Re: definition of "wave"

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

Digby Willard wrote:

> > A matematician, you are likely to agree, could not function without
> > a definition. Right?
>
> No.  Geometry works just fine without defining point, line, or plane.

You are right; "the most simple" of Euclidean geometry are assumed
to be self-defined (obvious) . A point is a point and a straight line is
an
infinite set of points arranged in an obvious ways. Perhaps a narrow
beam of line was at the base of that concept.

But this is very different from a situation in which each teacher has
a personal definition. Definitions are very useful. Sometimes we must
go ahead without them but it is better to have them.

So how to define waves in a first physics course? We train students in
mechanics that physical concepts, such as displacement, velocity,
kinetic
energy or acceleration are well defined, mathematically. They expect
us to do the same in the second semester? The partial differential
equation is a good starting point in a calculus oriented course. A wave
is a moving disturbance whose description is given by the equation. Real

waves are more complicated but at least it is a good starting point.

And something which does not satisfy the equation, even approximately
should not be called a wave. Here we are again with the dilemma of
common words versus their use in physics. If we have many similarly
looking phenomena but can not create an all-inclusive definition then we

should make several different definition and wait for a possible
unification.
We can even debate the desirability of unification. Does it make science

simple or more complicated?

Please do not ask me to define simplicity, it is a self-defined concept.

A proper unit for it would be [lifespan of learning] to reach the level
of
mastery. Leight wrote earlier today:

> The last person who knew everything died a long time ago, and there
> will never be another like her.

Ludwik Kowalski