Those among us who loathed high school calculus might feel some trepidation at the premise in this week's episode of Rationally Speaking. MIT Physicist Max Tegmark joins us to talk about his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality" in which he explains the controversial argument that everything around us is "made of math."Unfortunately, there was little substance.

Max, Massimo and Julia explore the arguments for such a theory, how it could be tested, and what it even means.

He explained Gödel's incompleteness theorem as disproving Hilbert, and making it impossible to disprove 0=1. He claims to avoid this problem by avoiding infinity. He gets this wrong. It is possible to prove the consistency of arithmetic, if you use a larger system to prove it. It is not clear why any of this has any physical significance, or why infinity matters.

He made a big deal out of using real numbers to describe nature, such as the constant that is about 1/137. But then his rejection of infinity causes him to reject the continuum of real numbers, so it is not clear that any physics can be described by math the way he wants it.

He repudiated his earlier proposal to test many-worlds by playing Russian roulette. Now he argues that the best evidence is a quantum computer, presumably using David Deutsch's argument that quantum computing is so mysterious that it must be taking place in other universes.

He gave an argument about how mathematicians think of the number 5, but it sounded more like physicist thinking to me. Mathematically, the ordinal 5 is often defined as {0,{0},{0,{0}},{0,{0},{0,{0}}},{0,{0},{0,{0}},{0,{0},{0,{0}}}}}. See Von Neumann definition of ordinals or Von Neumann cardinal assignment for details.

He did not give a coherent explanation of what his math multiverse hypothesis means.

I also criticized Tegmark's new book here, here, here, and here.

Update: Lumo explains:

Laymen (e.g. postmodern philosophers) interested in spirituality and physics (...) often talk about things like the "influence of Gödel's theorems about incompleteness on physics" and similar things. They usually want to believe that this theorem must imply that mathematics and science must be limited, leaving the bulk of the human knowledge to witches, alternative doctors, ESP experts, dragons, priests, and global warming alarmists, among related groups of unscientific charlatans.He is mostly correct about non-mathematicians talking nonsense about Godel and infinities. And yes, as long as you can do a physical experiment to test your formulas, then you do not need to worry about the math subtleties. But when there is some doubt about the correctness of the math, there is no substitute for the axiomatic approach, and the nonrigorous physicist approach gives wrong answers all the time.

With their restricted resolution, "Gödel's theorem on imncompleteness" seems to be the same thing as the "Heisenberg uncertainty principle". However, the truth is very different. The mathematical insight by Gödel has no relationship to the Heisenberg uncertainty principle and none of the two imply that the laws of Nature cannot be pinpointed precisely, anyway.

When it comes to the irrelevance of Gödels theorems for physics, the truth is actually much more far-reaching. None of the major developments in the post-Cantor efforts to axiomatize mathematics and set theory has any implication for physics. ...

If I were a politically correct opportunist, I could say that the culture of mathematicians (with their cardinals, ordinals, theorems on incompleteness, disrespect for continuity, semi-bans on integration, and the proliferation of inseparable Hilbert spaces that follows from that etc.) and the culture of physics (with their operators boasting discrete, continuous, or mixed spectra, complete embrace of integration, continuity, unified treatment of operators with discrete and continuous spectra etc.) are simply two different, inequivalent ways to formalize certain (or superficially related) mathematical concepts and to define rules they have to follow.

But I am not a politically correct opportunist so I will tell you the actual truth. It is the physicists' perspective on these issues that is vastly superior and more profound even from a mathematical viewpoint – simply because it's the perspective that has already undergone some actual tests ...

It's the physicists' approach to the notion of infinity, infinite sums, infinite bases etc. that is the deeper one, more likely to be related with future important discoveries.

Hitler's cosmology gig is up!

ReplyDeletehttp://youtu.be/U6_adWD5H-s

I think the simplest case David Deutsch makes for Many Worlds is that it is the only tenable explanation for what happens in the double slit experiment. He further issues the challenge (in 'The Fabric of Reality', Ch.9) of considering *where* a quantum factorisation is performed, given that a single universe has too few particles to hold the intermediate results of the calculation.

ReplyDeleteThe double-slit experiment is not so strange if you believe that light is a wave. The quantum speedup on factorization has yet to be demonstrated.

ReplyDelete>The quantum speedup on factorization has yet to be demonstrated

ReplyDeleteIt may be true that Shor's algorithm has yet to be implemented for large numbers, but it's uncontroversial that it works in principle, and physicists who believe in the Copenhagen Interpretation will make identical predictions to their Many Worlds colleagues. So the question of where such a calculation takes place is already legitimate and meaningful.

Yes, Shor's algorithm works mathematically, and quantum experiments can be re-interpreted to be elements of that Shor computation. But no one has shown any quantum speedup. There is no quantum magic that requires another universe to explain.

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