Everybody knows that Ptolemy was wrong: the earth is not the immovable center of a finite, spherical cosmos. The earth is a planet, and the sun rather than the earth is the center of the planetary system. Everybody also knows that Ptolemy’s Aristotelian assumptions were wrong: the heavenly bodies are not divine. The physical universe -- so most scientists seem to believe -- is simply matter moving in empty space according to fixed laws of nature. Matter is the same everywhere, and there is no fundamental distinction between the “down here” and the “up there,” between my throwing a rock at the wall and the revolution of Mars. Whereas Aristotle’s physics is aristocratic, modern physics is egalitarian -- and modern physics has prevailed. Indeed, its technological achievements are staggering. We know, as I have said, that Ptolemy was wrong. What, then, can we teachers and our students possibly learn from him? Why read Ptolemy?

      At St. John’s College, every student spends considerable time with Ptolemy’s great work, the Almagest. Freshmen take up the motion of the sun right after their long journey through Euclid’s Elements. Sophomores continue the study of the Almagest with Ptolemy’s complex account of Venus. This account of Venus in turn paves the way for the study of Copernicus as students move from the beautifully clear skies of the Mediterranean to the cloudy skies of eastern Europe.

      The sequence of the St. John’s curriculum suggests my first answer to the question “Why read Ptolemy?” The answer is very simple: One cannot hope to understand the so-called Copernican Revolution (and therefore the astronomical origin of modernity) without a close study of Ptolemy. We tend to have very fuzzy notions about why the Polish astronomer did what he did. We tend to believe, mistakenly, that somehow or other Copernicus observed something that Ptolemy didn’t. But if observation wasn’t the issue, then what was? Why was a revolution deemed necessary? I shall return to this question at a later point.

      Sozein ta phainomena, “to save the appearances.” Thus did Simplicius, commenting on Aristotle’s De Caelo, famously define the goal of the mathematical astronomer. This saving of the appearances is deeply connected with the mathematical character of Ptolemy’s book. Ptolemy begins with the grand assumption of a beautifully ordered whole, in Greek, a kosmos. Fundamental to this view is the distinction between the human and the divine, the deathbound and the deathless. Is there experiential evidence for this view? Yes. As we look around us with an eye unprejudiced by theory, we observe all sorts of things undergoing all sorts of motions. Flowers emerge from the ground, blossom and then die. Leaves change their colors, fall from the trees and then reappear. Various animals creep, fly or swim. This variety of motions reaches its peak with man, who not only moves physically but also changes his mind and is constantly beset by those inner motions known as the passions. As we turn our gaze to the sky, although we still observe motion or change, whether the daily arc of the sun or the whirl of the stars in the course of a night, we behold -- that is, we pre-scientific observers behold -- a realm very different from our own. To all appearances the brilliant Beings in the Sky neither change nor die: they simply move in place. And what’s more, they appear to do this one thing they do the same way all the time. In the realm of pre-scientific experience, nothing on earth, certainly not man, approaches this marvelous regularity of being and behavior. To the scientifically disposed human being, the inquisitive human being, this pre-scientific experience is the surest sign that the world is not only visible but also thinkable, that if we look for order we will find it.

      But order and regularity are not perfectly preserved in the heavenly appearances. There is overall order, but there are observable irregularities within that order. The sun always rises in the same place and sets in another. Its whole daily cycle takes the same amount of time every day. But the sun’s arc, its height above the horizon, changes as the year rolls on. Then there is the fact that if we measured the durations of the four seasons, we would find that these durations are unequal -- that the sun in its yearly course around the ecliptic seems to speed up and slow down. The irregularities become much more disturbing when we conduct careful and prolonged observations of the so-called planets or “wanderers,” which not only seem to move at an inconstant rate but also are observed to “stop” in their course through the fixed stars and then move backwards! To save the appearances the astronomer must rescue them from this apparent irregularity and disorder. The Ptolemaic astronomer is thus the advocate and defender of the visible gods to human beings: he defends these gods, these starry symbols of our better selves, from the hasty though not ill-founded charge of disorderly conduct. He does so by means of mathematical hypotheses. Armed with these devices, the astronomer seeks to demonstrate that apparent irregularity is really the product of a complex and not altogether apparent regularity. Why rescue these motions and not the manifestly irregular jumps, starts and vicissitudes of plants and animals, why limit the mathematical rescue of the appearances to the Beings in the Sky? Because they alone for Ptolemy deserve to be rescued, because they alone of all the things in the familiar observable world manifest themselves as deathless and admirably dependable in their motions.

      The heart of Ptolemy’s science is the mathematical hypothesis of regular circular motion. Such motion has the following theoretical advantages: first, it is eminently intelligible because accountable in terms of Euclid’s geometry and theory of ratio; second, regular circular motion accords with the divine nature of the Beings in the Sky; and third, that’s the way celestial motion by and large looks. In Book III, Chapter 3 of the Almagest, Ptolemy lays out his two basic forms of this hypothesis: the eccentric circle and the epicycle with its so-called deferent, that is, the circle around which the epicycle’s own center moves. (Pictures of these hypotheses are appended. It is important to note that the pictures always contain the observer, the perspective from which motion appears irregular.) So what does the Ptolemaic astronomer do with these hypotheses? Well, he starts by looking at the world and taking measurements of time and position for a given star or planet. On the basis of these measurements he constructs tables. The tables serve as a means by which the astronomer can “plot the course” of a star or planet. The next step is to wed the specifics of the table, the “facts,” to an appropriately adjusted mathematical hypothesis of regular circular motion. The astronomer must demonstrate that how the Beings in the Sky actually look, especially in their apparent irregularity, can be regarded as the result of some non-apparent, hypothesized regularity. It would be like taking the various events in the life of a human being and constructing the single story or plot to which these events belong -- or can be imagined to belong. Needless to say, the hypothesis must have predictive power: it must not only accord with chronicles of the past but also serve as the basis for tables of future times and positions.

      Now you cannot really understand Ptolemy by just extracting the doctrine from his book, by reading his general assumptions and conclusions. You must spend time actually working through his artful and sometimes confusing demonstrations. Generally speaking, a proper understanding of science can be gotten only from actually attempting to do the work of science. This is precisely what students do when they take up Ptolemy in the mathematics tutorial at St. John’s College. By immersing themselves in Ptolemy’s activity, our students counteract the defects of both the “history of ideas” approach to great works of science and the professional study of astronomy: they are compelled to take Ptolemy on his own terms.

      It is an eye-opener for teachers and students alike to realize what Ptolemy is not setting out to do in the Almagest. He 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. For all the circles we see in his book, not one of them is an actual orbit. We can, of course, generate the orbits that Ptolemy’s mathematical hypotheses would produce. But only in the case of the sun do we actually get a circle. The rest are elaborate floral patterns with petal-like loops. Nor is there a single, coherent picture of the cosmos. The absence of such a picture goes hand in hand with the absence of a single, mathematical account of the heavenly bodies taken as a whole. In other words, the Almagest is a sequence of separate “savings” of separately taken appearances. And yet Ptolemy never doubts that there is a single and coherent whole of things, a kosmos. We can only conclude that such a whole does not for Ptolemy emerge in the purely mathematical study of the heavens but belongs in the province of another science.

      The absence of a single mathematical account of the whole in the Almagest horrified Copernicus. But what really horrified him was something called the “equant.” At one point in his account of Venus, Ptolemy realizes that even combining the eccentric hypothesis with the epicyclic can’t account for the apparent irregularity of the motions of Venus. So what does he do? He lets the motion of Venus’ epicycle around its deferent be irregular and then postulates another center around which this irregularity is made regular. This “equalizing” or regulating center is the equant. The ad hoc hypothesis of the equant, which surely seems to compromise Ptolemy’s own veneration of regular circular motion, is eliminated at one stroke by the heliocentric hypothesis of Copernicus. Furthermore, under the heliocentric hypothesis all the celestial appearances are mathematically accountable together as belonging to a single coherent system. The Copernican hypothesis does all this -- but at a price: the world no longer looks like what it is. Terra firma seems to be at rest but in fact is not; the sun and stars seem to move, but in fact they don’t. From the Aristotelian perspective that Ptolemy holds dear, the ordering principle of the world, the natural “placedness” of things within a hierarchy, is gone. With the triumph of Copernicus, humanity has gained a system but lost a kosmos.

      These remarks should make clear that a careful study of Ptolemy is absolutely essential to an understanding of Copernicus and his world-shaking hypothesis. It should make clear that the great revolution in astronomy was generated, as it were, from conflicts within Ptolemaic science. What seems to be at stake in the revolution is not the facts of the science but the form of science itself, the scientificness of science. This issue -- the form of science -- is of central importance to the development of modern thought, from Descartes up through Kant’s Copernican Revolution in philosophy, and beyond to non-Euclidean geometry, relativity and quantum physics.

      But we don’t need the moderns to get at the problematic nature of Ptolemaic astronomy. Ptolemy himself stresses the perplexing character of his science. He thus encourages us to persist in exploring the question, What is astronomy? Ptolemy at one point warns us that we must be careful not to confuse the mechanisms of our mathematical models with the actual motions of the Beings in the Sky. Echoing Plato’s character Timaeus, Ptolemy refers to his mathematical accounts as likenesses or images. He reminds us that the Beings in the Sky move the way they do, not because they are subject to laws of nature and experience either inertial or accelerative force, but because, as Ptolemy says, they are free, free of the chance and impulsiveness that characterize the realm below the sky.*

      By way of conclusion, I propose the following list of answers to the question “Why read Ptolemy?” First, without a study of the Almagest, as I have said, we cannot hope to understand the Copernican Revolution and the origins of modernity: not to study Ptolemy is therefore a failure to know ourselves. Second, Ptolemy represents a magnificent example of how the visible world seems indeed to be mathematically ordered. Third, Ptolemy’s theory, the truth of the Copernican hypothesis notwithstanding, actually succeeds in accounting for all the motions that are detectable with the naked eye. Fourth, Ptolemy presents his science within a comprehensive philosophic view of the whole, so that by studying Ptolemy we are led to the deepest questions about being and knowing, truth and appearance, the human and the divine. Fifth, in working through the details of Ptolemy’s argument, we get first-hand experience of mathematical model-building in physical science. Sixth -- and forgive me if this sounds frivolous -- Ptolemaic astronomy is fun. The very limits and difficulties of the science are intimately connected with the imaginative play of telling “likely stories” about the visible world.

      My seventh and last answer derives from the Preface to the Almagest. Here Ptolemy, again echoing Plato’s Timaeus, tells us that mathematical astronomy is good for our souls. He speaks of the eros, the passionate love, “of the discipline of things that are always what they are.” In studying the motions of the Beings in the Sky, we become more like them -- regular, orderly and good. We thus acquire and cultivate the right perspective on the human in its relation to the divine. To study Ptolemy is to realize that knowledge of the visible world need not be a stranger to nobility. Yes, Ptolemy seems to have been wrong about the facts. But his theory does save one appearance, one important fact, that modernity seems bent on repressing: that when we mortals observe the Beings in the Sky, we are compelled to look up.

* See Almagest XIII.2, p. 429, “Great Books of the Western World,” Encyclopaedia Britannica, Chicago, 1975.