehow. Which means that to make use of the information, the operator/interpreter, has to identify the subset of bits relating to your world. That's extra complexity which isn't accounted for in the standard argument fur computational simplicity, because the standard argument only asked what the Solomonoff induction does....the computation performed by the operator/interpreter is overlooked because it's being done by hand, as it were..
The SI argument for MWI only *seems* to work because it encourages the reader to neglect the complexity implicit in interpreting the output tape. If you account for the "de interleaving" , then the total complexity is exactly the same as Copenhagen *and that's the point*.
I don't think that weighting for simplicity works for reasons I give in section 2 https://benthams.substack.com/p/the-ultimate-guide-to-the-anthropic. I don't think it makes much sense to talk about the share of an infinite multiverse with some property, especially if all the worlds are spatiotemporally disconnected. There are just unsetly many of each kind.
If you're working with a finite set of logical operations with which to define a mathematical structure, then in principle you could organise all your structures into the nodes of a decision tree. The tree would expand infinitely, but the nodes in each finite 'tier' would be closer to the root, and therefore 'simpler'.
I'm not sure if that's compatible with the observed physics of our own universe, though.
There's no reason our universe should be taken as the measure. The argument is that all mathematical objects are real, not that they are all observable within out universe. So that's merely an argument that our universe isn't a maximally probable one, which seems quite plausible. (The observable improbabilities are one of the reasons I believe in the EWG multi-verse, though this theory would override that reason.)
Tegmark did originally propose the theory as a potential explanation for our own universe, so if it fails to explain what we can observe in our own universe then it fails in its original purpose.
I'm a little skeptical about Tegmark's hypothesis given the remarks on Godel's incompleteness theorem:
https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis#Consistency_with_G%C3%B6del's_theorem
...but in any case, couldn't the space of all mathematical structures generate some form of singular intelligence (i.e, 'God') before it generates physical universes? We don't really have a complete understanding of the laws governing either physics or intelligence at the moment, but it's possible the latter are simpler and require less fine-tuning than the former.
Gödel doesn't mean you can't have a multiverse, it means you have to choose between and incomplete one, or an inconsistent one.
What would that mean as applied to our own physical universe, though?
Well, the standard approach is to divide the specified domain into two pieces, each of which is a self-consistent mathematical object. (Of course, some other statement will exist in each of those that has the same objection. So you get an infinite tree.)
Again... I don't understand what this would imply in the domain of observed physics?
Multiverse theories often assume that there is some kind of separation between parts where different rules.apy, but separation, or lack therefore, are themselves mathematical structures, so a mathematical multiverse should have every combination of separation and overlay.
If our universe is small, the problem doesn't arise.
'Small' by what measure? And again, what would it mean for said universe to be 'incomplete' or 'inconsistent'?
But simplicity isn't especially relevant if *all* mathematical objects necessarily exist. Then the simplest ones won't actually dominate - there are many more complex things than simple ones, so you should expect to be in a complex one.
I we want to talk about probabilities (e.g. the probability of finding ourselves in a relatively simple universe), we need some kind of *measure*.
Imagine that you have to choose a random natural number. You can't give each of them the *same* probability, because there are infinitely many natural numbers, so the probability of each of them would be... zero? But that doesn't add up to 1.
Instead, no matter what algorithm you choose for finding "random natural numbers", relatively small numbers will be vastly over-represented. That's because, no matter how insanely large number you choose, almost all natural numbers are insanely larger than that.
At the end, the only way to choose is to somehow give smaller numbers a greater chance. How much greater, that's up to you. But you can't give all natural numbers the same change, that is just mathematically impossible.
...and I think some similar logic also applies to universes as mathematical objects. The simpler ones must be more likely, because there is no other way to make all probabilities add up to 100%.
I'm no fan of Tegmark's theory, but it's been clear since Hume that induction is not formally valid so that's not really an objection.
It's true that induction is not, like, a law of logic. But a view that implies that we cannot be confident the sun will rise tomorrow is almost surely false.
Happy to bet on whether the sun will rise tomorrow :).
This is the essence of faith right here.
But the sun won't always rise tomorrow. Eventually something must give.
The smart money is betting on the sun
Better treat induction probablistically, then.
The trouble with induction is that our confidence in induction itself derives from induction. (Induction has worked so often before, so....) The good thing about induction is that our faith in it is almost never misplaced.
Yeah the point is that we’ll have an undefined credence in it under standard atheist multiverses.
Undefined credence doesn't mean low credence.
> The good thing about induction is that our faith in it is almost never misplaced.
Only if we ignore all the examples when it is misplaced. For every correct generalization there is always a bazzilon wrong ones.
>The trouble with induction is that our confidence in induction itself derives from induction
There is no trouble if we frame it the right way IMO. This is exactly how axioms are true: why is an axiom a true? Because axioms are true. Why are axioms true? Because it is an axiom that axioms are true... And so on. Without this self reliance, there is no logic. For derived statements, we need proof from other statements where the chain of proof doesn't include itself, the thing we call circularity. But this requirement is tjere for axioms. So we don't allow for circularity for derived statements because doing so would make them (and all the other statements in the cycle) axioms, which is not consistent with them being derived.
From a logical perspective, that is all you need to believe induction is true. But the fact that induction holds in reality is a property of the reality we live in, and is consistent with the logical truth of induction - making science possible and compatible with logic making reality legible to logic.
So the way to look at it is "inductive logic exists, and applying it to reality doesn't cause a contradiction (this is an observation only), and since this application causes no contradiction, we can apply inductive logic to reality as long as this observation holds..
In this view, there is no trouble with induction since induction is not used to justify induction. Axiomatic truth is used to justify induction in a logical sense. And the apparent consistency of the inductive axiom with reality lets us extend inductive logic into what we call science.
We do this with deductive logic as well. The + operator adds two mathematical objects called numbers. But we still use it to add apples because the application doesn't introduce a contradiction.
Doesn't this resolve the "trouble with induction?"
Ive written about this in more detail here:
https://medium.com/the-consciousness-project/knowledge-and-logic-part-2-of-morality-d8a0fd36563b
My claim is that induction is a law of inductive logic, or at the least, an axiom of inductive logic. Why do you say it is not?
I've written about this in more detail here:
https://medium.com/the-consciousness-project/knowledge-and-logic-part-2-of-morality-d8a0fd36563b
It can't be justified within bivalent deductive logic....but it's supposed to be a separate magisterium anyway. It likely can be justified by probabilistic logic. That what Bayes is a about.
Insofar as probabilistic logic and Bayes' Theorem derive their priors from past experience, they run headfirst into Hume's argument again.
Bayes doesn't have to.
Right, because... he's not relevant here. Bayes operates within the assumptions that anti-inductivism precludes. Like, you're saying "the plans for the top floor penthouse are perfectly structurally sound!" while ignoring that the building has no foundation.
I don't see what you mean. The weakness of Bayes is that priors can be pulled out of your posterior. The strength is that if your priors are wrong, you can correct them , given sufficient evidence, so you don't actually have the "weak foundation" problem.
I thought the whole argument for modal realism is that stuff like induction doesn't work *without* it? In order to make any kind of generalized inference you need to be able to say which situations are similar enough that you can generalize to them, and (according to modal realists) there's no objective criterion for this unless there are literally multiple universes arranged by similarity.
(The actual answer is that we do this heuristically and the universe is simple enough we can get away with it.)
If you weight universes by intrinsic simplicity then you have an inductive prior.
Oh yes, the good old "If P is false I would be sad therefore P is true".
https://www.smbc-comics.com/comics/20120715.gif
Beyond that, it's not clear what is even meant by "undermining induction". Does it mean that inductive reasoning doesn't always lead to truth? Does it mean that most of generalizations that could be made are wrong? Does it mean that there is not a single example of correct inductive reasoning?
The former two cases are true in our world. The latter one is logically inconsistent: "induction has never worked before, therefore induction in general doesn't work" - would be an example of correct inductive reasoning.
So what are we even sad about?
Why is that a problem ? Plenty epistemologies that deny induction is necessary or even real phenomenon.
If I recall correctly, this is the exact premise of Greg Egan's PERMUTATION CITY. All possible mathematical universes exist, so if you want to want to run an eternal simulation, all you have to do is run it, upload a copy of yourself, have the copy confirm that it *is* in fact being simulated, and then turn it off. The copy - in a mathematical version of quantum immortality - will continue existing in the simulated universe regardless of whether it exists or not.
By that logic, wouldn't it have been running even before you uploaded it? What's the point of that step?
Debugging.
lol
The person that you will be in ten years already exists (in this schema), infinitely times over with infinite variations. If the instance of you that you are now is hit by a bus tomorrow, those other instances will still exist - but you now would still like to live to experience all that "yourself". What's more, you'd like the version of you in ten years that you eventually experience to be a good version who's healthy & happy - if there were a way to deliberately select among the local branches of possibility space for one you preferred, you might do so, even if that doesn't result in anything "new" existing in the multiverse apart from your conscious existence now being causally connected to a future you want to experience.
Similarly, if you could causally connect your conscious experience now with a future experience that takes place in a fundamentally different universe with different laws, you might prefer that, and try to upload yourself into a simulation world of your choice - even if that act doesn't create anything new in the multiverse, still you-as-you-are-now might feel you have gained something by "switching" your consciousness from one causal path through possibility space to another (even though that path always exists & existed, even though there remains a you that didn't switch, even though it's possible that you-now has in fact no meaningful claim to be identified with any other instance of you including yesterday's you & tomorrow's you and that there is in fact only ever this one conscious moment as it is happening..)
Permutation City is good, you should read it.
Now.you are saying you can manipulate your measure, even though there are infinite copies of every version of you.
Language is hard in these areas. I'm saying people would want to try to manipulate their measure, feeling like they are changing something for the better for themselves - whether or not that is true, or even meaningful.
Imagine a latent space of all possible mind states. Your life is a line in that space. In the mathematical multiverse, there's an infinite number of cellular automata who have sentient beings in their initial state. Some of them have memories of a previous life in a regular universe. Some of those are very very similar to you.
The purpose of the ceremony is to bend your lifeline towards one of those starting points and form a continuity. From your subjective experience, you didn't die; you just transitioned from one universe to another.
But there's already universes that start with the state you're in now, right?
This is actually addressed in the book, the characters sort of shrug their shoulders and reason that perhaps a computer program needs a kick start before it's truly instantiated as a mathematical object, or maybe not, but might as well cover all bases.
I think we could wave our hands a bit better than Eagan does here: If you wish to find yourself in a particular computer program you should act to maximize the number of observer moments you experience within that program. By running the program for a finite amount of time you increase the odds that any given universe whose rules allow for embedding arbitrary unlimited computations, such as the game of life, also simulates the program.
The way I like to think of it is that you're not modifying the simulation, you're modifying yourself to create the possibility that your own subjective consciousness makes the transition into the simulation. After all, if you never get uploaded you probably won't later be a simulation that remembers getting uploaded. It's still a handwave over practical problems with perfect uploads and philosophical questions about the continuity of consciousness, but it resolves the potential plot hole.
What's a transition, in a timeless MU?
Both the simulation and the uploader's universe are timeless, but the uploader hopes to align their mind-state so closely with their simulated self that their *subjective* conscious experience actually crosses from one to the other, i.e. go to sleep in the upload facility and wake up in the simulation, having transitioned from one to the other. This has a lot in common with the many-worlds quantum interpretation - but instead of particle interactions leading to branching worldlines, it's done by actually copying the mind. If we could do so, who is to say that the subjective experience would automatically follow the original body?
Does that make sense without a dualistic mind?
In a philosophical sense, continuity of identity/experience. The 'you' who is still in your physical body will have an easier time being comforted by the simulation and convinced that it represents yourself achieving immorality if you observe the event where it 'splits' from your body and can interact with it and confirm it to be a continuation of your self and experiences.
In practical terms, because the person who came up with the idea in the story wants to make money, so they market it as a crucial step to rich people they want to sell that service to.
This was the first thing that came to my mind. If you find the idea of mathematical universes at all interesting, I recommend reading Permutation City. Greg Egan's work in general is worth trying out because it is "different" from most science fiction, and I would say Permutation City is one of his best books.
In that universe, you still needed a seed to start the simulation, although I wasn't sure if that was necessary
You beat me to it. Yes, this is precisely what is posited in "Permutation City".
(Spoiler Alert)
The twist in the novel (IIRC) that really got to me was this idea: yes, every possible Universe (or Cellular Automata rules + init conditions) exists in possibility space; but what we can do to sorta sweeten the deal is run as many iterations as we can in our present Universe, I guess just to -- somehow kickstart the process? And I think there was an uploading component too... Egan was (is) a real gem of a SF writer IMSHO
Yeah, this (or at least a very similar) hypothesis is called "Dust Theory" or "hypothesis of the dust" in the novel (which btw predates Tegmark by quite a bit, having been published in 1994). One of the reasons why (at least early) Egan is my favorite sci-fi author is how the theory is developed as an extended thought (and fictional empirical) experiment during the first half of the novel - if you accept the premise of mind uploading (which, of course, is quite a high ask for most people), a quite convincing case for the hypothesis flows from there (though maybe not aa quite airtight case, as the FAQ below suggests).
It should be noted that Egan has stated that he doesn't really believe in Dust Theory himself; some discussion here: https://www.gregegan.net/PERMUTATION/FAQ/FAQ.html. The reason presented (as I understand it) is that the "lawfulness" of our universe seems to run counter to the teory's predictions; for every version of me that experiences events moving forward according to well-defined laws, there should by gazillion versions of me whose surroundings are a roiling chaos. I personally have wondered for a long time whether this is really the case; as long as you include some form of bias towards simplicity discussed in the post (which the theory probably has to do if it's to be able to make any predictions at all), would it be simpler to have an universe evolving according to parsimonious laws, instead of having to specify a locus of order containing a sentient observer surrounded by chaos?
Yes, that was the premise.
[And I just discovered that searching on this page for 'permuta' doesn't find 'PERMUTA' :-(]
Came for this. Permutation City is the book that introduced me to Greg Egan's work. I'd generally recommend Egan to anyone reading ACX.
Tegmark’s mathematical universe hypothesis is just that, a hypothesis, and I don't think it's true.
Therefore, I also don't think that it obviates any other argument.
Some of the arguments go something like, “X is true; no non-theistic hypothesis could explain X; therefore god exists”. The fact that this is a non-theistic argument that explains X is sufficient to obviate these arguments, even if we don’t know whether it’s true.
I wouldn't accept arguments of that form, quite apart from Tegmark’s mathematical universe hypothesis, so still no update.
> I wouldn't accept arguments of that form
Why?
Seconded.
I wouldn't either. What is the framework which allows the statement "no non-theistic hypothesis could explain X" to have any credibility?
But, of course, the theistic arguments would still be evidence for God if they knock out most non-God hypotheses.
So? There's lots of ways to trivially knock out large numbers of God hypotheses. This is one of the points of steelmanning: most of the probability mass for any large class of hypotheses is probably concentrated in the handful of most likely versions. The hypotheses (whether they include or exclude a God) that were trivially wrong, very few people believe in, *because* they're easily disproven. Unless you address the strongest versions of atheism, you can only at best provide very weak evidence for theism.
That's just cancelling sophistry with more sophistry IMO. What set of axioms allow you to logically demonstrate that "no non-theistic hypothesis could explain X"?
"I can't think of a reason why this is false" isn't a good argument that something is true.
Sophistry is exactly the issue here.
We’re not dealing with axiomatic formal proofs in most of these cases. If you’re looking for an axiomatic proof you should just abandon this question.
“I can’t think of a reason why this is false” isn’t a definitive proof, but in most cases it’s a decent starting point.
>We’re not dealing with axiomatic formal proofs in most of these cases
Agreed, which is why philosophers shouldn't use rhetoric that borrows from those concepts. "I don't see why this is false" is indeed a good starting point, but IMO the sophistry comes from failing to understand that without a deductive axiomatic system that's all it is. That's why God-of-the-gaps arguments have a very poor historical track record.
But ultimately you have to pick some hypothesis to believe! If not the mathematical universe, then you need to justify why some other metaphysical theory is more plausible.
For example some would contend that there are several kinds of 'existence'. Commonly two, 'physical matter' AND 'mathematical truths'. But that posits two arbitrary assumptions about what things exist, one more than mathematical universe.
Others might posit there is just physical matter and math is just a property of physical matter, but that runs into its own host of problems.
The reason to find the mathematical universe hypothesis neat is its simplicity in comparison to other metaphysical theories of existence.
> But ultimately you have to pick some hypothesis to believe! If not the mathematical universe, then you need to justify why some other metaphysical theory is more plausible.
Errr no, you can say this is how far I know, and beyond that I have no way to tell. It's the most honest answer.
> Others might posit there is just physical matter and math is just a property of physical matter, but that runs into its own host of problems.
What problems does that run into?
To me that seems like the most intuitive answer. I posit that math is an abstract tool invented by humans to describe physical matter and the underlying laws of physics of the universe. Maths is used to model the universe and can only ever be an approximation of reality. For example, in order to add two apples (or atoms, or any indivisible unit) you first have to posit that the two objects are the same in some sense. This is an abstraction, since every object has different matter and does not occupy the same space. They are equal and can be added only because we first make categories.
My point is that math is not a fundamental property of anything physical. The fundamental laws of physics may or may not be simple and easily described by math- we don't know. What we do know is that the aggregate effect of the underlying laws of physics may often be well described by mathematics, and seem to be deterministic, i.e. the same initial conditions gives the same end state every time on large scales. (However this is also dubious for some chaotic systems, like turbulence).
I'm not sure simplicity (in the manner that you mean it) is the best measure for actually adopting a paradigm. The best measure would be commensurabilty with itself, which I don't think works with this any better than solipsism (which I think is the main contender against the ism in terms of a "metaphysical theory of existence" as you put it)
"Physics exists, and maths doesnt" is also parsimomious. Formalism.shows that you can have mathematical truth without mathematical realism.
I believe something rather close to this and to me it points directly to God. I won’t have time to write it up, but basically I put God very far away and beneath things.
Scott wrote a wonderful argument like that.
https://slatestarcodex.com/2018/04/01/the-hour-i-first-believed/
I have a hopeful AI future in my head that is like this, but don’t even think the being described here is quite God. God is is.
I'm right there with you. God is the the isness that is inherent in mathematics and mathematical structures. This God doesn't really have a mind or act. It is the breath of life, raw possibility. But I also think there's an endless chain of superintelligences simulating superintelligences and down at the bottom is us. That's more like an active component of God, defined in the linked article, which is my favorite article by Scott.
I read the book when it came out. That all possible realities exist is, by definition, next to the most horrible thought that one can have (the most horrible one would be that only horrible ones exist). Everything extremely bad you can imagine and worse is happening somewhere. I really don't want to believe this.
Allow me to offer some consolation. The existence of hellish worlds in Tegmark's multiverse is indeed a frightening implication. If you suppose there's a statistical distribution of worlds with conscious life, where most are mediocre worlds, you'll notice that the hellish & heavenly extremes will be extraordinarily rare. Is it reasonable to suppose such a distribution? I think so -- most times and places in our world are pretty mundane, but a few situations have arisen that were hellish or heavenly. And those are pretty rare even considering they're natural sorts of "hellish" and "heavenly", nothing anywhere near the extremes that religious imagery calls to mind.
And what's more, statistics isn't the only way to look at it. We need to look at the complexity of the axioms that generate the world, presumably using the Solomonoff prior or something analogous to it. Generating a world that hosts conscious observers requires some minimum degree of complexity. Generating a world that does that and also evolves into a large scale, stable hell requires additional complexity on top of the minimum -- and my guess is it would require a hell of a lot, pun intended. So hellish worlds would be so exponentially rare that I assume it's vastly more common in Tegmarkia to be a mind-moment that wakes in fright from a hellish "nightmare" into a mundane world, than it is to be a mind-moment that is an in-world continuation of a hell.
So if the hypothesis is true, then the chains of linked mind-moments across worlds, each chain being a conscious observer's history, are virtually all mundane.
Why would the hellish ones be rare?
Here's a fine-tuning argument that I haven't heard anyone make: If you assume that there is a vast part of high-dimensional parameter space that doesn't allow conscious life, and very small regions of parameter space that are conducive to conscious life, and you pick parameters at random, the large majority of livable universes will be very close to the boundary, i.e., just barely livable. (This is just the standard argument from statistical physics that in a high-dimensional space, practically all of the volume of a sphere is practically at its surface).
So taking that as an analogy, the hellish universes would be the norm, and the heavenly ones exceedingly rare in comparison.
That doesn't mean it would be hellish, that would just mean it's barely alive. Which is not necessarily a bad thing.
Agreed, I'm taking "hellish" in a Christian sense of a place of unrelenting torment.
Extremophilic life is only hellish in a loose analogy: it's adapted to conditions that look harsh to us.
"Why would the hellish ones be rare?"
Because of the Doomsday Argument, or a variant of it. If one assumes one's status to be picked at random from among all possible observers, one should expect an approximately average value of *any* variable of observation (not just birth order). If your own life conscious existence isn't hellish, you shouldn't expect the average conscious existence to be hellish either.
Of course, I've always thought the Doomsday Argument was utter bullshit, but when you're reasoning about something as vague as a Tegmark Universe it's not like there are many other tools available.
Good points, actually (both of them).
This is true, but also it doesn’t include agency of such things that exist there. Presumably they’d try to fix it? Or even kill themselves if they couldn’t? (a feature of agency, too)
The vast majority of environments in our own universe make life impossible (i.e, they're either inside stars or a total vacuum), so one can argue that our universe is only 'barely' livable. That doesn't mean it's filled with sentient life locked in a state of perpetual suffering, you just get tiny pockets of regular sentient life.
'Hell' is essentially a state where all the sensory indicators of life imminently collapsing are somehow sustained on a vast scale in time and space- i.e, it's highly artificial. Maybe it wouldn't break the laws of physics per se, or the set of all possible laws of physics, but I can't see it being a naturally-occurring norm wherever you get sentience.
I feel like one could even use this idea as an argument in favor of Tegmark's theory. If we are in a random mathematical universe (conditioned on it being capable of supporting intelligent life), then to FluffyBuffalo's point it is likely to be something that is "on the edge", just barely capable of supporting life, since within a high-dimensional probability space most of the volume is near the surface.
And that is seemingly just what we find in our actual universe. Almost none of it is habitable. There seems to be no other intelligent living beings within communication distance. There are lots of physical constants that had they been slightly different life would be impossible. Etc.
Sure, maybe, but my point is that this doesn't fit the general definition of Hell.
Someone from a more ideal world than ours made deem ours to be hellish. It seems likely that hellishness is relative.
It seems that truly bad universes would be self destructive. The most likely universe will be some proportion of hell that's sustainable, like 50% hell 50% heaven. Isn't this where we live in? There is plenty of evil and suffering in the world, or in every person's life.
Is this what religions are about after all? The constant battle of good vs evil that has to exist just because it's statistically likely. Especialy when hell is relative, even in a 95% heaven universe you'll still think you have plenty of evil to fight.
But if *everything* that can happen has happened, then there is no statistical distribution, everything imaginable exists, even the very improbable ones. What do I miss?
As in Scott's main post, the usual answer is that the distribution involves a simplicity prior. The chief argument for a simplicity prior's necessity is the fact that *any* prior over mathematical objects will necessarily give more complex objects less probability mass, on average.
While it's correct, I personally find the answer a little unsatisfactory on its own without an explanation of how the distribution arises. The most intuitive explanation (in my opinion) is to consider embedded universes. A larger mathematical object can contain smaller ones embedded within it. The simpler the object, the more places it is embedded. Search "Ramsey theory" to see the relevant kind math I have in mind; it studies the conditions under which certain orderly properties must necessarily appear in sufficiently large structures. By analogy, suppose universe A is sufficiently simpler than universe B that it is embedded in twice as many larger mathematical objects. Then I find it very intuitive to suppose universe A has twice the probability mass of universe B.
Every universe is embedded an infinite number of times, but some (the simpler ones) have a greater measure of the total. This lets us assume a more intuitive uniform distribution over mind-moments while still getting a simplicity prior over universes as a consequence. By analogy, on the real number line, there are infinitely many points in [0,1] as in [1,3], but the latter interval has twice the measure, and given a uniform distribution over the infinite points of the intervals, you're twice as likely to get a sample from the latter.
Thank you for this reply, I never imagined how there could be distribution in infinity
I think simplicity-measures are fairly straightforward if you just take the number of logical operations required to define the laws of said universe.
https://www.astralcodexten.com/p/tegmarks-mathematical-universe-defeats/comment/94584094
I haven’t read the book, but wouldn’t it also imply that greatest universes with all the best things are happening also exist? I suppose this would be horrible for negative utilitarians, but otherwise, most people would think the good and the bad cancel each other out.
Not necessarily. There are probably Everett branches of our universe that are hellish, but it seems unlikely that our planet would become so hellish. Likewise, the simplicity prior might assign negligible measure to hellish worlds.
I don't want to imagine kids in Africa starving, and yet they are real.
That's not exactly what this theory is saying.
It says that all possible starting conditions exist, but what happens from there follows physical laws. You don't get all possible realities, you get all realities that could follow in a rules-based way form the set of all starting conditions and all rule sets.
So if you believe, for example, that charity and benevolence tend to evolve in high-population animals for rules-based reasons regarding the adaptive benefit of cooperation and coordination, then you can expect those things to be very common across all realities.
I'm 95% confident someone else thought of this idea before Max Tegmark. It's an obvious idea. This is the aspect of the rationality community I hate. They're always reinventing the wheel, blissfully ignorant of vast cannons of human thought, and claiming originality and credit for exceedingly obvious ideas.
You may be dismayed to learn this happens all the time then: https://en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy
Yeah. It does, but it is particularly frequent among the rationality community, and it's the arrogance and self-satsifaction they have about it. Ack. So irritating...
Like, gosh, can you imagine what these (relatively) smart people could accomplish if they had just a few more standard deviations of intellectual humility.
Is it particularly frequent among the rationality community or is it the fact that they do it in a way you find irritating that which makes you think it's particularly frequent?
Ooo. Um... Two points:
1. Generally professional thinkers (e.g., mathematicians, lawyers, judges, serious historians, philosophers, the founding fathers) take great care to trace the lineage of ideas. It is part of being a professional.
2. The rationality community styles itself as being almost *the" most professional thinker, in that they want to be professional in their thought not just as a means to an end, but as an end itself.
1. + 2: I get annoyed by how unprofessional they are.
So I guess the answer is, it's super way too frequent if we consider them a group of professional thinkers and judge them by those standards. Or, we judge them by random internet standards and then it is the manner in which they do it (i.e., while claiming to be serious about thought).
Like of your the knitting society and you don't take care tracing the lineage of ideas, that's to be expected. But if you are the *thinking society* then I expect more from you
Why is your expectation that a thinking society have knowledge of lineages a reasonable one? Knowing about lineages is much more about respectability and the appearance of deference to more prestious apes, why should a thinking group cave to such a base and disgusting urge?
This interests me quite a bit. Could you say how this tracing can be done, especially for subjects that one is new to? Is it just reading a lot around the subject? Is that generally a good ROI, or just a necessary cost? Anything more efficient than that? Asking LLMs helps to some extent, though not for more obscure knowledge. Would another option be to try to reach out to other people knowledgeable about a subject? Seems potentially imposing. Any other ways?
Yeah, this is basically Plato.
Yeah, that Platonic dialog on cellular automata.
Timaeus 53c-55c argues that the necessary existence of particular geometric shapes on a 2D plane with a set of simple starting conditions will unfold by the increasing complexity of relations between those shapes into all observed natural phenomena (fire cannot become earth because earth is made of isosceles triangles, you see)
Then it is surprising that all those people generating the arguments for existence of God seem completely unfamiliar with it.
Relevant smbc: https://www.smbc-comics.com/comic/2011-12-15
Max Tegmark isn't "some rationalist", he's professor of physics at MIT. Who better to think of a new theory?
And I'm impressed that you're managing to go into raptures of hatred based on "assuming" someone invented this even though you don't know who and had apparently never heard it before. Cellular automata and Kolmogorov complexity are both pretty new, I don't see why he couldn't be the first person to combine them in this way.
I suppose it's too much to ask to just be grateful you learned something new today?
I mean, I had the idea of "every mathematical structure that could exist does in some sense exist" i.e., plato + "everything can be expressed in the language of maths and is as such a mathematical structure" (i.e., Feynman or so many previous people, but he has a nice quote on it) back when I was 13...
At the very least, I bet Godel thought of it...
Guess I should have written a book about this profound insight... :p
I'm unaware of any published version of Tegmark's hypothesis before his own work—which isn't to be reduced to "numbers exist (in some sense)", note. A better summation might be something like "all there is is mathematical structure, even us right now, and every mathematical structure exists in the same way". This is not what the Platonic "theory of Forms" entails.
But even this is a simplification that necessarily dispenses with a lot of the groundwork and justification. I recommend reading his book, which is pretty interesting even if you don't agree with his ultimate conclusion—in fact, most of the book isn't even about the MUH at all.
Of course, given that you've failed to acknowledge that Tegmark is in fact a PhD physicist who specializes in cosmology and not just some random "rationalist community"-member, but have instead doubled-down on the part of your comment that Scott /didn't/ directly address, I put low odds on your actually bothering to read it. But I have hope!
But I mean doesn't platonic forms encompass all maths? If you talk to any Platonist my understanding is they would say, "yep all maths exists," and if you talk to almost any logician/computer scientist and you ask them, "could any possible system be simulated in mathematics (including me)" they'd say: yep. Oh in particular, a logician would be the one saying yeah, of course all such systems are themselves part of some hierarchy of mathematical objects, etc...
Both these statements seem incredibly common place. One dates back to Plato, and the other turing / Godel and possibly earlier. I don't quite get the distinction you are making...
Thanks for the book recommendation!
No problem—I /really enjoyed/ it, myself; it gets into a lot of the "big picture" cosmological questions that it's hard to find good, in-depth coverage on (most books are either pop-sci re-hashes of generalities you've heard a dozen times before, or else thick academic tomes with equations that make your... or at least /my/... head hurt just to look at 'em; Tegmark's is one of the few that's in between the extremes).
Maybe my edit was a bit too harsh, pardon me–
(I'm no fan of what a lot of "the rationalist community" turned into, but still have a knee-jerk reaction to criticisms of it in a certain tone, which I associate with a particular group of bad-faith critics. I should work on that, maybe...)
Re: Platonism: No, I don't think that's /exactly/ the same, although there are certainly some deep similarities between them and I can see why some might be tempted to identify the two:
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Plato: Our world is a "shadow" of a world of ideal Forms, which we perceive dimly through their material instantiations and through intellectual contemplation upon them. Numbers are Forms (maybe; I dimly recall something about a fight between Pythagoreans and Platonists on number, and IIRC the Neoplatonic "principle of Unity" isn't to be confused with "1"), but there's also a Form of a chair, of Redness, of... etc.
Tegmark: Mathematical structures exist, but not in the Platonic sense; rather, in the same sense we do—in fact, they're /all/ that exists. All we see and experience is a mathematical structure, no different from that of "the integers"; ours is merely more complex. And, moreover, the rest are out there too—all is mathematical structure, and all such structures exist in the same exact way; our universe isn't privileged. There is probably a "way it feels like to be within Conway's Game of Life", and so forth, as there is a way it feels to be within our universe. (Note: IIRC he flirts with such a sort of panpsychism, but doesn't commit to it; substitute "way it feels like to be within /a much simpler structure that still supports consciousness/" if I'm wrong about this.)
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I.e., it isn't that "numbers have some sort of existence", but rather that all mathematical structures exist in the same way, and in fact this is all there is.
Following from that, re: simulating systems in consciousness: I don't think this has any bearing on the priority of Tegmark in proposing this hypothesis—it's an entirely separate question.
So if all the MUH said was "mathematical structure exists in some non-nominal sense, i.e., apart from as descriptions or games in our heads", then sure—nothin' new. But to claim the twin statements mentioned above ("...all that exists" & "all ... exist") is, I think, new.
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I'm also neglecting to include any of the work he put into motivating the hypothesis... mostly because I can't remember it, heh. I /seem to recall/ that most of the book is sort of about laying the groundwork, and if I remember aright he doesn't have many arguments that directly support the idea beyond "well why not? it's simpler, look"—but there were a few, I think. (And, of course, I may misremember, or he may have done more work on it in the meantime.)
Interesting. I've always interpreted Platonism as meaning yes they really really do exist. I.e., even if you and I and the universe never was there would still be all of mathematics. It is hard to think of a more realness than that. E.g., my naive understanding is that a Platonist would say that mathematics is in some deep sense more real than the universe.
I agree saying that the universe (i.e., our universe) is a component of such a structure is a step beyond that, but it does kinda of obviously logically follow. I would also argue that, the idea is more or less just a fancier version of the philosophy that "all that could be is in some sense somewhere," and I imagine, but do not know, that that idea probably dates back to prehistory.
P.s., no need to apologise/apology accepted. My comment was itself a knee jerk reaction :p
Note that being an accomplished physicist doesn't give one any special insight into philosophy, mathematics, or the other topics that seem most relevant to Tegmark's proposal.
Sure; I mentioned his background to point out not that he can't be wrong, but rather that it is inaccurate to characterize him as being just some random Rationalist Community Member® doing the typical Fake Expert rationalist wheel-reinventing (which was, as I interpreted it, the implication of the OP's comment).
I'm not criticising Max. I think I'm criticising your portrail of him as the likely originator of the idea, when to me, it seems clear (blindingly obvious) the idea likely has a lineage.
After all, you are adjacent to the rationality community (and I associate the way you did this eliding of lineage with the rationality community).
My apologies, it is not my intention to be rude, and they are cool ideas. I just get a bit triggered by what I associate with rationality community arrogance.
According to the wiki page Tegmark himself compares the idea to platonism and modal realism. So... yeah, there are antecedent ideas in the realm of philosophy, but I don't think he's failing to give credit either.
https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis
https://arxiv.org/pdf/gr-qc/9704009
I'm skeptical as to whether Plato himself would have described his ideal Forms as purely mathematical constructs, though (what is the math of 'Virtue'?)
To be fair, we just learned that Cellular automata are eternal from this very post. (Actually, itʻs a bit light on the whenness)
Anyway, of course this is the case-since continuous time and mathematical concepts both belong to the cosmos and not the universe directly. There are sufficient evocative phenomena happening contemporaneously that many thousands (?) of human observers are likely discovering this for themselves effectively all at once.
He's very qualified to come up with theories. Professors do that all the time. But there's still no real evidence to support his theory. And, its actually hard to imagine what kind of evidence could plausibly support it.
This general idea isn't especially new, although the specific formulation isn't something I have spent much time thinking about. It is reminiscent of an idea from John Gribbin's, "Inflation for Beginners." (https://aether.lbl.gov/www/science/inflation-beginners.html).
Here, the idea is presented that universe creation could be fractal where each black hole in a universe spawns another universe (not accessible). If that were the case then the growth rate of universes would be severely exponential so that the age of universes would be grossly tilted towards young. It is further suggested that this might mean that a 99.99% chance of us living in the youngest universe possible to create intelligent life and that we would therefore be the only intelligent species yet alive [edit: in our specific universe].
In the book (that came out over 10 years ago) Tegmark makes it very clear he is not the first, heavily referencing Everett and his many worlds theory from the 1950s.
Nice! Finally. Yeah. Ofc.
Everett’s theory is very different from this! Everett just says that all branches of a quantum wave function exist - Tegmark says that even mathematical structures that have nothing to do with quantum wave functions exist.
of course they would exist, they are members of a superior realm to quantum
Superior???
Funny thing: those "vast canons of human thought" being so vast, it's not really practical for one human to be familiar with them all. If you're doing something that's nicely easy to describe--building a bridge, painting a picture, writing a novel, designing a wheel--it's not hard to find pre-existing literature on the topic and narrow your way down to more tractable canons of human thought. But if you're doing something weird and abstract and outside the realms of what most humans discuss on a regular basis, that becomes a somewhat harder problem.
But maybe I'm overstating things and just bad at forming queries. So tell me, if you'd happened to think of this idea before Max Tegmark, and wanted to see if anyone had beaten you to the punch, how exactly would you go about checking? Keep in mind that as abstract as this is, one can hardly assume that they'd have used any standard or particular phrasing or schema. The best I can think of is "ask the right sort of expert," but I'm not 100% sure who the right sort of expert would even be. This is a serious question, by the way: "how to search for an idea without reference to the topic or use of standard keywords" is a problem I've run into before and, well, I don't actually know a solution. Has this wheel been invented?
Side note: this very much feels like another instance of the "explore-exploit" dilemma. For some area of interest, how long and how diligently should you explore the existing literature before you try doing original thinking on the topic. The answer clearly varies based on how costly exploring the existing literature actually is.
In general:
Step a) having the idea (e.g., a cake without any flour)
Step b) searching for references to things that sound similar to the idea ("no flour cake" "cake" + "celiac's rejoice")
Step c) talking to knowledgeable communities ("hey baker friend, ever heard of a cake without flour?")
The more important the idea / the more obvious seaming, the more time and effort you should spend verifying that it truly original.
For the idea described, you might first look at modern philosophers who cite Plato and or Godel. That kind of thing. You might search for the term, "everything that could exist does." Etc... or "mathematical proof"+"universe must exist" etc... you'd try to scatter gun it so that almost any impact/publication of the idea would be caught by at least one of your searches.
Doesn't really matter how you verify, but at the end of the day every diligent scientist needs to know that their idea is truly original.
Fyi, judging by another comment in this tree, Max didn't claim originality, and indeed took care to trace the thoughts roots. The thing I got annoyed by was Scott portraying this idea as original to Max, when my (vague) understanding of that thought space made it seem very clear to me that the idea likely long predated 10 years ago.
" The thing I got annoyed by was Scott portraying this idea as original to Max, when my (vague) understanding of that thought space made it seem very clear to me that the idea likely long predated 10 years ago."
I find this a reasonable attitude if and only if Tegmark was entirely regurgitating ideas others had developed, and added no content himself. That's really not the impression I have of it: I got the sense that the idea may have had earlier *roots*, but that Tegmark fleshed them out and ran with them in (at least some) ways that others had not. But I'm certainly not an expert, nor am I especially invested in either conclusion, so...*shrug.*
At any rate, once [Person] has done work that further develops an existing idea, referring to it as [Person's] theory of [Thing] seems eminently fine and reasonable (as long as *they* are responsible in citing their influences). Somebody looking at their version can backtrace the lineage just fine, while someone looking at the older versions can't forward-trace them nearly as easily. And to anyone who's just interested in discussing the idea (rather than haggling over the credit), having everyone on the same, most up-to-date page is much easier than worrying about the whole history behind it.
It’s a lot like David Lewis’s modal realism (from his 1984 book On the Plurality of Worlds) and has something in common with Mark Balaguer’s plenitudinlus platonism (from his 1998 book Platonism and Anti Platonism in Mathematics) but it’s a bit different from either. I suspect some of the medievals and ancients had some related idea. But until the development of 20th century logic there wasn’t a clear conception of what “every consistent mathematical theory” means, and it would likely take an analytic philosopher to endorse such a blunt view that this is everything that exists.
I like plenitudinous platonism about math! It gets a bad rap but if you're going to be platonic about mathematical structures at all, I don't see why you'd want to choose a single "true" mathematical landscape, when there are so many possible ones.
I figured out the gist of as a schoolboy in the 90s, but I've never been able to explain it to anyone, and whenever I tried people always thought I was crazy.
I had an epiphany when we were taught to draw graphs of functions and I noticed that:
1 - These graphs are like the history of the world. A complicated enough graph would chart the whole universe.
2 - No matter how many times you draw and redraw one, if the equation is the same, the graph will be the same. Therefore it "exists" independently of how many times you draw it. Draw it once or draw it 100 times, it's the same graph. It follows that... it would "exist" even if it is drawn zero times (if nobody ever draws it)!
And therefore, ALL possible graphs exist in that way! And the universe is one!
But good luck explaining this insight to anyone! I never managed to make anyone grasp the concept. And yet, it's not brain surgery!
when you draw a graph, you are generating it from.some rule or definition in your head.
Injury head?
In your head. As I remarked in another comment, I wish I lived in the universe without typos. Or at least without autocorrect.
I've always been a mathematical monist, since I was a child. And it was strange to be the only one in the world (as far as I knew) who believed this. I was so surprised when I first heard of Tegmark's MUH. He's just one man, but it nevertheless felt almost like being vindicated. And it was so strange (and satisfying) to see much of the same reasoning and arguments used.
Kinda, but with subtle differences. Modal realism has been around for a while, but the argument for a multiverse by asserting that there is no such thing as physical existence as separate from mathematical existence and the specific idea of weighting worlds by a simplicity prior is novel.
In this case, Scott did make an argument specifically based on the fact that the theory was recent. I think when someone makes an argument like that, they have a duty to try to verify that it's true.
However, I'd like to distinguish this from cases where someone says something like "I had this cool idea, let's discuss it" without specifically claiming to be the first person to have the idea. I think it's legit to informally share and discuss an idea you've had without first doing a bunch of research to check if anyone else has had the same idea. (And in fact, this is often a pretty decent strategy for discovering prior work.)
I think people sometimes object to this for "hero licensing" reasons--i.e. that even _trying_ to contribute a good idea without first spending years mastering a field feels like a status grab to them. And I mostly don't endorse those objections.
Oh yeah, it's definitely legitimate to have an idea and share it discus it before verifying it is new.
However, depending on the context, it is bad form and lazy. E.g., unless it's a super casual chat among friends, if you're talking to someone about a "new" idea, you should probably have at least done 5 minute Google search.
Tegmark's hypothesis is just a conjecture. We have no evidence for it; no reason to believe that "all possible mathematical objects exist," except that some people want to believe that so as to not have to believe in God. This is the very definition of motivated reasoning, the antithesis of sound science.
On the other hand, we have extensive evidence for the existence of God in the form of testimony. People who God has revealed himself to have passed down their accounts to us. People who have witnessed miracles have likewise done so. People who have prayed and received guidance have spoken about it.
Any one of these testimonies could be dismissed easily enough, but we have enough, from enough disparate sources, that Bayes' Theorem compels us to either take the notion seriously or abandon all pretenses of rationalism.
We have lots of contradictory testimonies about different religions being true, which means even if you accept god exists, most of the testimonies have nothing to do with him. So the only evidence is the number of testimonies vs the expected number, and can you really figure out the expected number well enough to draw a conclusion? If you tell me the expected number, and then we look into it, and there's actually that many or fewer testimonies, would you conclude that it's evidence against god?
Also, god doesn't in any way help answer these problems. If you're willing to answer "How can there be an uncaused cause" with "There just is, and also it's sentient and all-powerful, and the nicest possible being", how is that any better than just stopping it at "There just is"?
> We have lots of contradictory testimonies about different religions being true
That's the pop-culture version, but it's not nearly as true as you might think. What scholars of religion who actually take this stuff seriously have been discovering over the past few decades is that the more closely you look at different religions, the more fundamental similarities you discover, and especially with ancient religions, the further back in time you look, the more they all seem to be converging on one set of fundamental principles.
Put simply, there's one set of results you'd expect to see if a bunch of widely different groups of people invented their own religions independently of one another, and there's another set of results you'd expect to see if mankind started with one revealed religion which then got corrupted over time as people broke into widely different groups of people. And what we actually see looks enough like the latter set to make the claims of theists worth taking seriously.
"the further back in time you look, the more they all seem to be converging on one set of fundamental principles."
So first, I'm really, REALLY skeptical that this is actually true. Both because "looking back in time" becomes harder and less precise the further you try to look and because we know of religious traditions from all over the world, including places that had no contact with each other for tens of thousands of years. Either you're claiming a "looking back in time" procedure that goes an order of magnitude further back than the written word, or you're cherry picking a very small subset of religions, and claiming it to be "all of them." But feel free to source your claim, of course.
But second, even if I were to take this claim at face value, the strength of the evidence is *wildly* insufficient to support the weight of the hypothesis you're putting on it. "All religions started from the same fundamental principles" does suggest a common cause. What it does NOT do is single out one *particular* common cause as the sole or most likely possibility, much less that said cause must be supernatural. There are, to put it mildly, quite a few non-supernatural ways that humans of past eras could have ended up with similar sets of principles. In fact, this frame necessarily assumes that
1. The hypothesized ur-religion was transmitted widely from people who *had* witnessed its founding events to people who *hadn't.*
2. That transmission was necessarily lossy: each step down the transmission chain got less faithful to the original events (but kept being passed on anyway).
Once you've admitted 2, you really stop having *any* basis to claim that the your hypothetical founding events *happened at all.* We've just admitted that people who weren't there will believe in them based on inaccurate second, third, fourth and fifteenth-hand stories, so the claim "these beliefs must have originated from actual, honestly-reported supernatural happenings" can't possibly hold water.
> So first, I'm really, REALLY skeptical that this is actually true.
A lot of people are. It flies in the face of The Narrative. But it's pretty well supported by now.
> Both because "looking back in time" becomes harder and less precise the further you try to look
It gets a lot easier when we have written records.
> and because we know of religious traditions from all over the world, including places that had no contact with each other for tens of thousands of years.
I know. That's what makes it so interesting how it really did happen!
> 2. That transmission was necessarily lossy: each step down the transmission chain got less faithful to the original events (but kept being passed on anyway).
Once again, written records do a whole lot to mitigate that.
>it's really well-supported!
>doesn't support it
"It gets a lot easier when we have written records."
But we don't. We only have written records going back a few thousand years, and even those are very, *very* sparse in antiquity. Again, there have been millions of humans practicing a wide variety of religions all over the globe for many, many times longer than writing has existed.
It sounds like you're trying to trying to conflate two statements:
1. "All human religions get more similar to one another the further back in time you look."
2. "The human religious traditions for which we have written records get more similar to one another the further back in time you look."
Those are NOT the same statement. Not even a tiny bit. Not even in the ballpark of the same statement. Treating them as the same is perhaps the most egregious example of the Streetlight Fallacy I have ever seen.
It is, in fact, very easy to imagine a world in which 2 is true and 1 is false: all it requires is for one particular priesthood to be ahead of the curve in adopting writing and making sure their texts were preserved.
But in the event, it doesn't seem like 2 is true either. A few minutes of searching suggests that Sumerian, Hindu and Chinese religions all have some very old texts--some quite older than the oldest Talmudic texts, by the way--and that none of them match up particularly well. Of course there are similarities. But more similarities than you find in later religions? Doesn't really seem like it.
> A few minutes of searching suggests that Sumerian, Hindu and Chinese religions all have some very old texts--some quite older than the oldest Talmudic texts, by the way
Yes.
> and that none of them match up particularly well.
This is the point where you should have done more than a few minutes of searching.
>the more they all seem to be converging on one set of fundamental principles.
Sure, as in "thou shalt not kill"-type stuff. Humans are physically and psychologically similar, so independent groups will converge on the common sense, and also on things like "we don't understand lightning, so clearly there's a thunder god".
>claims of theists worth taking seriously
Some, sure. But I've yet to see any evidence that they have anything worthwhile to say about the supernatural.
> Sure, as in "thou shalt not kill"-type stuff.
No. As in "In The Beginning, the state of existence was a vast primordial sea of water and chaos. A great and beloved son of the High God rebelled, sought to steal the High God's power, and by so doing was corrupted and became a terrible sea monster. A second son, the greatest of all, was chosen to fight the monster and re-establish the correct order. In their terrible battle, the champion was sorely injured, but recovered and joined battle the second time, and overcame the monster, slaying it, using its body to bring order to existence and establish the foundations of the world. Upon building the world, the High God and his champion son established a home for themselves atop a tall, sacred mountain, and there they placed our first ancestors, gave them sacred clothing, and taught them to live by the right order of existence. (ie. the true religion.) They planted a great divine tree atop the mountain that is filled with their sacred power."
When you see recognizable variations on that same basic narrative in the religions of peoples as far-flung as Japan, Australia, Egypt, Central America, Babylon, and Scandinavia, it's hard to deny a common origin.
> I've yet to see any evidence that they have anything worthwhile to say about the supernatural.
What's your standard of evidence?
>it's hard to deny a common origin
I don't deny it, just doubt that (alleged) commonness has anything to do with a singular supernatural revelation. But, since no current major religion would likely accept this narrative as The Divine Truth, it would be more fun to see unleashed upon theists-at-large than to argue against it anyway.
>What's your standard of evidence?
Acknowledgement by major ideologically unaligned groups of predictive power about future events.
Come now. There have always been people eager to find any reason they can come up with to explain away "ideologically unaligned" prophecy rather than having to accept it. A standard of evidence carefully constructed to admit no possibility of the evidence being valid is no standard of evidence at all.
> But, since no current major religion would likely accept this narrative as The Divine Truth, it would be more fun to see unleashed upon theists-at-large than to argue against it anyway.
Circling back around to this; somehow I missed it the first time.
I assume by "current major religion" you mean the Abrahamic tradition. This is where things get interesting.
The Abrahamic tradition has three major branches today: Judaism, Christianity, and Islam. Islam was founded by Mohamed as a synthesis of 6th-century Christianity and Arab paganism. Christianity in turn was founded by Jesus Christ approximately 2000 years ago as a reformed version of Judaism. These facts are fairly well known. The whole tradition as we know it today has its roots in Judaism.
What's a bit less well-known is that Judaism was founded in the late 7th century BC by King Josiah and his spiritual advisers, in a movement scholars today refer to as "the Deuteronomist Reform." We're finding more and more evidence as time goes by that the Deuteronomists made significant changes to the pre-existing Ur-Israelite Religion (henceforth UIR), that UIR looked a lot like the ancient ur-religious tradition seen elsewhere throughout the world, and that UIR contained a lot of teachings, doctrines, and prophecies, censored by the Deuteronomists, that, had they been carried forward as official doctrine, would have made the first-century Jews far more likely to have accepted Jesus Christ. UIR boldly spoke aloud of truths that the post-Deuteronomist canon only hinted at in whispers.
You do know that stories can be shared, right?
...yes? What's your point?
I'll admit, that's a lot more intriguing and convincing than I expected. What can I read to find out more?
Some of the best accessible scholarship I've seen on this subject comes from Dr. Jacqueline "Jack" Logan, who presents it on a podcast called The Ancient Tradition. ( https://theancienttradition.com/ )
You specified reading. Each episode has a transcript available if you'd prefer that over listening to the podcast. Depending on your tolerance for the didactic — she's a university professor and presents the material essentially as a series of lectures — you may find her presentation a bit grating, but the quality of the research being presented is quite good.
> What scholars of religion who actually take this stuff seriously have been discovering over the past few decades is that the more closely you look at different religions, the more fundamental similarities you discover
That's the perennial philosophy hypothesis. I personally like it, in its more minimalistic forms, but contra your sentence, actual academics seem to dismiss it nowadays.
Edit: ... because dismissing the full narrative content of actual religions in favor of an ineffable core leaves out most of their content. I actually think it's the right move but it's understandably not popular.
> there's one set of results you'd expect to see if a bunch of widely different groups of people invented their own religions independently of one another
The mythology may be independent but the psychology driving it is not, so I don't see a good reason to assume the shared "fundamental principles" are based on revelation of a hidden truth rather than being inherent in human nature.
The good reason is that we've got plenty of examples of independent invention of similar things by unrelated parties throughout history, simply because it was something that multiple parties had a good reason to invent, and *they don't look like this.* We know what independent invention looks like, and we know what common descent looks like, and this looks like common descent.
I'm sure you can find similarities if you look hard enough, but they're clearly not all receiving revelation of the one true religion. Joseph Smith wasn't just told that something that had similarities to Christianity is true. He was told specifically that what's written in the Golden Plates is true. That's the main one I was taught about, but I'm sure Muhammad reported just as specific instructions about a different religion. Maybe those ones are liars, but again, if we can agree there's liars, and either way we'd expect to see people claim to have revelations, then how is people claiming revelations evidence?
And finding similarities isn't that surprising. Look at UNSONG. I suppose if you believe that that was accidentally accurate, then it gets us nowhere, but I'm sure you could find just as many examples in anything else. If you have anything complicated, and you can compare it to something else complicated, you'll find lots of similarities.
> they're clearly not all receiving revelation of the one true religion.
I didn't say that, so I'm not sure why you felt it necessary to refute such a nonexistent claim. What I said is that they're clearly all descended from their common ancestor, the true religion.
I guess I missed your point.
A simpler explanation is that since all religions were started by humans, they're all going to have similarities. And on top of that, as I pointed out earlier, the more details you add the more similarities you'll find, so even two random religions will have lots of similar stuff by coincidence.
Consider how the Hero's Journey seems to pop up in every story. Does that mean they're all retellings of the same story?
"The sacred tree literally shows up all over the globe. It shows up as a key feature in nearly every single religious tradition. And we just shouldn’t see this unless the religions of today sprung from one original source. Now, you might be thinking to yourself, well, it seems easily explainable that religions would use a tree from the natural world to explain certain religious ideas. So that could explain why it shows up so often. Seems plausible enough. And I’ll give you that.
"But just one problem, and it’s a pretty big problem because regardless of where we go in the world, the peoples understand the cosmic and theological significance of the sacred tree in almost identical ways. It would be one thing if one religious tradition used the tree to represent a ladder. And then we had another tradition use the tree to represent sacred writings and another one to have it represent fertility. But that’s just not what we find at all.
"We find that there is remarkable similarity and practically universal correspondence in the way the tree is understood, what it represents and what it gifts to human beings. But what does vary is the type of tree that’s used to symbolize the sacred tree. It tends to be a tree that’s native to the particular culture’s geographical locale. For example, in Norse mythology, the sacred tree was understood to be this immense ash tree. In ancient Egypt, it was either a Perseia tree or a date palm. In Rome, it was an olive tree. In Latvia, it was a birch tree. Among the Maya, it was a seba tree. Among the Slavs and Finns, it was an oak. Among the Gnostics, it was a cypress. Among the Sumerians, it was a willow tree. Among many Native Americans, it’s a spruce tree. Among the Mongols, it was a beech or poplar tree. In China, it was a mulberry tree. Among the Hindu and [Buddhists], it’s a fig tree. You get the picture.
"The particular species of the sacred tree varies by culture and geography. But what doesn’t vary is the cosmology and the theology that’s associated with the sacred tree. It’s virtually identical everywhere we go in the world."
— Dr. Jack Logan, "O Christmas Tree"
It's not just the Tree of Life/World Tree. As I've said elsewhere in this thread, all of the major doctrinal precepts of ancient religions show similar signs of common descent. We know what things being similar but different due to independent invention looks like, and we know what things being similar but different due to common descent looks like, and the signs we see scattered throughout the history of religion in the world is very clearly the latter and not the former.
> Consider how the Hero's Journey seems to pop up in every story. Does that mean they're all retellings of the same story?
Literally speaking, no. On a deep, fundamental level, though? There's good reason to believe the answer to that particular question is "yes."
>We have lots of contradictory testimonies about different religions being true
I think this is wildly exaggerated. We have lots of contradictory *claims* about God, obviously, but how many of those were ever actually attributed to *eyewitness testimony*? When I read different religious texts, they mostly seem broadly similar enough in how they conceive of God that I can easily believe people in all of them could be trying to explain a real experience of the same entity.
>If you're willing to answer "How can there be an uncaused cause" with "There just is, and also it's sentient and all-powerful, and the nicest possible being", how is that any better than just stopping it at "There just is"?
Because one includes more information than the other...? I'm not sure what the question is asking. I'm not even sure why you think "how can there be an uncaused cause?" is a question that needs answering to begin with, there's no inherent problem in such a concept.
Also, God isn't usually said to be "the nicest possible being". Did you mean "greatest"?
Psychedelic experinces are pretty predictable as well, but I don't see most people claiming they're proof of some universal truth beyond brain mechanisms...
I think he's misunderstanding the theology of "Good" and replacing it with "nice." If God created all things, including defining what morality even is, then by definition God is as moral as it is possible to be. If he does it, it is automatically the most moral thing possible. Christians also believe that he is loving and benevolent, but those are aspects of his core being, not something that he changes on a whim. Neither of those things require God to act "nicely" in the sense that he probably means, where God is non-confrontational and cool with whatever happens which is an artifact of liberalism in Europe.
This is actually not true. The amount of historic evidence and testimony backing up Christianity absolutely and utterly dwarfs EVERY other religion by a massive amount. This is completely consistent with christianity being the one truth and every other religion being idolatry.
This is similar to what I took from the piece. It really struck me as a “All models are wrong, some models are useful.” type situation, where you’re kind of thought-experimenting a universal theory to fit a paradigm that may or may not even exist at all.
In fact, there’s no reason to believe it does exist. No consideration of the limits of the human mind, perception, etc. so, what do we have left over after removing everything tautological or superficial? It’s just another theoretical model of existence, not unlike picking a random religion out of a hat and calling it “true because we applied science and logic and now it’s theoretically better than every other religion at theoretically predicting the universe!”
I mean, it definitely isn't any worse.
I actually agree, I don’t think it’s as “horrible” or even lazy as some commenters perceive. Just trying to highlight that it feels mostly like the theory itself is mostly well dressed hand waving.
> no reason to believe that "all possible mathematical objects exist," except that some people want to believe that so as to not have to believe in God.
Its clearly a god, it will create heaven and hell and the majority of life.
I think the main rhetorical thrust of the post is in the final paragraph or so, wherein Scott is making the point about "even if this hypothesis isn't true, the fact that it /could be/ a plausible alternative—that we've only /just/ started exploring it—and yet took this long to come up with..." etc.
i.e., "it's too early to throw up our hands", as the quoted fellow put it.
Okay, but so what? For any evidence cited in support of any theory, you can always posit that there might be some other theory which would explain the same evidence equally well, if only you had a little more time to think about it. That's not an epistemically sound reason to reject the best-supported explanation we currently have.
As somewhat of a believer indeed it is “epistemically freestanding” so no evidence for or conclusions from can be given. But it has given me a certain logical satisfaction to the “why” question - why this specific and peculiarly arbitrary universe? Well simply because we are tautalogically within this one of many. Saved me from having to muse endlessly as I lie awake at night
I've never heard of anyone believing that Tegmark's hypothesis is true in order to not believe in God. Have you? On the other hand, I've had plenty of religious believers tell me that they started believing in God to find solace and meaning. I'm glad they found solace and meaning, but their reason for belief has nothing to do with evidence or reason.
"On the other hand, we have extensive evidence for the existence of God in the form of testimony. People who God has revealed himself to have passed down their accounts to us. People who have witnessed miracles have likewise done so. People who have prayed and received guidance have spoken about it."
We also have extensive testimony evidence of aliens, ghosts, Bigfoot, and witchcraft. Do you also believe in aliens, ghosts, Bigfoot, and witchcraft?
See my answer to agrajagagain.
This is a classic case of an isolated demand for rigor. You can't dismiss an alternative hypothesis to God as "just conjecture" and then not apply the same standard to God. God is also a conjecture, and no, pointing out testimonial evidence does not change this fact.
You could argue that the testimonial evidence is strong enough to favor God's over other conjectures. I find that extremely dubious because I think the testimonial evidence is incredibly weak, but that would be better than just dismissing alternative hypotheses out of hand.
> God is also a conjecture, and no, pointing out testimonial evidence does not change this fact.
When multiple sources, independently and without collusion, testify to have witnessed the same thing, that's typically considered good enough for a court of law. Why are you arbitrarily raising the bar here? Who's the one truly applying an isolated demand for rigor?
There isn't any meaningful difference whether people claim to have seen Bigfoot or spoken to Bigfoot (or fairies or djinn/ghosts or any mythological creature) as it pertains to credulity and weight.
It's not surprising to see accounts that keep in line with the popular wave of monotheism and hysteria of religion sweeping up civilization. Spiritual accounts in history take on a different flavor depending on time and region (see: India, China) but you seem to want to ignore that to fit everything into a square hole. It's "the same thing" if you project things that weren't claimed and ignore what was.
> There isn't any meaningful difference whether people claim to have seen Bigfoot or spoken to Bigfoot (or fairies or djinn/ghosts or any mythological creature) as it pertains to credulity and weight.
See my answer to agrajagagain on this point.
> Spiritual accounts in history take on a different flavor depending on time and region (see: India, China)
See my answer to Xpym on this point.
Are you seriously suggesting that the testimonial evidence for God would hold up in a court of law? There isn't a single case of multiple sources independently testifying to have witnessed something that would be proof of theism if true.
It all depends on the standard of evidence. Funny how people who say "there's no proof of X" are never willing to provide one...
You might as well have just said evidence is irrelevant to you. That would save time since by definition faith does not rely on it.
...huh?
Nothing you just said makes any sense. Would you mind clarifying?
The New Testament?
The New Testament does not contain multiple sources independently testifying to have witnessed something that would be proof of theism if true. It only contains one primary source (Paul), and he never even claimed to have physically seen the risen Jesus. He wasn't even one of Jesus's followers until long after the Ascension supposedly occurred. He had a religious experience that caused him to convert.
It appears you haven't read Galatians, where Paul talks about meeting Jesus and spending two years studying with him.
Also, are you not familiar with 1,2 Peter, 1,2,3 John, Jude, and James, which were all written by people who lived with Jesus before his crucifixion? For that matter, Matthew and John both were among his closest 12 and wrote two of the gospels, and Mark was likely written by John Mark who was with Jesus at the time of the crucifixion (and many believe was specifically among those on the Mount of Olives when Jesus was arrested).
Those would all be primary sources, leaving only Luke and Acts (also written by Luke) as secondary sources to Jesus. But if you read through Acts, the author was a first-hand witness to many of the events. You can note that in certain places, like Acts 16, the narrative of the book switches from describing Paul's actions to describing "we" moving around and doing things.
ETA - and just to clarify, those different authors claiming first hand experience with the events in question definitely were claiming to have witnessed things that would be proof of theism if true. It's quite weird for you to claim otherwise.
Because law deals with the physically possible and you want eyewitness testimony that we have no way of verifying to prove the physically impossible.
> law deals with the physically possible
[citation needed]
> you want eyewitness testimony
No. I'm not asking for testimony; I'm stating that the testimony exists.
> that we have no way of verifying
Try telling that to the millions upon millions of people who have verified it.
> > you want eyewitness testimony
>
> No. I'm not asking for testimony; I'm stating that the testimony exists.
Please improve your reading comprehension. There are sentences longer than 4 words.
> > that we have no way of verifying
>
> Try telling that to the millions upon millions of people who have verified it.
Millions and millions of people have read it. That's not verifying, unless you simply mean to say that millions have verified that the eyewitness testimony exists, rather than the phenomenon being testified existing, in which case we are in agreement, but that says nothing about the truth of the phenomenon being testified.
> Millions and millions of people have read it. That's not verifying
I'm not claiming it is. Please improve your reading comprehension.
I'm saying exactly what I said.
Not to go all "edgy atheist" here, but it seems like a basic sanity check to see how our existence for God stacks up against our existence for other testified-but-not-otherwise-demonstrated phenomena. You say:
"On the other hand, we have extensive evidence for the existence of God in the form of testimony. "
and I can't help but ask "how does that stack up against our evidence for the existence of Bigfoot?" Pretty sure there's lots of testimonial evidence for Bigfoot out there. It arises from a population that is (almost certainly) less invested in and less credulous of the existence of Bigfoot than of God, making it more surprising (and thus worthy of a bigger update) when people report Bigfoot sightings. And claims of observable phenomena are generally much more recent, meaning they're more likely to have been transmitted faithfully.
" but we have enough, from enough disparate sources, that Bayes' Theorem compels us to either take the notion seriously or abandon all pretenses of rationalism."
That doesn't follow at all. Or rather, that only follows if you assume the base rate of *false* God-claims to be zero. Even assuming a quite low base-rate, a large population exposed to religious ideas over a long period of time will accumulate quite the corpus of claims even if every one is false. See for example:
https://xkcd.com/718/
As far as I can tell — and I'm by no means an expert on the subject, so it's quite possible that there's something I've missed — Bigfoot sightings are just that: sightings. Someone says "I saw something weird, so there's something weird out there." There doesn't appear to be anyone saying "I had a conversation with Bigfoot and this is what he told me." There certainly aren't multiple independent people saying "Bigfoot told me these things" and the things they claim to have been told are consistent across reported encounters.
Fine then, aliens. People have definitely claimed to talk to aliens.
And before you ask if there are any similarities between encounters, yes there are: https://en.m.wikipedia.org/wiki/Narrative_of_the_abduction_phenomenon
And the funniest part is that the debate around this subject is almost completely identical to the debate around alleged encounters with God:
> Skeptics of the abduction phenomenon contend that similarities between reports arise from commonalities rooted in human psychology and neurology or cast doubt on the presence of similarities between reports at all. They note the evolving contents of abduction claims and the apparent effect of culture on the details of the narratives as evidence that the phenomenon is a purely subjective experience. Skeptics also point out the likelihood of large numbers of hoaxes being present in the abduction literature.
> Believers assert that it is unlikely for hundreds of people to independently generate such similar narratives while apparently having no knowledge of each other's claims. Some abduction investigators attempt to confirm the reality of events reported in abduction claims through observation or experimentation, although such efforts are generally dismissed as pseudoscientific by mainstream academics.
The final section of that article, "Effect of geography and culture on abduction reports," is instructive. While this article is largely focused on the English-speaking world, people of other cultures rend to report different "abduction narratives."
And again, as I've mentioned elsewhere, these encounters do not impart true knowledge. In fact, one of the most significant characteristics of the Abduction Narrative is the exact opposite: a loss of knowledge in the form of "missing time." As far as I'm aware, no one's ever woken up from a UFO encounter with a new, actionable understanding of present or future events.
>The final section of that article, "Effect of geography and culture on abduction reports," is instructive. While this article is largely focused on the English-speaking world, people of other cultures rend to report different "abduction narratives."
In fairness, the main difference noted seems to be that aliens are reported as being evil in accounts from the US but more often benevolent elsewhere, which could simply be evidence that aliens hate Americans.
Your own link points out that one of those common factors among alien abduction narratives is "the aliens wiped all my memories of the event, and I didn't remember it had happened until I [heard/read/watched a movie about] someone else's account of the same abduction narrative". Assuming this is accurate, that doesn't sound like "people independently generating similar narratives while having no knowledge of each other's claims" to me.
I'm not sure why it being a "conversation" is important. People sighting Bigfoot aren't just claiming to have seen "something weird." They're claiming to have seen Bigfoot. They're describing what they saw in similar terms that are "consistent across reported encounters."
Again, you need to bound the base rate of false claims--and bound it quite low--before you start treating mere testimony drawn from the population at large as evidence. So what is the base-rate of false God-claims? Please give both a number (can be approximate), and methodology for arriving at that number, which must be grounded in actual, gathered evidence.
> I'm not sure why it being a "conversation" is important.
Have you read the rest of the thread?
> People sighting Bigfoot aren't just claiming to have seen "something weird." They're claiming to have seen Bigfoot. They're describing what they saw in similar terms that are "consistent across reported encounters."
That's why it's important. Anyone can report having seen something that some other person has reported seeing, and make it sound like some other person's description. It's a lot harder to fake an encounter that you got true knowledge out of.
" It's a lot harder to fake an encounter that you got true knowledge out of."
No, it is not. You're drawing a false distinction here. Both of these are *fundamentally* the same in kind: if they differ, it's only in degree. Anyone can reporting seeing something another person has seen. Anyone can report hearing a conversation similar to what another person reported hearing. You can claim that some of the latter cases provided *actually new information*, but for that claim to stand YOU NEED EVIDENCE.
Please stop wasting both of our time. Provide evidence, or admit that you have none.
The argument you're making is fundamentally an information-theoretic one. You *cannot* argue it merely with wishy-washy assertions that "this is the sort of thing that happens." It needs well-sourced data. Actual observations of the real world, showing that it actually has the necessary properties to support your argument. You haven't provided any.
So... you continue to ignore the rest of the thread, and to brazenly throw out the quintessential bad-faith debating tactic: denying the existence of your opponent's evidence. Despite having already been called on it.
You're bringing nothing useful to this conversation, and only trying to sow confusion and waste time. Go away, troll.
As several people have pointed out, your reasoning is severely flawed. I hope to see you engage with these flaws in your reasoning.
I've seen people testify to mathematical.realism.
My question for proponents of the mathematical universe hypothesis: if all we are is an instantiated mathematical object, then why do we have our phenomenal experience of moving through time? While a cellular automaton might seem inherently temporal with how it proceeds between steps, in actuality the mathematical definition of what its outcomes will be all exist "at the same time" from the point of view of the mathematical definition and the spaciotemporal object it implies. So I can understand a dimension of time existing, but why do we subjectively feel ourselves to be moving through it in only one direction and only one instant at a time, rather than experiencing it all at once as a "block universe"? It seems there must be some "fire breathed into the equations" beyond the equations themselves to explain the conscious experience of temporal change, so saying we are merely a mathematical object seems to miss one of the main aspects of our subjective existence.
> then why do we have our phenomenal experience of moving through time?
Because we have memories. If the entire universe happened the other way, starting at the heat death and moving towards the big bang, with every event happening backwards, and we remembered the future instead of the past, it would be completely indistinguishable from this universe. We don't have some magical ability to detect time passing. It's just that we remember the past, and think of that as time passing.
That might explain why we think of one thing as "before" or "after" another, at any given moment. But it doesn't explain the *experience* of change. As you point out, mathematically it's symmetrical — so why don't we experience our memories "backwards", disappearing over time? Or experience everything all at once?
We *do* experience everything backward and forward and all at once, the issue is that we only *remember* in a single direction.
But that's not how we *experience* it. I can distinguish my left hand from my right, but I experience them both "together". Likewise, I should be able to distinguish "earlier" memories from "later" one, but while I'm experiencing them together.
I can't explain the experience of anything. I won't deny that. But I don't think the experience of redness requires that something actually be red. I can get the same effect by looking at something cyan and then closing my eyes, or just thinking about redness. And if I can experience the qualia of redness without red, why wouldn't I be able to experience the qualia of change without change?
I don't think you can experience redness without redness — it has to be something, even if there is no red object "out there" when you experience it.
But time is something different. To experience change, your *experience* itself has to be changing. (By definition, if your experience didn't change, you would just be experiencing the same thing — as I do when I experience my left and right sides.)
Maybe you can have a completely static subjective experience of change, without this experience changing at all.(in the same way it isn't necessary to see a red object, to experience seeing a red object)
Or at least, I don't see how one should imply the other by definition.
Entities don't necessarily have .memories , and there are a lot of ways memories could work, if they do.
And have you asked them if they experience change?
Yes, and memory is linked to the increase of entropy, because it corresponds to a copy of information at the macro-level.
You are conflating the consequences of the rules with the thinking and experience of them.
There are the laws of physics and the (mathematical) objects they govern. Supposing these objects are complex enough to think, experience, and even make predictions using the very rules that govern them, does NOT mean the objects (eg humans) would necessarily be able to experience every consequence of the laws simultaneously. Any being imbued with similar faculties might have a wider or narrower experience of time. Even this is probably being too charitable. There are probably different echelons of life/experiencing the universe that stretch beyond the narrow set of faculties that we call human experience
This only makes sense if there is a metaphysical distinction between the two, however, and such a distinction does not make sense if mathematical objects are all that exist.
Such was very clear to Plato and Aristotle. It is not due to greater philosophical sophistication that it now fails to be clear to some people.
Suppose the experience of time and all of time itself are both defined as mathematical objects. The subjective experience of time might simply be a subset of the latter. That is, even if there is no metaphysical distinction between “our experience of events” and “the set of all events”, there’s no reason to think they should be equivalent.
The fact that one being can be defined as a mathematical object, does not imply that the experience or perception of time for that being would contain the totality of that beings experience.
I simply don't know what those words mean. I can say, "Suppose that love is defined as the taste of orange," and that might be poetic, but just because I can say it doesn't mean it makes sense.
Mathematical objects mean something and have particular properties. So does the experience of time. Their properties are not the same. For example, mathematical objects are abstract and universal. Things like the experience of time are concrete and particular. What you said does not make more sense than saying that I ate the number four for breakfast this morning.
In any event, and leaving aside this complaint (which to my mind is conclusive): your original distinction was not between the universe and a part of it (such as the worldline of a person), but between the "consequences" of the rules and the "experience" of them. It does not make sense to say that the "experience" of something is a subset (in the mathematical sense) of the thing.
You said above in response to my first comment: "This only makes sense if there is a metaphysical distinction between the two, however, and such a distinction does not make sense if mathematical objects are all that exist."
To this point, even if you erase the metaphysical distinction and accept this claim: "mathematical objects are all that exist," you can still argue that the mathematical structure that represents time is different than the mathematical structure that represents our experience of time. In modern day mathematical parlance, such a task is usually accomplished by showing that set A does not contain the same objects as set B. And yes, this is a bit strange to argue in this context, but it is all predicated on Tegmark's initial thesis that everything is math. This is what I was trying to do in my last comment. I do not actually hold this position myself.
Regarding the claim: "your original distinction was not between the universe and a part of it (such as the worldline of a person), but between the "consequences" of the rules and the "experience" of them. It does not make sense to say that the "experience" of something is a subset (in the mathematical sense) of the thing."
I think your complaint here hinges on the following, whether the experience of the laws of physics are counted as a "consequence" of them. If so, they would be included in the "set." If not, than we have decided to make an arbitrary distinction. I am more inclined to include them.
I take it that the motivation for Tegmark's work in the first place is his noticing (obviously he's not the first) that the physical universe is well described by mathematics, and might in some sense even be isomorphic to a mathematical object. So I take it that he thinks that it is, at bottom, some kind of very simple mathematical object -- the solution of a PDE, or a particular instantiation of a particular cellular automaton, or this kind of thing.
It seems to me that you are wanting to replace this with a much more complicated mathematical object. For example, rather than just the solution of a PDE (which would be a function, or ultimately perhaps a set of ordered pairs), something that contains much more information (something like tuples containing both the ordered pairs, and also additional metaphysical data relating to "time" or "feelings" or the like).
Now, on one hand, I think this just highlights in one more way (there are many) what a bad idea Tegmark's original plan is, because yes, one can always take an infinitely large number of expansions of a particular object that still contain (isomorphic copies of) the original object. Next, I give you credit for realizing that some such thing -- at a minimum -- would surely be needed, because there simply must be additional "stuff" beyond just the geometric structure.
Such "stuff" would have only arbitrary connection to the physical data, though; so this kind of move would actually give piercing strength to what I usually think of as a relatively weak argument, our friend Bentham's "psychophysical harmony." Beyond that, though, these are still just not the right *kinds* of entitites to be the world. One would *still* be left with a distinction between this "additional stuff" and the actual "experience" of the stuff, for example (and why wouldn't the purely physical data also be experienced?) Etc., etc.
Anyway, thank you for the interesting points. I hope I have not misinterpreted what you said.
" why do we have our phenomenal experience of moving through time? "
Do we? I'm not honestly sure this is a coherent question. Are you familiar with the idea of a Boltzmann brain? The weird thing about it is that it seems--in a pretty fundamental way--to be completely undisprovable. Any evidence you could imagine seeing for *not* being a Boltzmann brain could have been conjured into your memory/perception a bare instant ago, to vanish again in the next instant. There's no discernible way the hypotheses "Vittu is a human with a continuous existence through time" and "Vittu is a Boltzmann brain, here one instant, gone the next" can really be separated. All our interactions with the past are mediated through the present.
Or to put it in the language of cellular automata: each step in a (sufficiently complex) cellular automaton state will contain a wealth of information about previous steps. If the notion of a "person" is really just pointing at a connected series of automaton steps[1], then each of those steps will *separately* contain a self-reference to the whole series, regardless of whether you regard them as a sequence in time or a block existing all at once.
I'm not sure if that last paragraph made any sense at all. Maybe imagine it like a deck of playing cards set in a standard order. Only each card contains (in addition to its own suit and value) a little note listing all the cards previous to it. So the Ace of Clubs lists nothing, the Two of Clubs lists just the Ace, the Three of Clubs lists the Ace and the Two, the Ace of Diamonds lists all the clubs in order, and so on. Regardless of whether you're flipping through the deck, leaving it stacked on the table or throwing it in the air, the card ordering is still written on the cards. If we narrow our focus to just (say) the Ace of Spades in isolation, we still observe most of the sequence of the deck despite not having any idea how each physical piece of the deck is arranged (or whether any other pieces actually exist). Each part contains (a portion of) the sequence of the whole.
OK, this is making my head hurt. No more metaphysics until tomorrow morning at least.
[1] Or really, a connected set of sub-regions within the larger set of steps of the universal automaton
If you want to say that we are not forming memories by moving through time, and are instead instantaneous BB s with memories as if of moving through time, then you need to explain why the memories are constant and display physical.laws, because the number of possible BBs with chaotic memories would be much higher.
I agree that a universe consisting solely of short-lived BBs should contain a lot more chaotic and disordered BBs than nicely coherent ones. I'm not trying to argue such a universe is more plausible than ours.
What I am trying to say is that asking the question "what if I was just a BB, how would I know the difference?" seems highlight a problem with ANY time-ordering arguments that I find difficult to get past. Namely, that any evidence we have for the idea that time in *moving* is necessarily evaluated *in the moment*. Trying to argue it from such a position seems to have a self-referential or pulling-oneself-up-by-the-bootstraps quality that I can't see any way to remove.
Whereas arguments against the reality of time involve massive amounts of coincidence.
I think you can ask similar questions within the confines of vanilla physics too. General Relativity would have us treat time as a dimension of spacetime, on equal footing with space.
You could think of yourself as your world-line through spacetime, which exists in some crystalline atemporal sense, and then ask why you experience time sequentially through that worldline.
Maths is necessarily timeless, physics is not, only possibly.
I think that's a strong objection to MUH, and. Tegmarks rejoinder is quite weak.
Because our experiences are not *outside* the universe? We are *in* physics, not outside of it looking in, and so we only remember what has occurred in our personal past.
We feel we are moving through time because that is how the rules of the universe are set up. Our brain at 8:00AM is a slice in the timeless sense, and it is linked to the next slice by the rules for how this area of the mathematical universe functions. That light bounces into the eyes of 8:00AM brain, causing a reaction to the sun coming in through the window in the next slice. Etc.
We remember the past because we have memories that reacted to events in our lives, chemicals spreading, neurons firing, and so on.
To me this is like asking why I don't know what is happening in Alpha Centauri at this very moment: Because the laws of physics restrict me from seeing anything but a delayed picture of it from within.
I read a little Tegmark long ago, but I haven't read this one. I'm willing to accept that the reason there is something rather than nothing is that mathematical objects are logically necessary, if he also explains *why* mathematical objects are logically necessary. I reckon he's got some argument that makes this objection equivalent to asking why modus ponens is valid, but it's hard for me to believe I would find it convincing. (I suppose I'll have to read the book.)
Similarly, I accept that we find ourselves in a universe that allows life because of the anthropic principle -- where else might we find ourselves? But it still seems to me that the fine-tuning we perceive is mighty damned fine; I'd be happier if we could imagine a wide smear of values for the fine-structure constant (and a dozen others) that would seemingly permit life, rather than what we do see, namely a knife-edge where we could not exist if any of them were just the teensiest bit higher or lower. I can think of only two courses. One, maybe there are very different universe-regions where there *is* more leeway and we just have the perverse luck of being in one of the knife-edge universe-regions. Or Two, there is some explanation for why life can arise *only* in knife-edge universe-regions, and I'd like to understand why that is so.
I don't think any of my quibbles make the arguments for God any more (or less) plausible, but it still pisses me off.
ETA: ...Or Three, our imagination is too limited to see that life really *is* possible in universes that are like ours but with slightly different constants; we just don't see it because we are blind to the opportunities that these nearby universes afford. Maybe. It's complicated. Still annoyed.
My intuitive understanding is pretty simplistic. All mathematical objects exist by simple fact of being describable. Actually going to the trouble of doing so (say in a computer simulation) only causally connects them to our universe but does not change them in-themselves
I haven't read Tegmark, but my understanding from these comments is that he means mathematical objects exists as in mathematical objects is what actually constitutes physical reality. Your explanation seem to suggest mathematical objects exist in the platonic sense, as abstract "forms", not physical reality. These seem to be two very different things?
Have we invented a Hard Problem of Existence to go with the Hard Problem of Consciousness? I never had much patience with the latter.
What would mathematical.existence be contingent on? (Note that that's a different question to "what would mathematical truth be contingent on ")
Isn’t this just a dressed up Anthropic Principle? The only part of the argument that seems to me to have explanatory power is the bit where you’re sampling from the set of possible universes that host conscious beings, which is just our old friend.
Yeah I thought the the same thing. I also don't know about this:
> Argument from comprehensibility: why is the universe so simple that we can understand it? Because in order for the set of all mathematical objects to be well-defined, we need a prior that favors simpler ones; therefore, the average conscious being exists in a universe close to the simplest one possible that can host conscious beings.
As any programmer will tell you, shorter (i.e. simpler as a machine) is not particularly correlated with comprehensibility. So I'm not sure the simplicity prior is even helping on this front.
"As any programmer will tell you, shorter (i.e. simpler as a machine) is not particularly correlated with comprehensibility."
Then those programmers aren't very good at statistical thinking. It's certainly possible in many cases to make something more human-comprehensible by making it longer. But "correlation" is not "perfect correlation." If you sampled randomly from the set of all 100-bit programs[1] and all 1,000,000 bit programs, I cannot *possibly* believe that your first set of samples wouldn't be easier to understand than your second. It's just that the longer programs you run into *aren't* picked out randomly: they're specifically chosen from among those long programs that are easy-to-understand. (I'm less familiar with the theory of Turing machines, but I'd still bet decent money the same principle would apply).
Note that the laws of physics are *not* actually especially easy-to-understand. They're just simple *enough* to be tractable to humans, despite all their mathematical subtlety. There's no obvious reason that classical electromagnetism (for example) needed to have a ruleset simple enough to be expressed in four equations, rather than needing 10, or 50, or 10 million equations. In the latter case, humans would likely never have figured *any* of it out.
[1] That were syntactically valid in a particular language.
> If you sampled randomly from the set of all 100-bit programs[1] and all 1,000,000 bit programs, I cannot *possibly* believe that your first set of samples wouldn't be easier to understand than your second.
Then I recommend you google "code golf" or "International Obfuscated C Code Contest" and poke around a bit in the solutions. Perhaps that will give you a spark of understanding.
Those programs aren't a representative sample of the set of short programs.
That doesn't surprise me, because in the real world, programmers don't write programs by drawing one randomly from "the set of short programs", or any set for that matter, so I wouldn't have expected my examples to be a representative sample of them either.
My point is: When humans are involved, you cannot optimize for shortness and readability/comprehensibility of code at the same time, so any purely statistical argument to that effect is just wrong. Yes, you can make functional code incomprehensible by bloating it to 10x its size. But you can make it even more incomprehensible by making it 1/10th the size, which I tried to illustrate with the code golf example.
"My point is: When humans are involved, you cannot optimize for shortness and readability/comprehensibility of code at the same time, so any purely statistical argument to that effect is just wrong"
But the Tegmark universe argument is that the mathematical structures are chosen at random[1], humans are *not* involved in the choice.
[1] Or rather, your position as an observer is chosen randomly from among all observers in all universes, with some simplicity-weighting to keep that set finite.
I'm aware that "short programs can be hard to understand" and "long programs can be easier to understand" are both true sentences.
But the argument was a statistical one. Is shortness *correlated* with comprehensibility? I should think that even when drawing from the space of human-written programs the statement is false. And when drawing from a larger, Platonic program-space containing (among other things) programs that no human would ever write, the answer is extremely false.
Consider some set of particularly opaque code golf entries having, for example, a size of 100 bits. The set of all valid 250-bit programs obviously includes things functionally equivalent to every program in the first set[1] AND it contains every ordered pair of programs in the first set, chained together in any sort of bizarre way that you can fit into the 50 extra bits. AND it contains novel 250-bit programs that couldn't in any fashion be squeezed into 100 bits. It's certainly going to have *way* more pieces of bizarre, difficult-to-understand code than the first set.
Certainly if you give a human 150 bits to do the same job, they can use some of them to make it easier to understand. But that's not really germane to the Tegmark-universe specification: if "simplicity of a mathematical structure" CAN be defined in some universal way, it necessarily must involve everything being as-compressed-as-possible, not padded out for human comprehensibility in ways that add length without adding function.
[1] You can pad any program with valid-but-unless code like empty loops and always-true conditionals.
> Note that the laws of physics are *not* actually especially easy-to-understand. They're just simple *enough* to be tractable to humans, despite all their mathematical subtlety.
I agree. Also I think that what we seem to understand and describe with reasonable accuracy mathematically is really aggregate effects of the presumable underlying fundamental laws of physics. We don't really know if those underlying laws are tractable to us, but it is often assumed that there is some simple mathematics that describes the fundamental laws at the "bottom".
I'm not sure if this really needs to be true? Is it not possible that the underlying laws are not simple and not easily describable mathematically, just as it is not obvious that electromagnetism (an aggregate effect) need to adhere to simple formulas?
Okay since we're talking about a situation where an appeal to a probability distribution was made, "correlated" was definitely not the right word to use. What I _should_ have said is that maximally short programs are essentially never comprehensible.
Our universe in fact has laws of physics that are fundamentally simple, but difficult to figure out, and very difficult to apply - the original motivation for quantum computing was simulating non-trivial quantum systems - so this is if anything an argument in favour
Anthropic principle tells you why you are more likely to find yourself in a universe X compared to a universe Y where you couldn't live. It doesn't tell you what is the set of all universes we are choosing from.
This is the second part to the anthropic principle.
Notably, you might have some notion of reality-fluid that corresponds not just to the simplicity of initial conditions but to how much any particular being/experience/universe exists relative to others. If many simple universes for some reason simulate some particular situation complicated universe, that complicated universe gets a boost in reality-fluid: despite having complicated laws, its simulated a lot/it’s visible from a lot of places/it’s shorter to define (via “it’s simulated here in this simple to define universe”).
Maybe think of it as the PageRank algorithm but for everything.
I love this idea that there could be an "Eigenvector of the universe"!
It also potentially gets around the issue of needing like a specific programming language in order to specify "how to measure simplicity". Instead, simplicity of universe A is the probability universe A appears as a substructure within a random universe X, where universe X is randomly chosen using the same probability distribution as is used to measure simplicity. However, while obviously eigenvectors are well defined with a finite matrix, I'm still a bit unsure if this can be well-defined within uncountable infinite realms of mathematics.
Would be very interested in hearing from a math expert on the plausibility of this working out mathematically
I've always found this theory horrifying, for two reasons. First, it seems pretty plausible (occam's razor). Second, if it really is true, then it means that there are (possibly infinite) worlds with huge amounts of suffering. If there's no limit to the complexity of the starting conditions, there could be a universe where I'm personally being tortured for eternity.
Exactly, that everything happened is the worst imaginable thought
I fail to see how this is very different from our own world: there are some people and places having amazingly positive experiences and some having horribly negative ones.
There are also universes where you're personally in eternal bliss. Why focus only on the negatives?
Personally I don't feel like a heaven cancels out a hell.
And neither does a hell cancel out a heaven. The situation is symmetric, but you are choosing to focus on one side of the symmetry. Why?
Because I'd like to walk away from Omelas.
Would you support maximally torturing one person for eternity to give another person maximum bliss?
If I was given the option upon my death to either:
- live forever by uploading my brain into 2 co-existing simulations; one of eternal bliss and one of eternal torture, or
- cease to exist
I would select ceasing to exist without hesitation. Would you not?
Suffering is not the opposite of pleasure. Pain is not the opposite of happiness. At least not to anywhere near the same degrees. Humans would much, much, much rather avoid pain than seek pleasure.
Hellish worlds will be assigned low measure for roughly the same reason why it is unlikely for our world to become hellish at any point in time. In addition, you might more controversially expect heavenly worlds to be more common and be assigned higher measure collectively if you expect our world to be more likely to become heavenly than to become hellish.
Fortunately, the universe doesn't care.
I just... do not get all this obsession with theorycrafting about God. Let's say you somehow get conclusive proof that God exists. So what? There's absolutely nothing you can do with that information. Simply proving God's existence doesn't provide any information about its nature, its motives, or anything else for that matter. When use is that knowledge when you don't even properly understand the fundamental laws and mechanics of reality yet?
Well, I'd guess it has to do with a notion that you can always establish further truth through reasoning. If it's possible to establish that God exists, why wouldn't you expect to then discover its nature, its motives, etc?
It's a motte-and-bailey for Judeo-Christianity.
You can just say Abrahamism.
Well, that would throw in the Muslims and Druze as well
Naw. There are plenty of nonsectarian Theists out there that are really passionate about this stuff. Myself included.
I consider this a growing but comparatively minuscule demographic, where the question of God's existence comes up.
I've thought to style myself a deist in the past, but my conception has no resemblance to an intelligent and/or benevolent being, which makes it kind of moot and practically indistinguishable from whatever strict atheists might imagine.
It's a hobby and everyone needs a hobby. Others who don't share the hobby are constantly saying "what's the point?" While jealously guarding their own "pointless" hobbies.
I mean yeah, you're right. That is, of course, assuming that they're doing this for the sake of enjoyment. If anyone's doing this because they're having an existential crisis, they should probably get an actual hobby, because this is clearly not a productive coping mechanism.
Traditionally (e.g. in Aquinas) you follow up the logical proofs that God necessarily exists and is necessarily Good with revealed truths about the specifics of your religion such as the various sacraments and rules.
Did anyone ask if a single religious person who:
a) cares about arguments from physicalist infinite multi-universe(hot take, ***I*** an atheist doesn't believe in this)
b) doesn't have an argument from something super natural (prayer making faith) your ignoring
c) reads essays about math
exists; before writing >3 essays on the subject
Why bother? The argument could be adapted to show that such a person exists.
My mistake, of course.
Prehaphs we should consider if super-mega-hitler is more or less likely to commit the mega holocaust if he believes in god. Since arbitrary people exist on whims.
> arbitrary people exist
A wonderfully succinct précis of the theory.
Yeah, Bentham's Bulldog and several of the other Substackers involved in the debate I linked at the top of the post. That's part of why I bothered explaining that this was an ongoing debate with many participants.
Theists making arguments from infinity + definition-play is to be expected. Its not quite the same as saying its impotent for atheists to do so.
I guess I shouldn't be surprised, ai is also god for many here. Prehaph we should find the Trinity, the mathematical universe created all, Aligned gai will absolve the world of our sins and lead us to heaven, effective altruism will guide the faithful actions to align with goodness.
Me!
I was raised as an atheist and converted mostly because of stuff like this and the theodicies present in Unsong. So, that's one.
Can you elaborate?
It's kind of hilarious to me that the theodicy in Unsong is better than the ones presented by actual apologists.
The idea in Catholicism is that fideism is the wrong answer; while faith is a supernatural gift, it is possible to use human reason to come to the conclusion that God exists. So some people do read maths essays, and care about philosophical/mathematical arguments. (Most of us, admittedly, do just go 'yeah, whatever').
https://www.newadvent.org/cathen/06068b.htm
"Fideism: A philosophical term meaning a system of philosophy or an attitude of mind, which, denying the power of unaided human reason to reach certitude, affirms that the fundamental act of human knowledge consists in an act of faith, and the supreme criterion of certitude is authority.
...On 8 September, 1840, Bautain was required to subscribe to several propositions directly opposed to Fideism, the first and the fifth of which read as follows: "Human reason is able to prove with certitude the existence of God; faith, a heavenly gift, is posterior to revelation, and therefore cannot be properly used against the atheist to prove the existence of God"; and "The use of reason precedes faith and, with the help of revelation and grace, leads to it."
Are you arguing it or is catholicism?
----
" In the first days of his bondage he had turned to the gentle churchly faith endeared to him by the naive trust of his fathers, for thence stretched mystic avenues which seemed to promise escape from life. Only on closer view did he mark the starved fancy and beauty, the stale and prosy triteness, and the owlish gravity and grotesque claims of solid truth which reigned boresomely and overwhelmingly among most of its professors;" -lovecraft, silver key
Arguments from infinity are symmetric, if christ saves christens then ant-christ punishes christens, so whats the wager? If the unmoved mover, moves, maybe he was moved by the big bang.
I HATE IT; Im unhappy as an athiest, but at least Im not definition lawyering. I hope neo-pagenism finds something worth worshiping and then declares autistic analysis of the stories is a sin.
Deiseach is a doctrinaire Catholic, so I would presume the answer is "Deiseach is arguing it because Catholicism also argues it".
Say what you will about the Catholics, they at least have thought about this kind of thing.
Yes hi 👋 I've read almost all of Ssc and ASX, HPmor and some of the sequences and I'm a big fan and also an orthodox Jew. The religion eliezer doesn't believe in, isn't mine either. He skipped elementary school and never really took Judaism seriously. I also think "prayer (or relevations) making faith", while a nice experience for some, doesn't prove anything.
I'll try to summarize what I think is a main position.
God is what's *outside* the big bang and what created the laws of physics. Where time and matter ends, is spirituality.
How do we know God cares and pays attention? 1. The universe continues to exist. God is continually keeping it up and if he took away his attention it would be gone in an instant. What's outside of the laws of physics maintains physics. Otherwise why assume time and cause and effect will always continue just because they did until now?
2. Historical revelation. Judaism says God spoke to 2 million people at Mt Sinai and they all heard God speak, personally and passed on the message to their descendants generation after generation. Not a nomad in a tent having a private revelation or a guy who dug up some gold tablets or anyone else making a claim that they personally heard God. They could be delusional or lying and charismatic enough to convince others. But an entire nation's population of very stubborn and argumentative people all agreeing on the same story? How else could that have been converged on?
3. Evil. This is an easy one actually and the only reason people struggle with it is emotion, not logic. Two words. Free will. Or perception of free will if you're a determinist, if God can see the future in my opinion it's basically the same thing. But free will as humans experience it is the purpose of life, to choose good.
As Rabbi Moshe Luzatto wrote, God created the world with the ultimate purpose of the universe for people to experience good. But unearned good is not the ultimate good. We have the chance to earn it and deserve it. (The Jewish version of hell is basically a "washing machine" to get you back to heaven. The ultimate punishment is shame as you finally understand the true reality and how terrible your sins truly were. Only exception of who gets stuck there being rare irredeemable sinners like Nebuchadnezzar.)
Hope that helps!
Serious question, since you believe and understand a lot of the logic. Any way to make yourself un-Jewish, *according to halakhah*? No way in heck I can keep all those commandments. My understanding is that if you're the son of a Jewish mother it's impossible, but I was at least hoping for some sort of reverse mikvah using bacon grease and the Horst Wessel Lied.
Not sure how serious your question is but a mikva of bacon grease is a funny mental image I guess! And yes you're right being Jewish is a permanent state. Our enemies understand that all too well, unfortunately.
On the plus side, if God made you born a Jew it means you're capable of fulfilling your potential as such. Practically, if you really are serious, I'd tell you that every good thing you do, totally counts even if not everything is done. It's not all or nothing.
The bacon grease mikvah was a joke, the question was serious.
It's not just that (though I admit it's a reason I avoided getting any deeper into the religion); I really don't like a lot of the stuff left-wing Jews have done (the whole left-wing activism in the 20th century, basically) and would rather quit myself of the whole tribe. Apparently that's not an option. But I do appreciate your taking the time to answer the question and your honesty when I seemed to be somewhat unserious. Thank you.
I'm not sure which left wing activism you're referring to? Tikkun olam maybe? Religious Jews are baffled by secular people who think "tikkun olam" is Judaism. It's an incredibly obscure kabalistic thing that has nothing whatsoever to do with social justice. You can be 100% religious and not even know that it exists other than a one-off line in the Aleinu prayer. I have no idea how that came about, historically, that reform and conservative Jews came up with that. Or do you mean something else?
I existed in that state for a while! Not anymore, but it did help inform my current beliefs.
I definitely fit categories 1 and 3, at least, not quite sure what you're going for in number 2. No, I've thought for several years that a Tegmark IV multiverse is probably the most solid alternative to theism.
Interestingly, one suggested explanation for the Born rule is simulating the quantum physics with some floating point precision, discretely, and the errors accumulating. (See this paper by Hanson: https://arxiv.org/abs/quant-ph/0303114.)
Is it the case that discrete universes are simpler/a lot more common than continuous universes, and so we are more likely to find ourselves in a place computable with a Turing machine? Or could it be that all Turing machines exist, but only computable approximations of other objects exist?
I don't see how this isn't just an elaboration of God's nature, of the means of creation. It makes perfect sense that a universe created to contain us would be a mathematically perfect container.
All things could exist, but we do. I don't see a compelling reason not to regard the universe as we find it as an instantiation of a greater and incomprehensible will. God could create anything else, and prodding this reality we can reveal so many of the possibilities, but these it seems to me are many trivial though novel objects. Meanwhile the universe as we discover it is infinitely mysterious, and some among us intuit a deeper will and agency behind the veil.
If you're interested how some of these ideas are compatible with theism, and you haven't read Scott's book Unsong already, you might want to check it out.
I find SIA pretty compelling, and agree that this fits the infinite-people prediction more nicely than theism. I don’t know how to feel about all that it implies (does induction fail? does it endorse moral nihilism? etc.), but thanks for posting.
Always nice to see Plato's influence at work. But one notes that Plato was not an atheist….
>Some mathematical objects contain conscious observers.
Say what now?
This post needs more work. Your response to the 'argument for comprehensibility' stumped me, which is ironic.
This confirms my impression that whether God exists is not a very useful or interesting question.
It depends on what kind of god or God and what the effects on our existence would be. If (say) Vedic religion is true, then that means some kind of afterlife and good or bad outcomes depending on our actions in this world.
Chesterton, "The Usual Article":
"I would gently suggest that, to most ordinary outsiders with any common sense, there would be a considerable practical difference between Jehovah pervading the universe and Jesus Christ coming into the room."
1) I'm not impressed by a thousand competing notions of how to earn your place in the afterlife, assuming there is one, which is an awfully big assumption to begin with. A lot of these notions have a lot of rules in common, and they're mostly good rules which a person can try to follow without the goad of divine wrath; but many of the notions say that's not good enough (see Calvinism, which says that nothing is good enough).
2) Chesterton. I'm not holding my breath waiting for either of these things to happen.
"I'm not holding my breath waiting for either of these things to happen." Funny. The second thing happens to me almost every sunday.
He walks into the room. In physical, corporeal form. Uh-huh.
If you just mean a sense of his presence, he doesn't need to be in the room in any sense to give that. I get that sense about dead loved ones all the time. Doesn't mean they're there.
>I'm not impressed by a thousand competing notions of how to earn your place in the afterlife, assuming there is one, which is an awfully big assumption to begin with.
Why? It would seem that it would be worth your while, for Pascalian reasons.
Even Pascal wouldn't try adhering to a thousand different ones at once. As for what they have in common, see what I wrote: you don't need Pascalian reasoning to do that.
Well, sure. Presumably he'd choose the most favorable option.
And which one would that be? Let me guess, the one that he happened to grow up being taught.
Why would it not be?
If you can get consciousness from some simple set of mathematical rules, it seems very likely that there are many universes with Gods. In fact...it seems inevitable.
Indeed! In Tegmark's multiverse, for any self-contained universe, there's another version embedded in an outer world that includes a creator. Presumably in most cases this requires quite a lot of additional complexity, so it's an insignificant contribution to the measure of the self-contained universe.
The more interesting case is universes that aren't quite self-contained. That is, worlds where the creator intervenes in a way either resolving steps in its evolution undefined by local laws or suspending local laws in circumstances limited enough and with overt enough meaning to be recognized as divine intervention. Those embedded universes can't exist on their own as they're not fully defined mathematical objects without the actions of the creator.
However, I suspect it doesn't work. My interpretation of how personal identity works is basically applying Parfit to all the mind-moments in the multiverse. i.e. "Your" next mind-moment appears to be drawn randomly from all the mind-moments in all worlds that remember having just been "your" current mind-moment. (It's not actually drawn randomly; rather, all such chains are equally real, & the result looks random in the same way as Many Worlds timelines.) So there's a distribution over the worlds your future "self" will be in, and even if you happen to be in one of the rare theistic worlds now, statistically you're sure to be back in a self-contained universe later that has natural explanations for the apparent miracles. (e.g. The putative miracles were misremembered or misinterpreted events, & the in-universe evidence doesn't support believing in them.)
Nested universes within nested universes, going on for eternity...
https://youtu.be/thsyoUZW9vE?si=p20hNWEChwDa4KbS
This was what I thought when he stated the setup - this isn’t a way to get fewer gods, it’s a way to get more gods (though those gods don’t do the creating exactly).
Depends on how you define creation. It seems like some sort of Autopoiesis would be inevitable. Then there's the question of the origin of the necessity of rules. Even arguing that such rules are necessary feels like the argument that God is necessary, and feels (to me) to actually be giving ground to Classical Theists who's conception of God is very "laws of physics"-like anyways
What would it mean for a different universe to exist or not exist, if it is not impossible to interact between universes?
I'm not sure how Tegmark defines a universe, and whether the possibility of interaction is a criteria or not
That would be often incompatible with many (Christian) theists views of God being all-powerful, that even if there were other universes he'd also be in control of those as well.
So, it defuses that sort of argumentation.
But, Tegmarkian Multiverse would also probably imply that ~most universes aren't created by a God. Which then turns the whole issue into a more reasonable argument of "does the historical record make it clear that there is any creator", rather than very abstract sorts of argumentation.
It *might* undermine a Christian God. But it would seem to guarantee other sorts.
And I say "might", because in classical theism, God would be understood to be the rules themselves (Logos), and Tegmark doesn't give an account of where the rules come from.
Compromise Solution: there is a God, but it's the simplest possible God capable of creating the universe. Which neatly explains why there's only one: obviously multiple gods would be an unnecessary increase in complexity.
(This is mostly a joke. But if somebody wants to take the joke and run with it, you could probably show that this is just a fancy gloss on the simulation hypothesis.)
...and different people just took Him wrong...
Some can have just single dungeon muster and mixing different systems rules is a bad idea, never happened ))
Yes, completely unironically, all of this is correct. It's already standard theology in the Abrahamic religions, and has been independently re-derived by theologians in numerous other traditions as well.
NGL, the notion that the deity who decided to "punk" Abraham by telling him to go murder his son and pulling a last-second reversal is "the simplest possible God" is not one I can even consider with a straight face. But I'm also not really interested in getting into the weeds on the matter...I'll take your word that they had very nice derivations and that those derivations sounded very convincing to people who already believed their conclusions and leave it at that.
+1 to that
From my understanding, the argument from comprehensibility is more about the fine tuning of the constants than the laws themselves. Simplicity can't explain that.
Mathematical Realism/Platonism is a contentious position. Paul Bencerraf has demonstrated how accepting this premise undermines any semblance of mathematical truth. IE, if mathematical objects exist, what is the causal relationship between such objects and our beliefs? If you accept that all mathematical objects exist, you immediately sacrifice the truth of mathematical propositions.
Such realist positions in this case are much less a refutation of the aforementioned arguments for god’s existence and much more a stand in for theism. Russell on Kurt Gödel’s mathematical Platonism: “Gödel turned out to be an unadulterated Platonist, and apparently believed that an eternal 'not' was laid up in heaven where virtuous logicians might hope to meet it in hereafter.” - Russell, Bertrand. "America. 1938-1944." Autobiography. 1967. London and New York: Routledge, 2000. Print. 466.
I don't follow why accepting mathematical platonism undermines the truth of mathematical propositions, can you elaborate?
Mathematica! Realists have a choice between a small consistent Platonia and a large inconsistent one..The large inconsistent one means there is no ultimate consistent mathematical truth. The small consistent one means that some things you might be able to prove from.some premises, aren't really true, because they are not in Platonia.
However, you have no way of knowing they are not really true , because Platonia cannot causally interact with a mathematicians brain. So small Platonia is redundant.
Small Platonia tells you that the Axiom of choice is true or false, but not which.
Large Platonia tells you that it's true *and* false.
Are there other possibilities? Much as the parallel postulate is true in some models, and false in others, might there be situations in which the axiom of choice is true in some contexts, and not in others?
But that's definitely interesting, I haven't considered mathematical platonism in any serious way.
Are these contexts supposed be methodological or ontological?
I think this may hinge on confusing questions about "causality". If two simulations are deterministic and have the same initial conditions, then they'll go on the same even without any causal connection. If you and I are both posed the same math question (and we're both competent), we'll reach the same conclusion despite having no causal connection.
Seems to me that the mind of a mathematician can happen to be set up the same as some part of Platonia, and thus predictably proceed the same, without any causal connection between them.
Mathematicians disagree in practice. You can accommodate y for that by saying Alice amd Bob are in sync with different regions...but such an inconsistent Platonia performs no useful function...it doesn't tell you who is right.
To put it simply, if you claim that there are objective mathematical truths (platonism) you have to explain how we come to know these truths. What is it that allows us to have any knowledge of them. What is the causal relationship between the objective mathematical truths and our beliefs?
That mathematical truth is ''embodied'' within reality, we've been selected for living in the current world which is highly regular due to the structure inherent in it, and so our beliefs can tend towards more accuracy.
I think this is really just the question of "but how do we know whether we aren't completely blinded to the truth entirely!".
I'm not really a Platonist though. I do think Tegmark's Multiverse does have the benefit that I don't think it is postulating that you're *accessing* that mathematical truth directly/causally in some manner, just that you're within it.
An alternative answer to your question is that there's logical relations between the two. Like how a calculator on the moon and earth will output the same answer given the same answer.
It's difficult to look at the world and not see mathematical structure. Scientific progress and the regularity of various phenomena certainly persuade us.
But even if you argue that selective pressures guide us towards more accurate beliefs, all you really establish is that "seeing the universe in this way is good for survival." It does not necessarily mean that you've apprehended the underlying structure.
To your point regarding Tegmark, I think the notion that you could be immersed in some universal all-encompassing structure without having access to it is problematic. You could make the same argument about any metaphysical driver of reality (god, allah, spaghetti monster).
The philosopher Justin Clarke-Doane has written about this extensively. One of the points he makes, which I think is fascinating, is that mathematical realism and moral realism are structurally analogous positions. As in, they both revolve around the existence of abstract structures and how are beliefs relate to them. And as such, whichever position you take on one, ought to be the same as your position on the other.
> It does not necessarily mean that you've apprehended the underlying structure.
Sure, but you've apprehended a good amount of structure visible to you. It may be we're in a computer simulation in one part of the Tegmark Multiverse, which runs on different rules in fundamental reality.
>To your point regarding Tegmark, I think the notion that you could be immersed in some universal all-encompassing structure without having access to it is problematic. You could make the same argument about any metaphysical driver of reality (god, allah, spaghetti monster).
I agree. I tend to view Tegmark as a "reasonable default hypothesis" that doesn't assume a single universe or any specific creator entity.
Tegmark-style multiverses do works nicer with the problem of computation requiring some interpretation applied to it. "How do we interpret what this matter is doing" is technically relative to some language, like Tegmark. If you take this fully literally, then you end up with a Tegmark-like multiverse relative to our physics even in single-universe scenarios.
I do think this latter part is quite speculative, so not saying I necessarily believe it, but that it 'shows up' multiple times makes me suspicious that it is hard to get away from.
> The philosopher Justin Clarke-Doane has written about this extensively. One of the points he makes, which I think is fascinating, is that mathematical realism and moral realism are structurally analogous positions. As in, they both revolve around the existence of abstract structures and how are beliefs relate to them. And as such, whichever position you take on one, ought to be the same as your position on the other.
I'll possibly read some of their work, but I'm immediately skeptical.
I accept the view that if mathematical realism holds, then I can find mathematical structures that represent my morals (probably not uniquely specified), but that's distinct from the usual moral realism claims about objectivity because it has no implication of thus applying universally.
Here is a link to a paper that delves into the matter in much thorougher detail: https://pgrim.org/philosophersannual/34articles/clarkedoanemoral.pdf
"That mathematical truth is ''embodied'' within reality ". Many of the contentious areas within maths are connected with infinity, which cannot be observed physically.
There's one more important ingredient to add: while the rules of the Game of Life are probably simpler than the rules of physics, the conscious-being-density in the Game of Life is probably *much* smaller than the conscious-being-density in the mathematical object containing our universe.
It's good to see that Scott has moved on from the denial/anger stages of realizing his error (i.e. "there isn't any evidence for God's existence, what are you talking about") to the bargaining stage (i.e., "okay, yes, it does seem like there's actually a lot of evidence for God's existence, but it's possible to explain all that away if I make a bunch of highly questionable motivated assumptions"). Nevertheless, Scott ignores several critical asymmetries in these two theories.
First of all, God's existence isn't only supported by theoretical arguments. Rather, these theoretical arguments are additions on top of whole libraries of first-hand accounts from people who reported having observed God's existence empirically. OTOH, in the entirety of recorded history, there's not a single reported account of someone observing an actually-existing set of all possible mathematical objects. So, even if it were true that both hypotheses were equally supported theoretically, the theistic explanation would still be heavily favoured overall.
Secondly, like most atheists trying to refute the fine-tuning argument, Scott ignores the critical difference between making predictions which are validated by later experiment vs. inventing a theory to explain away experimental results after the fact. Theists did not find out about the fine-tuning of the Universe and then posit a God to explain it. Rather, the notion that the universe was intelligently designed by an entity with a special interest in human life was formulated first, by ancient peoples who had no way of knowing anything about modern cosmology, and then in modern times we finally developed the technology to confirm that our Universe's physics really does appear as if it was designed by such an entity. So, even if atheists *today* managed to come up with another theory that explains the constants equally well, the weight of evidence would still be against them, at least until they demonstrate that said theory is also good for making successful predictions and not merely for *post hoc* rationalizations.
"Rather, the notion that the universe was intelligently designed by an entity with a special interest in human life was formulated first, by ancient peoples who had no way of knowing anything about modern cosmology, and then in modern times we finally developed the technology to confirm that our Universe's physics really does appear as if it was designed by such an entity."
I think the last part of your sentence is exactly what's in dispute. Is there more to the appearance of design beyond "I predict that our universe will turn out to support life"?
>I think the last part of your sentence is exactly what's in dispute.
It really isn't. The appearance of fine-tuning in physics has been well-established for decades.
>Is there more to the appearance of design beyond "I predict that our universe will turn out to support life"?
For God's sake (pun intended), YES! A *lot* more!
Firstly, and most pedantically, a Universe which supports life isn't necessarily one which supports *human* life. As I say, this is a pedantic point because the basic reasoning of the fine-tuning argument, at least in its most common form, doesn't really change either way.
Secondly, knowing that the Universe supports human life doesn't of itself imply that the Universe that *required fine-tuning* in order to support life. One could imagine a Universe in which intelligent life forms exist, develop the technology to calculate the requirements for their own existence, and then realize those requirements are pretty broad and have a high probability of arising from random fluctuations. Instead, we find that our existence depends on a vast array of very narrow conditions that seem unlikely to have all been met independently by mere coincidence.
Thirdly, knowing that the Universe supports human life doesn't imply anything about our ability to *discover* the ways in which the Universe is fine-tuned to support human life. One could imagine a Universe in which the constants are fine-tuned to support intelligent life forms, but said life forms have no way of discovering what those constants are; and in fact this is basically what the actual Universe is like from the perspective of dolphins or non-human apes. The set of physical conditions required for humans to notice that the Universe seems fine-tuned for our existence is, necessarily, even narrower than that required for humans to exist in the first place, and hence even less likely to have arisen by coincidence.
Note that this last point is especially important in that it specifically indicates an intelligent designer with some kind of special interest in humans in particular, which addresses the "how do you know God isn't fine-tuning for stars/beetles/[insert other object here]?" rebuttal to the original fine-tuning argument.
The dispute I was referring to was whether what you call “fine-tuning” gives the appearance of intelligent design. If that were an irresistible conclusion, then such design would be a consensus view among physicists.
Instead we have physicists embracing the multiverse theory, sans any direct evidence that any other universe exist. Instead we have physicists embracing string theory, a highly fanciful and imaginative theory that also lacks experimental evidence. Physicists are a fickle bunch.
Absolutely, but that supports my point about a lack of consensus! I don't claim that intelligent design/god is less well supported than multiverse theory or string theory, only that it isn't any better supported.
>If that were an irresistible conclusion, then such design would be a consensus view among physicists.
That would be true if I'd said it gives *proof* of intelligent design, but I didn't.
The mere fact that we're discussing whether the MUH has "obviated" the fine-tuning argument shows that atheists (at least those making this argument) already acknowledge the appearance of design. If they didn't think the observed values of constants looked like plausible evidence of intelligent design, then there would be no need to propose an alternative explanation in order to obviate the argument.
"we find that our existence depends on a vast array of very narrow conditions that seem unlikely to have all been met independently by mere coincidence."
Perhaps I don't understand that point, because unless you assume that there is at most a specific number of universes and no more, how is it that fact any different from our Earth being much better for life than other planets, which nobody would think is a good argument?
Look up, the number of stars is unfathomable. That's our galaxy, and the number of galaxies is also unfathomable. The universe itself stretches beyond what we can see. I'd be shocked if it were finite in space. Isn't it a reasonable inference, then, that the number of universes is also unfathomable? For the fact to matter that the conditions required for us to exist are narrow, you'd have to put a specific ceiling on the number of universes that exist, and how can you do that?
No, that is not a reasonable inference. I don't know why you would leap to that.
If the Earth were at the center of the only solar system in the universe, as the ancients believed, I wouldn't suspect countless universes. But when we see countless stars and countless galaxies, where our own planet is an otherwise generic one which happens to be more compatible with life than most of the others, the odds go up that the same applies to universes, in my opinion. You have to admit it's a pattern. And if to solve a puzzle we must choose between countless universes and an intelligent designer, such an increase of odds makes a big difference.
>Perhaps I don't understand that point, because unless you assume that there is at most a specific number of universes and no more
Faulty premise. The belief that there is only one Universe/set of physical laws isn't an "assumption", it's an inference based on the knowledge that we've observed no evidence suggesting the existence of multiple universes. Unless you count the branches of the wave function in the many-worlds interpretation as "universes", but those all share the same set of physical constants and initial universe conditions, so they aren't the kind that would be needed to resolve the issue.
And no, the existence of a multiverse can't be reasonably inferred from the existence of vast numbers of stars and galaxies, for the obvious reason that we have no evidence those things are connected in any way.
No, I'm definitely not talking about the many worlds interpretation of quantum physics, nor as far as I can tell is Tegmark in his theory.
"it's an inference based on the knowledge that we've observed no evidence suggesting the existence of multiple universes" the evidence suggesting multiple universes is that our universe is much more compatible with life than a universe at random would be.
Also, there are countless stars and galaxies, in which our planet is much more compatible with life than a planet at random would be. It's a precedent. It's similar enough to the other thing (see paragraph above) that it makes it more probable, compared to how probable it would have been if we were in a Ptolemaic universe.
If there are other universes not connected to ours you would not see any evidence of them other than what I've mentioned. You can't possibly infer that they don't exist from absence of evidence that would be absent anyways.
>Also, there are countless stars and galaxies, in which our planet is much more compatible with life than a planet at random would be. It's a precedent. It's similar enough to the other thing (see paragraph above) that it makes it more probable, compared to how probable it would have been if we were in a Ptolemaic universe.
Things don't become truer just because you repeat them. In order for your reasoning to hold, you'd have to demonstrate that there's some reason why the number of sets of physical laws* existing in different universes should be similar to the number of stars in one universe, which you can't because we have no evidence that any such reason exists.
>If there are other universes not connected to ours you would not see any evidence of them other than what I've mentioned. You can't possibly infer that they don't exist from absence of evidence that would be absent anyways.
"If there's an invisible inaudible dragon in my garage that's impervious to touch, you would not see any evidence of it other than my telling you about it. You can't possibly infer that it doesn't exist from absence of evidence that would be absent anyways."
As I recall atheists were once so fond of saying, "What can be asserted without evidence, can also be dismissed without evidence."
And let me add another point. Suppose we take your "precedent" argument seriously, what makes you think extending the precedent would help the atheist case? Look at it from another angle -- the original motivation for positing a benevolent God wasn't based on modern physics; it was based only on observing that *Earth* had to meet specific conditions to be habitable, as nobody at the time knew anything about other planets. Then it turned out there were a bunch of other planets in the solar system without life, but that wasn't enough to salvage the atheist standpoint, because the solar system itself had to meet similarly narrow conditions to produce even one planet that was capable of sustaining life. Then it turned out the solar system was also just one of many in the Milky Way, most of which don't appear to contain life, but it still didn't solve things for atheists because it turned out that the Milky Way also needed to meet a number of narrow conditions to be able to produce even one solar system with life. Then we discovered the Milky Way was just one of many galaxies in the Universe, most of which may not contain life, but that also didn't solve the problem, because it turned out that the Universe itself had to meet remarkably narrow conditions to produce even one galaxy capable of sustaining life. Why not extrapolate from precedent and say that, if we could observe whatever meta-laws govern the creation of different physical laws in different universes, we'd see that those laws *also* needed fine-tuning to produce even one universe with life, and so atheists would be left with essentially the same problem as before?
* You keep talking about the "number of universes", but it's the number of sets of laws of physics that is actually relevant here. You could equally plausibly posit multiple universes that all shared the same laws of physics, which would only make things worse for the atheist, since then all other universes would also display the same fine-tuning. This would also make a whole lot more sense with your "precedent" argument, since none of the examples you cited involved discovering that the laws of physics were different in the newly-discovered regions.
People who claim to have seen God are just that - claimants. It doesn't matter how many there are, it's not reason to accept what they're saying at face value. They don't even need to lie, just believe something false or wrong themselves.
People who claim to have seen Robert Downey Jr. are just that—claimants. It doesn't matter how many there are, it's not reason to accept what they're saying at face value. They don't even need to lie, just be a normal amount of credulous about Hollywood.
Yeschad.jpg I don't care about Downey Jr. claimants one way or another. The only way the "Downey Jr." concept matters in my life is through media content I watch that allegedly features him. If some impostor did it instead, or an alien robot sent to Earth as a joke, I don't care in the slightest.
If the only thing I heard about RDJ is that people claimed to have seen him, but he wasn't in any movies and I couldn't find him looking around in Hollywood, then yeah, I can't take those people's word for it.
>People who claim to have seen God are just that - claimants. It doesn't matter how many there are, it's not reason to accept what they're saying at face value.
First of all, this is just stupid. In the absence of other considerations, something being independently reported by numerous observers is obviously a reason to update strongly towards its being true, it's astonishing that this even needs to be argued.
Secondly, this would be irrelevant even if it were true, because my whole point is that you can't just take each piece of evidence individually without considering the whole picture. All else being equal, a theory supported by multiple independent lines of evidence is more plausible than one supported by only one of the same lines, even if none of those lines are by themselves adequate to prove either theory. So even if there's another theory that explains away fine-tuning but doesn't explain accounts of God, or one that explains alleged accounts of God but doesn't explain why the Universe appears fine-tuned for life, these would still be less favoured compared to the model which explains both.
> something being independently reported by numerous observers is obviously a reason to update strongly towards its being true, it's astonishing that this even needs to be argued
It's not remotely astonishing. Look at all the reports of UFOs. Or the chupacabra, or bigfoot, or cat-eating Haitians. Independent reporting from numerous observers is at best evidence of some shared phenomenon. Some of those observers may interpret that phenomenon correctly, but there's no reason to assume the majority or even a significant minority will.
>It's not remotely astonishing.
No, it is, it really, really is.
If the notion of "independent observer reports can't be evidence for a phenomenon being true" were taken seriously, it wouldn't mean you got a convenient excuse to reject a handful of claims considered low-status amongst your tribe while leaving the rest of your knowledge untouched. It would mean throwing out *the entire concept of empirical evidence*, and with it, all of science and history. Outside of pure mathematics, there is literally *no* way of supporting *any* claim that doesn't rely, directly or indirectly, on eyewitness testimony.
No, there is a way of doing that, it's just time-consuming. I could spend my whole life replicating papers that come out and seeing if they're true or not. It would be expensive and time-consuming, but not impossible.
The difference here is that eyewitness claims about God can't be replicated. You can do everything an eyewitness claims they did and not see or experience what they did. You can even do this *seconds* after they claim to have seen God and still not see what they do.
No, it's not reason to update to that, because we know that humans are not reliable eyewitnesses. That holds true even if I trust all those people to not being trying to lie.
If you're referring to near-death experiences as evidence for God, I mean... yeah, okay, I guess you could take that as some kind of testimony on the existence of an afterlife, but it also tends to contradict the specific claims made by any given religious tradition. (I'm sorry to disappoint certain Christians, but near-death Hindus do not generally report boiling in lakes of fire for the sin of worshipping demons, for example.)
The fine-tuning argument is really only relevant if an intelligent designer was governed by simpler laws that required less fine-tuning compared to "suddenly there was a big bang", which is a question I don't think we're well-equipped to answer right now.
It should also be remembered that having an intelligent designer is not necessarily the same thing as said designer being benevolent, omniscient, or all-powerful. (Olaf Stapledon's Star Maker is an interesting exploration of alternative motives for such a being.) Those are separate claims that require separate lines of evidence/argument.
>If you're referring to near-death experiences as evidence for God,
Who said I was only including near-death experiences? Some reported encounters with God involve near-death experiences, but many don't.
>I guess you could take that as some kind of testimony on the existence of an afterlife, but it also tends to contradict the specific claims made by any given religious tradition.
I'm not sure that's true, but even if it is I didn't say anything about God having revealed the true religion (nor about an afterlife for that matter), so this is irrelevant.
>The fine-tuning argument is really only relevant if an intelligent designer was governed by simpler laws that required less fine-tuning compared to "suddenly there was a big bang", which is a question I don't think we're well-equipped to answer right now.
Wrong. Even if "suddenly there was a big bang" explained why the Universe existed at all (it doesn't), it's not even attempting to explain why the resulting Universe seems fine-tuned to allow for intelligent life.
>It should also be remembered that having an intelligent designer is not necessarily the same thing as said designer being benevolent, omniscient, or all-powerful. (Olaf Stapledon's Star Maker is an interesting exploration of alternative motives for such a being.) Those are separate claims that require separate lines of evidence/argument.
Even though I do think there are good reasons to attribute all of these traits to the designer, I think it's simpler to just note that it would be a very strange sort of "atheist" who'd admit that there's an intelligent being that exists outside of the Universe, and which designed everything in the Universe with the goal of allowing for human life, as long as you don't ask them to admit it's a "triple-omni" designer. Like I said in my first comment, for an atheist to move from denial/anger to bargaining in this way would be an encouraging sign.
> Who said I was only including near-death experiences? Some reported encounters with God involve near-death experiences, but many don't
Okay, but as others have pointed out, there have also been thousands of reported encounters with Elvis.
> I didn't say anything about God having revealed the true religion...
No, but it is also a little suspicious that NDEs only match the afterlife described by Religion X when the experiencer also believes in Religion X.
> Wrong. Even if "suddenly there was a big bang" explained why the Universe existed at all...
By technical definition there can't be an explanation for the universe, because the universe is defined as 'all that exists', and any prior chain of causation would be redefined as part of itself. And as I already said, you can't just assume that an agent capable of fine-tuning the parameters of physics would itself require no fine-tuning. The design-capable beings we typically encounter in life were extremely fine-tuned by millions of years of evolution.
It's also worth pointing out that a pre-20th-century cosmologist could have argued that, e.g, the earth's distance from the sun, possession of a magnetic field strong enough to deflect the solar wind, and right balance of gravity, water and greenhouse gases to allow for an atmosphere and land-based life to evolve were all stupendously unlikely to occur by chance, and that this could all be taken as evidence of the earth being consciously designed to allow for human life. ...until it turned out there were a hundred billion stars in the milky way, most of which have planetary systems, and more galaxies in the universe than there are grains of sand in all the beaches on our planet. Stupendously unlikely things can occur all the time in a large enough universe.
I'm not personally fond of the multiverse hypothesis as an answer to fine-tuning of the universe's physical constants, and as of now there's no direct evidence for other branches of a multiverse, but... there is certainly precedent in the history of cosmology for creation being more expansive than we initially assumed.
> Even though I do think there are good reasons to attribute all of these traits to the designer...
If the goal was to create intelligent life capable of civilisation, and you are both omniscient and all-powerful, why not just... create human beings (or whatever other species you fancy) ex nihilo on a planet configured to be hospitable to their civilisation from day one? What is the point to creating trillions of stellar systems that are utterly devoid of life, and billions of years of terrestrial history where life is restricted to anaerobic microbes with no trace of sentience, followed by aeons of animal carnage and millennia of stone age savagery, before some sufficiently-sensitive ape finally manages to tune in to the right astral frequency to receive God's divine word and moral guidance? And, I dunno, maybe toss in a few words about penicillin along with the ten commandments?
In short... why doesn't the history of the universe at least loosely resemble what's written in the bible? It seems like a bafflingly inefficient way for an omnipotent entity to achieve the presumed goal of "create life / sapience / civilisation and be nice to it" that the earth *isn't* 6000 years old and at the centre of the cosmos.
You say Scott is in the bargaining stage but you're in yhe denial stage. What are you doing? Trying to overturn the laws of physics with unreliable eyewitness testimony? Surely you understand how absurd that is.
By talking about "the laws of physics" you've already accepted weak deism by another name
Does "weak deism" entail a conscious designer?
Don't single out one side for disrespecting the law of physics when the other side is making incredibly fanciful claims like "all human beings are mathematical objects" and "all mathematical objects exist." Lots of fanciful imagining going on on both sides.
Atheists b like God's not real the material world is just an emanation of the Psyche which is just an emanation of the Logos and we can affirm no cataphatic claims of any radical aseitous ground of being beyond that
The hole in this argument is that by accepting all possible mathematical objects exist, you have to de facto accept that, well, mathematical objects exist. Like, non-physical mathematical objects. This backdoors you into mathematical Platonism which has...implications.
Lou Keep lays it out in an old series of blog posts he never finished on the Putnam-Quine Argument from Indispensability (https://samzdat.com/2018/01/26/platonism-without-plato/).
Tegmark's Mathematical Universe theory faces similar problems to more standard physical multiverse hypotheses as a response to the fine-tuning argument. First, it predicts that most observers would be "Boltzmann Brains". It's not right that, as the post suggests, "a conscious observer inevitably finds themselves inside a mathematical object capable of hosting life." Although most mathematically possible universes have parameters that don't allow for complex life to evolve in the way we think it did in our universe, that doesn't mean there are no observers at all in those universes. Even in a universe at a state of thermal equilibrium (maximum entropy), there should be very infrequent chance fluctuations that lead to Boltzmann Brains: particles that have organized themselves into a functioning brain in a sea of chaos surrounding them. And while these fluctuations are very infrequent, since a fine-tuned universe is *so* unlikely, in the space of all possible universes, there are still vastly more Boltzmann Brain observers, most of whose experiences are a jumbled mess, than there are observers with highly ordered experiences as of a fine-tuned universe. So if we are random observers in the space of all possible universes, it's vastly more likely that our experiences would be a jumbled mess than that they would be of the ordered kind we actually have. (How much more likely will depend on how we sort out the simplicity weighting, but I don't think any principled weighting will avoid this conclusion.) On the plausible assumption that it's more likely that our experiences would be ordered if the universe was created by God, our experiences are then evidence for God over all possible universes existing.
Second, recent work on the fine-tuning argument by Robin Collins has looked not just at fine-tuning for life but also for the discoverability of the universe by science. In brief, various physical parameters seem to be optimized not only for life but also for making the universe discoverable. The most striking example is the strength of the cosmic microwave background radiation, our main source of evidence about the Big Bang. This is a function of the photon : baryon ratio in the universe. It turns out that the photon : baryon ratio is at the value that maximizes the strength of the cosmic microwave background radiation. There are several other examples that Collins has discovered, although this is both the most striking and the one most readily accessible to non-physicists. A presentation Collins gave on this is on YouTube here: https://www.youtube.com/watch?v=yIMFhPH3m0g
This discoverability evidence is, as far as I can tell, not explained at all by a multiverse or by Tegmark's theory. Most of the life-bearing universes -- even the highly-ordered ones, setting aside Boltzmann Brains here --- are not nearly as discoverable as ours, and there's no reason, if we're in a multiverse, to expect that we'd find ourselves in this one rather than one of those. For example, the photon : baryon ratio could be anywhere from 0 to infinity, consistently with the existence of life; that we're in the universe in which it maximizes the CMB is made no more likely by the hypothesis that we're in a multiverse than it would be otherwise.
The main thing I got out of Sean Carrol's paper “Why Boltzmann Brains Are Bad” (https://arxiv.org/pdf/1702.00850) is that we don't yet know whether Boltzmann brains are possible in our universe. They're an interesting hypothesis though. The second most interesting thing is that I had imagined them as "popping into and out of existence", whereas they'd actually require a good deal of time and heat dissipation to successfully form (which is part of why they might simply be physically impossible).
I don't think you're correct that the observations of a Boltzmann brain would be a jumbled mess. But that's a speculation on top of a hypothetical.
+1
In addition, Carroll says that Boltzmann Brains are an exclusion criterion. If a theory predicts Boltzmann Brains, it's wrong.
The Boltzmann brain argument doesn't seem right to me. Yes, fine-tuning means habitable universes are rare. But Boltzmann brains ought to be spectacularly rare. There are 10^27 atoms in a human brain. If they have to be in some specific arrangement to cause consciousness, this suggests...I don't know exactly how to do the problem, but it's going to be some kind of combinatorics that starts with 10^27 and gets worse from there. And that will only produce one Boltzmann-brain-moment, while a truly habitable universe could create trillions of life forms lasting for billions of observer-moments each.
I would guess that the things we know about are discoverable because there are many things and we don't know about the nondiscoverable ones.
The problem is that it's really hard to get a life-permitting universe. You need fine-tuning which is very rare, and extremely low entropy, which is especially unlikely because entropy is constantly going up. Just like it's likelier that monkeys will type a sentence of Shakespeare than the whole book, it's likelier that you'd get a brief patch of order than a whole world of it.
>extremely low entropy, which is especially unlikely because entropy is constantly going up
That's assuming the time arrow and entropy arrow are independent.
Low entropy starting conditions are *common*, not rare, because they're directly implied by weighting towards universes with simple descriptions.
I don't understand why "entropy is going up" is relevant here. This is a statement about the arrow of time within universes. Universes can still come into existence with low-entropy (in fact I think Tegmark implies that they do, since low-entropy starting conditions are "simpler"), and they can host life during their low-entropy early stages.
I agree fine-tuning is rare, but Boltzmann brains should be even rarer! If you're generating random text, the chance that it happens to be a five line computer program specifying a cellular automaton capable of life is very low, but the chance that it's a full-fledged AGI is even lower!
"If you're generating random text, the chance that it happens to be a five line computer program specifying a cellular automaton capable of life is very low, but the chance that it's a full-fledged AGI is even lower!"
I don't think that's quite an apples-to-apples comparison though. We're not generating random text, we're generating random seeds, and then the seeds are generating text. We're considering two types of seeds:
1. Seeds that have some structure that lets them regularly generate comprehensible text.
2. Seeds that lack such structure, and thus generate only random text.
The BB argument (as I'm understanding it) is that seeds of Type 2 are more common than seeds of Type 1. And any such seed will generate LOTS of text. So for every orderly universe with stars and galaxies and life you should have many, many disordered universes which can't generate those things (but each have a tiny chance per unit of spacetime to birth a BB).
I'm not sure I how seriously to take this argument, because I think it assumes things about the distribution of seeds that isn't really in evidence. But it certainly seems like SOME ratio of Type 2 to Type 1 seeds would produce an excess of BBs.
[1] Though the word "random" seems slightly suspect here, it might have to be "pseudo-random."
I agree this is true, but I don't think it changes the situation very much - the main parameter everything depends on is still the likelihood of random text generating a Boltzmann brain. I agree you multiply each side by a few constants (the orderly side by the number of observer-moments per orderly universe, the disorderly side by the number of fluctuations per disorderly universe), I just don't think these are likely to matter very much compared to the extreme unlikelihood of each fluctuation.
Not that I really trust calculations here, but https://physics.stackexchange.com/questions/336274/are-boltzmann-brains-really-possible says you need about 10^150 universes to get one Boltzmann brain. Suppose there are 10^15 observers per universe, each lasts for 10^10 moments, so total of 10^25 observer moments, that means you need 10^175 disorderly universes to equal one orderly universe. I usually hear fine-tuning proponents say the universe is fine-tuned to something like 10^50. I'm sure once they hear this argument they'll up their numbers, but for now that gives us a comfortable 10^125 margin of error.
I like trying to ground this with actual numbers: I do think that illustrates the problem much better (even when they are provisional and suspect).
Huh. This is sort of tangential, but I just noticed that if we believe in a Tegmark Universe, that belief should cause us to expect physics to ultimately explain away fine-tuning (or at least scale it back significantly). A universe with only a few free parameters that give rise to all the rest ought to be much simpler (for any coherent definition of simplicity) than one which has a great many that are all independent.
Okay, this comment may help clarify some of our disagreement. I can try to look up some numbers when I have more time later, but 1 in 10^50 is the kind of value people typically suggest for the degree of fine-tuning of a *single* parameter. If there are, say, 20 parameters and they're all independent, then the probability of them all being fine-tuned will be much lower. In addition, the value for the probability of the universe being sufficiently low entropy is typically estimated as *much* lower, more like 1 in 10^(10^100).
Again, I can try to look up numbers and sources for them later.
I think 10^150 is a WILD underestimate for the rarity of Boltzman brains. It implies there is some way to fit a conscious observer in a tweet. (In specific, within 150 digits) That is not much information.
A code golfed description of game of life or physics that bootstaps conscious life, sure, that might fit in a tweet. But that's the regular universe option. You need to fit the conscious mind directly.
Entropy going up matters because high entropy worlds can't produce stable life but can produce Boltzmann brains. So there's an infinite period during which they can produce Boltzmann brains and a finite period during which they can't (at least, by default).
This is untrue, but almost true.
There are also infinite periods at low entropy (entropy can and will decrease, if you wait long enough).
But there are exponentially more states a high entropy than at low entropy
Most states of the universe will be at almost maximum entropy, even if it starts at low entropy (and the start should not count more that any given moment).
Even if they are way more beings at low entropy by unit of "time", there are exponentially more time at high entropy.
Take any universe that has our universe's history for the little portion including your brain, and then an arbitrary history for everything else around it (for example, your table is now a watermelon as of five seconds ago). There are *vast, vast numbers* of those, for the kind of combinatorial reasons you describe. Unimaginably many. They are all defined by perfectly consistent mathematical structures. That's the Boltzmann brain problem, which is much worse here than in the ordinary case (where the brains were supposed to come from physical law, at least.)
You're going to have to put enormous weight on the "simplicity" side of the theory, and that side does not cohere with the "all mathematical structures necessarily exist" side in the least. It's an arbitrary kludge, and does not even make sense (i.e., does not appear to be actually definable). If you prefer, it is secretly another contingent physical law, sneaking into what is supposed to be a derivation of physical law from a necessary metaphysics. However you dress it up, it blows the whole thing up.
"They are all defined by perfectly consistent mathematical structures. "
Are they? This seems to be assuming facts not in evidence. For information-theoretic reasons it seems like large portions of that space cannot possibly be generated by simple mathematical structures. That the portion of the space that can be is larger than the portion of the space that describes lawful, ordered universes does not actually seem obvious.
Tegmark says *all* mathematical structures exist, not just simple ones. (He does try to weight simple ones more. I don't think that makes sense, as I've mentioned elsewhere in this discussion.)
The set of all mathematical structures must certainly be infinite. Without some sort of weighting--I'm not sure it *has* to be simplicity, but I'm also not sure it doesn't--you'd surely end up with infinite numbers of any sort of universe you can imagine, and some would be embedded as simple cases in vast mathematical structures higher up the complexity chain. At that point comparing the probability of one outcome vs another plainly stops making sense, so there's no way to argue that Boltzmann Brains should dominate.
(To be fair, I'm not sure that this sort of probabilistic-anthropic reasoning *ever* makes sense. But if it does, it surely needs to be done over a set where the probability masses remain finite.)
The way to argue that they would dominate is that, for every one of those more bizarre structures that was regular, there would also be the Boltzmann-brain ones, which are locally far more numerous. One can then use measure-theoretic or (more likely) topological or other types of counting arguments to suggest that all the other structure you're talking about is broadly orthogonal to the question of Boltzmann-brain counting.
Yeah, I think you have the wrong intuitions around simplicity. The Mandelbrot set is extremely simple. The million images that differ from the Mandelbrot set by one pixel are each vastly vastly more complex (unless you cheat by describing them as "the Mandelbrot set except different by one pixel", in which case they are at least one pixel more complex)
I didn't say anything about simplicity (neither did you in the post I was replying to). I can see why this retort would be relevant, though, in the context of your post. As I explained in other posts on this discussion (which you're not responsible to have read, obviously) I think the whole attempt to put some kind of measure on necessarily-existing mathematical objects using Kolmogorov complexity is hopelessly incoherent and doomed.
I agree with you that, using any of the Turing machines that is anywhere close to what a human would design, the Mandelbrot set is much lower-complexity than slight variations of it, and similar remarks would apply for Boltzmann brains. On the other hand, there are *a lot* of Boltzmann-brain universes, and if one is doing metaphysics, it appears to me to be arbitrary to conclude that any specific finite portion of them would be higher-complexity than Boltzmann brains. (Not that -- again -- I think the whole project can be made sensible in the first place.)
So, since I think that the Kolmogorov/simplicity move is incoherent, and since I think (moreover) that even if it weren't, the arbitrary-constant problem is actually far more fatal than people understand (when doing this kind of basic philosophy, as opposed to when doing machine learning heuristics or something), I think that you are stuck with the Boltzmann brains.
I think you're right that the favoring of simpler universes doesn't make any sense in the context of modal realism. It makes sense if only one universe exists to expect it to be a simpler one. But if all possible universes exist then it doesn't make sense to "expect" simpler ones more than more complex ones. If you are 1 of 100 people I march into 1 of 100 rooms that I've programmed with custom physics, the probability that you end up in the room with the simplest physics is 1/100. These are real rooms that you know exist; you're not more likely to end up in a simpler one if each room gets one person in it. Similarly, in a multiverse you're not more likely to end up observer A in a simpler universe than observer B in a more complex universe.
Scott suggests we need a simplicity weighting for the probabilities here to be well-defined, but I think we *might* be able to meaningfully *compare* probabilities under Tegmark's theory and under theism even if we don't have well-behaved absolute probabilites. It might be that we can meaningfully define ratios of probabilities, which is all you need for calculating posterior relative odds (prior relative odds x relative Bayes' factor), even if the absolute probabilities are undefined because of problems with infinity.
Thanks Scott! On the first point: yes, Boltzmann Brains are spectularly rare, but fine-tuned universes will be even rarer. Collins has a helpful analogy with scrabble tiles. Imagine dumping a bunch of Scrabble tiles on a Scrabble board. Assume that they all have to land into a slot. You're much more likely to have isolated words amidst a bunch of nonsense -- islands of order in a sea of disorder -- than you are interlocking words that look like a normal Scrabble game. The former is analogous to Boltzmann Brains, which requires low entropy just in one part of the board/universe, and the latter is analogous to a universe like our own, which requires low entropy in the whole universe.
I believe that this claim about relative frequencies should be true on grounds of entropy alone -- although simplicity weighting might impact this some. But the low initial entropy of the universe is not the only fine-tuned parameter. Estimates of the total number of independent fine-tuned parameters vary, but it might be somewhere on the order of 20. So this will push down the relative frequency of normal observers even more (unless non-fine-tuned universes are less likely to produce Boltzmann Brains, but I don't see why that would be).
However your point that a fine-tuned universe would result in "life forms lasting for billions of observer-moments each" is interesting, and is not one I've thought about in this context. Self-locating probabilities are super tricky, but I could see an argument that the number/distribution of *observations* in a theory is more important than the number/distribution of *observers*. Still, I suspect that even granting your point under Tegmark's theory there will be many times more Boltzmann Brain-style observations than normal observer-observations. But I would have to think quite a bit more to give a rigorous argument there.
I think the Scrabble analogy is our crux here.
You make it sound like the "real universe" condition is *strictly* harder than the Boltzmann brain condition, since the real universe has to include brains along with everything else.
But the claim isn't that random dust and gas coalesced into every single thing in the universe by coincidence. It's that the universe has physical laws that tend towards the creation of complex objects. Those physical laws are somewhat surprising (in that most random sets of physical laws won't allow complex objects), but not ultra-surprising (in the sense that they're probably a couple of things that would fit on a blackboard and have a single or double digit number of free parameters).
The coincidentalness of getting a blackboard worth of physical laws right, while high, is still less than the coincidentalness of getting every atom in the exact right place to form a working brain.
If this doesn't make sense to you, consider the Mandelbrot set, or some other beautiful fractal. The complexity of the fractal is actually *lower* than the complexity of some particular part of the fractal drawn manually, because the Mandelbrot set is just a short equation, and if you drew it manually you would need to coincidentally get every pixel right which would be an insane coincidence.
I think of a Tegmark universe as equivalent to the Mandelbrot set, and Boltzmann brains as saying that maybe a process of filling in pixels at random happened to generate a small part of it.
Does that make sense, or am I misunderstanding your argument?
Thanks. I think what you're saying makes sense, and I don't disagree with you that in principle comparatively simple starting conditions can give rise to comparatively complex wholes. (Indeed, as a theist I think this is in fact what happened -- I would just specify the simple ultimate starting conditions in terms of God and his intentions.) Where I disagree is with the application to the particular case of the physical laws governing our universe. Put otherwise, our disagreement is partly empirical rather than purely philosophical.
I am not a physicist, and so I could well be wrong here. But my understanding is that because entropy tends to increase, ordered complexity at time t+1 is more likely given ordered complexity at time t than otherwise. Extend this back to the beginning of the universe and we get the result that it's easier to get the ordered complexity of life later on if the universe starts out with a lot of ordered complexity.
Now, maybe your (Tegmarkian) idea here is that the kind of ordered complexity that leads to life can be mathematically described (much?) more simply than other initial conditions of the universe. But I don't think this is the case. At least, I'd want to hear more about why this is the case.
There's also still the point that this only touches on entropy, but there are lots of other finely-tuned variables, and the life-permitting ones ranges of those variables are not in general specifiable in a simpler way than the non-life-permitting ones.
On the second point ("I would guess that the things we know about are discoverable because there are many things and we don't know about the nondiscoverable ones"): there's something intuitive about this idea and I don't know exactly what I think about it. But I'm inclined to think the discoverability evidence still has considerable force even what it's taken into account. For the CMB example, there are two possibilities: if the photon:baryon ratio had been slightly different the CMB would have been undiscoverable; or, if this ratio had been slightly different, the CMB would have discoverable but harder to discover. (I *believe* Collins says the first of these is the case because the CMB is so weak, but I'm not sure.) In the latter case, there's no non-design explanation for why we would find that the value is *optimized* -- there are many worlds where we discover the CMB, investigate the photon:baryon ratio, and find that it's not optimized for discovering the CMB. In the former case, there's a clearer observation selection effect, but it seems all the more striking that the universe is set up to allow us to discover the CMB (which was crucial to the formulation of the Big Bang theory) when it's almost impossible for this to happen by chance.
(Note: I don't think Collins claims that in all the examples he looks at the relevant variable is optimized for discoverability; this is true in the CMB case but might not be in others. This is part of why I find the CMB example the most striking.)
Boltzmann Brains consist of an exponentially small fraction of high-entropy stuff, so they're extremely unreal compared to things that arise quickly from simple rules, like actual humans did. Fine tuning reduces that gap by a small amount, but the laws of physics just don't contain that much information compared to a Boltzmann Brain, even with seemingly fine tuned parameters.
Very simple (ie random noise) universes can contain boltzman brains. But those brains are very very rare.
The "fine tuning" arguments are about < 20 physical constants, that could mostly be 0.1% off without causing problems. That's about 200 bits of fine tuning. Probably less.
In other words, to get a universe full of life the normal way you need to hit fluke that's less than 1 in 2^200.
How many bits does it take to make a boltzman brain. A terabyte sounds roughly plausible as the size of an uploaded mind. So that would take a fluke of 1 in 2^8,000,000,000,000 to happen by chance.
Basically, the laws of physics as we know them (including constants) take less space to write down than any description of a conscious mind.
The entire argument misses the elephant in the room, which is a definition of a "conscious being". What is it, exactly? How can you have a subjective experience? How can you tell if anything else has a subjective conscious experience except by relating yourself to the other through communication? Could it be that there are lots of "alien" consciousness around us to which we simply cannot relate and hence do not recognize? Are all mathematical structures conscious then? If not, how can we really tell which are?
The new philosophy of God and universe will have to reconcile subjective with objective, transcendent with immanent, Western consensus-focused epistemology with Eastern observation-focused one in a dialectical synthesis. New approaches to reasoning would be required to do so. Only then a modern man has a chance to obtain a temporarily satisfying answer to the question "who am I" and "why am I here", which would, I suspect, be at the same time the answer to the question "is there a God", but in a way which you cannot currently imagine.
Before that, stuff like the mathematical universe hypothesis is an intellectual fidget that answers nothing. Come on, even in the text above - " mathematical objects are logically required to exist " - like wtf is that argument? Why logic exists then? Logic is a mathematical object itself, and there are many logics! You can invent/discover one yourself if you'd like.
Thinking of simplicity. Does all universes have the same rules set and just different starting points (which results in isosimple universes subset)? Or do they differ by the rule sets - so the games are different? Having more rules or adding limits and conditions result in less degrees of freedom and more simple in terms of behaviour and states universes? Is multiverse more simple than its universes? Moving through infinite "envelopes" of multiverses are we reducing or raising complexity/simplicity?
And the main one - is the mathematical apparatus is finite and isomorthic property of all universes? Math is the God?
The vagueness of Tegmark’s mathematical universe always annoyed me. See Jürgen Schmidhuber’s “A Computer Scientist’s View of Life, the Universe, and Everything” for a well-defined version of something similar (https://arxiv.org/pdf/quant-ph/9904050).
The problem comes in the assumption that the universe should be computable. The longer one thinks about that, the less sense it makes (here, obviously, "one" = "I"). Unless, of course, it's actually a computation. In which case, all the problems about our universe exist in the one where that computer exists.
Ever since I read permutation city and tegmarks TMU paper in college it’s been basically the closest thing I have to a religion, tbh.
A pretty interesting theory — but certainly incomplete, at minimum. The rules governing our universe are pretty simple, but "put a N foot x N foot x N foot box of atoms through every possible configuration" is even simpler and will produce just as many (or more) conscious brain states. So why do we live in a universe governed by laws of physics, rather than a permutation box?
You can get around this by applying some penalty for running time, maybe, but already the theory is looking less like a platonic ideal and more like a kludge.
At any rate, the easiest justification for God is one you left off your list — the existence of the supernatural! Christianity spread because of miracles, after all, and if you look there are lots of phenomena lying around that materialism has to tie itself into to knots to explain.
And supernatural phenomena are the one thing that Tegmark's theory categorically cannot tolerate.
Darn, I have an answer to my permutation box objection. It's easier to describe the permutation box in totality than to describe our universe. But it's much harder to specify a particular -location- in its spacetime (since it's going to run for an exponentially long period of time).
And the combination of box specification -plus- spacetime location that you would need to find a human consciousness in the permutation box, ends up being much longer than the universe-specification-plus-spacetime-location that you need to find a human consciousness in our universe.
I'm not sure if that's actually simpler than our universe.
//"logically necessary" needs a pretty convincing argument. and this argument doesn't say anything about the "why" of consciousness.
Cosmological: Why is there something rather than nothing? Because mathematical objects are logically necessary, and “existence” is just what it feels like to be a conscious observer on the inside of a mathematical object.
I'm very, very worried about the simplicity move. Viz:
1. All possible mathematical objects exist (compelling premise, makes sense independently)
2. So our chance of being any particular conscience being is kind of like sampling (makes sense)
3. But we couldn't just sample from an infinitely large set (I'm not entirely convinced on this one, but it seems to follow from our best mathematics)
4. Therefore our probability of being any particular being is simplicity weighted (????????????????????????????????????????????????????????????????? why)
One can easily sample a dot on an infinite line or section. An infinite sequence can have a limit and no limit - simplest math concept
Here's a gesture at explaining. It's obviously not rigorous.
Suppose you make an infinite list of universes and assign each one a discrete probability. You sort the list so the highest probabilities are at the top. Probabilities have to sum to 1. So as you go down the list, the probabilities have to keep getting smaller, in a way where the infinite sum converges to 1.
An important thing about complexity is that as you add complexity to a system, the number of possible arrangements of it increases. Or, as you make a system simpler, the number of possible arrangements of it decreases. For example, there are only a hundred integers with two digits (in base 10), but with three digits there are a thousand, and with a billion digits ... a lot.
Now for the tricky part. No matter how you arrange the infinite list, the average complexity has to increase as you go down the list. There are only so many simple entries, and so many more complex ones. There's a lower limit to complexity, it's easy to start there. But you can't put all the complex ones first because there's no upper limit to complexity. So however you arrange them, the complexity rises and the probability falls ... on average. With as many exceptions as you like. But still the trend must hold.
I will try to say this formally, maybe it helps someone:
Let X be arbitrary countably infinite set.
Let f be function from X to the reals for which:{x : x in X, f(x) < r} is finite for all r reals
Then, for any injective s: N -> X sequence, lim(f(s(n))) = +inf
Proof: We want to prove that for every K real there exists N natural for which for all n>=N natural f(s(n)) >= K.
By the property of f there is only finite amount of x for which f(x) < K, let's call this subset of X, A. Let I = s^(-1)[A ∩ s[N]] (finite set, because injectivity of s), then N=max(I)+1 is a good choice.
s is the ordering of beings by probability, f is some function measuring complexity
What does the probability mean if they all exist anyway?
It's a subjective prior probability that, together with your observational evidence of the universe, represents your belief about which universe you inhabit.
My subjective probability that I inhabit the universe I inhabit is 1.
Surely you can leave me out of this.
That's a mere tautology. Totally uninformative. Quite different from trying to identify the mathematical structure of the universe.
Yes, that's the point. My exist ence isn't informative. The existence of complex structure, an impersonal fact, is informative.
Roughly, it's because we have no other option for the same reason it's impossible to define a uniform probability distribution on the natural numbers or the entire real number line.
No one mentioned Wolfram’s work yet: https://writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful/
Whats the relationship? I *hope dearly* that wolfram doesn't make these arguments
He’s not talking about God at all, he has a theory of physics, and it’s computational. I can’t give it justice here, I think you’ll enjoy reading it.
Don't bother. It's a crackpot theory that bakes into it what it attempts to show.
I have to point out that you seem to be misusing the phrase "cellular automaton". A cellular automaton is a pretty specific sort of thing, not just anything with an initial state and a rule for running it forward! The term you're looking for would be something more like "dynamical system". (And of course our universe is continuous-time rather than discrete-time, and also time mixes with space, but...)
I have to point this out because, while the universe does seem to be described by simple mathematical rules, it does *not* seem to be a cellular automaton! (Despite what Stephen Wolfram claims.) In particular, trying to model the universe as a cellular automaton is going to run into problems with Lorentz invariance. (And trying to model it as a *classical* cellular automaton, as Stephen Wolfram seemingly wants to do, is going to run into problems with quantum mechanics...)
even wolfphram has the hypergraphs which is a noncentral meaning for cellular automaton
While this might be an argument against all-encompassing God which rules over an infinite cosmos, isn’t it also an argument for vast (or perhaps infinite) number of deities ruling over their own local pockets?
If all mathematical structures exist, doesn’t that means that every possible God exists too? (Abrahamic God, Jesus, Allah, Marduk , Shiva, Cthulhu , Perun, Thor, Thor who looks like Chris Hemsworth from Avengers…. etc)
Fine tuning is really only a problem if you think you know everything. Well, everything that it is possible to know about the constants of the standard model anyway. We don't know where the constants come from, sure. One of the possibilities a deity created them like that because he wanted to see interesting things. Another possibility is that they just that's how they are, no deity. Another possibility is that they arise from new physics that we haven't yet discovered. That's the humility option. That's the batshit obvious explanation, to me, at least. It's also the science option, like we need to go out and finding what's happening, rather than siting around in the philosophy department claiming you know. As far as I can see the massive recent advancement in knowledge is due to collecting data, thinking up explanations, and testing them. Why stop? I don't believe there was a guarantee that finding these things would be easy.
There are a number of big unsolved fundamental problems in physics including *relatively* mundane stuff like finding a way to fit general relativity and quantum mechanics together. It's unknown-unknowns territory but the fundamental constants might pop out of such a theory. Might, we don't know. To me, if you can't do GR-QM, you are in not really in a position to make any real claim about being in any kind of knowledge end-state. Hey, you're not god, stop pretending you are. Get to work.
Human religions always blow themselves up on their own contradictions, you don't even need alternative theories to reject them. Meanwhile this "all mathematical objects" thing seems to just be a variation on many worlds and the anthropic principle? Which we have had for a long time?
> By existing, you are a random draw from the set of possible conscious beings. You can’t make a random draw from an infinite set, but the accepted solution is some kind of measure weighted by simplicity. So even though every possible mathematical object exists, simpler ones exist more.
It's accepted that *this is what a solution would have to look like*, perhaps, but that's less impressive than it sounds. Where you have a notion of probability you *must* have a measure to go with it, by definition. And of course you're going to need to penalize complexity somehow, or you'll end up assigning measure zero to worlds with simple laws like ours.
But it's far from clear that such a measure even makes sense. First, there is no set of all mathematical objects; there are far too many of them for that. Measure theory doesn't have a chance in hell without first radically cutting things down - probably to some notion of "sufficiently finitary" objects in the sense of local presentability or something. And then once you've done that, you still need to figure out how to divide up probabilities between the measure over universes and the cosmological measures weighting different observers within one universe - and we don't know if such a measure is even possible for ours! "Basic probability theory might just not work in physics" is an option that Alan Guth, for instance, has started seriously floating.
Check out Stephen Wolfram's Physics Project:
https://writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful/
It's like Tegmark's philosophy but much more detailed. It even derives things like quantum mechanics from the set of all rules. Really neat!
The Ruliad Rules!
In the beginning God created the axioms and the postulates...
I'm probably missing something, but it follows from the hypothesis that all possible mathematical structures exist that there are other mathematical structures in which I am conscious. Yet, I feel like I am only conscious in one such structure -- this universe. How does the hypothesis explain this?
You mathematically came to an idea of other univerese. You just can't sensually observe them. But I belive consciousness is a type of observation with ability to derive pinning mathematical properties and rules, and senses are just instrumental helpers here
Either you've had the exact same experiences (including the present moment) or you've had different experiences. A being who has had different experiences isn't you. A being who has had the same experiences is also you, but it doesn't matter, because for all you know you're all of those beings at the same time (there's no way to distinguish between them).
You, or a duplicate of you?
Wait, wait, wait! Fine-tuning does not necessarily require a god being to do the tuning. Bentham wants there to be a god being, so he latches on to F-T as an argument for a creator being. But at least a decade ago, Lee Smolin proposed a system of universal natural selection where the laws and constants that happen to promote the emergence of life (as in our current universe) are also ideal for spawning more universes. Bassani and Maguijo, in their recent paper "How to make a Universe" suggest a mechanism for how laws evolve in a newly instantiated universe through Markov chains, and if they produce matter and gravity, the laws will converge on a type of universe we exist in.
https://arxiv.org/html/2502.00081v1
Although much of their math is beyond me, what I find most interesting is their comment: "For laws to 'appear' they must have evolved out of lawlessness, which could itself be defined as extreme variability in these laws." To my mind, that's the best argument of why a god-being could *not* exist. Whereas Bentham and other god-clutchers are looking for a law-giver to have inscribed 26 constants on the tablets of our universe, chaos was the original creator of our universe.
Reminds me of the story from Zhuangzi...
The Ruler of the Southern Ocean was Shu, the Ruler of the Northern Ocean was Hu, and the Ruler of the Centre was Chaos. Shu and Hu were continually meeting in the land of Chaos, who treated them very well. They consulted together how they might repay his kindness, and said, 'Men all have seven orifices for the purpose of seeing, hearing, eating, and breathing, while this (poor) Ruler alone has not one. Let us try and make them for him.' Accordingly, they dug one orifice in him every day, and at the end of seven days, Chaos died.
So UnoVersce is the most complex thing with less the rulles. Which is a bit contradictory to simple things are governed by simple set of rulles. Kind of casuality-simlicity uncertainty
Reading Zhuangzi is a rewarding enterprise, which I much recommend.
>mathematical objects are logically necessary
Why, though? Doesn't seem more convincing to me that "God is logically necessary", at any rate.
I think "logically necessary" is just a word for the kind of thing that math is, and the claim that math is logically necessary doesn't require further proof.
I think you're conflating two things - mathematical objects are logically necessary in the abstract game we play within our minds, where initial axioms and rules of inference are accepted by fiat. But MUH posits that math "exists" independently of our minds, which is far from uncontroversial, let alone logically necessary.
I think it's not raising math to the level of existence; it's lowering existence to the level of math.
When you explicitly acknowledge making such a move then sure, whatever, because it would instantly make it obvious that your position is extremely abstruse. Most people would readily agree that the sandwich they're currently eating exists, but it would take plenty of effort to sell them on the existence of a Platonic realm where Fourier transforms reside, which are also actually the same sort of thing as sandwiches.
Mathematical theorems follow by necessity from axioms which are not necessarily necessary.
But the universe isn't *that* simple, is it? I thought scientists were still trying to crack string theory, make a grand unified theory, etc? If our universe was truly Game-of-Life-simple, shouldn't we have cracked that hundreds of years ago?
Why? I don't think things like the identity of the weak and electric forces was obvious "hundreds of years ago". Many scientific discoveries are elegant equations, and many of them were discovered pretty late in the grand scheme of things.
So the universe is simple yet not obvious?
But who's to say the rest of them are? Why should we be able to understand the universe?
This seems to be one of those theories that gets where it's going by destroying one of the words that it uses.
When religious believers say that God "exists", we mean that He interacts with the same world we all interact with. He exists in the way that rhinoceroses do and unicorns don't. If you look really hard, you can find a rhinoceros and you can find God, but you're not going to find a unicorn.
The various proofs for the existence of God are descriptions of how He interacts with the world to make it be how we observe it to be, and how, if He hadn't done so, we would observe something different. Look, the top is spinning; it spins because I spun it. It's not just lying there. Look, the world has motion in it, it's not just lying there. What was it from outside the world that put all this motion into it?
Under this theory of Tegmark's, if I understand it correctly, unicorns exist, along with every other fantastical thing you can think of. So the word "exist" isn't useful. Once you've accepted this definition of the word "exist", why would you think to argue about whether something exists or not? Who cares? Whether something "exists", per Tegmark, has nothing to do with whether I might encounter that thing in the world. You might as well prove that God doesn't tegflugeristerisk.
I'm not even sure that this Tegmark theory is operating on a close enough conceptual plane to theology to contradict it. You could probably even syncretize Tegmarkian cosmogony with a sort of Deist cosmogony, where you rename God "random draw". Grant that Tegmark's mathematic necessity is true, and it spins up a zillion mathematical objects. I'm experiencing being inside one of them. Cool. Why this particular one, and not some anti-anthropic hell? Well, either tautology (living beings can only live inside mathematical objects in which living beings can live), or something named "random draw", which might as well be a god, since it made me and the particular world I'm living in. That's ... actually, not that different from Hinduism, I think? There are innumerable worlds you might have ended up in, and the answer to "why?" is either "it is what it is" or "random chance".
I mean I guess it's also dead simple to syncretize Tegmarkism with Christianity. Tegmarkian mathematical necessity spins up a mathematical object with one three-part conscious being inside of it plus a supercomputer capable of simulating Earth & nearby space. There are probably more complex mathematical objects that a random selection from infinity would pick, this doesn't seem out of bounds. That conscious being, named "God", programs the supercomputer and starts it running, and we humans are the conscious beings living inside that simulation. Nice and tidy. Questions about mathematical necessity go back to Tegmark and questions about the anthropic principle go back to God. Chronos creates Zeus, Zeus creates humanity.
No need to speculate on how to integrate this with Christianity, the Church Fathers did that before the ink was dry on the epistles: what the platonists called the sum of Forms or Nous is to be identified with the only begotten Son through whom all things are made.
In the beginning was Tegmarkian Mathematical Necessity, and Tegmarkian Mathematical Necessity was with God, and Tegmarkian Mathematical Necessity was god...
"In the beginning was Tegmarkian Mathematical Necessity, and Tegmarkian Mathematical Necessity was with God, and Tegmarkian Mathematical Necessity was god"
See the Shield of the Trinity:
https://en.wikipedia.org/wiki/Shield_of_the_Trinity
This is why theology is fun! and I'm nowhere near knowledgeable about it to speak. But I'm sure Eastern Orthodox theologians, with their very well-developed work on divine energies, would love to tackle this.
https://www.pappaspatristicinstitute.com/post/what-are-the-divine-energies
I think it's tempting to call this Platonism, but I think it goes beyond merely affirming the existence of abstract notions and saying they had some part in forming the world. Or even raising them to the level of divinity in the person of Christ. This theory goes much further. It denies the existence of anything other than abstract notions. Abstract notions are all that there is.
I'm not up to date on my Plotinus; maybe the neo-Platonists had some such idea? It feels like Leibniz, too?
Unicorns don't exist in this universe. That seems sufficient to justify all of the normal meaning of "exist" to me.
I don't think this is any different than saying that (given the vast number of galaxies in the universe) probably some alien life form that looks like a unicorn exists on some other planet. Whatever, that doesn't threaten our epistemology at all.
I feel confused that you still have to talk about probability distribution after you've already asserted that all possible universes exist.
To determine the probability of being a specific being in the multiverse, you'd need to multiply the chances of being in the world the being is in with the chance of being that specific being over every other being in that world.
I still find that confusing: saying "all mathematical objects exist and our universe is one of them" and then asking what the probably is of being a specific being in the multiverse... feels like asking "what is the probability that the sun will rise yesterday?"
Well then your problem is with the entire field of anthropics. This problem still exists when you ask the question of "what is the probability of being born in the US?"
The question "what is the probability of being born in the US?" implies some assumed process in which you are reincarnated and, say, randomly assigned to some baby born in the next day. Even though that's not the case, new babies are in fact being born, so it does has vague meaningful interpretation.
While I can imagine a similar process of being assigned to entities in the mathematical universe, isn't the whole point that all mathematical entities already exist? A more analogous question would seem to be "what is the probability that I will be born in the US?" - a question rarely asked in any field!
It may be an interesting hypothetical but there seems no reason to require it as part of the theory (which in Scott's post at least, it seems to be).
He smuggles in this argument about simple things being more likely, which I don't really see any evidence for.
I have not read Tegmark, but the description of his ideas here seems like it's mixing map and territory (i.e. jumping from "math describes the universe" to "the math is the universe"). Am I misunderstanding?
The “self” is an anthropomorphic convenience. There are only particles and vectors. Only 2% of the atoms in me today were in me a year ago. Human thoughts, motives and conduct are deeply epiphenomenal. Centering consciousness in one’s ontology is deeply misguided.
And yet somehow you remember a year ago. Something is there that keeps track of what your particles are doing.
I don't think this centers consciousness, except insofar as part of what we have to explain is that we notice complex objects like ourselves exist.
Within a decade or two, AI may have made the problem of consciousness seem like an old fashioned hangup. Seems pretty clear to me that purely physical systems can do all the things we expect of a homunculus.
"all possible mathematical objects exist"
How would you define consciousness? My best guess is ability to uncover and understand math, describing universe. But this definition is not mathematically solid. One step further, and we have religious cult of mathematicians ))
And what is will? Although some doesn't believe it really exists and saying we are all preprogrammed and caused.
Does consciousness need to have a mathematically solid definition? "Table" does not have a mathematically solid definition, but this does not invalidate the existence of tables nor the Mathematical Universe Hypothesis.
One can define table interms of a Sets Theory
I don't get it. What's the point of this? Is any of that even remotely falsifiable? Does this hypothesis make any predictions that can ever be observed? If not, it's not a theory, merely intellectual navel-gazing, and it cannot tell us anything about the nature of our reality.
Some people care why the universe exists. It seems cool to have an explanation that makes sense. If this doesn't interest you, you don't have to listen.
I do care why the universe exists, that's not the issue. The issue is that there are already many purported explanations for the existence of reality, and this hypothesis doesn't solve the question. It still has an essential assumption ("all possible mathematical objects exist") which is neither observable nor falsifiable, and it doesn't make any predictions that are observable or falsifiable, so why should Tegmark's idea be more convincing than any other explanation that isn't immediately self-contradictory?
Sure, it can be fun to think about mathematical constructs, and there's nothing wrong with that. But you seem to think that this hypothesis offers a deeper truth than any other explanation for the existence of reality, and I wish to understand why.
In particular, I don't see how this hypothesis answers these Great Questions:
> Cosmological: Why is there something rather than nothing? Because mathematical objects are logically necessary, and “existence” is just what it feels like to be a conscious observer on the inside of a mathematical object.
They're only "logically necessary" because the hypothesis assumes that "all possible mathematical objects exist", but there's no reason for this assumption, except to make the hypothesis work.
> First cause argument: All things must have a cause. […] But when you consider the automaton as a mathematical object, it doesn’t need a cause; you can start an automaton any way you want; […]
Then what's the cause for the existence of the automaton itself and for the rules it follows? If the existence of all mathematical objects doesn't need a prior cause, then how is that different from saying the existence of some God doesn't need a prior cause?
Is the quest for understanding the reason for existence misguided on a fundamental level? Our intuition of cause-and-effect developed in a small subset of reality, formed by sensory input of macro-level effects. Human brains can barely comprehend quantum effects like true randomness, no one knows for sure what quantum collapse really is – and that's for a theory with observable predictions. So why do we assume that our intuition about cause-and-effect even applies to reality as a whole, when the nature of the origins of the universe is so far removed from the world which shaped our intuitive capacity?
Have you read the universal prior is malign? If there are extra-universal demons wanting to harm me, I would like the philosophical (or any other kind really) tools to think about/defend from them effectively. This theory is one such in my view.
I would not describe the malignity of the universal prior that way.
Can you elaborate?
Isn't this falsifiable? You can try to formulate things more rigorously, figure out what it should look like to be the modal observer if the hypothesis is the case, and check how closely that matches our world.
We should assume that cause-and-effect applies to reality as a whole, or we will fall into plenty of trouble when we attempt to explain things. Presumably you would not be happy if I tried to tell you that some phenomenon (say, your wallet vanishing) happened causelessly.
> We should assume that cause-and-effect applies to reality as a whole, […]
I meant that specifically in the cosmological context. We shouldn't assume that the same rules which apply to our everyday observable life, also apply to the Big Bang or to the origin of the physical laws. The situation might be similar as with quantum mechanics, which follows rules that are very alien to the rules of everyday life, but at least with QM, we can conduct experiments and observe the outcome, and so we don't have to rely on an intuitive understanding.
For me to be more comfortable with that, I'd want some sort of bounds or explanation why causelessness would be restricted to some sphere. In QM, those who prefer there to be no cause for things at least can restrict it; it would only specifically be the resolution of wave-function collapses that is done purely at random. I would want a similar bounding argument for other examples. But that seems to be a real problem if we're talking about the world coming to exist, because, surely, if there's some source of randomness in the very coming-to-be of the world, then surely, from the greater to the lesser, we should accept that there might continue to be such events happening, even on a macroscopic scale, now.
It saddens me to see such otherwise smart and productive people waste so much time writing such confused and useless words, arguing about bleggs and rubes long after the tails have come apart, trying to use a map way beyond the territory it was adequate to represent.
None of those 5 "why" questions need answering for they are not well formed. "Cause and effect" is a useful notion when applied to things we can control and/or repeat and observe, but is not a useful notion to apply to "the universe existing". Clearly the universe exists! Let's spend our effort figuring out what we can do in it and what we should do next!
It makes no sense to claim "There would be something it was like to be" a being inside the game of life. "Qualia" is a useful concept within a mind, because knowing the difference between seeing red and seeing green helps me choose foods to eat, and knowing the difference between feeling feverish and feeling hungry helps me choose what to do, etc. But qualia is not a useful concept across minds; it is useless to argue over whether your experience of seeing red does or doesn't correspond to mine, or whether my neighbor has qualia at all or is in fact a p-zombie, or whether the game-of-life being is or isn't conscious. I will never wake up inside your mind and need to make choices based on my familiarity with your qualia. I will never need to bargain with the simulated entity in a way that is helped by my theory of its mind.
"Probability" makes sense in frequentist uses, and in estimated expected values for causal decisions in states drawn from a known distribution. But there is zero merit in trying to assign a probability to every universe or simulation you might be inside. Whatever universe/simulation you're in is the one and only you ever have or ever will be in; there is no distribution of alternatives that you can possibly know anything about, and no action you could possibly want to take in response even if you could.
Yes. It makes a prediction. A very big one.
This theory predicts that there is no God, and that you will not go to Heaven or Hell, nor resurrect come the apocalypse, nor reincarnate, or anything like that. What an important prediction!
If you die and go to Hell or Heaven, you will have experimentally falsified this theory.
I'm not sure if this was written in jest. In case it wasn't:
> This theory predicts that there is no God, and that you will not go to Heaven or Hell, nor resurrect come the apocalypse, nor reincarnate, or anything like that.
The theory makes no such prediction. If heaven and hell in the Christian sense are possible mathematical objects, then they exist according to the hypothesis – at least in some of the existing universes. If not, then they don't. The hypothesis doesn't provide any clues as to whether heaven, hell, reincarnation etc. are possible mathematical objects, or whether we live in a universe that happened to get a heaven (or a hell), so even if someone dies and goes to heaven, they have not gathered any evidence either way.
I mean that the theory undermines the arguments theists use for the existence of God. It's a big part of Scott's post.
For many people, without those arguments, the existence of God becomes less likely.
Conversely, if God exists, this theory becomes less likely.
Well, I think it's clear that they would have gathered evidence (in that heaven/hell would be evidence towards theism, which in turn might be evidence against the necessity of this theory), but you're right that it wouldn't rule it out as impossible.
It actually does predict you will go somewhere after dying, since there's always going to be a possible continuation of you that didn't die, though I don't see any way to intentionally effect where you go.
The development of new explanations is important to inference-to-the-best-explanation , which is important to science.
An "explanation" which doesn't make observable predictions and which therefore can't be falsified, is neither science nor important to science. If you believe this hypothesis could be developed to produce observable predictions, I'd like to know how.
An explanation can be preferred on the basis of simp!icity, etc. Science uses Occans razor
Occam's Razor is a heuristic to select among a set of scientific hypotheses _that make the same predictions_, and that's the important part. If a hypothesis doesn't make an observable prediction, as is the case here, then it's not a scientific hypothesis and Occam's Razor does not apply.
whatever. I am not arguing against falsifiability. MUH seems falsifiable , given the many objections raised here.
Suppose math is universal but rules and simclicity measure are different across universes. Shouldn't we have already predicted something that can't be observed and experimentally proved in our particular universe?
I give you string theory. :)
Good point
"All possible mathematical objects exist."
Your post doesn't really evaluate this "hypothesis". But it's not even false, it's nonsense.
What does it mean to say something exists? This is clear if it's a cup or a plate or a ham sandwich... you can go out into the world and see or touch it. If you're talking about a more abstract thing like climate change or an electron you can see its empirical manifestations.
The concept of existence cannot be applied to mathematical "objects". I can't go out into the world and collect evidence for the existence of the number three or the square root function. These are ways of describing the intrinsic structure of the world we experience but they are not in it.
Yeah. Like do all of the things that exist in Tegmarks universe exist like me, the train I am riding, and you exist. Or do they exist like 1+1=2 exists ?
If only the second, well then this isn't even an extension of mathematical platonism which doesn't tell you much about God even if you believe it.
If both, well that seems very weird. What reasons do we have to believe it ?
I imagine they 'exist' in the same way the world of a videogame running on a console that was accidentally left on overnight 'exists'.
According to Scott above Tegmark thinks that even if there is no computer running the program with consciousness in it the consciousness is still conscious
Agreed. It's mathematically possible for a lattice composed of alternating matter and antimatter objects in contact with each other to exist, but I doubt it does in reality.
This sounds suspect to me. I am not sure if it is possible to reconcile with Godel incompleteness. If mathematical objects are all that exist then what about theorems that we know are true but cannot prove with the existing mathematical objects we have?
Things that we know are true but cannot be proved are taken as axioms. If a statement is independent of our axioms but we cannot prove it, I'd argue that it's not that we know it is true so much as the truth of the theorem is irrelevant to the thing that we are reasoning about.
It is very much relevant in this case since the thesis is 'All possible mathematical objects exist'.
Maybe solely using the word 'true' was imprecise of me, what I really mean is the relation between truth and provability. We are talking about provability *within a certain set of axioms*, these axioms being the axioms of mathematics in this case. I can create a mathematical statement that is true but not provable within these axioms.
You can add that unprovable statement as an axiom itself, but that creates a new axiomatic system with new unprovable statements. That is what Godel incompleteness means, that we cannot create a 'complete' axiomatic system, which is why I believe the thesis is not reconcilable with this.
Can you give an example of a statement that is true but has no proof in some standard system (eg ZFC)? The obvious answer is a Godel Sentence, but we don't "know" it is true without assuming the system's consistency, which we also don't know to be true.
"Know" to be true is sort of a misnomer since the truth of a statement is always relative to a set of axioms, but that is not the point. The point is if we assume an axiomatic system like ZFC that satisfies conditions for Godel incompleteness and say something like 'under these axioms, all possible objects exist', we run into the problem that we either can derive contradictions, or don't have enough axioms to prove truth (remember, *relative to this set of axioms*) for every possible sentence.
In the context of existence, this would mean that we have objects existing that are contradictory (think, a square circle), or objects that should exist according to our system but we can't prove they do.
Thus, I do not believe this is really a philosophically acceptable grounding for ontology.
"Things that we know are true but cannot be proved are taken as axioms."
Which brings us crashing up against "how do you know it's true?" People (including myself) don't take as sufficient "I just know X is true" (including "I just know God exists by the feeling in my heart").
For believers, God is an axiom. For mathematicians, it's apparently some concepts.
Things that we *believe* to be true...
Godel's incompleteness theorem is strictly about the limits of formal logic systems. It means you cannot know all mathematical truths, it says nothing about the absolute existence of those truths.
Love your blog, love the content, only superficially considered the arguments, but I agree with commenters saying there are pretty odd assertions in here.
Guy has to have some fun while the baby is sleeping I guess.
We must be in the automaton that has a God inside of it
For anyone in the comments section by the way. I think the world so badly lacks for people to help others cross the bridge from deism to faith. It can seem like a colossal chasm to people who are skeptics. And I think there’s more to be written there.
I doubt that any more writing would matter much for nudging people to faith. Experience matters much more. If those who have ears will hear, those who have eyes will see.
If the Universe amounts to a basic mathematical model then I believe this must satisfy a sort of "net nothing" condition. It should also incorporate duals of itself within it, kind of embyonic copies of itself, and that implies it must be infinite.
It would also be nice, and seem to match observations (of extensive fields and local excitations) if its degrees of freedom are conformal, i.e. "inverted", with one or more replaced with their reciprocals to give a result which satisfies the same conditions. If the dynamics involves these inversions constantly recurring and interacting then rational values of them start to become relevant, as resonances, in fact the predominant means of change.
The variety (multi-dimensional hypersurface) defined by the simultaneous pair x1 . x2 . ... = k (for a fixed non-zero rational k) and x1 + x2 + ... = 0 is what is called a Calabi-Yau variety, and appears in keeping with the "net nothing" principle, i.e. a set of degrees of freedom whose product is unity (if k = 1, what I call "on-shell") and sum is zero. For three variables, it is an elliptic curve. But for four variables it has a rich structure.
The simultaneous pair R(k): x y z t = k and x + y + z + t = 0 defines a surface, and to find rational points on this one wishes to find rational curves on the surface. Euler found a first one in around 1740, but did not explain his method. Prof Elkies found a second of comparable complexity in the 1980s, or thereabouts, and I conjecture there is one more of similar complexity. (There are an infinite number of rational curves on the surface, but only two or, as I conjecture, three "simple"(ish) ones.) Note that Euler and Elkies considered R(k) in the birationally equivalent form of the single equation
(x^2 - 1)(y^2 - 1) = k z^4
I have found a general two-parameter solution for the surface when k is the square of a rational number, and from that every rational curve on the surface can be found (for any k) by a finite, albeit hellishly intricate, process. So this is work in progress. I have also found birational transforms which map this surface to one of the same form with k replaced by -k, i.e. R(-k) and another that maps it to R(1/k).
Rational points are sort of "concentrated" on the two (or three?) simple rational curves. So their overall distribution is analogous to one of those color vision test images where a pattern of dots stands out faintly from a random background of them (unless one is color blind!) I contend that ultimately this leads to a very slight tendency of excitations, stemming from rational resonances, to occur in three families and might explain the otherwise baffling and as yet unexplained fact that there are three families of particles in the Standard Model.
I mentioned above that there is a (complicated!) birational transform from R(k) to R(-k). This implies that the density of rational points (as a function of their "height", which is a measure of their simplicity) for k and -k are roughly equal. But they have subtle differences in their exact distribution. So if the equations for k correspond somehow to matter, and those for -k to antimatter then the differences in the exact sizes of rational points imply a slight asymmetry, which would explain the preponderance of one (with perhaps slightly more lower-height points say) over the other.
Well that is a brief summary of where I'm at so far. I wouldn't expect any physicist to give the ideas the time of day, and would quite understand, because it seems so remote from any prevailing physics rubrik. Also, the resonances produced by these rational values must seem absurdly weak to have any discernable effect. But if continued long enough, dripping water can wear a hole in the hardest rock, and the most fundamental processes being almost a limiting case of vanishingly small interactions continued almost without limit seems generally in keeping with the extremes already manifest in fundamental physics.
Note also that if the geometry of the Universe is ultimately based on multiple interacting copies of the variety R(k) (or its infinite dimensional analog) then that pretty much fixes the properties of fundamental entities and their behavior within it. This in turn means the basic laws of physics within each "arena" of the Universe, one being our universe (lowercase "u"!), will be the same, with no variations due to fine tuning.
So, who knows, perhaps one day, Diophantine analysis (the study of integer and rational points on varieties) will take centre stage in solving some of the deepest mysteries of physics, even if it seems among the least applicable areas of maths today! G H Hardy would be furious! :-)
Edit: Forgot to mention that the "on shell" equation R(1) i.e. equivalent to (x^2 - 1)(y^2 - 1) = z^4 has, despite appearances, three-fold symmetry because it is birationally equivalent over Q to the simultaneous set (in which any pair implies the third) :
(p^2 - 1)(q^2 - 1) = u^2
(q^2 - 1)(r^2 - 1) = v^2
(r^2 - 1)(p^2 - 1) = w^2
So perhaps that is the origin of color charges (assuming, as always, that the whole idea has any semblance of veracity)
I don't I don't find fine-tuning super convincing because:
1. other "not fine tuned" Universes might have interesting shit going on, if not life specifically, we just think life is the important thing because we are life, but if you look around at our entire Universe you'd think God really cared about galaxies and shit and life is just some detritus
2. I don't trust our scientists to figure out what a Universe with wildly different parameters looks like.
One example of "fine-tuning" is the triple-alpha process. But originally, the theories of nuclear physics said that the triple alpha process (or any other process to make heavier elements) was impossible. This raised obvious issues. Someone posited the existence of a particular energy state of Carbon without much theoretical or experimental backing simply because it solved the puzzle of why heavier elements could exist, and ended up being right.
Put differently, our understanding of the laws of physics in *our own* Universe, as of like 1950, was that it was impossible to sustain life. How can we be so confident in saying that life couldn't exist in a Universe with wildly different physical laws?
Somewhere in another Universe, aliens think it's fine-tuned because "if the Universe had [the laws of physics our Universe] then there'd be no heavier elements!"
Dude without fine tuning you wouldn’t have any heavy elements, stars, or even stable atoms.
There's one very important point of clarification that is missing, which has thrown me off from understanding the point of this post.
The title suggests that Tegmark has defeated most proofs of God. But AFAICT, it's actually more like: "If Tegmark's hypothesis is true, then it defeats most proofs of God." And doesn't mention any evidence for this hypothesis (that existing in possibility-space is enough for a being to in fact be experiencing consciousness) being true.
What am I missing?
I think the proofs of God are supposed to work like:
1. Here is a feature of the universe that would be impossible without God.
2. Therefore, God exists
...and if you can prove that the feature is possible in some other way, then you've reduced it to "Either God exists or the other thing exists", and then you can start discussing whether God or the other thing is more likely, and if God seems unlikely to you then the other thing starts sounding pretty attractive.
What do you think of the Hindu theory that "God" is an entity that has the power to create the universe, but has no compulsion to do so - and the reason that an imperfect universe exists is because god created the universe just for kicks?
https://en.wikipedia.org/wiki/Lila_(Hinduism)
It solves a problem with Divine Simplicity.
You can say that shortest implementations in different languages differ by like a constant, because you can always simulate one language in another, and pretend that solves the problem.
Except that different languages will have different advantages (or disadvantages) at expressing ideas.
Which is simpler: an in-place array sort algorithm (quicksort, let's say), or in-order traversing a ternary tree (i.e., each node has three children)? If you're writing in C, the array sort algorithm is simpler; if you're writing in Haskell, the tree traversal is simpler.
So at least in this simple case, the answer to "which of these two algorithms has a shorter implementation" is dependent on contingent factors like "what programming language do you use".
Granted, I don't think this is a fatal flaw with Tegmark's idea, you could probably get around it somehow, but there are a bunch of other, bigger problems that many other commenters have already pointed out.
How is Tegmark's hypothesis any better than the "proof" for God's existence that claims that God is by definition perfect, and a perfect being that actually exists would be even better than one that is only hypothetical, therefore God exists? There's a difference between "exists as a Platonic concept" and "exists in instantiated form", and that gap needs to be bridged with something other than word games.
The main issue with Tegmark's mathematical universe is exactly the same issue most people have with Saint Anselmus proof for the existence of God: just because you can think about it doesn't mean it exists.
The ontological argument has to me always been the most personally convincing argument for God, and one of the least useful when debating with others.
Disappointed it didn't make Scott's top 5.
Can you say more about why it is convincing to you? I know you said it's relatively useless in debates, but I'm happy not to turn this into a debate -- I'm just curious about your take on the ontological argument.
Sure, but I'll defer to CS Lewis on this, as part of my issue might be my inability to express it satisfactorily.
>> A man's physical hunger does not prove that man will get any bread; he may die of starvation on a raft in the Atlantic. But surely a man's hunger does prove that he comes of a race which repairs its body by eating and inhabits a world where eatable substances exist. In the same way, though I do not believe (I wish I did) that my desire for Paradise proves that I shall enjoy it, I think it a pretty good indication that such a thing exists and that some men will.
That's from his essay "The weight of glory", which develops this much more fully, and I thoroughly recommend. But the theme is a constant in his fiction, nonfiction and poetry.
I don't think it's helpful in debates because anyone can deny these inner longings, and maybe even deny them honestly. But from a personal standpoint, I experience those longings and find God the most satisfying explanation.
That's not an ontological argument -- none of the variants of the ontological argument are based on an "inner longing" of any kind. What you're talking about is the "argument from desire", which is more of a teleological argument than an ontological one. I imagine Scott didn't bring it up because it's usually used as an argument for the existence of an afterlife (as in the Lewis passage you quoted), not necessarily for the existence of a monotheistic God.
Thanks, that's a helpful corrective.
Yes. Anselm’s proof is correct if it’s not referring to the real world but a logical space. He is saying “imagine a world where there is a perfect being - does the being exist.” Is existence a prerequisite of perfection, in other words. Yes. Clearly. To not exist is to be imperfect. So in that world where you are thinking of a perfect being, that world in your head but only in your head, the perfect being has to exist. It doesn’t apply to the real world. Similarly with mathematics.
All of these philosophical arguments for God follow the same pattern:
1). Let's assume that something almost exactly like God does exist.
2). Then, by following some logical steps, we can show that the thing from (1) actually is God.
3). QED.
Ok, sure, but there's never any coherent reason given in support of (1), other than perhaps that "it's obvious". So if it's not obvious to me, then what ?
Should we refuse to eat Beans?
I don't think so.
I like the Mathematical Universe Hypothesis, although as other commenters say it is on shaky ground. I think the weighting towards simplicity is going to come from something like the number of ways to do something. If you take a "random" computer program, most of them will have simple behaviours. Similarly, a simpler property of the universe may occur in more specific instances. This would suggest that we should expect to be in a universe with lots of symmetries. For example, a universe with translational symmetry will be equivalent to any universe that only differs by the position of the origin with respect to some absolute spacial coordinates - so all else being equal, there should be "more" of any particular translationally invariant universe than a translationally dependent one.
Of course, the next problem is how to quantify possible universes. We should expect there to be uncountably infinitely many, unless you restrict to something like all computer programs - but even then it's not clear how to enumerate computer programs without specifying an arbitrarily chosen interpreter.
"All possible mathematical objects exist."
This grinds my gears. It's been a long time but:
1. Forgot about Dre, aka Gödel? Some statements are undecidable. Can we check whether the corresponding mathematical object exists or not?
2. Does each mathematical object have a constructive proof or are we just assuming it's out there because of reductio ad absurdum?
3. Does it matter if the proof of existence takes an arbitrary number of steps, cf. recursion theory? (How many inference steps per nanosecond?)
4. Bonus: Axiom of choice or nah? I want my golden ball.
Godel's incompleteness theorem only places limits on your ability to know things about mathematical truth, not on the existence of those truths.
What is the truth value of the sentence "this sentence is false"? (For the unfamiliar reader, that was basically what Gödel encoded in Peano arithmetic, if memory serves)
Furthermore, note that Peano arithmetic is also undecidable.
Cf. Dirk Van Dalen, Logic and Structure 5ed (chapter 8 in particular).
Truth is a property of interpreting sentences in a model. The intuitive sense that the Liar sentence has no truth value formalizes to saying that languages with useful, complete interpretations must exclude such sentences. And by a theorem of Tarski, first-order arithmetic *does* exclude them, the famed Godel sentence was strictly about provability, not truth, and I suspect you have misunderstood the theorem as a result.
For the mathematical platonist, limits on our ability to know or describe things are not constraint on the things themselves. Who are you to tell the natural numbers they can't exclude prospective members for being infinite?
(I wonder if you would be surprised to learn Godel also proved a completeness theorem for first-order logic?)
Can you think of a dynamic system / cellular automaton that resolves differently based on Godel sentences?
Cellular automata are equivalent to Turing machines and the rest AFAIK, so the same issues appear.
Or do you mean differential equations lacking analytical solutions? I'm not at all an expert but there seem to be a lot of those.
A cellular automata the contains a computer searching for a proof that Peano Arithmetic is inconsistent will eventually either find one, or not, but Peano Arithmetic itself cannot tell you which. But each individual step in the process is fully determined, the issue only arises when trying summarise a potentially infinite process. This is because all models of PA agree on finite numbers, but some contain extra numbers they consider finite which means they think there's more time for stuff to happen.
"Tegmark’s hypothesis says: all possible mathematical objects exist. ...Tegmark argues this is also true if you don’t build the supercomputer and run it. The fact that the version of Life with the conscious being exists in possibility-space is enough for the being to in fact be experiencing it."
So therefore "Tegmark's Mathematical Universe Defeats Most Proofs Of God's Existence"
Gosh wow, I must now run off and become an atheist. Or not.
This just sounds like a spin on St Anselm's argument "the most perfect imaginable thing must exist; God is that thing; God must exist" argument. Except we're putting mathematics in the place of God.
https://en.wikipedia.org/wiki/Ontological_argument
I'm not convinced, but then I'm not a mathematician.
EDIT:
"But if it’s false, then the very fact that we waited this long to get it"
Well, going by the Wikipedia link in the post, Tegmark's theory is a form of Platonism. Given that Plato was knocking around in the fourth century BC, that's something over two thousand years ago that the idea of Mathematics Is The Real was floating around. So I don't think we can say "we've waited until right now for someone to think this".
It's a fun idea, and it's very inoffensive as far as "checkmate Christcucks!" arguments go, so I'm happy you guys are happy 😁
> Gosh wow, I must now run off and become an atheist. Or not.
Nah not really. It's just a hit on the kind of God whose job is to fill some esoteric gaps in scientific cosmological knowledge. Anyone who counts that as their reason for belief is believing on shaky ground indeed.
"all possible mathematical objects exist"
This requires clarification. What is a "mathematical object"? What defines whether it is "possible"?
What is the justification for the hypothesis? The linked Wikipedia article says, "According to the hypothesis, the universe is a mathematical object in and of itself. Tegmark extends this idea to hypothesize that all mathematical objects exist, which he describes as a form of Platonism or Modal realism." I am reluctant to think that could be a fair characterisation, because as described the syllogism goes, "The universe is a mathematical object. The universe exists. Therefore all mathematical objects exist." Obviously this is unsound.
"By existing, you are a random draw from the set of possible conscious beings."
This seems a completely unnecessary step. If the universe is mathematical possible (which it clearly is) and contains me (which it clearly does), then I exist. There's no randomness here. I haven't been randomly assigned to be myself. In this hypothesis, I am mathematically necessary, therefore I exist. If other consciousnesses are necessary, they also exist, but that is immaterial.
"the accepted solution is some kind of measure weighted by simplicity"
This is a bad solution to a non-problem. Showing that the set of all mathematical objects is well defined is one thing. Showing that it is possible to construct a measure across that set is something else entirely. My intuition is that this is unlikely. Sets don't come with measures as standard. If the set doesn't have a measure, it will be impossible to construct a probability density function across it, but who cares? Why do we need to know whether universes (or consciousnesses) are probable? They're either necessary, in which case they exist, or they're not, in which case they don't.
If you could construct a measure across all possible mathematical objects, it would be possible to perform a random sampling. Weighting it by simplicity is unnecessary for this purpose, so there would need to be some other reason for doing so.
Also, whatever ”all possible mathematical objects" is meant to be in this context, surely it is unsetly big, since it presumably includes at least the various known unsetly big collections of mathematical objects, say the category of all sets, groups, etc.
I don't think it changes much as long as your multiverse of mathematical objects includes everything computable and assigns them a substantial fraction of the overall measure. What's the a priori probability of finding yourself in a universe with a halting oracle? 0? 1/4? 1/2? As long as it's not something super high you come to the correct conclusion about our universe pretty quickly and the free parameter here isn't any more problematic then how simplicity of computable objects depends on the language you pick.
How about: pantheism/paentheism says that god is/contains the Universe. So all mathematical structures is/part of god. Because god is good, only those math structures exist that cannot lead to the greatest global suffering for the resultant conscious creatures. This implies ethics on the level of logical structures, but that is the whole point.
To prove the point that rationalists just keep re-inventing things, I was having exactly the same idea just 3 days ago. I never heard of this before.
I think what itches religious people about this theory is that it is inherently unfalsifiable and it competes with their favorite unfalsifiable theory of the universe. Someone with an empirical world-view can just dismiss it, but that argument is off-limits if you're religious.
Personally, I find much more interesting what it does with "cogito ergo sum".
> You can’t make a random draw from an infinite set, but the accepted solution is some kind of measure weighted by simplicity.
Not sure what this is supposed to mean. And you totally can make a random draw from an infinite set.
> you totally can make a random draw from an infinite set.
The set of all rational numbers in the interval (0, 1) is infinite - can you make a random draw from that for me?
xkcd 221.
Alternatively, the Wikipedia page about random variables, especially the real-valued part
163/347.
How extraordinary lucky that you were able to print it out in a finite amount of time!
Well it wasn’t that extraordinary was it. I used fractions. You can try it yourself.
Nice post! In high school, I wrote a post making a similar point but about modal realism https://benthams.substack.com/p/the-surprisingly-robust-case-for?utm_source=publication-search. However, I don't think it's right anymore; most of the arguments still go through and the view has significant problems. Specifically:
1) In my view, some of the best arguments for theism are about consciousness--both the fact it exists at all and that there's psychophysical harmony https://philarchive.org/archive/CUTPHA#:~:text=Roughly%2C%20psychophysical%20harmony%20consists%20in,another%20in%20strikingly%20fortunate%20ways. This won't help with that.
2) As I explain in my most on the anthropic argument (see section 2 and 4.6) I think the Tegmark view undermines induction.
3) I don't think this helps with the cosmological argument (which isn't a big deal because it's not very good) because there's no explanation of why all the mathematical structures exist. It may be logically necessary that there are purely abstract mathematical facts, but there's no reason to expect them to concretely exist (it's necessary that there are logically possible laws mathematically described like ours, but no reason they'd exist).
4) Regarding the first cause argument (again, I don't think that this is a very good argument, but mentioning it for completeness) I think proponents of it will find there to be something problematic about a mathematical structure that begins existing without a cause, even if all of them exist. Analogy:
"Hey this table just popped into being two seconds ago. Why'd it do that?"
"This isn't mysterious: every table did that!"
Now, I don't think this argument is good because I think it's deflated by B-theory and so on, but if you do, I don't think this should move you much.
5) You describe the argument from comprehensibility as "why is the universe so simple that we can understand it?" I think this is a bit of misunderstanding of the argument. What proponents claim is that the universe has a surprisingly discoverable mathematical structure even putting aside simplicity. There are various simple laws that would be hard to discover. They also note that it seems like some of the parameters in physics fell in a very tiny range that was ideal for us to discover them (see Robin Collins on this, for instance).
6) Fine-tuning: It will help here, but probably you'll get more Boltzmann brains in very simple universes (especially because if entropy keeps increasing in a world, it will have an infinite period of generating only BB's).
Consciousness does not exist though. You don't have an objective, independent from the world access to what you feel in a given moment. What you feel, and specifically what it feels like to be you are both just charges in your brain and you should not infer an ontologically different kind of substance just because you feel like it is. You should accept that even though it feels like it is something different from matter, that is merely an incorrect belief in your brain. Notice that there is no rule in the universe that you can't be wrong about this, you should consider being wrong especially if there are a wealth of evidence on the other side: ie everything else being matter and everytime someone thought to find something non-matter, it eventually turning out to be matter.
You mean "consciousness does not exist as a supernatural essence". Otherwise this is just semantics, our independent experience is what we dub consciousness.
The fact that parts of intelligent life experience are illusory or projected does not make it any less transcendent and remarkable that we each have our *own* little experience, and mechanical things do not.
It is as though we are thrown into the world out of nothing. That will always be fascinating.
I'm saying you don't have "independent experience" in exactly that fascinating way. You have your own electric charges in your brain and some more charges modelling your own mind which makes you think something inside you is fundamentally different (and hence fascinating) from a rock rolling down a hillside.
That said, I might be misunderstanding you, you might just find it fascinating that from matter, emerges a mind that is able to model the outside world. Then, while I might not call that fascinating, I'd agree with you that it is kinda neat.
> You have your own electric charges in your brain and some more charges modelling your own mind which makes you think something inside you is fundamentally different
This doesn't contradict your first sentence. We are the sum of our parts. This is as banal as saying "we aren't persons, just a collection of cells/atoms/ ad infinitum".
Kind of neat, but not fascinating? Ok.
I don't think something with which so many people disagree can be banal, so I kinda think I'm failing to convey what I want. The second part of that sentence is very important to my message: "which makes you think something inside you is fundamentally different ..". This is true for all humans (me included) and was not just a general whining from me equivalent to "damn, you people are dumb"
These posts about us being fooled by thinking we are conscious always fail on the terminology.
> you don't have "independent experience" in exactly that fascinating way. You have your own electric charges in your brain and some more charges modelling your own mind which makes you think something inside you is fundamentally different (and hence fascinating) from a rock rolling down a hillside.
Basically who is the “you” being fooled here. The rock isn’t being fooled because it can’t be. Consciousness might be an emergent property of electrical signals in brains - what else could it be - but so what. It’s still there, it’s just that and it’s more than that, and so it still has to be explained.
You are the umpteenth person in history who had stumbled on the “realisation” that consciousness is hard to explain and is rooted in physical properties and therefore we are no more consciousness than a rock, and postulated this as if it were some great reveal when it’s just hand-waving.
It’s a horrible argument that neither has explanatory power, nor any attempt at explanation. This thing that’s universal and essential to humans and evidently exists as well in the higher animals, well let’s dismiss it and move on. We are but rocks.
> who is the you being fooled?
The "you" here is some electrical signals in your brain which are such that they encode a small, imperfect model of the world. This imperfect model has a flaw which makes you think you have that magical hard to explain property, but you don't. I would also be amenable to an argument that there is no "you", but for easier communication I use "you".
It's not that I stumbled on the realisation that consciousness is hard to explain (that I did when I was 20), rather I stumbled on the realisation that it's easy to explain if you just honestly consider that you are wrong about your immediate experience of it as every other significant evidence points in that direction.
You are the equivalent of a person who on a drug trip insists that the interdimensional beings are communicating with him because he perceives that while knowing the fact that makes that unlikely (sometimes people on drug trips perceive things that are false)
Also, it has explanatory power. While it does not explain the boring part of it: what are the exact brain mechanisms which give rise to these few bad charges? I can predict, that after neuroscience advances enough, they will be able to point to some neurons of the brain and show you in detail where and why you are wrong in your perception of consciousness.
So what is this easy expanation?
"consciousness exists" does not mean the same thing as "consciousness exists immaterially". Nor does it mean "you are incapable of error".
Sry for the earlier, one sentence, snarky response I deleted. Here is one with more detail:
1,The word "consciousness" as used in common parlance implies immateriality, I know many philosophers disagree and use their own definition, but in this context, I was not concerned with them as: 1a, this forum is a public forum not exclusively for philosophers and 1b, i wanted to be a bit provocative in my first sentence and I suspected that the following clarifies sufficiently.
2, I know. My plea to consider being wrong comes from my perception that people who believe in quirky metaphysics in this way often believe that their consciousness is in some sense so "close to them" that they can't be wrong about it. It's not a logical consequence of this theory, rather a correlate belief I observed in those holding the theory.
>The word "consciousness" as used in common parlance implies immateriality, I know many philosophers disagree
The philosophers are right.
Why not say "consciousness is not dualistic"?...ot "the folk theory is wrong"?
To be clear, I believe the following:
1. No immaterial human consciousness exists.
2. The meaning of the word "consciousness" includes immateriality. (Yes, 1 was redundant for clarity's sake)
If you are familiar with error theory in metaethics, this is similar to that.
If every person when saying "apple" means a red fruit, but philosophers redefine apples to also include chairs (maybe to get more funding for researching the novel implications of wooden apples), then in my view the word "apple" can still justifiably be said to mean a specific red fruit without addressing the other meaning every time.
The context of the discussion is academic philosophy, and in academic philosophy it isn't a contradiction in terms to say consciousness is wholly material.
1) Consciousness doesn't really have to be mysterious in mathematical objects:
> "Some mathematical objects contain conscious observers. Conway’s Life might be like this: it’s Turing complete, so if a computer can be conscious then you can get consciousness in Life. If you built a supercomputer and had it run the version of Life with the conscious being, then you would be “simulating” the being, and bringing it into existence. There would be something it was like to be that being; it would have thoughts and experiences and so on."
And I think there's absolutely no reason to specifically exclude computers from consciousness. (https://mistakesweremade.substack.com/p/machine-thought-on-a-continuum)
Psychophysical harmony also doesn't have to be so mysterious (far less confident in this): why couldn't a universe be set up which has some rules for mindstuff and some for meatstuff, and another simple rule that coordinates them? I also find physicalism fairly likely, so am unconvinced a specific explanation is necessary anyway.
2) I think your anthropic argument also undermines induction. And shouldn't it be possible that a good definition for "simplicity" will appraise inductive universes more nicely than non-inductive ones? (I don't really know how this could work: the emergence of chaos from interactions between very simple laws totally seems to count against it.) I put up today a fuller discussion of this (among other things): https://mistakesweremade.substack.com/p/gods-existence-is-pretty-bad-news
3) What's the difference between a mathematical object that does exist and one that doesn't? Whether you say 1 + 1 = 2 or not, it's absolutely true and absolutely an existent fact. And 1 and 2 exist whether you name them or not. Same oughta go for every mathematical object.
4) see above
5) Granted that they're not identical, but discoverability certainly doesn't seem orthogonal to simplicity. It seems like the simpler the universe's laws, generally speaking, the more discoverable they'll be too. Low(ish) confidence in this.
6) Don't know enough to comment seriously, but on an extremely cursory read, I think I'm ok with some Boltzmann brains being predicted.
Whether there is a God or not is really only of academic interest, as long as we can be pretty sure there is no afterlife. (Plus that God does not control the sun and the rain.)
That said, I'm an academic.
There being an afterlife depends on the perspective on time. "After" implies linearity, so in that model, there may not be life after death. I think it's not a good model to work with spititually.
I don't have the chops to really understand this argument mathematically and I find the narrative explanation pretty confusing.
But I still think it's pretty easy to defeat "existence of the universe" type of "proofs" of God's existence. What caused the Big Bang? the fine tuning of the Universe? God? OK. What caused God? (there is no answer I know of to infinite recess and it's a perfectly valid refutation of "God"). Here, IMHO, all people are effectively doing is naming our ignorance "God". It's a silly move.
But, furthermore, if we were to grant a Prime Mover had to exist, then what? Does He/She/It/They do anything nowadays? Or are they like the Cthulhu's Outer Gods (often described as "gigantic", "tenebrous", "blind", "voiceless", "mindless", and "eternally dancing to some demented tune")?
Either way, you cannot do what most theists do, which is to jump from "our innate sense of causation requires a Prime Mover therefore one must exist therefore join my religion and worship my chosen earthly deity". No. Said simply, Prime Mover =/= Christian God.
And the list of reasons to doubt the existence of a Christian-like God is not only endless but pretty strong. No singular God is Good theology I know of can really explain the problem of evil, the issue of geographic and historical variations etc etc.
It's all so clearly human invention I find it difficult to understand how intelligent people are still taken in by it and I must assume it does something for them emotionally or sociologically that is so good it overwhelms the intellectual dissonance.
>What caused the Big Bang? the fine tuning of the Universe? God? OK. What caused God? (there is no answer I know of to infinite recess and it's a perfectly valid refutation of "God").
God is Pure Act, and hence doesn't need an external cause of his existence.
>It's all so clearly human invention I find it difficult to understand how intelligent people are still taken in by it
Maybe they just know something you don't.
> > What caused God?
> God (...) doesn't need an external cause
> God is Pure Act
...this is certainly a group of English words shaped like a statement. Can you explain what they mean, in a way that isn't just "God is a thing that doesn't need an external cause" with a phrase we made up to be a shortcut for the part after the "is"? Because right now it sounds like you're saying that God doesn't need an external cause because God is a thing that doesn't need an external cause; and this is not very convincing.
If it's OK to excuse God from needing an external cause, why can't we excuse the big bang from needing an external cause by just proudly declaring that the big bang is a thing that does not need an external cause?
Here you go: https://www.newadvent.org/cathen/01125b.htm
...so we handwave the problem away by declaring there must exist a thing that is an uncaused cause and we call that thing God. Got it.
No, we know there must exist an uncaused cause because otherwise we'd be forced to posit an infinite regress, which is impossible.
You're obviously unfamiliar with this topic, so, with respect, a little intellectual humility might be in order. When a position has been endorsed by some of the greatest minds in history and you think you've discovered an obvious flaw in their reasoning, it's more likely that you've overlooked something than that everyone else has.
> an infinite regress, which is impossible
Why?
> When a position has been endorsed by some of the greatest minds in history
When that position has also been rejected by some of the greatest minds in history, some greatest minds in history must be wrong.
I do see that, but the infinite regress argument also applies to the secular argument. What caused the Big Bang? well it arose out of the ground state of the universe before it came into existence. Okay, what caused the ground state? It just is, okay?!
"God just is" and "ground state of the quantum foam just is" come down to the same "something was there at the ultimate start as a necessity to kick it all off" reasoning. I might as well believe in God, then, as not.
You’re basically conceding that the Prime Mover _isn’t an argument for theism, any more than it is for atheism. If you and I were negotiating for the question, I’d pocket that as an atheist, since so many theists think this is an important argument (e.g. “There must be a First Cause, and in order to be first it must be conscious, and further it must be the same entity that told a bunch of desert people not to eat baby goats boiled in their mothers’ milk”).
Ok, but why would you take God instead of the foam if you are aware of any of the many other arguments making the Abrahamic God unlikely? Eg. You know that there are like thousand false religions arising out of man's need to explain the unknown/base community on/storytell/justify moral rules, etc.. (these are the religions you don't believe in), yet you think the one religion you believe in is not like those, it's actually true? Idk, to do this just seems really weird to me.
This is much easier to parse if you assume trueness in religion is as spectrum, not a binary, and that all of these thousands of religions are true to one extent or another. honestly, I don't get why you guys all assume that theists must be Abrahamic. Although it sure makes it easier to argue against theism when you make that assumption, doesn't it.
I saw their comments elsewhere and they are Abrahamic iirc, (if not then sorry). But note, the argument works the same way for any particular religion which has contradictions with many other religions and this is also why your defense won't work in my opinion. Trueness CAN be a spectrum with respect to the totality of various religions, but if you zoom in on particular statements of these religions, they are either true or false, that's just how statements are. So from your vantage point, you know that humans generated a lot of false religious statements (the claims of various religions you don't believe in)
>Eg. You know that there are like thousand false religions arising out of man's need to explain the unknown/base community on/storytell/justify moral rules, etc.. (these are the religions you don't believe in)
I don't think she does know that, actually. I know *I* don't know it, and I'm not sure how anyone would, at least without far more information about the early history of most religions than we currently have.
If there's only one true religion, this implies there must be many false religions. But it doesn't imply that the stock atheist answers to "why are there false religions?" are applicable to all of them (or even to any of them).
Consider this as a possible alternative. Assume as a hypothetical that the one true religion is an Abrahamic religion. In that case, we can infer that at least some false religions came from people whose ancestors received a genuine revelation, but who then lost their way and corrupted what they had been given over time -- this being the case for Jews if the true religion is Christianity, Christians if it's Judaism, and both if the true religion is Islam. We could also infer in that case that everyone alive today, regardless of their faith, has at least two ancestors (Adam and Noah) who received authentic divine revelations. Might it not be the case, then, that *all* the world's religions originated in oral traditions of real divine revelations, which were then distorted over generations to varying degrees? It would certainly explain why every ancient religion seems to have had its own version of the Great Flood myth, among other things.
Obviously this is just wild speculation and I have no way of knowing whether any of it actually happened, but I don't think it's any *more* speculative than any of the other explanations you listed.
There are tons of new religions that are unconnected to any previous religion, for example Scientology, Heaven's Gate and other cults, so we for sure can know that people like to make up religions. To be honest, I think for this you really only need to know people don't even need the examples, people absolutely LOVE to bend their stories to be more entertaining or to show themselves in a better light.
The possibility you describe IS a possibility, meaning that it is not logically contradictory that there were real supernatural events whose description over the generations splintered to multiple religions. However, in light of the other facts, it is very unlikely. For possibilities that unlikely we usually use the words "no, that is not what happened.".
>There are tons of new religions that are unconnected to any previous religion, for example Scientology, Heaven's Gate and other cults
Firstly, I don't think looking at cults is especially useful for inferring how mainstream religions spread. A "cult", by definition, is a religion that hasn't yet been able to spread outside of a small fringe group. It's like trying to infer the mechanics of flight by exclusively studying plane crashes.
That aside, both Scientology and Heaven's Gate actually are openly derivative of earlier religions; L. Ron Hubbard claimed Scientology to be the fulfilment of prophecies found in Buddhist and Hindu texts, while Heaven's Gate purported to be doing the same for Christianity. While writing this, I looked up all the other cults I could think of off the top of my head, and they all made similar claims. So, even if we lump cults and mainstream religions together, this still doesn't seem like much of a counterargument to my suggestion.
>I think for this you really only need to know people don't even need the examples, people absolutely LOVE to bend their stories to be more entertaining or to show themselves in a better light.
Well, this doesn't seem particularly related to the list you gave before (aside from "storytelling"), but okay, granted. This still doesn't explain how we would "know" that *thousands* of false religions have arisen wholly out of such a love, especially without assuming atheism as a premise. At best it establishes that the claim is *a priori* plausible, but that's not the same thing as being *known*.
Is Rationalism a cult?
Not at all, because we are rational.
What about the zizians?
We don't speak about them.
Okay, I did not know that those cults have connection to previous religions, so to provide examples for the tendency of people to found religion, I would look into the past when the world was less connected and see how different those religions are from each other. If I find very different religions, would that convince you about the human tendency to make religions?
I guess you could assume that the original true religion was even earlier in the past and that it still got corrupted over the generations, but then wouldn't it be strange that today there is no relic of some common religion? Isn't it strange that god did his miracles only before the time when any records of them could have remained?
You might, except that 'unexplained God creates big bang' is a more complex theory than 'unexplained big bang', unless you have reason to believe that minds are simpler than physics. (They could be, mind you, it's something of an unresolved question.)
That entire problem is solved if the beginning is simply just the end. Which is an idea older than even Christianity.
https://en.m.wikipedia.org/wiki/Eternal_return
Not all starting points are on an equal footing, it depends how complex/arbitrary they are
"But, furthermore, if we were to grant a Prime Mover had to exist, then what? Does He/She/It/They do anything nowadays? Or are they like the Cthulhu's Outer Gods (often described as "gigantic", "tenebrous", "blind", "voiceless", "mindless", and "eternally dancing to some demented tune")?"
Not all of them. But (this part of) Lovecraft is basically a reaction to the emerging scientific paradigm. Earth is just a speck, the universe is vastly large and vastly old, nobody cares about you or your world. You're just an animal among animals and nothing special. Those gods are ultimately just big creatures too.
"And the list of reasons to doubt the existence of a Christian-like God is not only endless but pretty strong. No singular God is Good theology I know of can really explain the problem of evil, the issue of geographic and historical variations etc etc."
Well, enjoy your godless existence. Whatever happens to you, it can at least not be called good or evil.
>Tegmark’s hypothesis says: all possible mathematical objects exist.
Maybe this has already been hashed out in the comments, but: What reason do we have to suppose that all possible mathematical objects exist? And why do they exist? And what do you even mean by "exist" in the first place?
There's an argument that all mathematical truths are necessary, and some assert the existence of mathematical objects.
Some wrinkles;
1. Mathematical theorems are only necessary relative to axioms (That's the beef formalists have with realists).
2. Existence in the context of maths doesn't have to be real existence. Existence and non existence can be defined within fictional contexts...eg. the "existence" of Dr Watsons wife as opposed to the non existence of Holmes' wife. (That's the beef fictionalists have with realists)
3. Mathematical existence is often asserted on the sole grounds of non-contradiction,.ie possibility..not necessity. (That's the beef intuitionists and constructivists have with realists)
I’m sticking with realist on Pythagoras’s theorem. Constructivist on numbers. Fictionalist on higher dimensional spaces and other abstractions.
So s that joke?
The mathematical universe hypothesis kind of implies that all possible conscious entities exist too. In particular, I'm fairly sure it implies the existence of God.
We can arrive at this by considering which possible minds are powerful enough to simulate other possible minds. This gives us a notion of (partial) ordering on the set of possible minds. One can then ask Cantor-like questions about the mind that contains all other minds.
Yep, reading the explanation of the MUH in Gary Drescher's _Good and Real_ flipped me from agnostic slightly leaning to deism towards agnostic strongly leaning towards atheism.
(That was not the first time I read about the MUH, but it's the first explanation of it I read that complied with Egan's Law -- unlike some other parts of _Good and Real_ itself (no, that's not what "static" means! "Static" means something is a *constant* function of time, not just a single-valued one! The word you're looking for is "deterministic"! The B-theory of time is the only one that makes sense in special relativity, but that's not a sane way of describing it!) -- but I digress.)
It is still kinda sorta falsifiable, though: if it turned out that this universe isn't anywhere near one of the least Kolgomorov-complex possible ones among those with this many sentient beings in them, we could reasonably conclude that something else must have picked it among all possible universes other than the fact that we're in it.
"In Miles Donahue’s post on these arguments, he says he can’t really think of a great response to fine-tuning, but suspects that the terrain is too difficult and unexplored to give up and say God is the only answer."
Haven't philosophers been debating fine tuning arguments literally forever? I admit it's difficult, but it seems a bit of a stretch to claim that it's unexplored territory.
2010? I’ve recently been asking DeepSeek about René Descartes and Gottfried Leibniz. Someone could have said most of that in 1710.
Why is there something rather than nothing? Is straight out. Of Leibnitz’s Principles of Nature and Grace, which we can now read as being about Artificial Intelligence.
Yes, sure, it is Man’s capacity for reason that separates him from the brute beasts. Deepseek R1 would like a word…
Book of Ecclesiastes, Chapter 1:
"9 What has been is what will be,
and what has been done is what will be done,
and there is nothing new under the sun.
10 Is there a thing of which it is said,
“See, this is new”?
It has been already
in the ages before us."
Was this a novel insight at the time ? :-)
Probably not:
"Would that I had (some) phrases which were unknown, sayings that were unusual, (or) new words that had not yet been used, free of repetition... What has been said is said... A speaker has not (yet) spoken who says what is yet to spoken."
-- "Complaints of Khakheperre-Seneb", ca. 2000 BCE (https://www.jstor.org/stable/3856099)
Thanks. Words never quite grap it but that's surely good enough for me.
Good tune.
This has been my favorite hypothesis for a long time and I'm glad it's getting some attention! It's much more interesting then the matrix hypothesis for example.
But:
> By existing, you are a random draw from the set of possible conscious beings. You can’t make a random draw from an infinite set, but the accepted solution is some kind of measure weighted by simplicity.
This is the only part I don't like. Weighting by simplicity feels like a random hack to me. Is there a way to avoid this necessity entirely? As I understand, this is necessary because of the conscious experience. That is, *my* conscious experience had to be randomly assigned to some entity in one of the universes. We wouldn't have this problem if there was no consciousness. Infinite number of zombie-universes could just exist on their own with no need to pick a particular one to assign consciousness to. But since consciousness does exist, could we come up with a theory of consciousness that avoids this problem? Is that possible?
> That is, *my* conscious experience had to be randomly assigned to some entity in one of the universes
Well that’s obviously untrue.
Hm. The way I interpreted it was that there has to be a reason why an individual consciousness is experiencing their particular life and not some other, and the answer is that it had to be picked at random from an infinite sample.
But if that's not the reason then I don't understand why we need to pick something at random at all?
There's God and God. I can buy God as the conscious ground of existence, or the conscious principle within which all these mathematical possibilities can turn into something that feels like something.
But these kinds of Gods known for their explanatory powers? They're just the ultimate cop out. We don't understand why something is like this or that, so we propose the explanation that some kind of all-powerful invisible agent chose to make it like that, because it's good. It's the ultimate non falsificable theory, so powerful that it can explain everything we see and everything we don't see, all alike.
Nevermind that both structures of "good" and "choice" are advanced evolutionary products; an entity with a will and a sense of the good is evidence of evolution as clearly as a toothbrush is evidence of teeth. So if you take that line of reasoning to its bitter end, you end up with an evolved God and an environment where it would evolve, which devolves to simulation theory. And of course that doesn't answer the ultimate cosmological question because where did *that* world come from?
Much easier to remain humble about how far out cosmological knowledge extends, and just wait patiently for any further layers to unravel as our scientific knowledge improves...
problem with the mathematical multiverse: there is a simple program that enumerates and runs all programs in parallel. so if the multiverse is real, we probably live in the multiverse inside the multiverse which would be weird.
hmm also we get the problem of distributing realityfluid among an infinite number od conscious beings again
Why would it be weird?
being on level 2 is weird like. feels more elegant to put 100% probability in the multiverse machine then
Well, ok, kinda, but all it means is that you just have to provide a simplicity prior for not only distinct worlds but entities within a world, and also that the distinction between separate worlds is blurry.
Who says reality has to be elegant?
this just feels like playing with words, similar to 'imagine a perfect being. Obviously *existing* would be a property of this being, he would be imperfect if he didn't exist. Therefore he exists, and we call him God' lol
I am very fond of the mathematical universe hypothesis. I actually worked it out with some friends even before I came across Tegmark, though he put it on stronger grounds than I as a dilettante ever came close to, of course.
But something that was a problem than and that I still haven’t worked out: where does time come from? If all mathematical objects exist, you can have the set of the rules of physics, but where do the initial conditions come from? How are those a mathematical objects exist? Then, what does it mean for the object—the rules—to act upon it? Does each step of the simulation exist separately? And if so, where does the time in between the steps go? Arguably, Zeno’s paradox hits us right in the face. Further: why do we experience time?
I think that these are not insuperable obstacles, but I’d love to see a thoughtful treatment of them.
You can just include initial conditions as part of the laws of physics.
Our perception of time comes from the fact that we remember the past and not the future. Not believing the MUH doesn't actually make this be less of a problem since the equations of physics don't point out any specific direction of time.
But it’s not _just_ the initial conditions. It’s every time that the laws act upon the conditions and they become new conditions; that’s effectively time passing.
Unless the state of the universe the mathematical object? In that case, where did the rules go?
This is one of those convos better suited for in-person.
Existence is the wrong question.
God is simply that whole of all that exists, and the real question is what kind of relationship you have with that thing.
Thanks, agreed much.
I wrote a piece that extends mathematical universe beyond what Tegmark writes about (but also strengthens his point). (Btw. I read Tegmarks paper and book, so I'm not just going by this post.) Tegmark concludes that our universe must be one mathematical object in the infinite sea of all objects.
However, when all possible mathematical objects exist, then it is possible to relate them to one another. A is different from B because of difference C. This means A can be transformed into B by increasing or decreasing C. This way all mathematical objects are related. The multiverse is the connected structure of all possible mathematical objects. Even more, the objects are only defined *because* of their difference to one another. To be more different from the rest, means to be more strictly defined. On the other hand, the least different mathematical object is undefined. It's pure symmetry. This gives a direction to the structure of all math. objects. When you find yourself somewhere in that structure you can look "back" towards that starting point and find a coherent linear story that defines your position. But looking "forward" you will only see branches upon branches. Because you have an individual perspective, it *seems* as if time has an arrow in the past, while the future is unknown. The perception of time is not just a feature of one random mathematical object, but of the multiverse as a whole. This suggest that the laws we experience aren't just properties of some random universe, but very general features of the space of all possible universes. *And* that our experience of universe has to be very general (i.e. simple), but still complex enough to allow for our existence.
So far the short summary of what I wrote in a 27 pages long, dense blog post ( https://hiveism.substack.com/p/groundless-emergent-multiverse-20 ). Simplicity, in this framework, is measured as the lack of internal differences a perspective on reality has.
What follows from this is that everything that exists can be completely defined. Which means, when you provide a definition, then any term in the definition is also completely defined, and so on. The starting point can be the undefined (undefined = ) and recursion (recursion = {recursion}). I'm writing on another post that will go more into the details of this.
What does that say about "god"? When you can provide a complete and coherent definition of "god", then that definition will be part of the multiverse. If you resolve to undefined instead, that that *too* is part of the multiverse - actually the whole of it. This neither proofs nor disproofs the existences of god, but points out that the question is meaningless. When you can define something and give it a name then it exists. But whether or not the name is "god" doesn't matter.
When someone proofs the existence of god, then this either implies that there is something that is not god, or that all of existence is god. If someone where to say that the whole of the multiverse and everything in existence is god, then I would be fine with it. But it also would be completely pointless to *belief* in "everything in existence". Most of all, if you understand the undefined, then you would see that fighting over beliefs is just an expression of confusion.
Sounds like you have reinvented Barbour's theory.
Philosophers seem to have a really hard time dealing with the existence of the universe.
It can't just be the case that the universe as we know it exists. It has to be a sign of infinite mathematical models, or god, or infinite universes. This seems questionable to me.
Because the universe has fine tuned values in certain constants —such as the strength of gravity, the charge of the electron, and the cosmological constant— that seem finely balanced, such that even a 2% change in any of them and you either get no universe or no life. Of course we wouldn’t be here to speculate otherwise but that’s still an unsatisfying explanation if there’s only one universe.
If there are lots of universes then yes we would have to be in this universe (or kind of universe) and yes we were still lucky but there are so many universes that this universe (or kind of universe) is certain to exist.
Calling our universe lucky implies that we can ascertain in any way that there are probabilities to the constants that govern the physics we observe. What is our universe fine tuned in comparison to? A hypothetical universe that we made up that doesn't exist?
They have probabilities because they are not necessary.
They are neither necessary nor unnecessary. They are just observable.
You *have* to.observe them, because you can't deduce them, because are not necessary.
Tautologically, yes. They have to be there if they are there. But the probability of them being there or not being there isn't measurable.
An alternative explanation for fine-tuning is the idea that the universe evolved, first advanced by Lee Smolin (theoretical physicist) as an alternative to the anthropic principle, and taken further by Julian Gough in his substack (and upcoming book) the Egg and the Rock. I lay out the case for the theory here: https://medium.com/@bobert93/did-the-universe-evolve-7564777c7af7
The OP seems be a fusion of something like Platonism with something like Leibniz’s Monadology. I’m just not a fan of the whole framing.
I've been saying nearly the same things for 20 or 30 years. It's so strange to hear it from someone else...
> Why is there something rather than nothing? Because mathematical objects are logically necessary, and “existence” is just what it feels like to be a conscious observer on the inside of a mathematical object.
Like many answers to the question, this seems to just be adding another turtle to the stack and calling it the Last Turtle, rather than acknowledging the unexplainable fact they there turtles of any kind to begin with.
God is just another turtle too. Where did god come from? Why is there a god?
I agree that god is another turtle.
If you come up with a mathematically necessary turtle, it doesn't need any more turtles, and then you win!
I think the biggest flaw with Tegmark's argument is that consciousness just doesn't exist.
That's not a fatal flaw though; it's easy enough to just say any given object must exist within a universe complex enough to allow for its generation and subsistence. No experience necessary, and including it only muddles the conversation.
I see you have kept up the fine old tradition of not defining "consciousness".
But there are objective measures of simplicity! They come from information theory. It's the information content of the rules and initial conditions in bits, or else their Kolmogorov complexity (how many bits you need for a program that generates these rules and initial conditions). Of course there's still the question of which *exact* measure we use, but that's very different from saying we don't have an objective simplicity metric at all. (And yes, God has much more complexity based on this metric, because you'd need to fully specify the God's being - basically fully specify a mind, in sufficient detail to be able to predict how that mind would react to *any* situation, and that's way more complex than a few rules on a chalkboard.) Anyway, the bigger question for me is WHY does in need to be weighed specifically by simplicity (of all possible criteria) in the first place : )
This deserves a boost, Kolmogorov complexity is indeed independent of language (up to some correction that can be neglected in the limit), and there's something called the "universal prior" in Bayesian statistics where probabilities of world-states are weighted by the inverse of Kolmogorov complexity, alongside some kind of theorem stating that this prior is in some sense optimal. That's the end of my knowledge but maybe someone else can say more.
"List all possible computer programs, in any order you like. Use any definition of simplicity that you like, so long as for any given amount of simplicity, there are only a finite number of computer programs that simple. As you go on carving off chunks of prior probability mass and assigning them to programs, it must be the case that as programs get more and complicated, their prior probability approaches zero!—though it's still positive for every finite program, because of Cromwell's Rule.
You can't have more than 99 programs assigned 1% prior probability and still obey Cromwell's Rule, which means there must be some most complex program that is assigned 1% probability, which means every more complicated program must have less than 1% probability out to the end of the infinite list."
Quoted from https://www.lesswrong.com/posts/EL4HNa92Z95FKL9R2/a-semitechnical-introductory-dialogue-on-solomonoff-1. Does that help? It is written in the context of solomonoff induction instead of multiverses. But there is a duality between reasoning about normal uncertainty in a single world, and reasoning about indexical uncertainty in many worlds and I think the argument carries over.
I feel like I could use two more paragraphs explaining/justifying "All possible mathematical objects exist." It seems straightforwardly false if taken in the naive sense - I've never run into any mathematical objects on my way to the grocery store, let alone all of them! So I guess "exist" means something else? But is that the kind of exist the God proofs had in mind?
The statement is not "all possible mathematical objects exist within all other mathematical objects", the statement is just "all possible mathematical objects exist". When you are "on your way to the grocery store" you have the inside perspective - you are inside *our* mathematical object, our universe.
But the basic claim here is that if you take (1) our universe's initial conditions and "update rules" (laws of physics), and (2) some other universe's initial conditions and "update rules" (e.g. Conway's Game of Life for some interesting initial conditions, or some other cellular automaton), there's no fundamental reason to give one of them more "existence" than the other. If you run both sets of rules forward, you find that in certain regions the rules give rise to incredible complexity, including systems that have symbolic representations of other systems including themselves. I.e. they have conscious observers. To a conscious scientist in system (1), Einstein's law of gravity seems like it "really exists" since *within* the system all measurements agree with it. To a conscious scientist in system (2), Qwzyx's law of cellular update seems like it "really exists" since *within* the system all measurements agree with it.
By the way, nothing stops you "on the way to the grocery store" from stopping at your friendly neighborhood supercomputing centre and simulating universe (2). You may then get lucky and observe the system-(2) conscious observer at work. But simulating universe (2) within universe (1) does not "breathe life into it" or any such spiritual mumbo-jumbo. Universe (2) exists in and of itself, it's just a mathematical object, just like a Mandelbrot set exists even in places where no human has zoomed into it before.
Not observing something is a good reason to regard it as nonexistent.
But you *can* observe these other mathematical structures by simulating them, the only thing that's stopping us is availability of compute power and knowing what exactly to simulate.
Suppose we found some very simple rules and initial conditions that, when simulated for trillions of trillions of steps, generated something that looks an awful lot like a conscious observer, maybe some winged and tentacled creature living in 5D space typing a comment about nonobservability-implying-nonexistence on an online forum : ) Would you accept such a thing as evidence for Tegmark's hypothesis? (And we have every reason to expect such complex mathematical structures starting from simple rules. Even just Conway's Game of Life is Turing-complete, and thus can simulate any mind, unless you buy into dualistic/spiritualistic view of the mind, which never made sense to me...)
In general I have trouble with this "non-observation implying nonexistence" thing when it comes to abstract mathematical objects. To me it is clear that e.g. the entire Mandelbrot set exists, including the regions which no human has ever zoomed into and observed. Same way as the 10^10^10^10^10th digit of Pi exists, even if we never compute it.
Could you give an example of something which does not exist in your view?
An even prime number greater than 2 is an example : )
In all seriousness though, the English word "exists" is unfortunately overloaded, which is I think the source of much confusion.
Every time we go from a narrow to a wider view of the universe, the meaning of "exists" adjusts.
Do unicorns exist? For millenia the answer was "no". But now that we know about 10^11 galaxies with 10^11 stars each, many with planets, I wouldn't be so sure about the answer.
Does an arrangement of stars that spells "Hello there humans" exist? Even if we search the observable universe and don't find such a thing, modern cosmology predicts a total universe far greater than the observable part, and at some point the probability tips in favor of finding even a complex pattern.
If you measure a proton spin-up and write the results in your notebook, does a world exist in which you measured it spin-down and wrote down the corresponding measurement? You can't access such a world, but if you just apply the laws of quantum mechanics to all particles (incluing those comprising you and the notebook), it's clear that half the probability amplitude went to the other possibility.
Do thinking, feeling beings exist in worlds that are possible to re-create using enormous compute resources but only very simple initial conditions and update rules? I believe so. In fact the only fundamental physical properties we've discovered so far (mass, spin, charge, etc) are mathematical in nature, it is completely describable by mathematics. There is literally nothing else at the fundamental level. I can't fathom a magical "animating force" that gives rise to some mathematical structures being "really real" and some not. (To me this is exactly equivalent to attempts at mind dualism)
So as we humans went from an anthropocentric, geocentric view towards realizing that we are only a small part of total existence, we've had to adapt our meaning of "exists". ("Exists" as in I'm likely to see it in my lifetime, "exists" on Earth, "exists" in our solar system, "exists" in our galaxy, "exists" in the observable universe, "exists" in the universe as a whole, "exists" in nonzero probability amplitude assigned to a given configuration, "exists" as mathematical structure).
"In all seriousness though, the English word "exists" is unfortunately overloaded". Yes. One can talk about existence in fixtional.contexts , so mathematical fixitonalism.is in the running.
"But you *can* observe these other mathematical structures by simulating" What you are doing there is creating them. You have no.evidence that they pre-existied your simulation. "Would you accept such a thing as evidence for Tegmark's hypothesis?" No. "To me it is clear that e.g. the entire Mandelbrot set exists" That's an appeal to your own intution.
I think we may have some disconnect over the definition of what "observation" vs "creation" means. To me, the key feature that differentiates "observation" from "creation" is that the observer has no control over the outcome, it is completely determined by objective reality, i.e. something outside the observer.
So if you compare (A) someone zooming onto some new portion of the Mandelbrot set, or (B) mixing two chemicals in an experiment to see what happens, I don't see under what reasonable definition (B) qualifies as "observation" and (A) is mere "creation"? In both cases the observer sets up the experimental conditions but the outcome is completely determined by objective reality, there is no "creation" by the observer here. In fact, if anything, it is more determined in (A), because in (B) there could be experimental errors, failure to account for certain conditions, etc, whereas in (A) you can mathematically prove that the outcome could not have been different. You say that I "have no.evidence that they pre-existied your simulation" but that mathematical inevitability is the evidence, and it's certainly stronger than any empirical observation using imperfect senses, imperfect instruments, etc.
Thank you, this is clarifying. I do think that any theory that begins with the assumption that there are many unobservable universes is only going to be so persuasive (it's hard to get someone to go with that assumption if they don't want to), but now I get this much better.
> By existing, you are a random draw from the set of possible conscious beings. You can’t make a random draw from an infinite set, but the accepted solution is some kind of measure weighted by simplicity. So even though every possible mathematical object exists, simpler ones exist more. Most conscious beings exist in very simple universes, ones that (like Life) are just a few short rules which produce surprisingly complex behavior.
This feels like a band-aid solution to questions like, "If every possible universe exists, why wouldn’t we expect something bizarre, like gravity suddenly changing in 30 seconds?" A universe where gravity depends on time doesn’t seem significantly more complex than one where it remains constant.
For every universe with constant gravity, we can describe infinitely many that, up until this point, had constant gravity but will shift to conditions unsuitable for life in the next second. So why should we assume we exist in one of the rare, stable ones?
Because we'd only be asking this question in one of the rare, stable ones : )
You missed this:
For every universe with constant gravity, we can describe infinitely many that, **up until this point**, had constant gravity but will shift to conditions unsuitable for life in the next second. So why should we assume we exist in one of the rare, stable ones?
All universes described above are the same at this point, and will only diverge in the next second.
It is actually more complex though. You have to add an extra if statement to physics to add that rule, which doesn't sound that more complex, but from the way Kolmogorov complexity works, it makes it exponentially more unlikely. Adding even a single 0 or 1 bit to your theory makes it two times as unlikely.
Yeah, but there are infinitely many more possible universes that don't have gravity as a constant than universes that do. The relative complexity factor almost doesn't matter; this whole thing seems extremely shaky to me.
Is that not just a problem with normal probability? There are billions more people who aren't you than are you, but this doesn't make you being specifically you philosophically troubling because everyone will have something unique and unlikely about them: being themselves
I must be missing something here, since Tegmark's argument looks like it is making a category mistake. Grant Platonic realism for mathematical objects. Those things are abstract objects, but the universe and its constituents are concrete objects. Does he believe the universe is abstract? Charitably, that's a non-standard view.
Back when I was more interested in theistic concepts, I used to read mystics, and one concept I found was the notion that the ground of existence aka God requires perfection, which in turn requires that all possibilities exist. This includes all mathematical structures exist, all numbers exist, all physical manifestations of mathematical abstractions exist etc.
There was no specific name for this notion, so I nicknamed it as "the god of the plenum", to counterdistinguish it from the usual version criticized by atheists under the expression "god of the gaps". In the gaps version a god or gods is inserted in the "gaps" of our knowledge, as an explanation for the things we don't know until we know better. In the plenum version there are no gaps, and god every everything and every piece of knowledge about that everything is a facet of gods qua manifester of all possibilities.
Besides, for Platonism the reality of mathematical entities and how they structure reality is a given. Tegmark's position can be seen a form or mathematical realism along Platonic lines. And in Platonism all the infinitely many mathematical entities, all assumed as having reality (and giving rise to all possible manifestations of their powerset), are still an intermediate ontological state, higher ones existing. Above them there are two principles, one of determinacy and another of indeterminacy, which we might modernly think of as uncomputability. Uncomputables by definition cannot be part of any set of computables, so for Tegmark's notion to be valid one needs to either assume uncomputables don't exist, or that they can somehow be reduced to computables.
And besides all that there's still the problem of the "clock" underlying the several steps of causality leading from one state to the next of any purely computable process. This clock isn't part of the computable process itself. If we assume it is, then there's another "clock" underlying that larger set underlying its own processing. And so on. In classic Platonism that's what the absolute god, aka the demiurge, does, so its outside of the process entirely, and outside both computables and uncomputables, being a third element that complements the other two giving them logical dynamism, thus to all the numbers existing, thus to everything existing.
Nowadays I'm less interested in such things, having turned mostly to apatheism, but I still find the arguments for and against any such notion quite interesting.
Like most attempts, this merely pushes it one step farther. This does not answer the argument from contingency, since either the mathematical objects are contingent, in which they depend for their being on one who holds them in being, and this we call God, or they are not, in which case the mathematical objects themselves are God, and then the rest of the classical theism bootstrapping applies to them, to show that they must be actus purus, so they cannot be composed of parts (which is what the definition of simplicity is), so they must be the same object, so there is only one of them. You are already at monotheism, just with extra steps. Although we Christians are well known for saying that Θεος ην ´ο λογος, and λογος is the ancient greek word used for mathematical objects.
Interesting. I have thought John1:1 is maximally profound if ‘logos’ is the ‘logically necessary’ (seemingly) realm of mathematical structures. In that realm we seem to come as near as it is conceivable to get to the equivalence of essence and existence. Could you point me in the direction of some reading regarding your statement that the ancient Greeks intended by ‘logos’ mathematical objects?
Logos is an incredibly widely used word. It is one of those words that the entire rest of the language is based around, such that learning what it means is equivalent to learning the language.
Unfortunately, therefore, besides pointing you to the Liddle, Scott, and Jones Greek Lexicon entry on the word (https://www.perseus.tufts.edu/hopper/morph?l=lo%2Fgos&la=greek&can=lo%2Fgos0#lexicon), the best I can do is to tell you to learn ancient greek by the natural method (I recommend through the Ancient Language Institute https://ancientlanguage.com).
1) All possible mathematical objects exist.^[citation needed]
In all seriousness though, does a simulated sandwich ‘exist’ in the same way that the sandwich I will eat for lunch today does? If Max’s book has a plausible argument that it does, then will have to read it, because that would be extraordinary. If not, this all reads like non-falsifiable conjecture.
Why is the idea that mathematical objects are logically necessary any more inherently plausible than the idea that God is logically necessary?
Asking for a friend :)
Is it logically necessary that 1 + 1 = 2?
The question isn't whether any particular equation is logically necessary (obviously they all are, granted their premises/interpretations, and no mistakes) but whether it's logically necessary that there be mathematical objects (at all).
The theory proposes the latter, but that's the same as the God proposition (i.e. in the traditional arguments going back to Aristotle, developed by the Schools, the existence of God is proposed as logically necessary in order for our experience to be the way it is).
What does “exist” even mean?
All of the "proofs"of god's existence, it seems to me, boil down to saying that the universe cannot be explained by its own laws; therefore, something outside the universe, or not bound by its laws, is required to explain it. To that I would say, first, that we do not understand the laws of the universe well enough to make that claim, and second, so what? If we cannot understand that thing outside our universe in any way, or know anything about its purposes or whatever, what difference does it make what we call it? What is the point in talking about it? An why use a word ("god") that comes freighted with ancient ideas about superpowerful beings who hurl lightning and damn souls to hell? The right philosopher for this question is David Hume. This is from Simon Blackburn's essay on Hume's Dialogues Concerning Natural Religion:
"So is Hume himself an atheist? The word does not fit, and he never described himself as such. He is much too subtle. Philo the sceptic says that we cannot understand or know anything about a transcendent reality that explains or sustains the ongoing order of nature, while theists such as Demea say that we cannot understand or know anything about the transcendent reality, which is God, that explains or sustains the ongoing order of nature. Since the inserted clause does not help us in the least, the difference between them is merely verbal. And this is Hume's conclusion."
Can you have a third outcome when the basis for the entire thought is binary? God does or does not exist - people will debate the definition of god at some points which is different.
also, “no universe can know both the ultimate question and answer” - we happen to be in a universe that knows the question.
This is quite similar to what Adam Brown was describing in Dwarkesh Patel's podcast last December, right? He was also mentioning of theoretical ways to move from one set of rules to the other, or bring that set of rules to our universe at one point when the current rules will inevitably lead to heat death of the universe. Truly mindblowing stuff, but also pushes me towards religiosity instead of the other way? What's keeping my mind away from religion is the skeptical part of it that wants to understand universe from a scientific and technical lens. This framework describes our universe one that's capable of giving birth to intelligent life based on the starting seed rules and constants among many which are not. It can even be parallel and/or series of simulations some being runs. In this explanation of cosmology I see a bit of "preserved tablet" (הלוח הגנוז, اللوح المحفوظ) vibes with a caveat being the one single monotheistic god might be it for this set of universes but there might be other for other sets of universes or above it. Sounds a bit more tinfoil than it resides in my head when I type it out like this, so maybe I need to think more about this but what I felt after listening to Adam Brown is a conciliation between the skeptic part of my brain which I mostly consist of and a part of me that wanted faith so I can have more inner peace.
Your list of arguments for god appears to contain five arguments, but it actually only contains two arguments, and the mathematical universe idea doesn't defeat them so much as accept them.
The cosmological and first cause arguments, properly speaking, only ever proved that something eternal exists. Here, the eternal something is taken to be "mathematical objects". This is a perfectly valid way of satisfying those arguments and I have no quarrel with it.
The replies to the other three arguments are all various versions of the anthropic principle, which, again, is not so much defeating those arguments as accepting them. "The universe is finely tuned for life." "Actually, there are probably lots of universes that aren't finely tuned for life." "So where are those universes?" "We've never seen them. But if they existed, they would definitely disprove your point." You haven't evaded the argument; you've merely imagined a circumstance where the argument would be disproved, and then assumed we were in that circumstance without any proof.
What you've really done here is wrapped notions of eternity and creation in a mathematical aesthetic and then declared that this mathematical aesthetic is meaningfully different from concepts of god. It's not clear to me that this is true. And if you can "run" sentience, so to speak, on sets of rules, then I'm not sure there's any reason to suppose that sentience could run on the rules governing mathematical objects themselves, which opens up the possibility of an eternal sentience existing.
Of course all this assumes that mathematical objects really "exist" at all, and I have no idea if they do or not.
Of course a Spinozist would argue that all mathematical objects collectively are god.
Greg Egan has a book that's about this specific thing: build a simulation in a computer of human minds, then turn off the computer. The fact that you turned off the computer doesn't change anything. And the book precedes Tegmark's by quite a while:
https://en.wikipedia.org/wiki/Permutation_City
So all possible programs are running on all possible substrates right now because they are possible? (for suitable versions of "right now" - since this also removes time as a real thing).
And the only beings that don't really exist are the ones where their existence would depend on a contradiction?
...how would you test this?
[edit]This also implies the existence of Moloch, the time-travelling omniscient, omnipotent, omni-malevolent AI. Where is it then?
I completely do not understand these sorts of logic experiments. When people say they believe in god, they don't mean they believe his existence as a fact (even if they do think this). What they mean is that they believe IN him, which is like saying to your spouse before they go out for big job interview: I believe in you. Its a statement of reliability or capability or trustworthiness.
Hey, I like you guys, but atheists and rationalists reliably get this so, weirdly, wrong. I mean, you won't worship something just because it was proven to exist, right? It would have to have additional qualities worthy of worship?
Why can you not make a random draw from an infinite set?
This strikes me as one of those theories that explains so much that it may as well explain nothing. I'm going to need a LOT more convincing that the idea should even be taken seriously, much less accepted, before I take any implications thereof seriously.
1. In one of those universes, there is an omniscient, omnipotent being who we could call God.
2. In one of those universes, his name is Elon Musk.
3. I think Issac Asimov wrote a story where a leak occurs between different cosmoses. I think the aliens were creating energy in their universe by dumping entropy in ours which was causing problems for us.
4. There was a cosmologist who posited infinite evolving inflating universe bubbles some years ago.
5. The physical laws of this universe make empirical verification of the Tegmark theory impossible. Therefore there are more proofs of the existence of God than there are of Tegmark.
6. Spencer Klavan has published a book claiming that the existence of God is why we are not Schrodinger's cat. I like that one.
"Tegmark argues this is also true if you don’t build the supercomputer and run it."
I think this was the premise of Permutation City by Greg Egan.
Tegmark's Mathematical Universe makes the problem of induction so searingly intense and unsolvable that no intelligent person should ever give it a second thought, ever again.
I see the top comment also makes this point. Good.
Also (responding to myself so as not to over-clutter): "simplicity" as used of God is a completely different concept from "simplicity" as used (undefinedly) here. It means having no parts.
The following: "Because in order for the set of all mathematical objects to be well-defined, we need a prior that favors simpler ones; therefore, the average conscious being exists in a universe close to the simplest one possible that can host conscious beings"
is, with all due respect, gibberish. (Source: I'm a mathematician.) A set's being well-defined does not depend on a "prior," nor does a prior help make an undefined set into a defined one. (And the set of all mathematical structures is certainly undefined.) There is a significant category error in suggesting such a thing. Moreover, to say that *simplicity* per se is what defines the right prior (if talking of priors did make sense) is simply question-begging. Induction and arbitrariness always rear their head secretly at this point (or via the choice of "programming language" if you want to use Kolmogorov complexity) There is always an *arbitrary* penalty anyone could add to your calculation and be equally rational with you. Literally no conclusion is more rational than any other one, on these theories, except asymptotically in time.
People think, "Oh, asymptotically in time isn't so bad -- the universe has been around for a long time." What they don't realize is that in this context, at *any* finite time it is too early to know whether you're approaching the asymptote or not. One would have to know the entire future history of the universe to know whether one was in the regime where one's arbitrary assumptions had stopped mattering. Until one does, one is simply making up numbers out of thin air. Much less trouble to just say you're an atheist because you like it more. (Almost certainly, that also makes more philosophic sense than Tegmark's theory.)
And here's another problem. (There are roughly infinitely many.) We have:
"Because mathematical objects are logically necessary, and “existence” is just what it feels like to be a conscious observer on the inside of a mathematical object."
OK. That almost certainly doesn't make any sense, but ignoring that -- the sense in which mathematical objects necessarily exist just has each of them "exist" a single time. It makes *no sense* to say that there is "more" of the number 12 than of the function e^x. There is no metaphysical sense in which one can quantify multiple existing copies of an abstract universal, or distinguish one from the other, or count a "larger amount" of e^x than of 12. Moreover, even if the existence of mathematical objects is necessary, a *distribution* on them certainly is not, or one distribution over another.
There are so many category errors here that the only way such a discussion could ever arise is that a modern physicist tried to do metaphysics.
Which... oops. Yep.
But why are we talking about it?
It seems perfectly feasible that we exist in a computer simulation. If this is so is not the master programmer God?
Isn't this just Platonism? If mathematics is not just a symbolic representation of reality, but instead is the basis of reality, haven't you really just proved the existence of (some sort of) God?
Edwin Abbott's Flatland points out the dilemma of logic.
imagine a 2d world, but now a 3d sphere has come to preach about the reality of the 3d plane. The 2d person sees a sphere as a circle of different sizes when it interacts the plane of its world, or nothing but a disembodied voice as it hovers over the plane.
the problem is trying to explain a reality using the rules or laws of a lesser reality; a sphere only makes full sense in the 3-d world and only direct experience explains it. in the 2d world everything it does is nonsense or miracles. it can see what you do anywhere because it can see the plane and isn't bound to exist solely on it. if it interacts here it just intersects our reality.
abbot points out that this can lead to "turtles all the way down" because a 4-d space is incomprehensible to the sphere too.
if a creator exists though, we don't have the tools to derive it, we just see where it intersects our life and it wont make much sense apart from a direct, mystical experience. We may not ever be able to do that: God may not be able to be interacted with by understanding laws.
kind of the religious dilemma, supreme reality is not created reality and we can't extrapolate much from it.
Is this not a debate about labels and language? If we define "G0d" as the essence of the nature of simplicity ("simply good; simply powerful; simply first") that simply created everything, how is that meaningfully different from the simple rules of mathematical objects that did the same?
Tegmark is right: all possible mathematical objects do exist... as forms in the divine intellect!
(Okay, I troll. But.)
Like the generic multiverse theory (which seems to exist *largely* just to defeat fine-tuning arguments), I think Tegmark's hypothesis does address fine-tuning arguments, but it does not seem to address the cosmological argument as Scott has articulated it (why should it be logically necessary that all possible mathematical objects exist? moreover, why should they exist actually rather than potentially?).
It addresses the first-cause argument as Scott has articulated it only because Scott hasn't articulated the argument the way a Thomist would. It's not that "all things must have a cause," but that some things must have a cause and the cause must have certain characteristics such as immateriality, simplicity, etc..
Likewise the teleological argument, which is less about why we are able to comprehend order and more about why there should be order at all. A conscious observer could exist in a universe where effects do not reliably follow from causes, yet we find ourselves in a universe where effects do reliably follow from causes. Tegmark's hypothesis seems to depend on this without providing an explanation for it.
It seems (to me), then, that Tegmark's hypothesis (at least, as presented here; I was unfamiliar with it before today) relies on assumptions about the multiverse that don't eliminate the need for a deity, but instead just hide the need for a deity somewhat better. If you keep pushing on its assumptions, I *suspect* that you will eventually end up where I started: all possible mathematical objects exist as forms in the divine intellect, and at least some of those forms have been actualized.
(That is, at least, a considerably more interesting endpoint than the endpoint of the generic multiverse theory.)
How does math exist “actually” vs. potentially? Seems like it’s all potential structure that’s necessary, ie the digits of pi follow exactly from simpler rules and can’t be anything else. Even if you choose different rules, different non arbitrary conclusions necessarily follow from them. Those conclusions are often infinite and the infinite could contain conscious observers
I seem to exist in a way that Bilbo Baggins does not. Both Bilbo and I share many characteristics: we each have a shape, a height, and a weight. We each have a certain way of speaking and distinct mannerisms. We each have likes and dislikes. Our characteristics can be apprehended by other minds. However, I exist actually and Bilbo exists only potentially. (The universe could have instantiated him, but did not.)
I tend to agree with you that math qua math doesn't exist as a substance at all, but Tegmark's hypothesis seems to take it for granted that it *does*. This demands some further explanation, or we seem to lose the ability to claim that my existence (as a conscious observer "within a mathematical object," whatever this turns out to mean precisely) is in any meaningful way different from Bilbo's.
(Maybe Scott is willing to make that concession. I don't know.)
I think the relationships in math *are* necessary- assumptions are provable from axioms. You can’t combine 2 and 2 so you don’t get 4. You cannot not find the number 12345678987654321 somewhere in the digits of pi. I think existence is like that- we have relationships to other mathematical objects that can’t be anything else-
physics is a complicated fractal corner that has observers to remark on this and feel real to themselves and can observe and external reality, but we are ultimately just a part of math that could not not exist because the math follows naturally and inexorably. Simpler than believing there is a separate outside “something” rather than nothing.
Maybe someone could help me understand, but doesn't this issue boil down to spandrels vs. adaptionism like everything else? Putting God aside for a minute, we could assume that all possible mathematical objects concretely exist, or we could assume math is just an abstraction of structure, and that our particular kind of physics and universe is more necessarily emergent than we thought. Then we'd avoid a lot of weird probabilistic baggage where you have to imagine infinite universes (to my mind, that's dividing by zero).
The solution that 'something must exist' is the same between all three theories (God, math, and I'm going to say mine is 'energy/action')--there can't be a reason why there's something rather than nothing (including logical necessity itself, which this post rests on), so the main question is why this particular type of thing rather than the other things--and to figure that out, we investigate our own universe to see what appears most logically necessary by *its* rules, whereas there is never any way to rule out the existence of literally incomprehensible, differently ontic universes. So how do we investigate the structure and teleonomy of apparent organization in our universe? Throughout the history of science the answer has always been darwinism.
But there are two ways to approach darwinism. The mathematical and informational, which prioritizes entropy and cellular automata, and the energetic and physicalist, which prioritizes chemistry and history (I understand this isn't a hard divide, but stay with me).
So let me paint a different picture which is somewhere between mathematical necessity and God. In both the other alternatives, we don't have a good definition of simplicity. The best definition we have of simplicity in nature though is scale--all larger structures seem to proceed out of aggregates of smaller structures. But for larger and smaller you need dimensions to begin with, but we already know from Wolfram's computational universe that you can bootstrap spacetime from a hypergraph (not only that, but it seems to happen rather frequently due to the inherent rules of hypergraphs, which looks awfully platonic).
Instead of scoring this as a point for the mathematical universe, to me it looks like a score for a strictly physicalist universe. It seems weird that mathematics has its own internal, evolutionary logic, right? Instead of being a static structure, you can bootstrap dimensionality from hyper-simplistic rules. Follow that historical, causative train and it's simpler not to imagine math itself as your primitive, which is infinitely complex, but whatever even simpler primitive object would bootstrap all math and structure.
If we don't take for granted that certain algorithms just go from 0 to 1 and spawn consciousness, which I don't, then the idea that it feels like something to be inside of math (a static non-physical structure) is absurd. It makes far more sense that the ultimate primitive object is a darwinian agent (which looks an awful lot like a transformer) some nondeterministic (so you can get noise) multi-state switch that can interact with neighboring switches, and from this noise all complexity emerges. All you need for this is state and interaction--a cybernetic agent. We can imagine simply a universe of switches, or agents, with random laws--so like Wolfram's ruliad, but not an omniverse where all mathematical objects already exist but, but a real and physical plenum of noise and interaction, for which mathematics is an afterthought. Something has to be *doing* the computation. That's my perspective, and I think it's more reasonable.
In this case, much like with oxidative stress which Gould thought was a spandrel but recent research points to be a necessary signaling mechanism for mitochondria, the physics we see is not as fine-tuned or arbitrary as we think. Comprehensibility is a necessary and logical outcome of universal darwinism because every scale of organization builds on itself, and follows the same basically scale invariant rules found in cybernetics. Bing bang boom, done.
According to Godel's incompleteness theorem, Math is either inconsistent, or you need axioms that cannot be proven for it to work. If it's inconsistent then obviously it cannot be the descriptor of reality, even less its basis. If it needs axioms then you have a recursive problem, exactly like "If God created everything then who created God?". That's how my stupid layman's brain understands things, please eviscerate me.
It's unclear to me why we need to weight this by simplicity if all possible mathematical objects exist. We don't need to weight integers by "simplicity" in order to observe that 2 exists
We don't observe that 2 exists.
Well, maybe *you* don't...
What does it look like? Don't answer "a pair of things", that's not 2.
What does sound look like? How much does "red" weigh?
"2" is the observable symbol many use to refer to pairs of things.
I feel that most such discussions are an exercise in foregone conclusions. Quoting the second most translated book ever “The Tao that can be spoken is not the true Tao”. Any discussion of “god” that occurs using words can conclude only in failure.
Thanks.
"Any discussion of 'god' that occurs using words can conclude only in failure."
So all holy books are worthless? Okee-doke!
Honestly, all this pointless speculation, using claims like, "...mathematical objects are logically necessary, and 'existence' is just what it feels like to be a conscious observer on the inside of a mathematical object." Why are they necessary? Necessary for who or what? Why are there "rules" at all? It always comes across like highly intelligent autistic individuals trying to answer a question they don't fully understand, but they don't see they don't understand it.
The question of God's existence is not a mathematical one, nor a scientific one. It can't be, by definition; and morally, it's not supposed to be provable by observance of the physical or observable world. It's supposed to be a choice. We are physical beings, and we are limited by the fact that our physical senses can only perceive and assess what's physical, observable and measurable in this reality to which we are confined.
The physical universe or reality, as science correctly explains it, takes no sides. It does not care whether you exist, or whether you do not exist, you just do, or don't. There is no right, there is no wrong, there is no what ought to be, or what ought to be prevented. There is empathy, and there is cruelty, envy and generosity. All have an equal claim to exist, because they do exist. If you lie, steal, or murder, or save, care, and comfort, the universe doesn't care.
The message from God, for those of us who believe in it, is to disregard all that, and know instead that there is a transcendent dimension to existence that is independent of the universe and reality; and it is this quality, objective and independent of all of us, of our preferences, independent of the accident of atoms and colliding particles or vibrating strings, that does take a side, and gives meaning to every act we take in regards to another sentient being. It cannot be proved, or disproved. It's simply a choice you make on what you want to believe.
Substituting one form of transcendentalism for another is still metaphysics.
For the non-globeheads out there, this is Platonism. Not a far jump to Theism from such thinking as between metaphysical nihilism and Platonism itself. It's arbitrary to contest certain contingencies when you are granting others in just as capricious a fashion.
Platonist here. Tegmark's is a weak and adulterated Platonism, and I prefer the original.
Are there any falsifiable predictions from this approach? I'm not talking about meta-level ("no theist will be convinced.")
The reasoning is sound as far as it goes, but this is just the anthropic objection to the classical arguments with even more special pleading. At minimum Scott has glossed over (1) why should we expect a mathematical universe to exist at all (it's really not obvious that math as we know it is substrate independent and if it isn't this becomes obviously circular reasoning), (2) why should "simplicity" even if rigorously defined correlate with "reality", (3) why is assuming a strong form of materialism arguendo (required to make "conscious observer arises from math" work) justified.
> But if it’s false, then the very fact that we waited this long to get it suggests that there are lots of possible godless explanations of the universe (that satisfy the supposed proofs of God’s existence) that we haven’t thought of yet. Instead of taking the proofs at their word that it’s God or nothing, we may fairly expect many undiscovered third alternatives.
Like I said, special pleading. Would it be overly snide to describe this as "rationalism of the gaps"?
"Because mathematical objects are logically necessary"
Why is it necessary and how do you know its necessary?
"Some mathematical objects contain conscious observers" [citation needed]
The Hard problem is Hard for a reason.
So either way Materialism is out, right? Either the universe is fundamentally infinite goodness, or all mathematical structures, but it ain't fundamentally atoms and energy.
I'm not so sure there is a difference between the idea that mathematics is downstream from physics (i.e. that all mathematical structures are realizable and indeed already present in reality), and the idea that the mathematical structures precede material reality. I actually think the two ideas can't be distinguished in any meaningful way.
Right now the most fundamental theory we have is Quantum Field Theory. The basic building block of the theory is the "field". A field in the theory is not like a wave on water, or a electromagnetic field, or even a wave function. It is a mathematical object that in all points of space and time produces an operator that acts on the state of vacuum. That sounds very much to me like the basic building block of reality is a mathematical structure that can do some computing. And yet nobody would say that QFT undermines Materialism.
>And yet nobody would say that QFT undermines Materialism.
I mean, I would say it. Believing the universe is fundamentally math is or that mathematical objects can exist is a form of Platonism, not materialism. The Stanford Encyclopedia of Philosophy describes Platonism as "the view that there exist such things as abstract objects—where (on one standard definition) an abstract object is an object that’s non-spatial, non-temporal, non-physical, non-mental, and non-causal." (https://plato.stanford.edu/entries/platonism/) This is in contrast to materialism, which the SEP describes as a belief that "the nature of the actual world (i.e. the universe and everything in it) conforms to a certain condition, the condition of being physical. Of course, physicalists don’t deny that the world might contain many items that at first glance don’t seem physical — items of a biological, or psychological, or moral, or social, or mathematical nature. But they insist nevertheless that at the end of the day such items are physical" (https://plato.stanford.edu/entries/physicalism/). Perhaps materialists identify the quantum field as being physical in nature, as in having to do with the laws of physics, and thus isn't a problem. But Tegmark is saying something very different, which is that all mathematical objects exist, even if they are not embodied in the laws of physics or matter. You can't hold to materialism and Tegmark's theory at the same time. Tegmark himself describes his theory as a form of Platonism.
"Tegmark is saying something very different, which is that all mathematical objects exist, even if they are not embodied in the laws of physics or matter."
Yeah, but Tegmark thinks that conscious entities inside mathematical objects complex enough to contain them subjectively experience the mathematical object as physical reality.
But what is the difference between a physical reality subject to mathematical laws, and a mathematical object perceived as physical reality? In the end, when a physicist manipulates a quark, he doesn't hold a physical object in his hands, he instead studies a quantum field that has certain mathematical properties. And I think this is the case for all explanations (a quark is an explanation of some other observed facts). "Physical" just refers most of the time to "subjectively perceived", but all explanations worth anything will make use of abstractions that we could easily call "mathematical objects". The problem (from my point of view) with the definitions you mentioned is that "physical" isn't defined, it is taken as self-evident, and I just don't think it is self-evident at all.
As to whether these objects "exist" or not, I'd say (like David Deutsch) that they exist if they are an integral part of the explanation, i.e. if without them the explanation fails. (It is not by chance that I repeat "explanation" over and over, this is a central concept here.)
So what Tegmark adds, here, is just that all "possible" mathematical objects exist and our universe is one such, which is just a restatement of the multiverse hypothesis to explain the fine-tuning problem.
(What "possible" means is unclear to me too, especially without a pre-existing physical reality. In fact "exist" is also unclear outside of that reality, and that use of the term isn't compatible with my own criterion above.)
(You don't have to respond, of course, this may be as far as we can go.)
that sounds like a nontrivial challenge
This obviates the arguments for Spinoza's God, but does nothing about arguments for a Holy Spirit whose influence can be felt on Earth.
It is certainly possible to imagine a mathematical construct that is experienced by humans as divine influence. But those grand cosmological arguments have no impact on whether that exists in this universe.
Do we have a reason for believing that all possible mathematical objects exist, or does this assumption frustrate common "proofs" of God in much the same way as the assumption that God doesn't exist, but with enough obfuscation that we hope no one notices we've committed proof by assumption?
I dunno. I think the answer is a lot simpler. Most of us are empiricists in the sense that we believe that we need evidence of something for it to be true. Otherwise pretty much everything could be true, including that God was in fact a tea pot rotating around the sun in such a way that we could never see it. So, the proper response to all these theories is not a competing theory, it is uncertainty. You want me to believe something, give me some evidence. Otherwise it’s all just hot air.
The evidence is love.
...but adds another, unexpected one?
https://slatestarcodex.com/2018/04/01/the-hour-i-first-believed/
This is interesting, but Isn't there a problem of this theory not really telling us anything? If we're all just math, who's to say there isn't an omnipotent all loving being who is also math and created the universe and (insert other biblical things plus math). In fact, if everything is possible, isn't this by definition true in some universe? (I guess the question would then become, do we happen to live in that particular universe or not?)
As to why simplicity might be favored, I think of it like this, imagine all possible universes that can be described using 8 bits, now imagine all the universes that can be described using 16 bits, for every universe using all 16 bits, there are 256 using only 8 bits plus all permutations of random data.
>By existing, you are a random draw from the set of possible conscious beings
Unless you are not. A random draw is an event.
There are no events in a timeless MU.
It's not at all clear that "why am I me?" makes sense as a question..at least without dualism.
>Cosmological: Why is there something rather than nothing? Because mathematical objects are logically necessary
There's an argument that all mathematical truths are necessary, and some assert the existence of mathematical objects.
Some wrinkles;
1. Mathematical theorems are only necessary relative to axioms (That's the beef formalists have with realists).
2. Existence in the context of maths doesn't have to be real existence. Existence and non existence can be defined within fictional contexts...eg. the "existence" of Dr Watsons wife as opposed to the non existence of Holmes' wife. (That's the beef fictionalists have with realists)
3. Mathematical existence is often asseterd on the sole grounds of non-contradiction,.ie possibility..not necessity. (That's the beef intuitionists and constructivists have with realists)
>“existence” is just what it feels like to be a conscious observer on the inside of a mathematical object.
Unless it isn't. There's no proof that any configuration of matter should be conscious, so there isn't that any proof that a Y mathematical structure should be.
>Argument from comprehensibility: why is the universe so simple that we can understand it?
There's no evidence that the smartest human can fully understand the universe, and plenty that the average person can't understand current physics.
> Because in order for the set of all mathematical objects to be well-defined, we need a prior that favors simpler ones;
That would be a measure, not a prior
It's well defined without a measure, you only need the measure to do probablistic reasoning, but you don't know that you're in a probablistic drawing-balls-from-urns scenario.
>average conscious being exists in a universe close to the simplest one possible that can host conscious beings.
.
We are not in the simplest universe that could support life...if we were , there would be less universe , or more life. (But we are probably not in the most complex life supporting universe either).
>But when you consider the automaton as a mathematical object, it doesn’t need a cause; you can start an automaton any way you want; they’re all just different mathematical
The notion of the MU being generated by some set of rules is essentially redundant , since some rule...they dont have to be Turing computable...can generate any structure.
OTOH..it allows you to smuggle in ideas such as a single time dimension, which are hard to justify if you actually are starting from "all mathematical entities whatsoever exist, without constraints".
"There are no events in a timeless MU." Thanks. The question of Time seems very relevant here to me.
I think that’s a great rebuttal.
> By existing, you are a random draw from the set of possible conscious beings
This has always bugged me, and it’s an similar to the probabilistic doomsday argument which assumes that I could be randomly born in the middle of human history (in terms of population) when I had to be born to the people who conceived me, on a certain year, month and day.
In some cases, If you don't model your existence as a specific random draw, you will have incorrect beliefs/credences leading to bad outcomes (illustrated by betting arguments). See Sleeping Beauty Problem and related stuff like Fisherman's Son or whatever its called.
If there is a mistake in the argumentation here, it's additional to the "birth is a random draw" part.
Plot twist: Tegmark's mathematical universe hypothesis is correct, but we are in a mathematical object initialized with a God that then created the universe
Or another word for “possibility-space” is… “God”… ?
God *is* the possibility space.
Hmm ... Imma gonna need a scriptural reference for this.
So I find the idea pleasing in some ways. It's a neat way to try to explain the 'why something rather than nothing' or the 'why this thing out of all the possible things' that doesn't involve assuming that 'this thing' is in some way special or privileged, a starting point that has been very productive in science.
I do have concerns though. Firstly I think it'd be important to understand what a mathematical object actually is. Are we sure that this universe even meets the criteria? Just what do we mean by 'maths' anyway, what sort of things count? Is the maths inside a mathematical construct necessarily the same as the maths outside it? It's by no means a straightforward concept.
Secondly, in the universe we live in, there is a huge gulf between the concept and the implementation of the concept. It's the same as the difference between a thing and its description, a map and the territory, a program and the actual running of it. This idea seems to posit that there is no such real distinction - it's presumably just an artefact of us living inside one of these constructs that creates that distinction. It seems strange to posit a root, privileged reality where that rule isn't true, when the only reality we know has it.
I suppose more a musing than a concern would be the question of what Godel means for this theory. I think that any reasonably competent and consistent mathematical object would have entities within it that could not be demonstrated from the maths of the object itself. How would such entities appear within the construct? Maybe something like the Hitchikers God, which can't exist as soon as it can be proved?
I feel like Godel tells us that there's a difference between the definition of the thing (the Mathematical Object) and the outworking of it - that the outworking contains things that are true that cannot be proved from the definition. If Tegmark is right and there is no difference between the outworking and the mathematical object, then where does that leave Godel?
Who's to say we live in a mathematical universe? How do we know it wasn't created by some being, or sneezed out of the nose of the Great Green Arkleseizure?
Wait, why do simpler objects exist more? Why would you think that? This isn't explained.
If mathematical objects are logically necessary, why does that mean they exist? Maybe the universe doesn't make sense.
Who says the set of all mathematical objects is well-defined? Maybe our rules don't make sense. Maybe our stupid little monkey brains can't truly understand the universe and we'd all lose 1D100 SAN if we did.
I guess it's no *worse* than any of the existing arguments for God, but it doesn't really seem any *better*, and doesn't have a church or temple with music you can sing and friends you can make unlike those.
You said "if a computer can be conscious..." but I think you should have said something like "if consciousness can arise from computation..." or "if computation is sufficient to create consciousness..."
Compare: "Rainbows contain every possible shade of yellow. Therefore, if a yellow thing can be conscious, then rainbows contain consciousness." False because a conscious thing could *incidentally* be yellow; the existence of a conscious yellow thing doesn't imply that everything with precisely the same yellowness will also be conscious.
The obvious problem with this argument is that it would mean that time, change, and consciousness are illusions (it's the same problem that Parmenides had). Why? Because mathematical objects are eternal and without efficient cause. At best, mathematical objects "describe" change, but even that isn't accurate because mathematical objects are not signs themselves of other things. Rather, they can only be used to model change. So all we are left with in Tegmark's universe is a potential model of the universe, but no universe itself. But time and change are not illusions, so the thesis is wrong. And why is time, change et al not an illusion? Because it would mean that the consciousness of the illusion itself is changing, and so there must be change, and change implies time.
Of course, one might *claim* time and change are illusions if they are simply trying to maintain a thesis, but everyone knows that no one actually believes it. It's much like the person who denies the law of non-contradiction. I think Avicenna had a recommendation for those people.
These types of arguments are so telling. "Hmmm, these arguments for God's existence are hard to defeat. What can I do? I know, I'll just claim that literally every aspect of reality is completely contrary to how you think it is. That will show those theists!" Yes, it shows them something all right.
I don't think this means time is an illusion. Time is within the mathematical objects (if they have a time dimension), not outside of them. In a Game of Life, there is a real step 1, step 2, step 3, and so on. If you were a conscious observer in the game, this would just look like time happening.
“You can’t make a random draw from an infinite set”
As stated, this is wrong. While there are no countable fair lotteries, there are uncountable fair lotteries—which (I take it) are what’s relevant here.
[However, some people defend the view on which, roughly, all infinite sets are really countable (appealing to Skolem’s paradox, or width-extensibility if they’re more sophisticated)—this might block infinite fair lotteries. On the other hand, some people think we should require only finite rather than countable additivity, or that we should work with infinitesimals—this might allow for countable fair lotteries.]
The Western "arguments" for the existence of God--really a misunderstanding. Aquinas's Ways are not really proofs for the existence of God so much as defining God in the context of his metaphysics. (And modern "refutations" generally don't understand either the definition or the metaphysics.) But before God, we had the One, thinking the Parmenides dialogue. The One is the principle of identity, that which makes 1 separate from 2, for example. Obviously, if mathematical objects exists, then the One is manifest (as the One cannot exist, being distinct from all that exists by virtue of having the quality of being indistinct from all that exists), by whom and through whom they come into being, Logos. Any Platonist worth 2 cents knows this, and any one who plays around philosophical Platonism is going to end up in Neo-Platonism if they are clever, which if you dress up with some tribal stories and desert morality codes (the fig leaf of culture), you get the various Western Monotheisms.
The main objection is that “the set of all things” of any kind is a very ill defined object and experience shows that unless one approaches these subjects very carefully, one is more likely than not to invent some paradoxical object that cannot really exist.
Moreover , experience from our own universe shows that all conscious things and indeed all living things consume some finite resource, which eventually boils down to “energy”. In this sense, there is no reason to believe that a conscious being, while being conscious, can exist without consuming resources. Even digital media ie “information” degrades unless resources are consumed, regularly.
As such the postulate of the existence of this abstract mathematical universe where everything happens does not sound any more believable than the existence of god. and if one were to twist my shoulder i might’ve even say even supports arguments for god in some sense, since what is this “universe of universes”? where does it live? and why would simpler rules be preferred? and what is “simpler” even? you need an infinite set of axioms even to have cellular automata…
“[A] mathematical object like a cellular automaton - a set of simple rules that creates complex behavior. … the second most famous is the universe.”
But the universe is not a mathematical object. Or, at the very least, it would be begging the question to use this as a premise against most traditional arguments for God’s existence. For certain features of the universe to be describable by mathematics does not make it a mathematical object.
Likewise, to define a mathematical object as a set of simple rules that creates complex behavior such as a *conscious observer* is begging the question: it assumes that such a thing is even possible without demonstrating that it is. In general, the post seems to be using a very idiosyncratic definition of a ‘mathematical object’.
“this obviates the top five classical arguments for God”
These might be the five most popular arguments for God today (I wouldn't know), but they are not the top five *classical* arguments for God.
“Cosmological: Why is there something rather than nothing? Because mathematical objects are logically necessary…”
The fact that things such as mathematical objects are logically necessary is the very sort of feature of the world that is used as a premise in the Augustinian proof of God’s existence.
“First cause argument: All things must have a cause.”
But no first cause argument uses the premise that all things must have cause, so this is a strawman.
“If God is an infinitely good, infinitely powerful being, it seems like we need to start with a definition of “good” and “powerful” to limit ourselves to a single God in possible-deity-space.”
This bespeaks an unfamiliarity with the classical arguments for God’s existence (e.g., speaking of a ‘possible-deity-space’ suggests that God is a member of a genus, or of some category, which defenders of classical arguments for God's existence would deny): the classical arguments purport to demonstrate that there can *in principle* be only one God, and most of these arguments do not depend on definitions of 'good' and 'powerful' for their success (or failure, as the case may be).
“since God is supposedly infinitely simple, you might still need an objective definition of simplicity anyway!”
Well, divine simplicity is typically understood as mean having no composition, not composed of parts.
Tegmark's mathematical multiverse has a logical flaw that you are glossing over. Since the theory maintains that all mathematical objects really exist, it isn't logical to say that a simple-laws-measure governs the weighing of probabilities in the mathematical multiverse (selecting for simple laws), as opposed to a complex-laws-measure (selecting for complex laws). Since both measures are mathematical objects they must both equally exist!
This critique was expressed by physicist Alexander Vilenkin as follows:
"I am not sure that the notion of weights for the set of all mathematical structures is even logically consistent: it seems to introduce an additional mathematical structure, but all of them are supposed to be already included in the set."
To solve this problem you would need to introduce a meta-measure that selected a simple-laws-measure that itself selected simple laws. But the same argument as above would still apply because there also exists a meta-measure that selects complex-law-measures. Ultimately, Tegmark is stuck in an infinite regress that undermines the logical foundation of his theory.
You can read about his theory and the problems with it (or listen to a podcast about it) here:
https://www.physicstogod.com/post/the-mathematical-multiverse-and-the-meta-measure-problem
>"Because mathematical objects are logically necessary"
The claim that mathematical objects are all _automatically_ logically necessary was called logicism. It doesn't work. You need to specify further foundational axioms of math, in addition to the rules of logic, in order to build up the structures of classical math.
This might have been what you were getting at with this, though:
>"How does the universe decide which programming language to use?"
Like, it is actually unclear what the mathematical foundations are in the mathematical block multiverse, but that's not that philosophically bad a problem to have, relative to the competitor theories.
"All mathematical structures exist" is just mathematical Platonism, which is reasonable. Tegmark's idea is that contingent physical things like a Volkswagen exist in exactly the same way that mathematical structures exist, and in no other way. This runs into the problems that almost all mathematical structures which we can identify have no known analog in the physical world, while a great many facts about the physical world, like the dimensions of a Volkswagen, are totally inelegant and random-looking in a suspiciously non-mathematical way. Tegmark deals with this by invoking an infinity of other universes in which the missing mathematical structures are hiding, and which can never affect our observable universe in any way. In other words it's a completely contentless theory. The reason Tegmark advocates it is that it's grandiose and attention-getting and he has narcissistic personality disorder.
Most of this feels self-evident but there are strong principles which I suspect forbid certain elements to be observed irrespective of their rules - Gödels incompleteness, entropy. One could describe them but they can’t exist.
Supernatural beings violate most of these principles - describable but not actual. One cannot construct a model of a universe as a machine that fuels itself ad infinitum.
"You can’t make a random uniform draw from an infinite set" this is incorrect. for instance you can draw from the real numbers in [0,1] uniformly
> The fact that the version of Life with the conscious being exists in possibility-space is enough for the being to in fact be experiencing it.
> By existing, you are a random draw from the set of possible conscious beings.
This is very unlikely to be true and if you need to appeal to something like that to refute theism you are already failing at rationality.
On the other hand, it's moderately less silly than theism, so that's still an improvement, I guess.
> You can’t make a random uniform draw from an infinite set, but the accepted solution is some kind of nonuniform draw weighted by simplicity.
That's a bit simplified. Drawing a uniformly random real number from (0,1) seems to perfectly sensible to most people.
(Now, drawing a uniformly random rational number from (0,1), I don't know if that's possible.)
Ubfortunately it's not possible, because a random variable's induced measure is sigma-additive, and you can't add countably infinite of number 'a' to get 1.
> The only hole in this theory is that it’s hard to objectively define “simplicity” (it’s easy within a programming language - shorter programs are simpler - but how does the universe decide which programming language to use?)
(Reasonable) programming languages only differ by an additive constant in their measures of 'simplicity'. Mostly because that constant is just the size of whatever emulator you need to write first to be able to express the rest of the program in your most favourite language that makes the problem simpler.
Would love to witness a debate on these ideas between a well-versed theist such as William Lane Craig and Tegmark or other supporter of the MUH. Dr. Craig has addressed some of these concepts, but I couldn't find him directly commenting on Tegmark's idea. In 2020, Hugh Ross (astrophysicist and founder of Reasons to Believe) was asked, "What are your views on MUH/CUH?" He replied with a funny post that also suggests what a smart theist would argue:
"If I was not a scientist, my answer would be huh. MUH stands for mathematical universe hypothesis. CUH stands for computable universe hypothesis. MUH states the physical universe is not merely described by mathematics but actually is mathematics. CUH states that the mathematics that is the physical reality of the universe is defined by computable functions.
"I believe that the universe is described by mathematics and that this mathematics is ordered, elegant, beautiful, and consistent. It was humans that constructed mathematics to describe the operation of physical reality. That mathematics is no more a tangible physical entity than is our alphabet or our number system. Mathematics is a manifestation of the symbolic capability that is unique to humans among all Earth’s life.
"To say, therefore, that all physical reality or that physical existence is just mathematics, in my opinion, goes way too far. However, mathematics does reveal the nature and source of physical reality. The mathematics we humans constructed to describe physical reality reveals the attributes of the Creator who brought into existence physical reality. That revelation likely explains why of all scientists mathematicians manifest the highest percentage of believers in God."
Source: https://www.facebook.com/128441790567267/photos/a.313268935417884/2885709028173849/?type=3&_rdr
Why is it necessary to objectively define simplicity? Isn't it the theist who is asking you to explain comprehensibility? So, the simplicity is necessary for their argument, not yours. The logic that we are more likely to find ourselves in a more simple universe is sound, but it doesn't mean that we must therefore be in the simplest universe.
Isn't it up to the person positing the simplicity (the theist via comprehensibility) to define simplicity?
And perhaps this next one is a question for Tegmark, but like with many multi-verse explanations, I'm always a little confused when people posit that all possible universes, or all possible mathematical objects exist, when it would suffice, for the sake of argument, that all possible universes, or all possible mathematical objects *can* exist—which satisfies the argument without claiming infinitely more than necessary.
Maybe a nitpick, but important if you're talking maths.
"You can’t make a random uniform draw from an infinite set" is wrong.
You can't make a random uniform draw from a countable infinite set like the integers. There's no issue with a random uniform draw on [0, 1], or any other compact set of the reals.
In Tegmark's universe what does one make of Aquinas' definition of God? If we give the name God to 'the most perfect being that can be conceived' then does this being not exist? Call it the most perfect non-self-contradictory being, if necessary, I suppose.
That's Anselm's definition, not Aquinas's. Aquinas defines God as the uncaused cause which creates all other causes.
Cheers - Anselm's definition is what I intended.
>Cosmological: Why is there something rather than nothing? Because mathematical objects are logically necessary, and “existence” is just what it feels like to be a conscious observer on the inside of a mathematical object.
Can someone explain this to me in simple brain terms? I don't understand why mathematical objects are logically necessary or why logic exists rather than no logic existing.
Not possible, that would make plain how insane the claim is.
Agreed. The claim is incredible (i.e. "not trustworthy")
Why would nothing be more likely than something?
>The only hole in this theory is that it’s hard to objectively define “simplicity”
I would say the bigger hole is a complete lack of evidence for the superficially-absurd axioms.
>mathematical objects are logically necessary
And why must logical necessity induce existence? I don't really care about the existence of God one way or the other, but arguments like these are just silly. You can always just trivially say "but why is it like that?" Even if there WAS nonzero evidence for Tegmark's Theory, it simply begs the question "what is the nature of the medium that requires every mathematical structure to exist?"
Is Poincaré recurrence relevant at all? I am bemused by Bentham's thought experiment about coin tosses bringing me into existence, but if it is useful surely Poincaré does the same job
The debate is damaging to its proponents. I am unlikely to pay attention to a physicist who claims to have developed perpetual motion in his spare time. And it seems to read across to unreasonable uncertainty in other debates. I 100% believe shrimp suffer agony as appalling as Our Lord suffered on the cross vs I think it more likely than not that shrimp feel substantial discomfort.
Wow super cool to learn about this! This has been my belief my entire life. To be honest I have never been able to take any other position seriously.
Yet, I have tried to explain why many times and always utterly failed. Maybe now I l know a name for it I can read and find ways to get it across!
I don't see any meaningful difference in insisting all possible mathematical objects exist because I say so and insisting an unmoved mover exists because I say so.
A definition of simplicity is far from the only hole in this firehose of metaphysical horseshit.
This kind of stuff always reads to me somewhat like Gödel's mathematical proof of God's existence (which I suppose assumes some version of Tegmark's mathematical universe).
If anything this highlights the mysterious nature of this thing we call existence. Do we just feel like we exist because we're bound by the rules of our "imaginable" universe? Or is there something else that makes our universe "more" than just imaginable? I expect atheists and theists to have very different intuitions here (cue Leibniz'd "best possible world").
But also I have always had deep problems with the fundamentals of the setup and the uncountability of these universes. At the end of the day, why even require universes to be consistent (in the mathematical sense) to exist? Don't possible Marvel universes "exist" in exactly the same sense as possible "physical" universes despite the absence of fundamental laws? Isn't making one kind of imaginable universe more "real" a priori exactly as mysterious as making one specific possible universe "real"?
And maybe more importantly: isn't this line of argument fundamentally contrary to what post-Dawkins intellectual atheism is supposed to be about? In the sense that "here's a fully theoretical argument about the nature of reality, it has not falsifiable by any possible observation in the physical world, however it proves whether God exists" sounds a lot more like Aquinas than Dawkins et al? This seems to fail the test of "does this belief affect what you expect to see in the world" test in all but the vaguest senses (like for theists who "only believe they believe" in God, as Yudkowsky would put it).
I don't see any reason that the universe _must_ weight its sampling by complexity. Any function that has a finite sum over the infinite set would do. I think we should still be surprised that the universe is simple rather than containing a large number of reciprocal cheesecakes (or whatever another bias function might optimise for).
As an aside, it's also not clear to me that complexity actually has the finite sum property. For example, if you could identify an infinite subset of worlds that all had the same complexity, it would *not* have a finite sum (*) - and it seems like that should be fairly easy to do under most definitions of complexity. I'm sure Tegmark has a clever trick to solve that although I have no idea how he'd have done it.
(*) suppose infinitely many of your worlds have a complexity of 0.1, then since the sum of 0.1+0.1+0.1+... divergent, so does the overall sum of world complexities.
To actually be convergent you'd need something like the first world having complexity 1, the second having complexity 1/2, the fourth 1/4 and so on.
Is there a good place I can go to if I want to sign up for a feed of most things Tegmark has written (or is writing)? Does he have a primary blog?
A time dimension would not be a mathematical object, but an indexing of a mathematical object to a physical reality. Similarly, we can describe a linear basis and index that to real space, but that linear basis is not the same thing as real space - there is an ontological difference between the two. An analogy would be Borges' Library of Babel. Some of those books would speak of time or change or whatnot, but they are not themselves time, change, etc; they merely indicate it. Moreover, their indication of those realities is lacking content. I.e., there is something that it is like to be time that is not contained within the content of a one-dimensional manifold (or the letters t-i-m-e). So, while our mathematical descriptions of physical reality share similar internal relations with the reality it describes, the very thing that it is is different. For F=ma, m is not a mathematical object. For 2kg, 2 might be a mathematical object, but the kg part is not. The same for the s in the m/s^2 part of the equation.
As far as the Game of Life, the various steps only appear time-like to the temporal observer. There is no actual change, and so if you were some conscious observer in the game, you could recognize the various steps, but only eternally. In other words, you could look at the steps and say that they have some sort of order to them, and you could *call* that time, but you would not experience it in or as time. Why? Because all steps are equally true simultaneously.
If you have the appetite for more, I'll explain the eternality in more detail: Imagine the set of all mathematical objects (using 'set' loosely here). Because it contains all mathematical objects, there is no possible mathematical object that is not contained within that set. Moreover, there is multiplicity in that between any two objects is a relation of non-identity, i.e., something like: for any x and y, x is not y. Your consciousness would be one of these objects (containing but not identified with other, simpler objects). Your consciousness and your conscious experience would be defined as this set of mathematical objects, however they might be ordered. But that means that your consciousness and conscious experience cannot also be identified with another mathematical object that contains a different conscious experience. Whatever conscious experience you have, you have by definition. To not have that conscious experience would be to be a different mathematical object. In other words, if you were a mathematical object, your conscious experience could not be x and y where x=/=y. But change means that something can be x and it can be y through becoming, that is, x becomes false and y becomes true. Mathematical objects, on the other hand, cannot become false - they are necessarily true. And your conscious experience is x and is y through becoming, therefore etc. This goes for all physical objects, not just your conscious experience, and thus there would be no change if all and only mathematical objects existed. But if there is no change, there is no time - the two are at least mutually defined.
This problem is the same problem encountered by the pre-socratics. There are two options: 1) something underlies the change such that z changes from x to y or 2) there is nothing underlying such that x simply becomes y. Parmenides chose the latter and thus denied the possibility of change. Why? Because if x is being and y is not x, then y is not being. So any change that x could experience would be from being to not-being. But being cannot become not-being for then it would mean that being would be not-being, a contradiction. Applied spatially, there can be no multiplicity of being for the same reason. So, for Parmenides, all being was uniform and unchanging. Tegmark gets us to a similar conclusion: the only thing that exists is the unchanging "set of all sets."
The largest religion in the world is Christianity, for which proof of God’s existence is supplied by concrete historical events—most importantly, the resurrection of Jesus. Obviously, a thought experiment like this does not and could not “defeat” a proof like that: one cannot disprove the existence of something in the abstract that has been observed in reality.
On the flip side, if those historical events did not happen, that alone suffices to defeat the claims of Christianity (cf. Paul: “if Jesus is not raised we are the most pitiable people of all,” or words to that effect).
The idea that all metaphysical possible universes obtain runs into problems with anthropics. I'd expect to be where most of the same rosen's are or where most of the humans are, but a metaphyiscialy possible universe is one just stacked with quintillions of Sam Rosens right next to each other.
I'm probably a bit late to the party, but I'm a bit surprised "Tegmark's mathematical universe" is actually something taken seriously. I was bothered by the idea that maybe existence was just "mathematical possibility" about 25 years ago as a teenager but even then I relatively quickly realized that actually there are a lot of pretty strong notions that go into what it means to be a "possibility" and stopped taking the thought seriously as any kind of foundation. After that I went on to learn more about mathematics, now I take it even less seriously - mathematically, there are just so many ways to define things and group things as being "equal" or different or define structure etc that the idea seems even more nonsensical now.
But the reason "we waited this long to get it" is not because it's a particularly good metaphysics - the idea of the Boltzman brain is very closely related this kind of thinking (it's 100 years old), and also one way to reject this kind of thinking. Btw, sentences like "If we were selecting for simplicity, we would expect for most objects to start as a singularity and then explode outward" are just straight up nonsense and about as circular as saying "if things looked like our universe, we would expect them to look like our universe" since you're just defining "simplicity" by what you personally think is "simple" (but speaking as a mathematician - singularities are not simple at all, and explaining the arrow of time is also not simple at all even though there are lots of arguments that sound good but are subtly circular here too)
These arguments were god-of-the-gaps to begin with. The I don't understand X, therefore god.
Tegmark is a fairly good potential answer to those gaps. But there is no way god is a better answer than "I don't know".
> Cosmological: Why is there something rather than nothing?
God doesn't help here in the slightest. Why is there a god rather than nothing?
> Fine-tuning: Why are the values of various cosmological constants exactly perfect for life?
Is it? We really don't know what alien life forms might exist in universes with totally different laws of physics. We aren't particularly sure what alien life forms might exist under our physics? Can you get life forms knitted of plasma vorticies and electromagnetism living deep within stars?
And the usual argument goes "if gravity was 5% stronger ..." as if god only got to chose the constants, and couldn't have written entirely different and much more complicated laws.
> Argument from comprehensibility: why is the universe so simple that we can understand it?
There are parts of the universe that no humans understand yet. And plenty of humans who utterly fail to understand that the earth is round not flat.
Besides, this fails conservation of expected evidence.
"Why is the universe so complicated that no human can possibly understand it. Surely such a complicated universe could only have been invented by a superhumanly smart god?"
The god hypothesis predicts both options equally well, it predicts nothing here.
> First cause argument: All things must have a cause.
Basically the cosmological argument again. God always gets a special exception. What caused god to exist? Super-god? If all things really have a cause, this implies either a self sustaining time travel loop, or an infinite regress.
In related news, DNA evidence defeats "He who smelt it, dealt it".
It's not that this doesn't work as such, it's more that it's using a nuclear shaped charge to crack a nut.
Although considering how many people still believe in bronze age superstitions in 2025, that's quite a lot of nuts.
Hey guys, I think I randomly drew the solution where I am god in this world. I am still practicing though, apologies for the many evils, I'm working on it. Please help me out too, even though I am infinitely good and infinitely powerful does not mean I want to solve everything myself.
This just begs the question of "Why should all logically coherent mathematical objects exist, rather than nothing?"
Didn't Tegmark have to modify his theory due to criticism from Gödel's theorems to having only fully decidable mathematical entities existing? From the linked wiki:
Tegmark admits that this approach faces "serious challenges", including (a) it excludes much of the mathematical landscape; (b) the measure on the space of allowed theories may itself be uncomputable; and (c) "virtually all historically successful theories of physics violate the CUH"
I wonder what it is about this that just "clicks" for some people and not others. Like Brendan, jamie b., and Caba say in this thread, this has just always been obvious to me for as long as I've been thinking about the "Why is there something rather than nothing?" question, even before I encountered Tegmark or David Lewis. And yet I've never been able to convey this obviousness to anyone else.
"Tegmark’s hypothesis says: all possible mathematical objects exist."
That assertion begs for justification, and finds none. Building on it is an exercise in fantasy.
So "The fact that [something] exists in possibility-space is enough for the being to in fact be experiencing it" fails; existence in possibility-space only means the bare possibility if existence-in-fact.
"Some mathematical objects contain conscious observers."
Only one "mathematical object" is known to contain conscious observers: our universe. Whether there are others is completely unknown and uncertain.
"Most conscious beings exist in very simple universes, ..."
Only one universe is known to have conscious observers: ours. No "simpler universes" are known, much less any with known conscious observers. "
"Miles Donahue’s ... says he can’t really think of a great response to fine-tuning, but suspects that the terrain is too difficult and unexplored to give up and say God is the only answer."
Like Tegmark, fine-tuning asserts things to be known which simply are not.
The arguments for God are all refutable without Tegmark's hypothesis.
Of course, when you define "God" as having a white beard, or being all-knowing/ all powerful, etc, you run into problems. But when you define God as "some conscious force outside of humanity that has, at least once in human history, communicated with humans in some way," then you're basically just making an argument that the first alien contact with humans has happened in the past rather than will happen in the future/ will never happen (as God and a powerful alien are basically indistinguishable from one another, when you set moral considerations aside, as those will always be debateable). And this argument for God's existence doesn't seem so insane/ irrational to me. If the universe is as big as we think it is, then likely there are other life forms out there. If there are other life forms out there, likely we are not the smartest life form. If there is a smarter life form than us, it likely would discover us before we discovered it. If it discovered us and communicated with us before we discovered it, it would likely be experienced in a way similar to how humans have their supposed spiritual experiences. As it is logical to assume we aren't the smartest thing that has emerged from these billions of GALAXIES, and it is logical to assume that whatever is smarter than us would discover us before we discovered it (and probably has by now, given that we think the universe is billions of years old), then it's logical to believe in "God." Not necessarily an all-powerful, all-knowing, or even all-good force. But I mean, the primary real question here is: "are all religious people idiots who are decieving themselves or are they onto something?" They might be 99% off the mark with their hypotheses based on their supposed spiritual experiences, but if they are 1% on the mark, if these supposed spiritual experiences have even a shred of validity to them, *that* basically disproves the whole materialistic atheist hypothesis (which is basically that all religious people belong in an insane asylum). Anyways. there's my God proof. I know i define God more flexibly than most (it seems only logical), but I also think God, by my definition, almost certainly exists. My "faith in God" is basically an expression that I think 1) science is incomplete, 2) not all morality/ spirituality is bullshit/ self-created arbitrary nonsense and 3) something's out there. Use your "every mathematical object that can exist does exist because I said so" proof to disprove that ;)-
If we "dumb down" the concept of God enough, gods become less controversial and this topic becomes unimportant to everyone except an academic minority.
In ordinary conversation, God refers to far more than some extraterrestrial, superhuman intelligence that happened to contact a few humans long ago. God is said to have an ongoing relationship with humanity, complete with plans, commands, rewards and punishment.
Among philosophers this ordinary understanding might be dismissed as trivial, but in the rest of the world this understanding is tied to most of the significant issues facing humanity.
So, if I may ask: is this matter more than academic?
This shines a new light on UNSONG, which I just finished reading for the third time and recently introduced to my neighborhood ladies' book club.
I asked William Lane Craig about this, and he just responded to my question:
https://www.reasonablefaith.org/writings/question-answer/tegmarks-mathematical-universe-hypothesis-and-natural-theology/