Harry Veeder wrote:
I am calling your bluff. ;-)
Not a bluff, though it involves some fuzzy reasoning. The difference
between a "proof" and an "explanation" has bugged me since junior high,
when I found out that most mathematical facts are "proven" without ever
being "explained".
As I said before, a "model" may predict what's going to happen but will
never tell you why. Using a model is a tacit admission that we don't
know what the "reasons behind" things are, or even if there are any such
reasons.
What is the difference between an explanation and a model?
You have said something substantive about models, but nothing substantive
about explanations, except to say that explanation is not a model.
Or is it just an issue of semantics?
Maybe it's just semantics, but I actually think it's more a matter of
gut feel, and "satisfaction level". If you look at the link Terry gave,
the author's objection is that physics doesn't say "why" magnets
attract. Well, what would it mean to say why they attract?
This is the heart of the issue -- just exactly what is an explanation?
In physics it's hard to say, for me, at least, because I don't know of
any explanations. As far as I know modern physics has none.
In math it's easier to see the difference. For example, we can find pi
by integrating the arctan function, or by integrating sqrt(1-x^2), both
of which are stunningly opaque approaches. We can prove that the area
of a circle is pi*r^2 using calculus, which is, again, an amazingly
opaque approach. Alternatively, we can find the circumference and area
of a circle using Pythagoras's theorem and some simple drawings, and we
can extract a value for pi that way. I would call the latter approach
an "explanation", because, to me, it "explains why" the circumference
and area of the circle are what they are.
But something this is pointing up is that the word "explanation" is
rather slippery. I could struggle with it a bit more, and perhaps say
that an explanation works from simple things which we "know" to be true
to show that other more complex things follow inevitably from those
simple things -- but the phrase "know to be true" is already flirting
with vagueness. So I'll just let it go at saying that an explanation
leaves one feeling satisfied; a model may not...
By the way, the derivation of pi from Pythagoras's theorem to which I
referred, and the derivation of the area of a circle and volume of a
sphere using geometric arguments, are here:
http://physicsinsights.org/pi_from_pythagoras-1.html
http://physicsinsights.org/sphere-volume-1.html
You may not feel these pages actually "explain" anything, of course!
:-) That was, however, part of the reason for putting them together,
and perhaps these pages will give you an idea of what I think an
explanation is. Or maybe not...
