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Recently, Stephen Wolfram wrote an interesting article about his proposed relationship between maths and physics (https://writings.stephenwolfram.com/2022/03/the-physicalization-of-metamathematics-and-its-implications-for-the-foundations-of-mathematics/#some-historical-and-philosophical-background).

There, Wolfram talks about the physicalization of mathematics and adopts some sort of platonic position saying that mathematics does really exist in some sense or another because mathematics and all the relations between abstract concepts would exist in a space he calls "ruliad" (more information in the article).

This reminded me of Tegmark's thesis of the "Mathematical Universe Hypothesis" where all mathematical structures would exist as separated universes. (There's even a comment in that article asking what is the relation between Wolfram's and Tegmark's ideas, but unfortunately nobody replied).

Therefore, basically my question is: Since Wolfram says that mathematical concepts and structures would exist in the ruliad, and the rulial space is what makes reality and every possibility is realized by it, couldn't we say that all the universes proposed by Tegmark would exist in some way according to Wolfram's ideas?

Thank you

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    I only gave Wolfram's thesis a cursory look when I heard that it had come out, and he seemed (from what I remember) to limit the base for universes to a specified set of mathematical structures. Tegmark, too, I've heard, went on to collapse the range of objective possibilities (to computable worlds?). I wouldn't be surprised if the ramifications of their ideas were so similar, seeing as their premises are at least somewhat similar, too. Jul 11, 2022 at 23:09
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    Ruliad is about the common low-level foundation of math and physics, while MUH is a more radical Platonism view that observers, including humans, are "self-aware substructures. In any mathematical structure complex enough to contain such substructures, they "will subjectively perceive themselves as existing in a physically 'real' world". In MUH math (structures) are the lowest level reality, and Wolfram's ruliad posits these are just intermediate level human perceived artifacts... Jul 12, 2022 at 1:04
  • @DoubleKnot yes that is true, but from what I've read in Wolfram's writings, he proposes that all possibilities (all possible rules, all computational processes, all formal processes...) are realized in the ruliad, and that we percieve the physical world and mathematics as we know them because we are sampling a specific part of the ruliad. But, does this mean that, in other parts of the universe (or in different universes) different mathematical structures and rules are realized and therefore all mathematical structures could exist as different universes in that sense (as Tegmark says)?
    – vengaq
    Jul 12, 2022 at 11:21
  • I read quite a bit of that link and was not able to tell if the author is a Platonist or a platonist (Quine's decision to call Fregean realists, platonists was extremely unfortunate). It's especially confusing when you mention physics because some famous physicists such as Einstein were arguably Platonists in the sense that they seemed to attribute causal powers to mathematics. Jul 12, 2022 at 13:43
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    Even on earth here bats may sample a different part of the ruliad than ours thus they may perceive different math in a sense although they live together with us in the same universe, while MUH only posits a common math structure of our universe. Also to account for elementary logic issue Tegmark had to concede to the much smaller space of CUH, while in ruliad there seems no such immediate incompleteness concern since there's no issue if the intermediate assembly language (axiomatic system of math) sampled by us describes an incomplete structure as it's not the ultimate machine language... Jul 13, 2022 at 1:33

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…all the universes proposed by Tegmark would exist in some way according to Wolfram's ideas?

I’m more familiar with the Wolfram’s theory and I think that it approximately equals and is continuously approaching the Tegmark’s level 4 multiverse (the ultimate one).

Wolfram’s model is digital, so things like circles and infinities are not continuous but consist out of emes (points of space or simplest dots). But Wolfram supposes that computations create more and more emes, effectively making the universe more and more continuous and I suppose more and more infinite.

Wolfram proposes a way to grow the universe step by step out of mathematical rules: all the computations are performed again and again. Each computation creates/removes emes and creates/removes relations between them.

According to Wolfram no hyper-computations exist, so we cannot travel forward in time or predict when any computation will halt without performing all the steps of it.

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  • just a correction. It is incorrect that Wolfram proposes that hyper computations do not exist or that they are completely impossible (see the hyperruliad) @AntonK
    – vengaq
    Nov 13, 2022 at 18:56
  • He specifically addresses this. As far as I remember, he says it’s possible that we live in the hyperruliad but the simple ruliad is more than enough. He said, the hyperruliad will allow travelling forward in time and he doesn’t believe in it. @vengaq
    – AntonK
    Nov 14, 2022 at 19:24
  • what do you mean with "he doesn't believe in it"? Can you give any reference? @AntonK
    – vengaq
    Nov 14, 2022 at 22:26
  • He doesn’t believe we can jump forward in time because to do this we need the hyperruliad. He writes: “At a purely formal level, there’s nothing wrong with hyperruliads. They exist as a matter of formal necessity just like the ordinary ruliad does. But the key point is that an observer embedded within the ruliad can never perceive a hyperruliad. As a matter of formal necessity there is, in a sense, a permanent event horizon that prevents anything from any hyperruliad from affecting anything in the ordinary ruliad.” writings.stephenwolfram.com/2021/11/the-concept-of-the-ruliad @vengaq
    – AntonK
    Nov 16, 2022 at 1:02
  • Okay that makes more sense now. Just one more question: If to jump forward in time one would need the hyperruliad, would one also need it to jump back in time (to the past)? @AntonK
    – vengaq
    Nov 21, 2022 at 22:51

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