On Oct 18, 2008, at 12:03 AM, Edward Cherlin wrote:
2008/10/17 michel paul <[EMAIL PROTECTED]>:
"We should abandon the vision that physicists seek an ultimate
mathematical
description of the universe since it is not obvious that it exists.
I disagree with this attitude. We can seek an ultimate mathematical
description, since it is not obvious that it does not exist. We should
also be aware that we do not have one, and have some idea of the range
of validity of our models. This will help us to avoid mathematical
absurdities, particularly the infinities that result from calculations
on unphysical point masses and point charges.
a consequence of the Godel theorem is that even if a complete
mathematical description of the universe exists, and we find it, we
cannot prove it is complete. We can only prove it works for those
phenomena we have observed.
I say the goal if to seek a comprehensive effective theory that
describes and explains observed phenomena.
The job
of the physicist is that of modeling phenomena within the physical
scales of
observed events.
True much of the time. Another part of the job is to model outside the
scale of the observed, and go make the new observations needed, as in
the case of General Relativity.
General relativity describes observed phenomena. It was so even at
times of Einstein (orbit of planets)
For some systems, the modeling can be done more effectively
using algorithms."
As a mathematician, I don't know what that means. Every algorithm can
be represented by a system of equations in a number of ways, and every
system of equations can be solved, at least approximately, by various
algorithms.
Mathematical formulas described relations between quantities.
Algorithms described a process (for example a process to solve a
mathematical formula).
If you believe you can find a ultimate model for everything, it has
to be described in mathematical terms. If you believe you cannot do
better than explain known events observed with a finite precision,
then numerical algorithms provide an efficient way to model the
physics. I am not saying one can have one without the other. I am
saying it is easier to teach Newton's gravity using Euler's
approximate algorithm that it is to do it using symbolic integration.
As a teacher, I know very well what it means. Some representations are
easier to understand, or easier to work with, or easier to learn from.
Various thinkers, including Babbage, Whitehead, and Iverson, have
commented on the effects of the way we represent problems on our
ability to think about them, and not only they but luminaries from
Fibonacci to Einstein have labored to invent or teach new notations
and representations.
I agree.
Massimo
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