I happened to come across a theorem called Gödel’s theorem, which roughly states this: in a complete theoretical system (one in which every theorem can be proven true), there must exist a proposition P and a proposition not-P (on the premise that P and not-P must be one true and one false). In other words, in any theoretical system there must exist propositions that can be proven neither true nor false — meaning all theoretical systems are incomplete. At first I thought it was some “expert” daydreaming in a vacuum, dressing up his own nonsense in professional language to pass it off as a theorem. Later I learned this theorem is actually a mathematical one, and a proven one at that (I still find this hard to believe — apparently if you’ve studied mathematical logic you’d just get it)! And it once overturned Hilbert’s philosophy of mathematics. Thinking it over carefully, this theorem tells us not just its own content, but also that humans can never fully comprehend this world. There’s another theorem that gives me a similar feeling — the uncertainty principle — which likewise hints that people can never fully grasp the entire universe.

These past few days I keep thinking of something Joseph Ford once said: God and the whole universe play dice, but the dice have been tampered with. Humanity will never know all the laws of nature — if humans ever did know all the laws, humanity would go extinct, because at that point people would try to change those laws, and the only result of changing them would be extinction. P.S. This reminds me of a blog post by Hua-something that was similar to this one — its last line captured perfectly the strange wonder between humans and the world. I looked at it again carefully today, and it seems the uncertainty principle doesn’t actually say that all particles can’t be measured.