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.
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