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Feynman on Conceptual vs Mathematical Models



Feynman on Conceptual vs Mathematical Models:

"Sometimes I wonder why it's possible to visualize or imagine reality at
all. . . . It's easy to imagine, say, the earth as a ball with people and
things stuck on it, because we've all seen balls and can imagine one
going around the sun - it's just a proportional thing, and in the same
way I can imagine atoms in a cup of coffee, at least for elementary
purposes, as little jiggling balls. But when I am worrying about the
specific frequencies of light that are emitted in lasers or some other
complicated circumstance, then I have to use a set of pictures which are
not really very good at all - they're not good images. But what are
"good images"? Probably something you're familiar with. But suppose
that little things behave very differently than anything that was big,
anything that you're familiar with?

Animals evolved brains designed for ordinary circumstances, but if the
gut particles in the deep inner workings of things go by some other
rules, and were completely different from anything on a large scale,
there would be some kind of difficulty, and that difficulty we are in -
the behavior of things on a small scale is so fantastic, so wonderfully
and marvelously different from anything on a large scale! You can say,
'Electrons behave like waves' - no, they don't, exactly; 'they act like
particles' - no, they don't, exactly; 'they act like a fog around the
nucleus' - no, they don't, exactly. Well, if you would like to get a
clear, sharp picture of an atom, so that you can tell correctly how it's
going to behave - have a good image of reality, in other words - I don't
know how to do it, because that image has to be mathematical. Strange!
I don't understand how it is that we can write mathematical expressions
and calculate what the thing is going to do without actually being able
to picture it. It would be something like having a computer where you
put some numbers in, and the computer can do the arithmetic to figure out
what time a car will arrive at different destinations but it cannot
picture the car. . . .

For certain approximations, it's okay. With the atom pictures, for
example, the idea of a fog around the nucleus, which repels you when you
squeeze it, is good for understanding the stiffness of materials; the
idea of a wave is good for other phenomena. The picture of atoms, for
instance, as little balls is good enough to give a nice picture of
temperature. But if you ask more, and you get down to questions like
'How is it that if you cool helium down, even to absolute zero where
there's not supposed to be any motion, you find a fluid with no
viscosity, no resistance - it flows perfectly, and it isn't frozen
solid?' Well, if you want to get a picture of atoms that has all that in
it, I just can't do it. But I can explain why the helium behaves as it
does by taking the equations and showing the consequences of them is that
helium will behave as it is observed to behave, so we know we have the
theory right - we just don't have the pictures that will go with the
theory.

I wonder whether you could get to know things better than we do today,
and as the generations develop, will they invent tricky ways of looking
at things - be so well trained that they won't have our troubles with the
atom-picturing? There is still a school of thought that cannot believe
that the atomic behavior is so different than large-scale behavior. I
think that's a deep prejudice, a prejudice from being so used to
large-scale behavior. They are waiting for the day that we discover,
underneath the quantum mechanics, some mundane, ordinary balls hitting
each other. I think nature's imagination is so much greater than man's
that she's never going to be defeated!" - Quoted in "No Ordinary Genius
....", Christopher Sykes


Bob Sciamanda sciamanda@edinboro.edu
Dept of Physics trebor@velocity.net
Edinboro Univ of PA http://www.edinboro.edu/~sciamanda/home.html
Edinboro, PA (814)838-7185