Bigger than his umlauts.
He should be in the pantheon of late night references- smoking a pipe with Einstein and Tesla; warily watching Schrodinger’s cat play with those very small strings. Instead he is hidden by the fog of that rolls in when people hear ‘math’.
Einstein said he sometimes went to Princeton just to have the pleasure of walking home with Gödel. This is who we miss in the fog. We miss the man who starved to death because he feared food that wasn’t cooked by his wife. She fell sick for six months and he died. We miss the revolutionary.
Don’t worry, I’m not going to get into the math. Generalities and speculation: that’s what I’m into.
In the early 1900’s people thought they were finally going to get it. Physics had been cruising along describing the universe as a bunch of billiard balls bouncing around. They were close to figuring out the right angles and hustling the whole game.
Math wanted a piece of that pie too: that absolute, unassailable truth pie. Mmmm- kinda bitter and dry.
So a bald guy with a round face and his white haired student wrote the most torturous book ever. There are few things more tedious then trying to prove all mathematical truths from the rules of logic. You start with ideas like: ‘the opposite of a true statement is false’. And you end with calculus. It’s like trying to build a cathedral by making your own rocks: it’s a very stale piece of pie.
But, after three volumes they thought they succeeded.
People talk about working within the system to change it: young teachers fight to become a wrench instead of a cog; lawyers know they will stand for the little guy; we all do this to keep our dignity. Gödel should be our patron saint.
Using their own work he showed their goal was impossible. He popped the balloon with its knot.
They wanted to build a cathedral to hold every mathematical truth. Gödel showed that there would always be a truth left out. You could build an extra room for that guy. But then another one would pop up. In other words, there will always be facts that are beyond the grasp of logic.
So what? If you’re not a mathematician this may all seem irrelevant.
In the early 1900s science went through a number of transformations. Nobody I know completely understands relativity or quantum physics, but everyone I know is at least a little enthralled. That fascination is our attempt to understand how they remake the world.
What Gödel did was as revolutionary. Perhaps moreso since math is the foundation for science. Quantum physics and relativity make us question the concrete world we live in. Gödel seems to say that we’ll never have The Answer.
Further- many philosophers believe that our minds mimic very complex logical systems. If that’s the case, then Gödel’s proof implies that there are facts about the world that our minds cannot even dream of.
We live in an intellectual earthquake: everything’s moving. Authority was shook by the renaissance and reformation when we retreated to personal experience and reason. But now they too are getting shaky. So what’s left to hold onto?
Maybe the real question isn’t what to hold onto, but whether holding on is a good strategy at all.