Is the universe made of math? That’s a question going around internet science-fan circles of late, and it’s a pretty difficult question. Roughly, a cosmologist named Max Tegmark believes in a very concrete form of mathematical Platonism - the idea that math is “real” in some sense. Now I and many other people agree that math isn’t just something we humans made up out of thin air (the formalist position) because math simply works too well. The richness of mathematics and mathematical physics is not something that was planned out from the start, which leads me to think mathematics is built in to the universe independently of anyone in the universe to write it down.
Now that’s a much weaker statement than “the universe is made of math”. Take Tegmark’s view:
I said there could be a whole universe that is nothing more than a dodecahedron, a 12-sided figure the Greeks described 2,500 years ago. Of course, I was just fooling around, but later, when I thought more about it, I got excited about the idea that the universe is really nothing more than a mathematical object. That got me thinking that every mathematical object is, in a sense, its own universe.
Tic-tac-toe is formally and completely described by math (as is the machine code of the Barbie Fashion Show computer game, for that matter), but the idea that somehow there’s an actual tic-tac-toe universe out there seems… far-fetched. At the very minimum there’s a lack of corroborating evidence, and not much hope of getting any.
He has a factual error as well:
But if space goes on forever, then there must be other regions like ours—in fact, an infinite number of them. No matter how unlikely it is to have another planet just like Earth, we know that in an infinite universe it is bound to happen again.
Not quite. There’s an infinite number of prime numbers, none of them are the number 15. Infinite trials do not necessarily lead to every result. There could be an infinite number of earths, but there doesn’t have to be even if the universe is infinite in extent. I notice John Derbyshire on (of all places) the National Review website has also pointed this out.
It’s not a bad attempt at an answer to Hawking’s “How come existence?” question, but for the moment I think it’s better to take the wet blanket stance on this particular idea. There aren’t any experimental ways to check it, and so it’s speculative philosophy but not yet anything approaching science.