
p.s. for the record, Barbour is no clown, but a serious cat -- he is also the guy that wrote "Absolute or Relative Motion / the Discovery of Dynamics" which is a bedrock treatise on Machian ideas in physics
He didn't start with that hypothesis, he came to it after multiple tries at fitting other models like an equant (an offset circle with angular speed controlled from the opposite offset, which is actually a good first-order approximation to the Kepler-law motion at small eccentricity).
> Only after repeating his procedures 70 times did he offset his computational errors. With a little less patience, he wouldn’t have proved his theory, and elliptical orbits would have eluded us for longer.
I skimmed the paper, and it seems to be about Kepler fitting an equant instead of an ellipse. Apparently he used an iterative method, stopping after 70 iterations? And his numerical errors seem to be responsible for it not converging faster. That makes more sense to me than my misunderstanding that you were saying he ran through the whole calculation from the start 70 times. I jumped to a conclusion about that part, and I'm sorry.
Julian Barbour's The Discovery of Dynamics explains what Kepler did in detail (it's not the whole topic of the book, but a big chunk of it). A great book -- I didn't really appreciate Kepler before reading it. Both brilliant and very human.
Of course his work was not done in a vacuum.
1) Lightman's description of his hallucinationish experience at the age of nine, wherein he perceived all time in one instant [or had the sensation of doing so], reminds me of Julian Barbour ["The Discovery of Dynamics"] and his hypothesis that all spacetime exists simultaneously -- not in a Minkowski-eque 'loaf,' but in a static collection of mathematical configuration spaces, each of which represent a "now" [which word, coincidentally, concludes Lightman's article].
2) I can relate to Lightman's notion of 'Nothingness' as it relates to quantum field theory -- when I first cracked Tony Zee's "QFT in a Nutshell," I'm pretty sure I experienced the same feeling of complete inconsequentiality described by Lightman, though for totally different reasons.