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I learned about Fourier this way from an old "American Scientist" book. The writer had a very powerful remark at the end. He explained how Ptolemeus first used epicycles as a base model to explain planetary motion [edit: their paths]. The criticism that led to the demise of this model was basically "yeah, well, you can make planets have square paths this way". If someone connected the dots at that point we could have had Fourier transform a couple of hundred years earlier. Maybe we did, but the documents disappeared.



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