[redhat-reallyp]

> It's the simplest hypothesis to date that I know of. Therefore, I assign at least a non trivial probability to it.

I don't think it's simple at all. What is the role of "mathematics" in the conjecture - what is the word supposed to mean, and what about this new definition of mathematics results in the creation of physical realities? It seems unrelated to the discipline I know of by that name, which at its most general, is an approach to defining, analyzing, and using formal models. Essentially Tegmark is saying "all formal models (of a universe) must have a concrete realization", but why, and what is the point of introducing formal models into the picture - what role do they play?

It comes down to this comment of yours:

> we try to express the laws of physics with pure mathematics since Newton, if not earlier. I think it at least indicates a hope that reality may be accurately described by pure math. Provided we can, good luck trying distinguishing that, and "being an incarnation of math." No way we can test it from within.

To test a claim, the claim first has to be stated coherently. Mathematics is an approach we use to describe and model things, including the universe. It simply isn't some sort of creative force existing independently of the minds that can contemplate it. So when someone says "the Big Bang and cosmological evolution of the universe arose out of pure geometry", they are speaking incoherent nonsense, because "pure geometry" is simply not the sort of entity that can produce such an effect.

For this to make sense, someone would have to describe the nature of this creative force that they're calling pure geometry, and then the only connection to what we normally call geometry is that ordinary geometry would be a way of describing the effects of that creative force.

Geometry or mathematics are approaches to modeling, and are neither physical phenomena themselves nor the cause of those phenomena. As soon as someone claims that "it" is the cause of phenomena, they have committed an equivocation fallacy and begun talking about some other "it" which they haven't defined.

> You mean, current evidence speaks again the level IV multiverse hypothesis? Or something else? Anyway, please name three.

I was responding more to your characterization than to Tegmark's actual definition: if "every mathematical structure just exists" and "the simpler ones ... have greater weight", then it should have observable consequences, but we don't observe such consequences. For example, we might expect things to be constructed from pure Platonic solids, we might expect the subatomic realm to be less fuzzy, etc.

> With enough double and triple checking, computer-verified proofs… we can be rather sure we did find the simplest explanation.

Actually I don't agree with that. Finding simplicity does not always lend itself to formal process. But I'm saying that although Occam's Razor can remind us that a better explanation could be simpler than the one we currently have, it does not tell us that this is the case.

> I was just saying that when I hear someone claiming something that I don't find very surprising, I generally take that as serious evidence that the claim is true.

We differ on that. The fact that something is not surprising is not evidence. Many claims that are not surprising turn out to be false. To be more likely to believe something that seems unsurprising to you implies that you're choosing beliefs based on personal bias.

> Quantum mechanics has to do with complex amplitudes, whose square determine the Born statistics. Plus, the wave function as we know it is deterministic.

None of this contradicts what I was saying. Those complex amplitudes are complex to deal with superposition, and once that is taken into account, probability densities in QM are described perfectly by probability theory, so I don't know in what sense you mean that the relation is "tenuous". This has very little to do with one's position on interpretations, it's there in the math whether you like it or not.

[loup-vaillant]

(If you want to continue this conversation offline, you can reach me by e-mail —see my profile and my website.)

Okaay.

By "simplicity", I mean something like the inverse of Kolmogorov complexity. I know it's not very well defined, but given a Turing complete language, there is a proof that a given program is the shortest of its equivalence class —if it is.

I said "simplest", not "easy to grasp for a human brain", or even "simple". It's just that "poof magic we have simple mathematical rules on which the universe runs" is a simpler hypothesis than anything else I have heard from (such as the God Hypothesis). There's also a certain… elegance in positing that every set of mathematical rules are actualized. That way, we don't have to pick a particular rule, making the master program even simpler.

On Quantum Mechanics, okay, I guess you're right. Just remember that while amplitudes are out there in the world, probabilities are in the mind.

Do you think plausible that we could, in principle, find a mathematical model that perfectly describes the universe? To me, the answer is obviously "yes", even though I'm not certain that we could find this model in practice. Now, assuming our universe does run on math, it is quite impossible to test for different kinds of ontological existence. Do we live in a simulation? If the simulation isn't buggy, we don't stand a chance at root escalation, and we can't tell. Does the mathematical rules exist, like "poof magic", or do they need some exterior force or entity to be actualized? Again, we can't tell, because there's just no way out of our universe.

> For example, we might expect things to be constructed from pure Platonic solids, we might expect the subatomic realm to be less fuzzy, etc.

Maybe not. The actual laws of physics may be even simpler than that, despite the complexity that arise from them. We'll see when we find them. Occam's razor doesn't favour surface simplicity, it favours simplicity at the deepest level.

> The fact that something is not surprising is not evidence.

Indeed. It is prior information, which is just as important as evidence. Without prior information, you don't stand a chance at interpreting evidence. Data can't speak for itself.

> To be more likely to believe something that seems unsurprising to you implies that you're choosing beliefs based on personal bias.

Or, it could mean that I tailor my surprise to my actual probability of the thing being true, based on the information I have. Heck, I have emotions, I might as well use them. By the way, didn't you notice that you're not surprised all the time? That emotion isn't as irrational as a Straw Vulcan would believe.

I'm not sure what "personal bias" you speak of, but there's no escaping the fact that different people have access to different prior information. They will inevitably make different probability estimates, even if they are perfect Bayesians.

You should read Probability Theory: The Logic of Science. It's an excellent book.

[redhat-reallyp]

> poof magic we have simple mathematical rules on which the universe runs

I'm not arguing against the idea that the universe might be described by simple mathematical rules - after all, we have a fair amount of evidence that it can be, for some value of "simple". But it's an enormous unsupported jump from there to the idea that the mere possibility of such rules somehow gives rise to a universe that follows them, ex nihilo, or variations on that idea.

Generally, such handwaving is not accompanied by much serious exposition. Even Tegmark's writing on the subject doesn't get into it in enough depth to seriously evaluate. It's an amusing conjecture, but I'm not aware of anyone having developed it beyond that point.

It's also strangely reminiscent of other attempts to delegate the creation of the universe to a mysterious unexplained force: is "mathematics did it" really any different than "a god did it" as an explanation? Neither are actually explanations, they just give the superficial appearance of explanation via a sleight of hand in which the entity in question is implicitly assumed to somehow have the necessary wherewithal to do the job it's accused of. To me, "mathematics did it" is about as good an explanation as "the Great Penguin did it".

> Now, assuming our universe does run on math, it is quite impossible to test for different kinds of ontological existence. Do we live in a simulation? If the simulation isn't buggy, we don't stand a chance at root escalation, and we can't tell. Does the mathematical rules exist, like "poof magic", or do they need some exterior force or entity to be actualized? Again, we can't tell, because there's just no way out of our universe.

I agree with this mostly, although again I'll point out that the entire idea of seeing our models of the universe as being somehow responsible for its creation runs the risk of being a huge category error, so I don't take it for granted that the universe actualizes mathematical rules in that sense. The rules we like to model may simply be an occasionally emergent property of a chaotic physical substrate, and we find ourselves in a predictable corner of some randomly organized multiverse by virtue of the anthropic principle.

But to your larger point that it's likely to be impossible to test the ontological status of mathematical rules, that's a major part of why strong claims in this area seem incoherent to me.

> Occam's razor doesn't favour surface simplicity, it favours simplicity at the deepest level.

Occam's Razor is a simple heuristic that has no such bias. The only simplicity it favors is the removal of redundant aspects of a model, and redundancy can exist anywhere, whether superficial or deep. Further, "redundant" can be relative to one's purposes. Many physical models are deliberate simplifications of the phenomena being modeled, e.g. gases, fluid flow. This often seems to be forgotten when people start to confuse mathematical models of the universe with the universe itself.

> By the way, didn't you notice that you're not surprised all the time? That emotion isn't as irrational as a Straw Vulcan would believe.

I distinguish between everyday claims, like someone telling me they went to a movie, and claims about new discoveries about the universe. You don't need to revise your theories about the universe to provisionally accept the claim that someone went to a movie, for example.

But a claim that entails revision of a theory needs to be treated differently, and in that context, being "unsurprising" is not really particularly relevant - such claims can and should be evaluated on the basis of whether they are supported sufficiently strongly.

> Heck, I have emotions, I might as well use them.

I disagree with using them to justify a conclusion about the validity of a scientific claim. Certainly many people seem to operate on this basis, but it leads to a great deal of irrational behavior.

> You should read Probability Theory: The Logic of Science. It's an excellent book.

Thanks, I'll check it out.

[loup-vaillant]

On "poof magic": I agree, with a tiny minor reservation: when we say "mathematics did it", we stand a chance at speculating how.

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> […] the entire idea of seeing our models of the universe as being somehow responsible for its creation runs the risk of being a huge category error […]

Oh yes. When you think of it, actual models are encoded in brains, paper, computers… Which aren't exactly responsible for the existence of the whole universe. So,

> I don't take it for granted that the universe actualizes mathematical rules in that sense.

Neither do I. I just give it enough credence to put it in a shelf, and look at it again once we know more.

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> I distinguish between everyday claims, like someone telling me they went to a movie, and claims about new discoveries about the universe.

So do I. This is not a new discovery about our universe, however, not yet. This is a new discovery of a mathematical simplification. I wouldn't be surprised if this one yields no easily testable prediction, much like the Many Worlds Interpretation.

Anyway, I suspected for some time now that the fundamental laws of physics were simpler than they looked. I expected someone to eventually find simpler models. So, when some people claim they did, they at least get my attention. If you did not have the same expectation to begin with, then of course you would reach a different conclusion from seeing the claim.

That said, I do agree that

> such claims can and should be evaluated on the basis of whether they are supported sufficiently strongly.

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> I disagree with using them to justify a conclusion about the validity of a scientific claim.

No no no, that's not what I was trying to convey. Actually, that's about exactly the reverse. First, I try to have correct beliefs about the world. Then I try and tailor my sense of surprise to those beliefs. That way, when I make an observation (such as reading about a claim), I can use my surprise (or lack thereof) as a hint (no more) about the credibility of this new information.

I won't try to use my sense of surprise to justify anything to anyone. It's only a descriptor of my own beliefs. It's a valid argument only to the extent you trust my beliefs. Which would be foolish: I'm just a random guy on the other side of the internet.