Max Tegmark
2007 · arXiv
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.
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11 selected excerpts · 11 total mentions
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 for the PEQ and much more worth reading than Tegmark's book).
> 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 would just direct you to https://arxiv.org/pdf/0704.0646 >What madness to is it to say that mercury in a thermometer not only acts as-if it is in coffe, but in its nature, acts as if there is an entire world that it is moving through -- and its motion up and down is always according to laws and principles as if such a world existed? Yes, that is exactly what is being proposed. Causality is an illusion. But how? Imagine an idea of a "definable world". Imagine that all definable worlds "exist", but imagine consciousness appearing only in "regular" worlds, with uniform laws and behaviors..
>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 thought expiriment where I try to "prove" this. You probably not want to read it. It is not very well written. https://sras.me/the-root-of-all-existence.html Later I came across Max Tegmark's paper, which describes the same thing.. https://arxiv.org/pdf/0704.0646.pdf
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
> 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. https://en.wikipedia.org/wiki/Mathematical_universe_hypothes... https://arxiv.org/abs/0704.0646 https://space.mit.edu/home/tegmark/crazy.html
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 Tegmark's idea that the universe is math: https://arxiv.org/abs/0704.0646 But it's nonsense that the natural numbers require two dimensions. Time appears nowhere in the Zermelo–Fraenkel axioms: https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory
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
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 on a stochastic path such that the conscious awareness we currently inhabit is one of many the many possible paths through the large phase space. From the "outside" the universe is a infinitely dimensional, phase space that evolves deterministically through time. That way I reason about it is that the big bang was a single "pixel" of super high energy in an infinitely dimensional phase space and…
the laws of physics are a Hamiltonian "kernel" that evolves the phase space in a similar way to the heat equation. Thus this kernel acts on the phase space from the big bang, mechanistically acting out the laws of physics, all the way until the heat death of the universe: effectively the fixed-point of the universe kernel. This may all sound like bullshit to a physicist, but it's the application of my limited understanding of physics and mathematics to the thought experiment. Good reading here: http://en.wikipedia.org/wiki/Mathematical_universe_hypothesi... http://space.mit.edu/home/tegmark/mathematical.html http://arxiv.org/abs/0704.0646
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 , http://arxiv.org/abs/0704.0646 (cliff's notes: "The [...] postulate in this theory is that all structures that exist mathematically exist also physically, by which we mean that in those complex enough to contain self-aware substructures (SASs), these SASs will subjectively perceive themselves as existing in a physically ``real'' world." Which means: take http://xkcd.com/505/ , and abstract it enough times so that you decide that the rocks themselves are not needed anymore.) -> if anyone has any comments about the MUH, would be interested to hear them. My head is kinda-still-aching from the last time I tried to decide how seriously I should take his ideas.
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 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."
> 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": - http://arxiv.org/abs/gr-qc/9704009 - http://arxiv.org/abs/0704.0646 - wiki: http://en.wikipedia.org/wiki/Mathematical_universe_hypothesi... The basic idea being, all internally consistent (viz., mathematical) structures exist (whatever the notion pertains to), and those containing 'self-aware substructures' are perceived as physical realities by virtue of those SASes being embedded within a particular given consistent…
structure (and hence having a from-within vantage point). Sounds fishy, but it's a hypothesis alright, and there have been (AFAIK) some attempts to provide falsifiability conditions (thus making it a testable scientific hypothesis), but one would first have to address the problem of proper operationalization, i.e. defining the damn concepts at hand; it's probably too all-over-the-place for now - but nevertheless interesting and (heh) internally consistent. Also see (for those interested), e.g. http://plato.stanford.edu/entries/computation-physicalsystem... (nice overview of related problem spaces)
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