Gödel

I've been somewhat hesitant about posting this topic. This is just an idea that's been rolling around in my head for several months. It's gotten to the point that I think I have to post about this just to get it out of my head and move on!

Douglas Hofstadter's book Gödel, Escher, Bach contains an interesting statement based on Gödel's incompleteness theorems: "In short, Gödel showed that provability is a weaker notion than truth, no matter what axiomatic system is involved." In plain[er] English, in any formal system there exist truths that are unprovable.

I'm sure Dr. Hofstadter will be appalled by my lack of understanding of his book, the parallels that I make to his statements, and links to a Wikipedia article that "kind of depresses [him]". But I'm not about to let that stop me :-)

Reading the statement of incompleteness gave me sort of a thrill. There are few things in science that match the rigor and thoroughness of a formal system. And yet, they are fundamentally incomplete.

I had a stunning epiphany about this: the idea of mystery is so deep that it's ingrained into the fabric of the Universe! It's the way everything is designed; you cannot escape it. No matter how tall we may try to build our modern tower of Babel, there will always be a Heaven above it. There will always be something beyond our grasp.

We are not built to know everything, we are designed to learn. There's always some new truth out there waiting to be discovered.