Oh Jesus, I've Seen the Light!!!

Years ago I read about an experiment in which people blind from birth were taught to draw objects with which they were familiar by touch in perspective. After some training, one after the other, they would suddenly "see," understand how visual perspective worked and, I think, become able to visualize objects. And they were thrilled.

And do I ever get it! I've been slogging through a heavy math book all summer at an average rate of 4 hours per page. (I'm not very good at math and I never got beyond 2 years in high school). I diligently worked through every example and every proof--mercifully the proofs are short and the logic I know.

I opened that book today and looked at a couple of the theorems I worked through yesterday to prepare to push on to the next section. And today I saw what they meant, could draw the pictures, could see how they showed what all the set theoretical symbol-pushing was about. I saw, in particular, how the closure of A is the intersection of all closed sets containing it. It's embarrassing because it's so blindingly obvious and I'd missed it because I was so nervous about the whole thing, because I was continually paging back to re-read definitions. And because it takes me a while: I'm one of the mathematically blind. Then I saw the theorem that the closure of A in a subspace Y of X is the intersection of the closure of A in X and Y, again after I'd worked through the proof, paging back to definitions and other theorems, still not feeling I'd got it even though it was a short proof. It's incredible, though embarrassing that I didn't see it before.

This is so good that I don't think I want to push further today--in a way not press my luck. I just want to hold onto this and record it so that I can come back to it. It seems so trivial when put into words, like some platitudinous description of a religious experience--the sound of one hand clapping after years of diligent meditation. And so obvious. But this is the kind of thing that knocks your socks off and makes life worthwhile. I'll probably become embarrassed about this post and zap it in a few hours, but right now I just want to shout!