Interesting point from a response by mathematician Sheldon Glashow to Daniel Kleitman’s review of Max Tegmark’s 2015 book, Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, again in Inference:
Chapter 9 is devoted to what can only be called mathematical epistemology. Tegmark alleges the plausible hypothesis that there exists an external physical reality completely independent of us humans to imply a rather more startling Mathematical Universe Hypothesis: that our external physical reality is a mathematical structure.8 The Level IV multiverse, it turns out, is nothing other than the set of all mathematical structures, each of them constituting a universe unto itself.
According to Tegmark, our universe is (rather than merely “is described by”) the long sought
Theory of Everything, or ToE, from which all else can be derived… [S]uch a complete description must be devoid of any human baggage. This means that it must contain no concepts at all! In other words, it must be a purely mathematical theory… [An] infinitely intelligent mathematician should be able to derive the entire theory tree [including all of science, engineering, sociology, psychology etc.] from these equations alone, by deriving the properties of the physical reality that they describe, the properties of its inhabitants, their perceptions of the world, and even the words they invent. This purely mathematical theory of everything could potentially turn out to be simple enough to describe with equations that fit on a T-shirt.9
And our ToE is just one among an infinity of mathematical structures, each of them its own universe. If Tegmark is correct, there must exist a slightly different mathematical structure, whose equations are emblazoned on another T-shirt, wherein I am Tegmark’s psychiatrist rather that a physicist. I do not believe a word of it. Paraphrasing Danny, I may be a blockhead but I am certainly not a mathematical structure akin to a triangle. More.
Tegmark is what happens when cosmology tries to become a philosophy instead of just sticking to facts. It sells books.
See also: We have infinite selves in a multiverse? No, sorry, goodbye all youse, says math prof “Since the laws of nature would thus be different [in a multiverse], you could not be you.”
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