Re: [Vo]:Three Words That Could Overthrow Physics

[Stephen A. Lawrence]

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...