**From:** Don Winterstein (*dfwinterstein@msn.com*)

**Date:** Fri Sep 05 2003 - 04:28:44 EDT

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Richard wrote in part:

*>I think you have characterized the situation exactly backwards. It seems you
*

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.

Don

-----

From: richard@biblewheel.com

To: asa@calvin.edu

Sent: Thursday, September 04, 2003 9:36 AM

Subject: Re: The Unreasonable Effectiveness of Traditional Christian Hermeneutics

From: "Don Winterstein" <dfwinterstein@msn.com>

Richard wrote in part:

"Moorad wrote:

">One ought not to confuse our mathematical

* >description of nature with nature itself.
*

* >Remember a map of a city is a useful construct
*

* >but it should never be confused with the real city.
*

"Agreed. But it has not been demonstrated that the mathematical description

of Reality is "our construct." On the contrary, it is eminently reasonable

to view it as our *discovery* of God's design. Remember, the revelation of

Almighty God declares that "In the beginning was the Logos, and the Logos

was with God, and God was the Logos." What then could be more logical (i.e.

pertaining to the Logos) than the view that the Divine Logos designed

Reality according to the absolutely astoundingly overwhelmingly beautiful

mathematics that we behold all around us? "

Moorad has made a good point for a reason so far not explicitly cited here:

The real world rarely or never precisely complies with our "astoundingly

overwhelmingly beautiful" mathematical representations. Real phenomena are

too complex to fit our equations. The equations are precise only for

simple, isolated systems, which physicists love but are never more than

approximate. For planetary motion, for example, first order approximations

are often good enough; but if you want precision, you have to deal with the

full many-body problem. So the maths are analogous to Platonic ideas: they

look "beautiful" as abstractions but find implementation only in the

simplest systems.

Don, speaking as an ex-experimental physicist/geophysicist

======================================================

Don,

I think you have characterized the situation exactly backwards. It seems you

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

own example proves this point. There is absolutely nothing *approximate*

about the equations governing the many bodied problem. We can write them

down with perfect exactitude. The approximations are introduced only because

we are unable to *solve* the exact equations.

Concerning the relation between Beauty and Physics, there have been many

excellent books written. My favorite is A. Zee's Fearful Symmetry which I

quote on my site to help people understand its application to the structure

of Scripture. Here's the article:

http://www.BibleWheel.com/RR/AZ_Fearful.asp

Here's a quote from page 3 of his book:

"Physicists have discovered something of wonder: Nature, at the fundamental

level, is beautifully designed. It is this sense of wonder that I wish to

share with you."

And here is his estimation of the spiritual beliefs of physicists:

"[Their beliefs] range over the entire spectrum, from the militantly

atheistic to the deeply devout, with the distribution dropping sharply

towards the devout end. I think that many theoretical physicists are awed by

the elegant structure that underlies fundamental physics. Those that have

thought about it are struck dumb with astonishment, as was Einstein, that

the world was in fact comprehensible."

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" (to use Zee's phrase quoted above).

In service of Christ,

Richard

Discover the sevenfold symmetric perfection of the Holy Bible at

http://www.BibleWheel.com

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