Written: Aug. 13, 2014
I have recently finished reading Max Tegmark's fascinating (but very annoying!) Our Mathematical Universe, subtitled, My Quest for the Ultimate Nature of Reality.
The main title "Our Mathematical Universe" is not that annoying, taken literally. We humans do mathematics, and that body of knowledge may be called our mathematical universe. But of course what Max means is "Universe" in the sense of physical universe, and that it is mathematical. Who are you Max (or anyone else for that matter), to tell us what IS our universe, when we, lowly humans, don't even know what is is, not even Kant, Frege, Kripke, Derrida, and Bill Clinton. If the physical universe is a mathematical structure, then YOU, Max, is your Social Security Number, or your finger-prints, since there is a one-to-one-correspondence between citizens of the US and the set of nine-digit social security numbers.
But the subtitle, "My quest for the Ultimate Nature of Reality" is yet more annoying. Guess what Max, you (or anyone that belongs to your species, the so-called homo-sapiens) would never ever know the "ultimate" nature of reality. At best we would know a tiny, trivial part of it, good enough for our short-term survival.
On some level I admire your chutzpah, and platonic naivete, and your metaphysical gibberish (that makes Kepler's one-to-one correspondence between the platonic solids and the planets seem super sane). But I also agree with the senior scientist who was annoyed that you mixed regular-science-physics with your speculative metaphysics.
On a methodological level, math did lots of good for physics, but it also did lots of harm. Modern physics has gotten way too abstract, trying to emulate the over-abstract, 20th century Bourbaki-style math. Now that we have the computer, we can go back to the basics and explore mathematics concretely, and empirically, like good-old experimental physics, before it was ruined by abstract math. Thanks to computer algebra, even "abstract" mathematics (the part that makes sense), can be treated concretely, using symbol crunching.
While in abstract mathematics (and logic), A=B iff B=A, in human discourse, A=B means something completely different than B=A. While you claim that Physics=Math, making Math central, I hold that Math=Physics. In other words, whatever little math that we lowly humans (only a few orders of magnitude smarter than amoebas) can do, should be explored like old-time experimental physics, using as much as possible our beloved silicon colleagues.
So let's be humble, and give up any claims to ever knowing the "ultimate" nature of reality.