Tegmark's mathematical universe hypothesis is very interesting (https://en.m.wikipedia.org/wiki/Mathematical_universe_hypothesis) but it has virtually no support among physicists because it is too philosophical. It only relies on the assumption that mathematics has physical existence, but it does not provide a possible physics-basis like it would have in string theory for example.

So is there any physical model that could reproduce all the universes proposed by Tegmark? All universes described by all types of mathematics? Maybe using the holographic principle...?

  • It’s basically Pythagoreanism in modern dress. Except when Pythagoras came up with the idea it was something new, novel and pregnant with a host of possibilities that Tegmarks notions simply don’t have. Apr 18, 2019 at 3:12
  • Nothing can produce "all universes described by all types of mathematics" since "all" has no fixed meaning.
    – Conifold
    Apr 18, 2019 at 16:30
  • is tegmark definitely saying that abstract mathematical entities exist? or does he just mean that mathemtical structure about the world is real? @Conifold you'll probably know the answer to that??
    – user38026
    Apr 18, 2019 at 18:40
  • 1
    It appears that even Tegmark himself does not really know what he means, see Does Tegmark's Mathematical Universe hypothesis allow existence of alternative mathematics?
    – Conifold
    Apr 18, 2019 at 18:52
  • "If this theory is correct, then since it has no free parameters, all properties of all parallel universes … could in principle be derived by an infinitely intelligent mathematician" suggests that he is saying that abstract mathematical entities exist independent of whether or not they are they appear in the structure of physical theories... thanks, that answered my question (i think?) @Conifold
    – user38026
    Apr 18, 2019 at 20:02

1 Answer 1


Max Tegmark answers the question Is the physical world isomorphic to some mathematical structure? with the claim that "The physical world is completely mathematical" and "Everything that exists mathematically exists physically." (page 1)

This would be a claim than any physics model, as a mathematical structure, exists in some universe or somewhere physically. So any physics model would illustrate Tegmark's hypothesis. Finding a physics model would not help justify it.

Bertrand Russell commented on bare mathematical structure in The ABC of Relativity (page 138):

The theory of relativity has accomplished a very great deal in this respect, and in doing so has taken us nearer and nearer to bare structure, which is the mathematician's goal - not because it is the only thing he is interested in as a human being, but because it is the only thing he can express in mathematical formulae.

Russell suggests there is more going on with reality than what can be expressed by this mathematical structure and illustrates this by comparing the structure present in a musical score with the actual music played by an orchestra: "you can infer the music from the score and the score from the music". However, if you were stone-deaf from birth would you be able to enjoy the music?

The value of the music would be completely unimaginable to you, but you could infer all its mathematical characteristics, since they are the same as those of the score. (page 137)

What Tegmark needs to find to justify his hypothesis is not whether there exists a physical model that fits his hypothesis (they all do), but rather does an argument exist justifying the claim that mathematical structure is all there is to reality. That is a philosophical question and it is something Russell suggests is worth doubting.

Russell, B. (1958). The ABC of relativity https://archive.org/details/in.ernet.dli.2015.187959/page/n1

Tegmark, M. (1998). Is “the theory of everything” merely the ultimate ensemble theory?. Annals of Physics, 270(1), 1-51. https://arxiv.org/abs/gr-qc/9704009

  • Thank you for your answer @FrankHubeny, althuough I think there are few things that you misunderstood in my question: I was asking more for a physical model that would contain literally all the universes proposed by Tegmark. I mean, all models would fit in Tegmark's hypothesis since they all are mathematical, but I was asking about a model that would contain all Tegmark's universes. I was asking for a model that would have as much "diversity of universes" as Tegmark's hypothesis does. Apr 18, 2019 at 16:48
  • Also, the difference between Tegmark's hypothesis and other models is that while Tegmark's relies only on a philosophical assumption, other multiverse theories like string theory rely on some mathematical models that make sense (in a "physical" sense). That's why string theory is seriously considered as a hypothetical model of physics, while Tegmark's model is considered only as philosophy or even fantasy @FrankHubeny Apr 18, 2019 at 16:48
  • i had a conversation, one time, about justifying that with phenomenology. the reading list they set me was too much for me though, definitely outside formal study anyway
    – user38026
    Apr 18, 2019 at 18:27
  • @SueKDccia You might consider Tegmark's own mathematical universe hypothesis to be the model you are looking for. Apr 18, 2019 at 18:30
  • if that exists you should link to it @FrankHubeny i'm really confused by what the holographic principle is and what relevance it is to modelling all mathematically coherent structures.
    – user38026
    Apr 18, 2019 at 20:06

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