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Wheels Within Wheels

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PostPosted: Sun Nov 19, 2006 6:49 pm    Post subject: Wheels Within Wheels Reply with quote

I remember watching Jacob Bronowski's the Ascent of Man. At one point they spoke of the ptolemaic solar system, with all the planets and the sun and moon orbiting the earth. Then the heliocentric theory, but with circular (Copernican) orbits. Models were built to simulate the movements, and these were great watchmaking, of wheels within wheels within wheels. They were adjusted and readjusted until the paradigm no longer fit the data -- and the elliptical model of Kepler.

We have always wanted an absolute, regular, Platonic we can predict things. What we end up with is a messy, unpredictable one. In fact, the whole history of 20th Century physics seems to be a vast retreat from the goals of 16th Century physics. We threw up our hands and said -- we can't model this!

I think of probability and the importance in our thinking. We guess at how likely something is to happen. We never imagine that we can absolutely predict these things. Is probability a measure of the likelyhood of something happening, or is it a reflection on our ability to predict absolutely, anything.

To me the key is geometry and the modulus. The modulus gives us wheels within wheels in our numbers. The Riemann geometry turns indecipherable events in one plane, into the puppet strings of another.
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