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Bugmaster comments on Rationality Quotes March 2012 - Less Wrong
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To be perfectly fair, AFAIK Ptolemy thought in terms of a finite (and small) number of epicycles, not an infinite series.
And so for the curves in question, the Fourier expansion would have only a finite number of terms.
The point being that, in contrast to what was being asserted, Ptolemy's concept is subsumed within the modern one; the modern language is more general, capable of expressing not only Ptolemy's thoughts, but also a heck of a lot more. In effect, modern mathematical physics uses epicycles even more than Ptolemy ever dreamed.
That's good point; I haven't thought about that. Go epicycles ! Epicycles to the limit !
ducks and runs away