I would be surprised to learn that 90% of physicists even know what the MUH is.

It is very popular in certain subcultures but it is definitely not a topic of discussion in physics circles.

@FedericoRottoli But for 90% of physicists to agree that MUH is false (i.e., for this market to resolve NO), they must know what MUH is. So I don't think this is necessarily a reason to buy NO.

@WinstonOswaldDrummond i agree, i bought NO because i think the MUH is (not even) wrong, not because I expect the market to close any time soon. Since i don't expect the market to close, i treat it as a keynesian beauty contest

@FedericoRottoli That’s fair :)

Selling because there's no reason this should ever resolve. I think good physicists probably wont ever think they know whether it's correct or not.

If this was likely to resolve anytime soon, I would bet it all the way down to 0%. I don't think the mathematical universe hypothesis is even logically coherent, let alone likely to be true. It's basically just the reification fallacy turned up to eleven.

@JosephNoonan The hypothesis is not testable and never will be, as there is no way to interact with the other mathematical universes. I am even in doubt in this context the word "exists" makes a good sense. At would you be so sure about the outcome in such situation? (I would be keeping a lot of uncertainty about whether the answer is yes / no or even that the question did not make a good sense).

@Irigi The reason I'm so sure of NO isn't because I think it will be tested and fail (hence why I'm only making a small signaling bet here, rather than a large bet that will never pay out). It's mainly on logical grounds - like I said, the hypothesis itself isn't even coherent. The reason for this is that the mathematical Universe hypothesis says more than just "Every mathematical structure describes an actually existing universe", but "Every mathematical structure is a universe, and our universe is one of these mathematical structures." That's just straight-up nonsense - to say that the universe literally is a mathematical structure rather than just that it has a mathematical structure would mean that the universe is an abstract object. It's a category error. In fact, the very first example of a category mistake given in the Standford Encyclopedia of Philosophy is "the number two is blue", i.e., attributing physical properties to mathematical objects.

Though there are also good empirical grounds for believing it's not true (and that it's maybe-more-coherent variants, like "there are universes with every possible mathematical structure" aren't true). Mainly that the universe is believed to operate under a set of relatively simple laws, whereas, if every mathematical structure describes a universe, the vast majority would have no describable set of laws at all. In fact, the proportion of mathematical structures that we can actually explicitly define (insofar as this proportion is a well-defined concept itself) is zero, since we can only define countably many. So what we should expect to see on Tegmark's hypothesis is a universe that's as chaotic as it can be while still allowing for intelligent life. Consider the fact that, for every orderly mathematical structure, there's another that makes a completely random change to it - for example, in addition to the mathematical structure that defines the laws and evolution of our universe, there are infinitely many describing a universe that starts out with the same laws as ours and follows the same evolution until last Tuesday, when they suddenly switch to a completely different set of laws. So we shouldn't expect there to be consistent physical laws under Tegmark's hypothesis - in fact, the chances of there being any are zero.

@JosephNoonan Sorry for replying slowly. Thank you for the detailed answer.

> to say that the universe literally is a mathematical structure rather than just that it has a mathematical structure would mean that the universe is an abstract object. It's a category error.

In this aspect, I understand MUH as follows: Every coherent mathematical description has physical realization. Then it is not a category error, is it? It is just very strong statement about multiverse.

I am not sure whether MUH goes into detail of what mathematical properties need the object have to have physical realization. There is probably many variants how this could work.

Toy example of a mathematical universe: Let's say, that only fundamental object that exists is some generator that runs all possible algorithms with all possible initial data on a Turing machines. If it happens that the sequence of its states represents some state of a possible universe, it gives it existence. It is in a way similar to the simulation hypothesis: simulation is just realization of some algorithm in the physical universe. If "the physical universe" is just this generator, all possible simulations (describable by a Turing machine) are realized by it. (This would be example ontology, where all algorithms are realized, but I could imagine similar generators for different classes of mathematical objects: not necessarily all of them, but all that have some key properties.)

I am not a big proponent of MUH, in fact, I am rather skeptical, as it does not really give many testable predictions, but it does not seem incoherent. (Maybe just underspecified?)

@JosephNoonan To the second part: Interesting! Regarding the chaos argument ("we would essentially be Boltzmann brains embedded in mathematical structures that allows brain-like patterns then"): What if there is some weighting on how often does given structure appear in the mathematical universe? E.g. in my toy model, let's say that the algorithms appear proportionally to the Kolmogorov complexity of the algorithm + initial data? Then you should expect to see universes with simple rules with low initial entropy - which is pretty much what we observe. (Am I wrong in this?)

I would even argue such a model gives an upper bound on complexity of the universe rules + initial condition: It should be much smaller than complexity of our brain, otherwise we would see the "Boltzmann brain chaos" you described. (It is not very specific prediction so it does not, as I see it, justify the complexity of the MUH hypothesis, but at least it gives some prediction :-) )

@Irigi

In this aspect, I understand MUH as follows: Every coherent mathematical description has physical realization. Then it is not a category error, is it? It is just very strong statement about multiverse.

Yes, this is not a category error. But the MUH does explicitly say that the universe is literally a mathematical structure, not just described by one. According to the Wikipedia article: "Tegmark's MUH is the hypothesis that our external physical reality is a mathematical structure. That is, the physical universe is not merely described by mathematics, but is mathematics." In most cases, I would agree that the charitable interpretation of the hypothesis would be as a statement about a very large multiverse, but the MUH specifically says that that's not how it should be interpreted.

I am not sure whether MUH goes into detail of what mathematical properties need the object have to have physical realization. There is probably many variants how this could work.

It doesn't go into detail because, at least in the original formulation, the answer is "every mathematical structure." The idea behind the MUH is that mathematical and physical existence are the same, so there would be no restrictions on what structures exist. You could restrict the theory to a set of structures that more closely resembles physical reality, but then it wouldn't be the same theory. Plus, that adds a variable to the theory (what types of structures are included), which Tegmark originally wanted to avoid (he claims the theory is favored by Occam's razor because it has no free parameters).

So basically, yes, if you restrict the MUH to only certain kinds of mathematical structures, and you get rid of the claim that the universe literally is math rather than just being described by it, you can get a coherent, and maybe even testable theory. But it wouldn't be the theory this market is asking about.

@Irigi

What if there is some weighting on how often does given structure appear in the mathematical universe?

I don't think weighting would work in the original version where every possible mathematical structure is a universe, but in your version where each universe is produced by a Turing machine, I don't see why it wouldn't work. I'm not sure if it would entirely solve the problem (e.g., a computable function with a single jump discontinuity added in isn't that much more complex than one without it), but maybe it would if the weighting is extreme enough.

@JosephNoonan Thank you for the responses. I did not know the MUH is so specific as you write. Then you are probably right about the original formulation.

> a computable function with a single jump discontinuity added in isn't that much more complex than one without it

The idea was that the weigth is initial condition + algo. In our universe, this would hypothetically correspond to few kB of data (rules + initial quantum noise, unless the underlying algorithm is even something weirder than QM). Swapping the state at any given later point would be costly proportionally to the complexity of the structure being swapped. If you meant swapping one universe originating from initial condition to another such universe, then it is also probable that the space of the initial conditions (being only small in description) does not describe all possible configurations of the evolved universes. So in every such universe, the memories are consistent, and the universes in which they are not are not reachable by setting proper initial conditions (because this space is much smaller). They are therefore selected with much smaller weights than the simple initial conditions ones.

@JosephNoonan Hmm, but thinking about it, it would really depend a lot on the exact weighting. For the algorithm describing our universe, there would theoretically be many very similar ones only with additional "if time > now, erase this electron" - which, as you say, does not have too much added complexity, and definitely would be observable.

@Irigi Yeah, the whole "add in an extra physical law to change some thing after some particular time" idea was what I was referring to. It could be gotten around by de-weighting higher complexity universes so much that the increase in complexity by even a small change like that is enough to overcome all the extra possibilities. Which I guess would predict that our universe should be about the simplest universe possible where observers can still exist.

Eventually the Everett debate is going to force physicists to take a stance on whether it's meaningful difference between something being possible, and something actually existing at some rate, and they are going to decide that there is a meaningful difference, and then they are going to apply that reasoning to MUH and realize that it is making a meaningful claim that every conceivable entity actually exists, this claim cannot be justified, solomonoff induction does not justify it, no experience we can have will ever justify it.

I'm personally intrigued by Tegmark's hypothesis, but very pessimistic about the possibility of 90% of physicists agreeing on anything like it: https://arxiv.org/abs/1612.00676

Surveying the Attitudes of Physicists Concerning Foundational Issues of Quantum Mechanics

Even though quantum mechanics has existed for almost 100 years, questions concerning the foundation and interpretation of the theory still remain. These issues have gathered more attention in recent years, but does this mean that physicists are more aware of foundational issues concerning quantum me…

I buy into the mathematical universe explanation because it is the most parsimonious (the universe is the math describing it with the math itself having substance, rather than the math describing it being actualized in some substance separate from the math itself). However, I buy into panpsychism for the same reason (consciousness is what existing in itself "feels like," rather than being an additional quality correlated to but separate from base physical existence). Which ultimately means that mathematical constructs are conscious, and that at a much lower level than the constructs we embody, one could meaningfully say there's something it "feels like" to be an ideal equilateral triangle or the number 1. Which is a bullet I'm willing to bite.

@Dfe2f Why not a subset of all the math, like a particular turing machine running a particular program? It's less simple, but why not?

By MUH here do you include: "all structures that exist mathematically exist physically as well"

@NoaNabeshima Yup

@NoaNabeshima oh man, I think there are many things that are MUH-flavored that are not literally this. MUH is very simple/natural but even still.

@NoaNabeshima Yeah, IDK the details on the different versions of MUH. I was going off my understanding and the Wikipedia page I linked to in the description, which says this: "Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well."

Do you think I should change the market or clarify things better?

@WinstonOswaldDrummond Oh, no the market is great! I made the comment to explain my prediction behavior

@NoaNabeshima Sweet!