Yet what makes this book really worth reading is the last quarter where the ideas about the Mathematical Universe are explored.

The author has a really pleasant way of covering the history of cosmology, making the story like a mystery novel, using detective work to explain one mystery after another. Tegmark seems to still be hoping for a resolution of the Measure Problem. Thus any assignment of probability to such constructs is nonsense. The underlying problem is in any reality, it is simply not possible to take a random sample from an infinite set. I think Tegmark underestimated the depth of the Measure Problem. Also a good new model in fundamental physics should address multiple issues in physics, but Tegmark does not use his ideas of the Mathematical Universe to clarify the understanding of quantum mechanics (particularly Bell’s Theorem) and the problem linking General Relativity and Quantum mechanics. He seems to reject continuums and infinities and randomness as unreal (which is what I think), but then he continues to refer to, and use, these as if they were real. It may just be awkward editing or just these ideas are heady stuff, but by the end of the book Tegmark seems a bit schizophrenic. I was led to my conclusions by a much different path (Bell’s Theorem & Bell Test Experiments) and take these ideas to even greater extremes than Tegmark, but this is the best (the only?) popular presentations of these ideas I have seen. I really thought I was alone in being a strong proponent of this Mathematical Universe idea, so I have quite pleasantly surprised to find this excellent presentation.

The relations defined by a mathematical structure is all that is needed for us to believe all we see and feel is real. Then the book gets really interesting! The author proposes that math does not model the universe, but that math IS the universe. The first three-quarters is good, but is just a nice rehash similar to a bunch of other speculative physics books covering a brief history of cosmology leading to the theory of inflation and various levels of multiple universes, Boltzmann brains and such, finally culminating in the Measure Problem (one cannot assign consistent probabilities to infinite sets). I think these ideas are, by far, the most likely to lead to progress in physics. The last quarter of this book has some of the most interesting ideas in physics I have heard.

Great ideas and great narration makes this a great audio book.

Tegmark our mathematical universe