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From: B. Harris)
Subject: Re: Strongest Muscle
Date: 10 Apr 1999 16:09:11 GMT

In <7el1na$5ii$> "mjdgdc"
<> writes:

>Why differentiate the "sciences" from "mathematics"? When I was studying
>physics, we learned that while much of physical science was "discovered"
>by experimentation, much was also derived with pure mathematics. Let's
>pick a physicist as an example, say...Einstein. Not much of an
>experimenter there. No lab. No little books of data. No measuring how far
>the ball falls when thrown at an angle. Just ideas, formulae, and
>profound mathematical ability. Add them up, and we have a revolution in
>physics, with curved space, relative time rates, and big holes in the New
>Mexico sand.

   Well, Einstein of course had data, but no data that everyone else
didn't also have.  So you have a good point.  Does something count as
human knowledge if it's implied in the math but nobody has been smart
enough (clever enough, talented enough) to see it?  I would say not.
Knowledge means somebody knows.  In scientific knowledge, anybody can
look it up at a library.  It doesn't mean something that is still
hidden from everyone, but still logically implied.  Is Fermat's last
theorum true?  We didn't have this KNOWLEDGE until very recently.  Is
black or white always guaranteed to win (or at least force a draw) in
any chess game?  In which the other is guaranteed to always lose?  We
have come far enough to know this is so.  Chess is like tic-tac-toe or
NIM in that.  We just don't know which color it is.  Or how to play
that well.  The knowledge is implied in the rules, but we're not smart
enough.  Does it count as knowledge?  I don't think so.

    Einstein's math was okay, BTW, but not his strong suit.  It took an
old teacher (Minkowski) to point out to even Einstein that his theories
implied a non-Euclidean geometry.  He hadn't realized this.  And then
when he realized he needed geometry for the general theory, it took an
old math friend (Grossman) years to teach Einstein enough math to put
his great theory in mathematical language (a great mathematician--
Hilbert-- when he finally understood what Einstein required of the
math, did the whole thing in a couple of weeks.  Einstein barely beat
him to publication).  And after all THAT, there was the humiliation of
having another mathematician (and a female one to boot) look at
Einstein's final theory, and remind him that it made conservation laws
superfluous, since they were already automatically built in, though the
math.  Einstein hadn't noticed.  He was delighted, but chagrined.

   But all that is not to detract from Einstein.  He could do hard math
when he had to, but his strong suit was knowing when to push a
contradiction in theory until there wasn't one. And he knew which parts
to fiddle with, and they weren't the obvious ones (to say the least).
How did he know?  That's the genius.  Nobody knows how he knew.  But he
knew most of it BEFORE doing the math.

                                            Steve Harris

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