Date: Fri Sep 05 2003 - 12:21:38 EDT
We seem entangled in the ancient war between Pragmatic Experimentalists and
Abstract Theorists. My primary protagonist, Albert Einstein, seemed to be
quite aware of this tension, but oddly, (he was an odd fellow), he also
seemed to take both positions simultaneously. Here is a quote from him that
agrees with your perception:
"As far as the laws of mathematics refer to reality, they are not certain;
and as far as they are certain, they do not refer to reality. "
Quoted in J R Newman, The World of Mathematics (New York 1956).
This sounds very much like what you said, and if this were all Einstein had
to say on the topic, I would have to concede your point. But the fact is
that he is the primary protagonist for the "truth (mathematical, physical,
etc.) is beautiful" school of thought. A. Zee paraphrased Einstien's
approach with the words:
"Let us worry about beauty first, and truth will take care of itself."
The bottom line is that the points are not actually mutually exclusive. We
are both correct. In the abstract, beauty rules; the devil is in the
details. Everything we have discovered about the *fundamental* equations
govering the universe can be described as astoundingly beautiful. But the
implementation of this knowledge quickly becomes a quite mess, as you well
Discover the sevenfold symmetric perfection of the Holy Bible at
----- Original Message -----
From: "Don Winterstein" <firstname.lastname@example.org>
To: "asa" <email@example.com>; <firstname.lastname@example.org>
Sent: Friday, September 05, 2003 1:28 AM
Subject: Re: The Unreasonable Effectiveness of Traditional Christian
Richard wrote in part:
>I think you have characterized the situation exactly backwards. It seems
have confused the approximations necessary for numerical analysis with
incompleteness of fundamental theory. The problem is rarely that we can not
write down the correct equation because it is too complex. The problem is
that we can not *solve* the exact equation because it is too complex.
You may be able to write good-enough equations for practical purposes, but
they would still not be strictly exact. In the case of planetary motion, we
simply don't know enough to include all influences. For example, we don't
know all the asteroids, comets, etc., much less details of the Oort cloud.
For extreme accuracy you'd have to include effects of stars, etc. While
you could write generalized Hamiltonian equations that include the real
world implicitly, you don't know enough to include the real world
explicitly. And this applies to all mathematical formulations of physical
theory. To what degree this truth is relevant to anything will vary
according to the branch of physics being considered. But whether it's of
any practical relevance or not, the point is that the math never exactly
represents the real world.
Math formulations that include the real world explicitly would lose elegance
and not be beautiful by most standards.
>You said "The real world rarely or never precisely complies with our
"astoundingly overwhelmingly beautiful" mathematical representations." While
you are certainly free to hold this opinion, I would be doing you a
disservice if I failed to inform you that it is *not* the consensus of those
"who have thought about it..."
"Those who have thought about it" were probably theorists looking at the big
picture and ignoring lots of details.
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