I: Introduction

Peter Kalkavage captures best what motivated the Polish astronomer Nicolaus Copernicus to overturn the ancient Greco-Roman astronomical model solidified by Ptolemy in his Almagest. Kalkavage writes: “[Ptolemy] is not setting out to ‘explain the world’ in the sense of getting at the true causes of motion and paths of the heavenly bodies. […] The absence of a single mathematical account of the whole [universe] in the Almagest horrified Copernicus” (Kalkavage, pg. 6). What Kalkavage elucidates is Copernicus’s motivation to upend the astronomical model presented in the Almagest because, for all of Ptolemy’s brilliance, he was unable to explain his many hypotheses on cosmic motion with a single unified system. That is to say, Copernicus saw that Ptolemy was unable to unite his various theories on how the motion of the night sky revolved in pattern by a singular cause. Instead, Copernicus saw Ptolemy’s explanations as disjointed: the movement of the sun looked nothing like the movement of the planets, and the movement of the planets were dissimilar in several cases themselves.
This paper will explore the most fundamental ways in which Copernicus and Ptolemy differ in their approaches to ordering the heavens. Although both sought to answer cosmological questions for the sake of the divine, Ptolemy sought to explain the “eternally unchanging” for the sake of Aristotelian wisdom (Almagest, 1.H7) and Copernicus sought to explain the workings of the universe as a means of exalting God. Where both authors diverge is not their motivations, but their methodologies: while both authors use circular motion as a way of explaining the wanderings of the planets (Almagest, 1.H27; Revolutions, 1.Ch4), Copernicus states that this is due to a “constant law” that, from the observer’s vantage point, merely appears nonuniform (Revolutions, 1.Ch4). This is significantly different than Ptolemy’s methods, which, by simply matching circular-movements to data, fail to produce uniform orbits for the planets. From these investigations it becomes apparent that the difference between the two authors is a fundamental one; specifically, that Ptolemy lacks a general “principle governing the order in which the planets follow one another” (Revolutions, 1.Ch9) analogous to that which Copernicus uses to construct his cosmological model. This paper will explore and contrast these two author’s methods, and seek to explain the pertinence of their work.

II: Ptolemy’s Circles

Both authors rely on circles to explain the phenomena of the heavens. The reasoning for this is simple in both cases: both authors seek to explain the movement of stellar objects – the Sun, the Moon, and the “wandering” planets — in a way that is A) uniform, in a non-erratic manner, and B) repeating, composed of discrete intervals that return to their original positions. We see these conditions satisfied in Ptolemy:

[…] the sun, moon, and other stars were carried from east to west along circles which were always parallel to each other […] and that the periods of these motions , and also the places of rising and setting, were, on the whole, fixed and the same (Almagest, 1.H11).

And in Copernicus:

[…] the motion of the heavenly bodies is circular, since the motion appropriate to a sphere is rotation in a circle. By this very act the sphere expresses its form as the simplest body, wherein neither beginning nor end can be found, nor can the one be distinguished from the other, while the sphere itself traverses the same points to return upon itself (Revolutions, 1.Ch4).

Both authors clearly agree that circular motion best describes how the stellar objects move predictably and seem to return to their original positions. However, these two authors vary on how they treat the influence of this circular motion.
Ptolemy uses circular motion to explain particular stellar phenomena individually and not systemically. Instead of arguing that all stellar objects move in the heavens using a single circular motion, he argues that many different circular motions might compound into a single, non-uniform motion. To understand this progression, one must first examine how Ptolemy explains the movements of the Sun.
Ptolemy answers the phenomena of the non-uniform motion of the Sun by compounding several circles onto each other. He tackles the phenomena of the Sun in Book 3, where he lays out two hypotheses to describe the Sun’s motion. According to Ptolemy, the Sun moves around a motionless Earth on either an eccentric circle, or on an epicyclic circle traveling itself on a deferent. This creates a sort of planetwide optical illusion: the Sun appears as though it’s traveling in a non-uniform motion, but in Ptolemy’s model that is only because the eccentric or epicyclic circles create a displacement effect between the observer’s position and the unseen circles guiding the Sun’s motion in a uniform manner.
Ptolemy uses the tools of these hypotheses to construct far different explanations for the planets. In Book 9, Ptolemy sets out to explain the planets’ paths about the Earth in a similar fashion to the Sun. However, unlike his two models on the Sun’s motion, Ptolemy’s new hypotheses don’t result in circles in the sky, but swirling ribbons. He returns to the use of epicyclic and eccentric circles to explain apparent non-uniform motions circularly: placing a planet’s epicycle on a deferent also eccentric to Earth. Attempting to explain the odd, non-conforming case of Mercury’s movement, Ptolemy introduces an “equant point”:

For Mercury alone, the centre of the deferent is a point whose distance from the centre of the circle about which it rotates is equal to the distance of the latter point towards the apogee from the centre of the eccentre producing the anomaly, which in turn is the same distance towards the apogee from the point representing the observer (Almagest, 9.H253)

Ptolemy produces a center for the deferent widely off from the rest of the planet’s rotations. Ptolemy’s sky then becomes a swirling ballet of planetary rotations, with the Sun moving uniformly in a circle, while the other planets move steadily in loops and ribbons around a static Earth. Although Ptolemy uses consistent logic in his method of adducing planetary motion, he seemingly modifies his hypotheses with no care for systemic consistency — preferring instead to find ad hoc solutions for his problems. By creating the so-called equant point, he introduces an additional convention to explain his hypotheses that is inconsistent with the rest of his premises in the Almagest. This is the core of the pseudo-scientific Ptolemaic model: piecemeal alteration of hypotheses without regard to a singular, governing principle. This is what Copernicus found so revolting.

III: Copernicus’s Circles

Copernicus, on the other hand, set out his cosmological model with consistency in mind. In Book 1, Chapter 4 of Revolutions, he lays out a case for ultimate uniformity of circular motions in the heaven. Speaking of the planets, Copernicus at first states, “[…] their motions are circular or compounded of several circles, because these non uniformities recur regularly according to natural law” (Revolutions, 1.Ch4). However, as he advances his argument he modifies this claim, portending that stellar bodies cannot be ascribed these “compounding movements” due to the motion of a single sphere. He concludes that these motions merely “appear nonuniform to us” (Revolutions, 1.Ch4), and that in actuality they make uniform orbits around the sun (Revolutions, 1.Ch10). He arrives here by a reversal of Ptolemy’s fundamental principles: the Earth now orbits the Sun, rotates on its own poles from west to east, and wobbles on its own axis (Revolutions, 1.Ch11). This monumental departure — from a geocentric solar system to a heliocentric one — wasn’t made lightly on Copernicus’s part. He was upending centuries of astronomical dogma with his new heliocentric model, but it was a conclusion delivered with even-headed logic. Copernicus could demonstrate his new model with a consistency Ptolemy lacked. By assigning Earth these three motions instead of the heavens, Copernicus was able to keep the heavenly bodies moving around the Sun in simple, uniform circles — the apparent non-uniformities in the sky coming from our own wobbling, twirling view looking up at the static Sun and the planets revolving it.
These phenomena are described most beautifully by Copernicus in Chapter 11. Setting the Sun in the center, Copernicus has the Earth rotate around it over the course of the year. The day/night motion will combine with our own rotation to cause the appearance of the Sun traveling through the order of the Zodiacal signs, when in actuality it is due to our rotation around the Sun. The axial tilt and its “wobble” effect — the Earth rotating around its poles unevenly, like a slowing teetotum — then produce appearance of a speeding or slowing Sun by shifting how much of our local sky is exposed sunward in a year. In one deft maneuver, Copernicus explains the illusion of the Sun’s movement and an accurate timing of the seasons. This same phenomena would produce the appearance of “wandering motions” of the planets, which are actually following fixed orbits. Copernicus’s system of a static sun and a moving Earth is an example of how he used circles as governing principles of his work. Instead of needing special cases like Ptolemy’s equant point, Copernicus constructs a system that is self-consistent with its base assumptions, requiring no deux ex machina convention to remain logically sound. The circular motion of Copernicus was what ordered a flighty heaven, and produced a consistent model predicated on conformity rather than exception.

IV: Conclusion

In “Why We Read Ptolemy”, Kalkavage explains to St. John’s students that they read Ptolemy, in part, to understand the weight the Copernican Revolution had on antiquity’s model of the cosmos. As Kalkavage rightly points out, Copernicus did not observe an additional critical “thing” that Ptolemy failed to perceive (Kalkavage, pg. 2). If one inspects Ptolemy expecting ineptitude they will be harshly surprised: his sprawling proofs, even in his first book, out-punch Copernicus’s. What Copernicus did to overturn Ptolemaic thought was not produce vital new information, but maintain a set of self-consistent premises that required no outside postulates to remain congruent. What this paper has found at the end of its exploration is thus a celebration of two brilliant astronomers, and a clear moral lesson regarding their methods.
However, more can be gained by the study of Ptolemy than mere context for Copernicus: what Ptolemy and Copernicus represent are two competing ways to solve problems. Ptolemy demonstrates an intensive exercise in constructing complex hypotheses to explain data. Ptolemy makes constant reference to the ancients who preceded him and catalogued the heaven’s movements. Copernicus makes comparably fewer references to the hard data, but ultimately modern scholars have found Copernicus, not Ptolemy, correct. The two authors even used similar geometric tools to aid their explorations, and yet Ptolemy fell far short. At the end of its exploration, this paper suggests that Ptolemy was attempting to explain each phenomenon in systemic isolation, while Copernicus was viewing them as part of a system ordered by concordant governing principles. Both skills demonstrated remain vital today — both in mathematics and in life’s general toolbox. A study of Ptolemy can instruct one on a rigorous tutorial on how to formulate ideas faced with reams of data — and the perils of doing so without consistent principles. Ultimately, what reading Ptolemy and Copernicus might demonstrate is how best to utilize the information presented to us, and how best to employ the circles in our logic.

Works Cited

Copernicus, Nicolaus. On the Revolutions. Translated by Edward Rosen. Edited by Jerzy Dobrzycki, John Hopkins University Press, 1992.

Ptolemy. Ptolemy’s Almagest. Translated by G. J. Toomer, Princeton University Press, 1998.

Kalkavage, Peter. “Why We Read Ptolemy.” Fourth Annual Conference of the Association for Core Texts and Courses, 17 April 1998, Asheville, NC.