In order to get the actual motion of the planets correct, both Ptolemy and Copernicus had to bolster their models with many more epicycles, and epicycles upon epicycles, than shown in the above figure and video. Copernicus even considered introducing an epicyclepicyclet — “an epicyclet whose center was carried round by an epicycle, whose center in turn revolved on the circumference of a deferent concentric with the sun as the center of the universe”… (Complete Dictionary of Scientific Biography, 2008).

Pondering his creation, Copernicus concluded an early manuscript outline his theory thus “Mercury runs on seven circles in all, Venus on five, the earth on three with the moon around it on four, and finally Mars, Jupiter, and Saturn on five each. Thus 34 circles are enough to explain the whole structure of the universe and the entire ballet of the planets” (MacLachlan & Gingerich, 2005).

These inventions might appear like remarkably awkward — if not ingenious — ways of making a flawed system fit the observational data. There is however quite an elegant reason why they worked so well: they form a primitive version of Fourier analysis, a modern technique for function approximation. Thus, in the constantly expanding machinery of epicycles and epicyclets, Ptolemy and Copernicus had gotten their hands on a powerful computational tool, which would in fact have allowed them to approximate orbits of a very large number of shapes, including squares and triangles (Hanson, 1960)!

Despite these geometric acrocrabitcs, Copernicus theory did not fit the available data better than Ptolemy’s. In the second half of the 16th century, renowned imperial astronomer Tycho Brahe produced the most rigorous astronomical observations to date — and found that they even fit Copernicus’ data worse than Ptolemy’s in some places (Gingerich, 1973, 1975).

Jacob Lagerros, *The Copernican Revolution from the inside*, 26 October 2017

Added to diary 15 January 2018