Edward Frenkel at The New York Times:
Math is so effective in describing the world, he says, because physical reality is a mathematical structure. He calls it the Mathematical Universe Hypothesis (M.U.H.). What exactly this means is a big question, which is never fully answered. Mr. Tegmark’s argument is that all physical properties of an electron, say, can be described mathematically; therefore, to him, an electron is itself a mathematical structure — as is everything else, including us. “You’re a pattern in space-time,” Tegmark says, and he is not just speaking metaphorically. Well, it’s true that the trajectory of a human is a pattern in space-time, but does it mean that a human is this pattern? What accounts for consciousness, for example? “I think that consciousness is the way information feels when being processed in certain complex ways,” Tegmark says.
I tried to process this information, but didn’t feel much. Let’s go back to the notion of “mathematical structure.” We read in the book that it is a “set of abstract elements with relations between them,” like the set of whole numbers with operations of addition and multiplication. However, there is a lot more to math than such mathematical structures. Objects other than sets are necessary, and they have now become widespread. Moreover, there is an effort underway to overhaul the foundations of math in which set theory is no longer central. So mathematical structures constitute but a small island of modern mathematics. Why would someone who believes that math is at the core of reality try to reduce all of reality to just this island?