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I'm looking for further reading about the Mathematical Universe Hypothesis. I'm intrigued and would like to know to which degree this has been discussed.

I'm aware and have been looking at Tegmark's work on the subject and commentary on his work but I can't believe he'd be the only one working on it? I'm looking for philosophy journals or widely published monographies, blog posts and such can nice but not what I'm looking for.

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    did you look for citations of his original paper in google scholar?
    – nir
    Feb 10, 2016 at 21:01
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    I wish Tegmark wouldn't call "reality is made of math" a hypothesis, which suggests that it might be something scientific. Penrose at least distinguishes between his Platonist speculations and actual hypotheses that they inspire him to make.
    – Conifold
    Feb 10, 2016 at 23:37
  • Hm, well I just adapted his terminology on the thing but I suppose if you want to go by definition, then it is not a Hypothesis. However, String Theory is a Hypothesis and not a Theory and yet everybody calls it String Theory nonetheless. Doesn't mean it's okay but unfortunately terminology is rarely strictly adhered to. Thanks for the remark.
    – MM8
    Feb 11, 2016 at 0:52
  • There is an extended review paper arxiv.org/abs/1406.4348 by Jeremy Butterfield at the arxiv (and possibly other work e.g. this arxiv.org/abs/1105.4278 ).
    – sand1
    Feb 11, 2016 at 9:25

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David Deutsch's strong version of the Church-Turing thesis, and the overall topic of digital physics (the universe is a computer) are closely related to Tegmark's hypothesis.

More disputed and controversial, but still somewhat related is Stephen Wolfram's idea that everything can be described by computations and cellular automata (equivalent to Turing machines and therefore related to Tegmark's hypothesis) as described in his book "A New Kind of Science".

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    Your answer doesn't mention any of the criticisms of Tegmark or the other ideas in your post, some of which were proposed by one of the people cited in your answer.
    – alanf
    Feb 11, 2016 at 11:57
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Tegmark's theory is no good. The problem is that if you consider the set of all logically possible universes, there is no particular measure on that set that is privileged. As a result, there is no way to count the universes in Tegmark's theory to explain any feature of the way the world works and the theory is worthless as an explanation. See "The Beginning of Infinity" by David Deutsch, Chapter 4, the last section, which is called "Fine Tuning", Tegmark is refuted starting on p.101.

I should also comment on the misuse of the Turing principle: the principle that any physical system can be simulated by a universal computer with finite resources. In addition, a universal computer can be simulated by computational networks built using of a single type of simple computational gate. Any classical computation can be done by composing Toffoli or Fredkin gates. Any quantum computation can be using almost any two qubit gate. People often seem to imagine that this means the universe could be a computer or something like that. In fact, it rules out the idea that the universe is a computer. Because of universality, if the universe were a computer, we could never know anything about the hardware. Any hardware capable of doing the simple gates mentioned above can simulate any physical system we could observe, so we can't tell what hardware is actually used. In other words, if the great simulator theory was true it would be impossible for us to discover the laws of physics. The significance of the Turing principle is not that the universe is a computer, but that it helps explain why the universe is comprehensible. The universality of computation allows us to model proposed explanations and either rule them out or use them to solve problems.

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    Just from reading the first paragraph of your comment, it seems to me that you are misrepresenting or misunderstanding Tegmark's idea and I have only really read his original paper and some of his book. That said, I wasn't asking for pro and con arguments, as I stated in the Q. Thus your answer does not respond to my question but instead argues for/against a certain view, which is simply not what I was asking for. Thanks either way. Discussions come after reading. I was asking for books to read, so thanks for the Deutsch reference.
    – MM8
    Feb 11, 2016 at 18:20
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    I didn't mean to sound rude, but the last sentence of the first paragraph of your answer was really all I was asking for. I never said I care about Tegmark or his views specifically, I just wanted to know more about the idea of the Universe being mathematical.
    – MM8
    Feb 11, 2016 at 18:25
  • @Kurow: (1) You say I'm misrepresenting Tegmark without giving any examples. (2) Also, it doesn't make sense to recommend a reference without saying anything about the argument. (3) People might come across this who won't read the reference but will now know of a serious problem with the argument. The second paragraph is necessary to reply to a misrepresentation of the Turing principle in an earlier answer.
    – alanf
    Feb 11, 2016 at 23:55
  • what about the alternative statement that the observable universe is a computation?
    – nir
    Feb 12, 2016 at 20:06
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    The measure problem doesn't invalidate the basic idea that our universe is a mathematical structure. This idea is as solid as natural selection.
    – Ron Inbar
    Feb 24, 2021 at 11:08
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I found your question when searching for the same answers. I am somewhat perplexed that the hypothesis of the mathematical universe, and Tegmark's book and papers, have not resulted in a flurry of philosophical debate on the subject. It is common scientific thought that biological and mental processes are chemical in nature and that chemical processes boil down to physics. And physics certainly distills down to math. So ought not everything be as its basis math, or emerge from mathematical constructs such as logic and pattern? It is only our famously unreliable and subjective experiences and culture that persuade us there is anything else that is fundamental. Of all things in time and space it is only math (and logic) that might escape time and space. It is only mathematics that can be eternal. We should ask, not why math is fundamental to our universe and everything in it, but why anything else should exist at all except as illusion. And we should ask how the physical world and the mental world emerge from the abstract and pure realm of Plato's ideal forms, how the world we see emerges from the perfection and purity that is logic itself. Everything we see, think, feel, and love, everything that is breathtakingly beautiful and everything sad and unfair, is at it's heart just math being math. The concept is not, or should not be a source of despair; rather it is a concept that is liberating. And to me it rings true, and seems natural and reassuring.

So to really answer your question, I have found no meaningful exploration of the subject of the mathematical universe, except derisive criticism. Nothing that delves into it while supporting the hypothesis, only negative criticisms that to me, so far, don't fly.

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    Thanks for the comment. Your concerns seem to be similar to mine. It's good to know that I'm at least not the only person interested in a further discussion / exploration of this topic in the philosophical literature.
    – MM8
    Jan 28, 2017 at 19:18
  • I appreciate that, Timon G. I think there is a lot more to come on the topic, in time.
    – R. Gold
    Jan 31, 2017 at 4:36
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There's a good book out last year - Spooky Action at a Distance by George Musser.

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Check out a paper called "Towards a theory of universes: structure theory and the mathematical universe hypothesis", it gives more background and theory.

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