Editing Deferent and epicycle (section)

==The number of epicycles==
According to one school of thought in the history of astronomy, minor imperfections in the original Ptolemaic system were discovered through observations accumulated over time. It was mistakenly believed that more levels of epicycles (circles within circles) were added to the models to match more accurately the observed planetary motions. The multiplication of epicycles is believed to have led to a nearly unworkable system by the 16th century, and that [[Copernicus]] created his [[heliocentric system]] in order to simplify the Ptolemaic astronomy of his day, thus succeeding in drastically reducing the number of circles.

{{Blockquote|With better observations additional epicycles and eccentrics were used to represent the newly observed phenomena till in the later Middle Ages the universe became a 'Sphere/With Centric and Eccentric scribbled o'er,/Cycle and Epicycle, Orb in Orb'.|[[Dorothy Stimson (historian)|Dorothy Stimson]]|''The Gradual Acceptance of the Copernican Theory of the Universe'', 1917<ref>[[Dorothy Stimson (historian)|Dorothy Stimson]], {{ws |[[s: The Gradual Acceptance of the Copernican Theory of the Universe|''The Gradual Acceptance of the Copernican Theory of the Universe'']]}} (New York, 1917), {{ws |[[s: The Gradual Acceptance of the Copernican Theory of the Universe/Part 1/Chapter 1#14|p. 14]]}}. The quotation is from [[John Milton]]'s ''[[Paradise Lost]]'', Book 8, 11.82–85.</ref>}}

As a measure of complexity, the number of circles is given as 80 for Ptolemy, versus a mere 34 for Copernicus.<ref>Robert Palter, ''An Approach to the History of Early Astronomy''</ref> The highest number appeared in the ''[[Encyclopædia Britannica]]'' on Astronomy during the 1960s, in a discussion of King [[Alfonso X of Castile]]'s interest in astronomy during the 13th century. (Alfonso is credited with commissioning the [[Alfonsine Tables]].)

{{Blockquote|By this time each planet had been provided with from 40 to 60 epicycles to represent after a fashion its complex movement among the stars. Amazed at the difficulty of the project, Alfonso is credited with the remark that had he been present at the Creation he might have given excellent advice.||''Encyclopædia Britannica'', 1968<ref>''Encyclopædia Britannica'', 1968, vol. 2, p. 645. This is identified as the highest number in Owen Gingerich, ''Alfonso X''. Gingerich also expressed doubt about the quotation attributed to Alfonso. In ''The Book Nobody Read'' (p. 56), however, Gingerich relates that he challenged ''Encyclopædia Britannica'' about the number of epicycles. Their response was that the original author of the entry had died and its source couldn't be verified.</ref>}}

As it turns out, a major difficulty with this epicycles-on-epicycles theory is that historians examining books on Ptolemaic astronomy from the Middle Ages and the Renaissance have found absolutely no trace of multiple epicycles being used for each planet. The Alfonsine Tables, for instance, were apparently computed using Ptolemy's original unadorned methods.<ref name=Nobody/>{{rp|57}}

Another problem is that the models themselves discouraged tinkering. In a deferent-and-epicycle model, the parts of the whole are interrelated. A change in a parameter to improve the fit in one place would throw off the fit somewhere else. Ptolemy's model is probably optimal in this regard. On the whole it gave good results but missed a little here and there. Experienced astronomers would have recognized these shortcomings and allowed for them.

In fact, in Ptolemy's ''Almagest'' the Sun has one cycle and the Moon has three: the deferent, an epicycle, and an inner small circle or "epicyclet". Each outer planet has four: deferent, epicycle, equant, and latitude wheel.  Venus has two more latitude wheels than the outer planets, so six.  Mercury has all of Venus’s cycles plus an epicyclet, or seven. If we include the sphere of the fixed stars, and another sphere to account for the precession of the equinoxes, the total number of cycles and spheres comes to 31.<ref>{{cite web |last= Weiss|first= Michael |date= May 20, 2025|title= From Kepler to Ptolemy 15|url= https://diagonalargument.com/2025/05/20/from-kepler-to-ptolemy-14/|website= Diagonal Argument |location= |publisher= |access-date=May 20, 2025}}</ref>