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.
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.
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.
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."
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.
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.
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.
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"?
"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.
"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.
>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.
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.
> 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.
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.
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?
>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"?
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 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.
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.
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.
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:
>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.
" 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.
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 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?
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.
This theory, the Mathematical Universe Hypothesis (MUH), alongside the Computational Universe of Stephen Wolfram, can be seen as a modern derivative of Pythagorean ontology ('All is number') grounded in the immutable cosmological model of Parmenides, the founder of the Eleatic School in the 5th century BC. I explore these kinds of views on my Substack.
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.
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.
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.
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?
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.
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.
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.
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.
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.
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.
They have probabilities because they are not necessary.
You *have* to.observe them, because you can't deduce them, because are not necessary.
I give you string theory. :)
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.
Thanks, agreed.
Why bother? The argument could be adapted to show that such a person exists.
> 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.
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?
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."
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.
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.
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.
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"?
"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.
>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.
>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.
>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.
You do know that stories can be shared, right?
I'll admit, that's a lot more intriguing and convincing than I expected. What can I read to find out more?
> 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.
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.
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?
>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"?
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 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.
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.
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.
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.
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.
Because law deals with the physically possible and you want eyewitness testimony that we have no way of verifying to prove the physically impossible.
> > 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.
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/
>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.
" 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.
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.
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 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?
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.
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.
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.
This theory, the Mathematical Universe Hypothesis (MUH), alongside the Computational Universe of Stephen Wolfram, can be seen as a modern derivative of Pythagorean ontology ('All is number') grounded in the immutable cosmological model of Parmenides, the founder of the Eleatic School in the 5th century BC. I explore these kinds of views on my Substack.
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.
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?
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.
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.)
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.
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.
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)
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/
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?
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.
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.
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.
"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: