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Re: [Phys-l] status of Occam's razor



Don,
The idea of accuracy historically in science is a moving target. In fact I think it is a moving target among our introductory students, but at least we have statistics for a model as to how to handle it. The Copernican theory was simpler on some calculations then the Ptolemaic model, but it is hard estimate which was more accurate. For example Christopher Clavius, sometimes called the last Ptolemaic astronomer, conceded that some calculation using the Copernican system were easier.
Tycho Brahe being an observer had a good grasp of observation error. He use a technique to subdivide his instruments that he knew was not precise but whose errors were less than what he thought he could measure. He even produced an error table to correct these result if he felt it was necessary.
Kepler of course built his laws on Tycho's data. He found that he could fit the Copernican model with this data to within seven minutes of arc, but he felt that Tycho's observations should be accurate to at least a minute of arc and that motivated him to through out epicycles and uniform circular motion and find another curve that would fit the data.
The deviation of the motions of the planets from Kepler's Laws is at most about fifty seconds of arc. I have wondered what if Jupiter had been more massive so the perturbations were the order of a few minute of arc, would Kepler have found his Laws? He was a real stickler for accuracy. Many astronomers would have been very happy to be within 7 minutes of arc or about one fourth the diameter of the moon.

Gary Karshner

At 12:54 PM 8/2/2007 -0400, you wrote:

On 08/02/2007 11:09 AM, chuck britton wrote:
> An Historical Question concerning Occam's Razor -
> Devil's Advocate Hat On:
>
> When did the Copernican Theory of our Solar system become as precise
> as the Ptolmeic Theory?
> Did Newton work out the perturbations required - or am I totally
> bonkers in believing someone who claimed that all the cycles and epi-
> cycles DID give more precise predictions than did Copernicus (and
> Kepler)?

The textbooks we used in the History of Science course I taught for
several years claimed that the Copernican Theory, as proposed by
Copernicus himself, was not as accurate as the Ptolemaic Theory (much
simpler, of course, but just not as accurate). However, Kepler's
modification of circular to elliptical orbits gave the "Copernican"
Theory just as much accuracy as the Ptolemaic with many fewer
assumptions and parameters. Newton provided the theoretical basis for
why the orbits had to be elliptical and started, at least, to consider
the effect of "perturbations" like three body versus two body problems.
Of course, the remaining vexing unexplained perturbation of the
precession of Mercury's orbit required Einstein's general relativity to
finally resolve.

Don Polvani
Northrop Grumman Corp.
Undersea Systems
Annapolis, MD
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