Michael Brady quotes Cheerskep:
> > Admittedly, though Godel's imagination was "technical", it did
> > produce a startling new insight. But it stopped there. The insights
> > of such folk are into mathematics -- not how we think.
>
> Michael then comments:
> I disagree with (what appears to be) your assumption that insights
> into mathematics are not--do not include, do not address, exclude
> (some notion like that)--insights into how one thinks.
>
> Isn't all of mathematics--or for that matter, all of any discipline,
> and all of all disciplines and metiers--insights into how we think.
>
Nah. We often do things without examining our thought processes as we do
those things. Put it another way: Mathematicians' insights are into numbers,
not
into HOW we think -- even about those numbers. They remark on how numbers
work,
not on how our heads work. I'd certainly agree to call what mathematicians do
"thinking", but few of them talk about HOW they do that thinking. Often they
haven't the slightest idea about that.
As a kid playing football, I was the guy who used to receive kickoffs and
punts. In my small, sluggish town I was always the least sluggish kid on the
field, and yet I used to catch the ball and move up the field slowly, using
quick
only when I had to. It wasn't till many years later that realized why I did it
that way: The guys rushing downfield toward me were of varying speed, so they
arrived in only ones and twos. I could always dodge one or two guys in front
of me. If I'd caught the ball and sprinted up field, I would have run into a
wa
ll of eleven guys with no gaps between them because they didn't have a chance
to break away from each other because of their varying speed.
When Gale Sayers was a great running back for the Chicago Bears, his back-up,
the "understudy" who got to play only when Sayers didn't, was Brian
Piccolo. Piccolo ask Sayers, "Gale, when you run with the ball, do you think
about
it, or do you just do it?" Gale said, "I just do it." Brian responded, "Well,
would you mind thinking about it?"
When I watched Sayers run, I could see an immense amount of "thinking" behind
what he did. I could "feel" the way he'd run in a certain direction at 80%
speed to suck the would-be tackler toward the point where the tackler figured
they would meet. At the last second Sayers would ram his speed up to 100% and
the tackler met only air. But Sayeer's insight was into DOING it, not how he
thought about it.
**************
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