One More Thought on Mysticism and Science

I realize that this Science and Mysticism topic may perhaps be getting a
tad old to some of us, and perhaps had "iffy" value on the tuning list, but
I'd like to one more comment following from Bruce K.'s comment that the
axioms (axia? - whatever) of science can be thought of as mystically
chosen:

One of the axioms of Science is what defines a "good" model of ... well,
whatever you're modeling. Historically there have been two basic ideals
for choosing models:
1. Is it useful?
2. Is it simple?

The first one is essentially says that a Scientific model is "good" if
it sets the groundwork for useful technology. Cast in a mildly cynical
light, this could be characterized the old addage about the winners writing
the history books: If a theory produces positive effects upon your life,
then it is more likely to become accepted, and accepted also as the basis
for the next advance.

The second one harkens back to the ancient Greeks. It says that a good
model depends on the smallest number of axioms, but the largest number of
interactions between those axiomatic elements.

To illustrate by extreme case, consider a vibrating air column, say of a
flute. Conceptually, I could precisely describe how it vibrates by taking
each individual air molecule in the tube, and describe its movement through
the tube, down to the nanosecond of time and the millionth of a millimeter,
and beyond. Once I've described the movement of the first air molecule, I
then then choose another air molecule, and describe its movement, and so
forth for each of the untold quadrillions of air molecules in the tube.

That would be an unfathomably, mind-bogglingly complicated model, but
there's no denying that it would exactly describe the air column's
vibrations to form a flute sound.

The other extreme is to describe the air column by rule. You model it
in terms of air pressure, density and temperature, and how they interact to
propagate sound waves through a tube. That model, altough certainly not
trivial, describes a flute tube in terms of less than a dozen measurable,
verifiable quantities. It is therefore many quadrillions of times more
simple than the other model.

Is that second model a better model? It almost certainly is if you're
interested in describing more than one particular flute tube, if you're
interested in a model that can be described in writing in a book small
enough to fit into the known universe, or if you're interested in a model
whose underlying concepts can be adapted to other types of instruments.
But is it INHERENTLY better? Can you be completely certain that every
single human being that will ever trod this earth will agree that it's a
better model?

Well... I suppose one could claim that my choice of the second sort of
model as inherently better is based upon mysticism, or perhaps upon
prejudice.

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