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arXiv:0704.0646gr-qc

The Mathematical Universe

Max Tegmark

Abstract

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.

arXiv comments
Replaced to match accepted Found. Phys. version, 31 pages, 5 figs; more details at http://space.mit.edu/home/tegmark/toe.html
Journal reference
Found.Phys.38:101-150,2008
DOI
doi:10.1007/s10701-007-9186-9
Subjects
gr-qcGeneral Relativity and Quantum Cosmology astro-phAstrophysics hep-thHigh Energy Physics, Theory

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Linked by 12 identifiable commenters in 14 comments across 14 threads, from Oct 2010 to Sep 2026. Found in 3 HN submissions from Apr 2009 to Jul 2023. Open submission discussions.

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Discussed in comments14 threads

  1. Earth's organisms developed via evolution. What if the cosmos did, too? 1 comment

    • I am a total layman. But I believe that MUH (Max Tegmark) is the real thing. I was once looking at fractal animations on youtube. At one point, I thought I saw things move in it in a way that resembles physical movement. That caused me to ask if there could be a fractal where…

      qseraView on HNParent context

  2. It is time to give up the dualism introduced by the debate on consciousness 1 comment

    • > its not an answer to any question It is. It is the theory of everything. > what is this "consiousness" in the end, which has in its nature, the production of all material reality to serve as a fixed causal basis for perception? If you haven't already came acrosss M.U.H, I…

      qseraView on HNParent context

  3. Why does anything exist? 1 comment

    • >The Universe is "just" mathematics.. I have come to this conclusion as well. It came to be when I was looking at a fractal animation, and it appeared that things moved in it as if obeying some laws of physics. I have expanded on this idea here, and have described a sort of…

      sras-meView on HNParent context

  4. Ask HN: What's the best paper you've read? 1 comment
  5. Ladder of Algebraic Structures 1 comment

    • Max Tegmark has a larger diagram for math in his paper: Is "the theory of everything'' merely the ultimate ensemble theory? https://arxiv.org/abs/gr-qc/9704009 and a sketchy one for physics in his paper: The Mathematical Universe https://arxiv.org/abs/0704.0646

      mikhailfrancoView on HNParent context

  6. Sub-Acute Effects of Psilocybin on Empathy, Creative Thinking 1 comment

    • > We are made out of math. There's plenty of sober people who think this idea is entirely possible, maybe even probable. The idea goes by the name the Mathematical Universe Hypothesis, and the foremost proponent is Max Tegmark.…

      peopleeaterView on HNParent context

  7. Is the Universe Made of Math? 1 comment

    • Skip the book (and the article), read the original paper: https://arxiv.org/pdf/0704.0646.pdf IMO, Tegmark has a solid argument that the MUH is more plausible than any of the other suggested possibilities (https://www.amazon.com/Why-Does-World-Exist-Existential/dp/0... is good…

      ravenouswolves6View on HNParent context

  8. Steven Strogatz on chaos theory, game theory, and why math isn’t boring 1 comment

    • Yea, mathematics is more fundamental than physics, in the sense that it would be possible for different universes to exist with different physics, but it's not clear at all that universes could exist with different mathematics. What would that even mean? You may like Max…

      zeroerView on HNParent context

  9. Why Understanding Space Is So Hard 1 comment

    • Couple that with Max Tegmark's ideas about multiverses. The idea is that all possible combinations of dimensions exist as a universe. We see 3+1 dimensions because this is the one combination that's most likely to develop life. http://arxiv.org/abs/0704.0646

      spacehomeView on HNParent context

  10. The Grand Illusion: Does time have a future? 1 comment

    • Max Tegmark has some really good writing on this. I quite like the idea that the "universe Hamiltonian" acts deterministic in phase space such that the universe's wave function evolves deterministic. From the "inside" of the system, the atoms in our brain are just carried along…

      brotchieView on HNParent context

  11. The Mediocrity Principle 1 comment
  12. When does a physical system compute? 1 comment

    • Two somewhat-related-pointers for people who decide that they're curious about these things: * a light and nice read: https://www.frc.ri.cmu.edu/~hpm/project.archive/general.arti... (an oft-cited article) * the madness of Max Tegmark: http://arxiv.org/abs/grqc/9704009…

      wfnView on HNParent context

  13. Saturn’s Strange Hexagon 1 comment

    • > Strictly speaking, math has to yield to the laws of nature as it does not exist outside the laws of nature (as mathematics is in our minds) There are (within academia) alternative views to this one, e.g. Max Tegmark's "Mathematical Universe hypothesis"…

      wfnView on HNParent context

  14. USPTO likely to adopt 'peer-to-patent' (Feb 2010) 1 comment

    • Ok, this isn't an answer to your points, but have you read Tegmark's Mathematical Universe Hypothesis?http://arxiv.org/abs/0704.0646 "I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of…

      JabavuAdamsView on HNParent context

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