Thursday, August 27, 2009

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!


Anonymous said...


Don't feel bad about the excitement of having a "Eureka!" moment while learning. It's common among those people who are actually trying to learn difficult things.

Used to happen all the time when I was at the Defense Languange Institute, many years ago. Students would beat their heads against grammar and vocabulary for weeks and months ... and then suddenly wake up one day and it was working.

Brava! and congratulations.


PS: Death to Chinese comment spam.

H. E. said...

Oh, my. I didn't think anyone but the Chinese spam-bots were reading this blog. I just trashed the Chinese spam.

Yeah, eureka is good. I get eureka moments occasionally with math and logic, but for all my efforts with foreign languages, eureka just doesn't happen. Worst of all, I watch other students in the class one by one get over the hump and start to fly with the language while I'm still struggling with flash cards, can't understand a word when the language is spoken, and have to run through the complete conjugation of every verb before I utter a sentence.

But this is encouraging. Thanks!

Anonymous said...

> for all my efforts with foreign
> languages, eureka just doesn't
> happen. Worst of all, I watch
> other students in the class one
> by one get over the hump and
> start to fly with the language
> while I'm still struggling

Age makes a difference. It has something to do with the speed at which new neural pathways are laid down as we age, but I'm out of my depth as to specifics.

Most of us at DLI were in the 19-22 year old range. A friend once told the story of some field-grade officer in his early 40s (they thought) in a class, who would get absolutely red-faced that the enlisted scum were just blowing by him in acquiring the language. Tee hee. :)

But apart from his flawed social perceptions (we had to sign agreements not to go to OCS just to get in there), the simple fact is that it takes longer when you're older (modulo individual aptitude, etc.).

Hang in there, it will work eventually. It's frustrating, I do know, but be encouraged.


PS: Other than age and speed of learning, no comparison between yourself and the red-faced field grade is intended. :)

H. E. said...

I think I've heard of this language school. Daughter, who is about to go to Turkey and do an intensive program in Turkish said they can teach you Turkish in 11 months. Korean takes three years. French, for English-speakers, 12 weeks. Sounds about right.

Mercifully, I'm just working on Italian--not Chinese!

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