Jan Coffey wrote:
>
> --- Doug Pensinger <[EMAIL PROTECTED]> wrote:
>
> > But you have to memorize math too - you don't just figure things out
> > every time you do a problem do you?
>
> Actualy yes, I do.
OK, 2-part question:
1) Did you take Differential Equations?
2) If so, derive the Heat Equation. >:)
That's what killed my husband in DiffEq -- he derives things on the fly,
has a hard time memorizing formulae. But you can't just derive the heat
equation in a couple of minutes when you're confronted with it on a
test. One day at lunch, someone claimed to be able to derive whatever
he needed on the fly; he was known for using napkins to figure things
out over lunch, so Dan told him, "Derive the heat equation. Here's a
napkin." The other guy allowed as how maybe he couldn't derive
*everything*, then.
I can memorize equations more easily than that, and can apply them
properly. But I ran into a problem in high school, taking physics. The
physics teacher we had wasn't qualified to teach physics (in fact,
*nobody* in the science department was, pathetically enough), but boy
did she know her chemistry. On tests, we were each allowed one 3"X5"
file card, and I'd just put the equations on there -- I could tell which
one it was by looking at it, but had a hard time memorizing. Then one
day, she gave us a standardized test, told us she didn't expect anyone
to do well on it, but that we should just do our best. No file card,
but no constraints. Use the margins of the question sheet to figure
things out. So I used the *calculus* I'd known for 2 years already and
could utilize in my sleep, and totally, totally blew the curve. (I
could look at any of the questions where calculus would be useful, and
know how to set up the equation, and get the right answer, no sweat.)
Linear acceleration? The stupid *formula* wouldn't stay in my head, but
I could get the right answer with calculus in almost no time. (If I had
to use the stupid equation and show my work, I'd either have to look at
my card, or *derive* the stupid equation through calculus in my head,
write it down on the paper, and take it from there. Stupid, stupid,
stupid.)
> > Unless you use your fingers every
> > time you add, you have memorized basic addition.
>
> No, I do it every time. And no, I don't need my fingers to do it. I can just
> see it. Not that it is a vision, it's an abstraction, I process it every
> time.
>
> Even if I did use my fingers I could count to 1023 on them anyway. :)
"Never trust anyone who can count to 1024 on their fingers" is what a
friend of mine said on another mailing list. I guess you'd need an 11th
finger to do that, and, well, have you seen "The Princess Bride"? :)
> > Do you figure out pi
> > every time you need to use it?
>
> No I do have pi "memorized" to 3 digits, but when is that suficient? It's one
> of those things I use a computer for. Why waste your brain on remembering
> something if you can look it up in the same amount of time? Knowing why pi is
> pi is what is really importat anyway.
And any memorization of digits out to any arbitrary place is *not* pi,
just a closer and closer rational approximation. I had it memorized to
about 106 digits or so once (don't remember exactly, but it was over
100), and then someone tripped us up with that, and I slowly began to
forget. Don't think I could rattle off more than roughly 20 digits or
so now.... But it doesn't really matter. Other numbers that you can
only memorize a rational approximation of include e and that number
which is its own cosine (measured in radians, I mean), cool numbers, but
not *necessary* to memorize out to a zillion places. (By "zillion", *I*
mean "more than necessary". It can be a very useful term, if the people
with which I use it understand that that's what I mean by it..)
(I did the *horribly* geeky thing my junior year of high school coming
to school on Halloween as pi. Some teachers were amused. The rest, and
the other students, just thought it was *weird*. The next year, I went
as a hippie. That was OK with everyone.)
Julia
babbling again -- waiting for dinner to arrive, and feeling just
generally uncomfortable, and looking a lot like a grape today, what with
the long purple shirt I'm wearing :)
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