Re: definition of "wave"

[John Denker <jsd@MONMOUTH.COM>]

At 09:05 AM 1/27/00 -0500, Ludwik Kowalski wrote:
> A matematician, you are to likely agree, could not function without
> a definition. Right?

Two answers:

1a) Mathematicians can use definitions and axioms to create artificial
worlds from scratch.  Such definitions are exact, by definition.

1b) In contrast, the physical world already exists;  it is not created by
physicists.  Many definitions will be only approximate.

--

2) Mathematicians and physicists use definitions to define terms that help
us communicate.

The problem arises when the real world presents us with a complicated
situation and the students demand a simple definition.  There is no easy
way to communicate a difficult concept, and asking a definition to do the
impossible only makes matters worse.

Example:  suppose we try to classify creatures by asking questions such as
        A) Warm blooded?
        B) Lays eggs?
        C) Nourishes its young with fluid from a special gland?
Then the conventional "pat answer" is to define
        mammal = [yes, no, yes], and
        bird = [yes, yes, no]

That's wonderful until you come across a creature that lays eggs *and*
nourishes its young with fluid from a special gland.  Is it a bird, or a
mammal, or both, or neither?  A mathematical deduction based on the
foregoing definitions is guaranteed to be unsatisfactory.

Hint:  andihce, noegip