Comment by MichaelZuo | Hacker News Reader

Comment by MichaelZuo | Hacker News Reader

"Trick though it is, it has real physics in it. The gravitational path integral doesn’t distinguish replicas from a real black hole. It takes them literally. This activates some of the latent topologies that the gravitational path integral includes. The result is a new saddle point containing multiple black holes linked by space-time wormholes. It competes for influence with the regular geometry of a single black hole surrounded by a mist of Hawking radiation."

Ah yes, the complex of wormhole interlinked blackholes surrounded by mists of Hawking radiation...

This style of writing, without the actual math, seems to more so obscure true understanding than reveal it for such a complex construct as english words are very likely insufficient for actually capturing the true meaning.

Adding the (partial?) equations of the path integral and/or the matrices would allow for an actual understanding without the confining nature of human words.

In fact just thinking and writing this comment made me more confused, just a few paragraphs prior the path integral could not be fully calculated, but now here it is certain that "the gravitational path integral doesn’t distinguish replicas from a real black hole". Just how powerful is this 'mathematical trick'?

>Adding the (partial?) equations of the path integral and/or the matrices would allow for an actual understanding without the confining nature of human words.

Go read the paper if you want that. Quanta isn't a journal its a popular science mag.

"But in terms of making sense of black holes, this is at most the end of the beginning. Theorists still haven’t mapped the step-by-step process whereby information gets out. “We now can compute the Page curve, and I don’t know why,” said Raphael Bousso at Berkeley."

So it does not seem that the physicists fully understand their calculation results either.

Edit: here's the arxiv link: https://arxiv.org/abs/1911.11977

Thanks for the link. I find it very frustrating when pop science magazines refuse to link to the actual paper. I don't want to read their attempt to put what the paper says into layman's language; their attempts are usually way off. I want to read the actual paper.

Edit: I was finally able to find links to actual papers in the article:

https://arxiv.org/abs/1810.02055

https://arxiv.org/abs/1905.08255

https://arxiv.org/abs/1905.08762

https://arxiv.org/abs/1908.10996

https://arxiv.org/abs/2002.08950

https://arxiv.org/abs/2004.05863

These appear to be the papers giving the various calculations the article discusses. There are also links to some previous work that was built on:

https://arxiv.org/abs/0804.0055

https://arxiv.org/pdf/1304.4926

https://arxiv.org/abs/1408.3203

I'm a layperson. Does this mean there's no firewall but they don't know how?

To someone like me, who believes that the universe is, must be, fundamentally a computer, the actual academic paper is hardly any better. Whatever the paper is doing is not describing any kind of computational process. It's a mille-feuille of semi-rigorous mathematical abstraction that sounds far more like a kind of liturgical incantation than a description of the software our universe is running.

That's not to say it is definitely not useful! It could be that, for some bizarre reason, reading the mathematical tea leaves of our current incomplete (and incoherent) theories might well yield insight into post-quantum physics. I do doubt it though.

To someone like me, who believes that the universe is, must be, fundamentally a computer...

Why do you believe that?

It'd be hard for it not to be yet remain consistent with observations and conservation laws.

Depends what you mean though. Define "computer".

See this sibling comment for context https://news.ycombinator.com/item?id=24948188

The definition you are looking for is very well established and intensely studied in physics and theoretical computer science. This is a good place to start a wikipedia exploration of the topic: https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis

Because I don’t think infinite amounts of information, and uncomputable numbers, exist. They are fantasies, and relatively recent ones at that. Unfortunately those fantasies came to dominate 20th century mathematics, and in the guise of string theory obtained a death grip on fundamental physics. Fortunately a new generation of smart people, with intuitions honed on computers, is well placed to capitalize on this arbitrage opportunity.

Heartening to see that unusual perspectives and opinions are rewarded with downvotes.

I suspect the downvotes are due to (1) the lack of intellectual humility and (2) misrepresentation in your comments. Plenty of physicists agree that uncomputable numbers are unphysical and the idea that infinite information density can not exist is in no way new or controversial (it is pretty much the starting point for the holographic principle, one of our main paths to a theory of everything). They are beautiful ideas worth discussing, but you used your knowledge of them to disparage people and fields which it seems you only have passing familiarity with.

Yes. It is dogmatic, not scientific, to suggest that a paper is worthless because the authors didn’t frame their argument under some set of axioms you just really identify with, conceptually.

> those fantasies… in the guise of string theory obtained a death grip on fundamental physics

What? The real numbers, with all the uncomputable reals included, are used in every corner of physics, not just in string theory. There is no treatment of calculus (with any semblance of popularity) that does not feature the usual real line.

Nothing in physics has infinite precision. Math is an abstraction - which is to say a stylised representation - and while you can imagine processes and representations with infinite precision, that level of precision is metaphysical.

This confuses Platonists who seem to believe that differential equations really exist - somewhere.

But that's like arguing that you will clock up air miles by zooming around Google Maps.

The set of operations you can perform on representations of reality is in no sense identical to the set of operations you can perform on reality itself.

If this still isn't obvious, try to differentiate a rock.

I don't know why you’re being downvoted. This is a rather good analogy. And it doesn't mean the initial comment of this thread is not presumptuous. In other words, the why should the expectation be that general authors assume universe be computational in nature, is sorely missing. But it doesn't invalidate an explanation of how analytical and discrete systems are yet unreconciled (and may never be).

I'm not disagreeing that the real numbers have no physical basis; that would be silly. I'm disagreeing with the absurd claim that "uncomputable numbers … in the guise of string theory obtained a death grip on fundamental physics". The real numbers are used in every single part of physics, and physicists do not care to distinguish between computable and non-computable reals, because that makes the theory much more complex with no known practical benefit.

I also wish that the person I initially replied to would expand on their vague claim that

> Fortunately a new generation of smart people, with intuitions honed on computers, is well placed to capitalize on this arbitrage opportunity.

What? The real numbers, with all the uncomputable reals included, are used in every corner of physics, not just in string theory. There is no treatment of calculus (with any semblance of popularity) that does not feature the usual real line.

First of all, there is no application of physics where uncomputable reals make one bit of difference. Unpopular treatments of Calculus that only deal with computable numbers exist and produce the same results for physics.

Secondly, physicists have a well-known disregard for whether official mathematical constructions support how they are using them. To name but two examples, both the Dirac delta and renormalization were in wide use long before any formalization existed that could justify them.

Given that, there is no way in which the use of mathematics by physics serves as justification for the reality of the obscure mathematical notions that mathematicians have developed.

> Unpopular treatments of Calculus that only deal with computable numbers exist and produce the same results for physics.

I'd really appreciate if you named them. I've seen synthetic differential geometry, which isn't nearly well-developed enough for use in all of physics, and I've seen nonstandard analysis, which obviously doesn't do away with the uncomputable reals at all.

> there is no way in which the use of mathematics by physics serves as justification for the reality

I am not saying the standard reals are real. I am saying that they are more convenient than any existing alternative, and fulfil the current needs of all of physics. I am also saying that the parent's claim that "uncomputable numbers … in the guise of string theory obtained a death grip on fundamental physics" is absurd, since string theory and uncomputable reals are pretty much unrelated.

I was thinking intuitionistic math, such as smooth infinitesmal analysis.

And yes, they are less developed than classical analysis, and harder to work with. But should not produce different results.

As someone who does lots of constructive math, intuitionistic math can't reproduce a large number of results on the reals and this is a kind of well-known thing. Even basic notions of continuity can't be reproduced in the same way and as a result there are multiple competing formalisms. It is possible that there are alternative ways to reproduce results of interest to physics but that's far from obvious.

The world of SIA and SDG is a very, very different world to that of classical analysis. If you think that they "should not produce different results", then

(a) you're either wrong or incredibly optimistic regarding our ability to carefully rephrase the statements of classical analysis in a way that works constructively.

(b) what would be the point of a harder-to-use system that offers exactly the same results, anyway? The whole reason I find SDG interesting is that it will eventually be simpler to use, and because it provides an entirely fresh of the number line.

Thank you for answering. My apologies for not engaging previously with your answer.

I agree that computation is likely a better model than string theory. However I have the humility to not insist that reality must match any set of concepts that I have.

In particular in this case results like the ones discussed at https://www.scottaaronson.com/blog/?p=3827 and https://www.scottaaronson.com/blog/?p=4372 say that quantum mechanical systems can perform operations in ways that are different from and fundamentally impossible for classical computers. Therefore it seems likely to me that classical computing is going to break down pretty hard as a model for how things really work.

In defence of the idea, if all physics is found to have a logical and mathematical basis, then doesn't all physical expression and interaction become computation?

Couldn't it be the reverse? Couldn't computation be the closest approximation to pure expression and interaction? Seems to me that this is more natural.

Also, I will bet 500$ that no one will be able to prove that all physics has a logical and mathematical basis within my lifetime :)

I bet the same. I'm not sure that hard determinism could ever be proven, even if it were the case.

"Computable" is a bit more strict than "logical and mathematical". We can define many perfectly consistent processes with perfectly consistent "observable values", which are inherently uncomputable (as in, there is no algorithm, even an inefficient one, that runs on Turing machines, capable of calculating the observable).

Here is my favorite example: https://en.wikipedia.org/wiki/Chaitin%27s_constant

I guess much of what I'm saying counts on hard determinism, and computation that isn't limited to what can be achieved with boolean logic. I'm talking out my ass here a little, but I picture quantum annealing as a form of computation where quantum physics effects are the actual execution engine.

Quantum effects are still things we can simulate on a Turing machine with a program that halts (just inefficiently slow given our current knowledge of complexity theory). Bringing in quantum effects does not make things uncomputable.

I now see the distinction you're trying to make about computability, so does this revised claim satisfy you?

> if all calculation of physical effects are found to be reducible to mathematical procedure with definite outcomes, then aren't real-world physical effects execution of computation?

There's probably room for semantic disagreements here. It does seem that the definition is somewhat tautological, but I'd claim that that's because the two are equal.

To an extent, but I think there is still a counter example that gets to why this is such a subtle distinction (computable vs "reducible to a mathematical procedure").

Consider an "analog" computer that is in principle noise-free (i.e. elementary operations like addition on this hardware are performed by adding up two analog quantities, e.g. voltages or currents, and these quantities are infinitely smooth, not discreticized/digital, and not disturbed by hardware imperfections and noise). I can create a model of such a device in theory and if I use only the axioms of classical physics (which we now know are wrong), then such a device will be capable of computing and representing numbers that can not be expressed by a Turing machine (i.e. it would be not just faster than a Turing machine or a quantum computer, it will be capable of things that a Turing machine can not ever do).

This is a device that one can imagine existing, and to quote you it is "reducible to mathematical procedure with definite outcomes". It just happens to be a mathematical procedure we find to be rather unreasonable for our universe (because of unavoidable classical thermal noise and non-classical quantum effects that cause discretization).

Some physicists and computer scientists (me included) like to take this as a starting point, as a reason for why certain theories of physics are probably wrong. I personally find this to be a very elegant, powerful, and subtle approach, up there with Noether's theorem or the second law of thermodynamics. "A theory of physics can not be true if it permits the construction of a computing device that can solve the halting problem" seems pretty much on par with "A theory of physics can not be true if it disobeys conservation laws / causality / locality / entropy considerations". All of this with the caveat that one should not be dogmatic about these vague statements, rather just take them as a general guideline.

I agree with what you're saying (as much as one can as an outsider). But, going back to the original claim, could you say the physical systems that bind our particular universe could be classed as executed 'computation', given that they likely could be computed by a Turing machine?

Side-question: is computation, by definition, strictly limited to that achievable by a Turing machine?

I do not think we have an answer to the first question. At the end it does not really matter whether our universe runs on an actual computer or is simply equivalent to a computable process (as opposed to an uncomputable one). However, for aesthetic reasons some scientists guide their work in theoretical physics by studying specifically only physical laws that are, in principle, computable. Said in other words, some scientist take the "Extended Church-Turing Thesis"[1] as an axiom of physics and work from there.

To the side question, yes, that is a typical definition of "computable" (usually what a CS theorist means by the word). The reason we believe it is a useful practical definition is that (1) such a definition ends up equivalent to a number of other interesting definitions and such a net of equivalences usually ends up being interesting and empowering (2) Turing machines form a "universal" modality of computation because we have proofs that they can "efficiently" simulate other theoretical models of computation (3) We simply do not know of other modalities of computation that can exist in our universe (which is a bit of a circular statement in the context of this conversation) (4) It simply seems to be a useful formalism that enabled us to prove a ton of useful results, so even if it was not as elegant as I claim, it definitely ended up being a productive and practical way of thinking. Side note: Quantum computing muddles the water a bit in terms of what is efficiently computable, but if something is not computable for a Turing machine it is still not computable for a quantum computer (however there are a few things that seem to take exponential time on a Turing machine while taking only polynomial time on quantum computer).

[1]: https://www.scottaaronson.com/papers/npcomplete.pdf

Thanks for your long-form reply. Super informative and entertaining.

For #1, wasn't speaking of the 'universe as simulation' hypothesis specifically, I think an assertion either way is indefensible. It was more about unpacking semantics, i.e., what is the most reductive form of a computation? Does there need to even be an operator that seeks to know an answer? Is computation something that only exists in human context, or can it simply be the unfolding consequences of the 'seed' of the universe? Just rumination on abstract inconsequential ideas :)

#2. I'm familiar with some of the nomenclature is regards to 'computing' complexity, and my question, in retrospect, seems a little silly. Computation is computation. I still only have a lay understanding -- as much as I need to know for perf and the differences between algorithms -- and I'll have a look at that paper and hopefully understand the subject a little deeper.

Thanks again.

I think most of my colleagues that care about such distinctions would say that in the most reductive form one does not need an operator or a goal for the computation. This is the typical assumption I would have when discussing this formalization of the laws of physics.

By the way, if you are fan of SciFi, Greg Egan has very fun stories that play with these ideas (nothing rigorous or seriously scientific, but certainly fun).

Stephen Wolfram takes that view too, but it seems like a fairly narrow lens to peer at the universe through. I suspect it may be true, but that doesn't even mean it's necessarily particularly useful for solving many classes of problems. In fact, are there any actual problems in Physics that have been solved by this approach?

Lots of things are true that aren't much use. Much of science, including physics doesn't describe computational processes. Does that make most of science and physics equally useless?

I'm not sure what to make of this comment. I'm not going to pretend I understand any of this at anything short of an extremely superficial level but you argument sounds like something a religious fundamentalist might say; just insert their belief system.

"To someone like me, who believes that the universe is, must be, fundamentally a construct of god, the actual academic paper is hardly any better. Whatever the paper is doing is not describing any kind of god process... sounds far more like a kind of liturgical incantation than a description of how god is running our universe."

I might be wrong, my understanding is limited, but you shouldn't dismiss something because it doesn't fit with you beliefs; you beliefs may be wrong g.

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