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AnnaSalamon comments on Were atoms real? - Less Wrong
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I realize that. But his epicycles were still easier to use than the Ptolemaic epicycles model.
I'd consider mentioning the equant as the elimination of it seems to be where most of the theoretical elegance was gained. There were fewer epicycles (were they used differently?) but I'm not sure how much of the epicycle elimination was due to genuine improvement and how much just left the theory as less accurate (more epicycles usually means more precision).
In what sense were they easier to use?
Well there were fewer of them... but Anna may mean something else.