My next podcast is my review of Ptolemy’s Almagest. To listen, click below:
There are few phrases more annoying or more effective than “I told you so.”
This is my second encounter with Thomas Kuhn, and again I emerge deeply impressed. To do justice to an event so multifaceted as the Copernican Revolution a scholar must have a flexible mind; and Kuhn is fully equal to the task. He moves seamlessly from scientific data, to philosophical analysis, to historical context, and then back again. The result is a book that serves as an admirable introduction to the basics of astronomy and a thorough overview of the Copernican Revolution, while raising intriguing questions about the nature of scientific progress.
Kuhn first makes an essential point: that the conceptual schemes of science serve both a logical and a psychological function. Their logical function is to economically organize the data (in this case, the position and movement of heavenly objects); their psychological function is to make people feel at home in the universe. Belief is only necessary for this second function. A scientist can use a conceptual scheme perfectly well without believing that it represents how the universe ‘truly is’; but people have an obvious and, apparently, near-universal need to understand their place in, and relation to, the cosmos. Thus, scientists throughout history have insisted on the truth of their systems, despite the history of science being littered with the refuse of abandoned theories (to use Kuhn’s expression). Even if this belief cannot be justified philosophically, however, it does provide a powerful emotional impetus to scientific activity.
Another question Kuhn raises is when and why scientists decide that an old paradigm is unsustainable and a new one is required. For centuries astronomers in the Muslim and Western worlds worked within the basic approach laid down by Ptolemy, hoping that small adjustments could finally remove the slight errors inherent in the system. During this time, the flexibility of the Ptolemaic approach—allowing for fine-tuning in deferents, equants, and epicycles—was seen as one of its strengths. Besides, the Ptolemaic astronomy was fully integrated within the wider Aristotelian science of the age; and this science blended perfectly with common everyday notions. The fact that the Ptolemaic science broke down is attributable as much, or more, to factors external to the science as to those internal to it. Specifically, with the Renaissance came the rediscovery of Neoplatonism, with its emphasis on mathematical harmonies—something absent from Aristotelianism—as well as its strain of sun-worship.
Copernicus was one of those affected by the new current of Neoplatonism; and it is this, Kuhn argues, that ultimately made him dissatisfied with the Ptolemaic system and apt to place the sun at the center of his system. We often hear of science progressing as a result of new experiments and empirical discoveries; but no such novel observation played a role in Copernicus’s innovation. Rather, the source of Copernicus’s rejection of an earth-centered universe was its inability to explain why the planets’ orbits are related to the sun’s. His system answered that question. But this was only an aesthetic improvement. It did not lead to more accurate predictions—the essential task of astronomy—and, indeed, it did not even lead to more efficient calculations. The oft-reproduced image of the Copernican universe, consisting of seven concentric circles, is a simplification; his actual system used dozens of circles and was cumbersome and difficult to use.
But the most puzzling feature of Copernicus’s innovation is that it achieves qualitative simplification at the expense of rendering it completely incompatible with the wider worldview. Aristotelian physics cannot explain why a person would not fly off of a moving earth. And, indeed, the entire cosmological picture, such as that painted so convincingly by Dante, ceases to make sense in a Copernican universe. For centuries people had understood the earth as a midpoint between the fires of hell and the perfect heavens above. Now, hell was only metaphorically “below” and heaven only metaphorically “above.” Besides that, the universe had to be expanded to mystifying proportions; the earth became only a small and unimportant speck in an unimaginably vast space. Strangely, however, Copernicus seemed blind to most of these consequences of his innovation. A specialist concerned only with creating a harmonious system, his attempt to render it physically plausible or theologically palatable is, at best, half-hearted.
This leads to the irony that one of the greatest intellectual revolutions in history started with a man concerned with technical minutiae inaccessible to the vast majority of the public, who had access to no fundamentally new data, whose system was neither more accurate nor more efficient than its predecessor, and whose main concern was qualitative harmoniousness. Copernicus was no radical and had no notion of upsetting the established authority; he himself would likely have been appalled at the Newtonian universe that was the end result of this process.
Yet this simple innovation, once proposed, had ripple effects. Though the earth’s motion was near universally rejected as a fact, its use in a serious astronomical work kept it alive as an option. And this new option could not be laughed away when, in the next generation under Tycho Brahe, better observations and novel phenomena upset the Ptolemaic world order. The heavens could no longer be seen as perfect and unchanging when Brahe proved that supernovae and comets do not exhibit a parallax (as in, they do not to change location when the observer moves), and thus could not be atmospheric phenomena. Further, Brahe’s unprecedentedly accurate observations of the planets were incompatible with any Ptolemaic system.
This seems to be one of many cases in the history of science when novel observations followed, rather than preceded, a theoretical innovation. us
Granted, this incongruence led Brahe to propose his own earth-centered system, the Tychonic, rather than adopt a sun-centered universe. But this new system used Copernican mathematics, and embodied the Copernican harmonies. In any case it is hard to see how the Tychonic system could ever have been anything but a stopgap, since the jump from Ptolemy to Brahe was scarcely easier than the jump from Ptolemy to Copernicus. Besides, it struck many as dynamically implausible that everything in the universe would orbit the sun except the earth and the moon.
Kepler and Galileo were among those unconvinced by the Tychonic system. The two very different men were both of an independent turn of mind, and their work finally made the Copernican universe unequivocally superior. Kepler particularly made the decisive step with his three laws: that planets orbit in ellipses with the sun at a focus, that they sweep out equal areas in equal times, and that they orbit the sun in a ratio of the 3/2 power (the orbital axis to the orbital time). But in Kepler we find further ironies. Far from the dispassionate lover of truth, Kepler was a Neoplatonic mystic, bursting with occult hypotheses. Many parts of his work strike the modern reader as scarcely more rational than the ravings of a conspiracy theorist. Yet the hard core of Kepler’s astronomical work lifted Copernicanism into a league of its own for accuracy of prediction and efficiency of calculation. If the orbits of the planets were related to the sun in such simple, elegant ways, it was difficult to see how earth could be at the center of it all.
This is my best attempt at summarizing the most salient points of the book. But of course there is far more in here, most of it worthwhile. I particularly enjoyed Kuhn’s chapter on the oft-ignored medieval research into physics, such as the impetus theory in the work of Nicole Oresme. The only weak point of the book was the rather brief epilogue to Copernicus. In particular, I would have appreciated an entire chapter devoted to Newton, since it was his Principia that was, in Kuhn’s phrase, the “capstone” of the revolution. But on the whole I think this is a superlative book, serious yet accessible, informative while brief. Kuhn captures the reality of scientific progress, which is far less neat that we may like to believe. Most striking is how a revolution which was guided by many extra-logical considerations—the Neoplatonic belief in celestial harmonies, the desire for mathematical elegance, the weakening of the religious worldview, the need to feel at home in the universe—fueled a process which, taken as a whole, resulted in a science definitively better than the Ptolemaic system it replaced.
Kuhn makes no mistake about this. Here is what the reputed relativist has to say:
The last two and one-half centuries have proved that the conception of the universe which emerged from the Revolution was a far more powerful intellectual tool than the universe of Aristotle and Ptolemy. The scientific cosmology evolved by seventeenth-century scientists and the concepts of space, force, and matter that underlay it, accounted for both celestial and terrestrial motions with a precision undreamed of in antiquity. In addition, they guided many novel and immensely fruitful research programs, disclosing a host of previously unsuspected natural phenomena and revealing order in fields of experience that had been intractable to men governed by the ancient world view.
… it is not fitting even to judge what is simple in itself in heavenly things on the basis of things that seem to be simple among us.
In my abysmal ignorance, I had for years assumed that tracking the orbits of the sun and planets would be straightforward. All you needed was a starting location, a direction, and the daily speed—and, with some simple arithmetic and a bit of graph paper, it would be clear as day. Attempting to read Ptolemy has revealed the magnitude of my error. Charting the heavenly bodies is a deviously complicated affair; and Ptolemy’s solution must rank as one of the greatest intellectual accomplishments of antiquity—fully comparable with the great scientific achievements of European Enlightenment. Indeed, Otto Neugebauer, the preeminent scholar of ancient astronomy, went so far as to say:
One can perfectly well understand the ‘Principia’ without much knowledge of earlier astronomy but one cannot read a single chapter in Copernicus or Kepler without a thorough knowledge of Ptolemy’s “Almagest”. Up to Newton all astronomy consists in modifications, however ingenious, of Hellenistic astronomy.
With more hope than sense, I cracked open my copy of The Great Books of the Western World, which has a full translation of the Almagest in the 16th volume. Immediately repulsed by the text, I then acquired a students’ edition of the book published by the Green Lion Press. This proved to be an excellent choice. Through introductions, preliminaries, footnotes, and appendices—not to mention generous omissions—this edition attempts to make Ptolemy accessible to a diligent college student. Even so, for someone with my background to attain a thorough knowledge of this text, he would still require months of dedicated study with a teacher as a guide. For the text is difficult in numerous ways.
Most obviously, this book is full of mathematical proofs and calculations, which are not exactly my strong suit. Ptolemy’s mathematical language—relying on the Greek geometrical method—will be unfamiliar to students who have not read some Euclid; and even if it is familiar, it proves cumbrous for the sorts of calculations demanded by the subject. To make matters worse, Ptolemy employs the sexagesimal system (based on multiples of 60) for fractions; so his numbers all must be converted into our decimals for calculation. What is more, even the names of the months Ptolemy uses are different, bearing their Egyptian names (Thoth, Phaöphi, Athur, etc.), since Ptolemy was an Alexandrian Greek. Yet even if we put all these technical obstacles to the side, we are left with Ptolemy’s oddly infelicitous prose, which the translator describes thus:
In general, there is a sort of opacity, even awkwardness, to Ptolemy’s writing, especially when he is providing a larger frame for a topic or presenting a philosophical discussion.
Thus, even in the non-technical parts of the book, Ptolemy’s writing tends to be headache-inducing. All this combines to form an unremitting slog. So since my interest in this book was amateurish, I skimmed and skipped liberally. Yet this text is so rich that, even proceeding in such a dilettantish fashion, I managed to learn a great deal.
Ptolemy’s Almagest, like Euclid’s Elements, proved so comprehensive and conclusive when it was published that it rendered nearly all previous astronomical work obsolete or superfluous. For this reason, we know little about Ptolemy’s predecessors, since there was little point in preserving their work after Ptolemy summed it up in such magnificent fashion. As a result it is unclear how much of this book is original and how much is simply adapted. As Ptolemy himself admits, he owes a substantial debt to the astronomer Hipparchus, who lived around 200 years earlier. Yet it does seem that Ptolemy originated the novel way of accounting for the planets’ position and speed, which he puts forth in later books.
Ptolemy begins by explaining the method by which he will measure chords; this leads him to construct one of the most precise trigonometric tables from antiquity. Later, Ptolemy goes on to produce several proofs of spherical trigonometry, which allows him to measure distances on the inside of a sphere, making this book an important source for Greek trigonometry as well as astronomy. Ptolemy also employs Menelaus’ Theorem, which uses the fixed proportions of a triangle to establish ratios. (From this I see that triangles are marvelously useful shapes, since they are the only shape which is rigid—that is, the angles cannot be altered without also changing the ratio of the sides, and vice versa. This is also, by the way, what makes triangles such strong structural components.)
Ptolemy gets down to business by analyzing the sun’s motion. This is tricky for several reasons. For one, the sun does not travel parallel to the “fixed stars” (so called because the stars do not position change relative to one another), but rather at an angle, which Ptolemy calculates to be around 23 degrees. We now know this is due to earth’s axial tilt, but for Ptolemy it was called the obliquity of the ecliptic (the angle of the sun’s path). Also, the angle that the sun travels through the sky (straight overhead or nearer the horizon) is determined by one’s latitude; this also determines the seasonal shifts in day-length; and during these shifts, the sun rises on different points on the horizon. To add to these already daunting variables, the sun also shifts in speed during the course of the year. And finally, Ptolemy had to factor in the procession of the equinoxes—the ecliptic’s gradual westward motion from year to year.
The planets turn out to be even more complex. For they all exhibit anomalies in their orbits which entail further complications. Venus, for example, not only speeds up and slows down, but also seems to go forwards and backwards along its orbit. This leads Ptolemy to the adoption of epicylces—little circles which travel along the greater circle, called the “deferent,” of the planet’s orbit. But to preserve the circular motion of the deferent, Ptolemy must place the center (called the “eccentric”) away from earth, in empty space. Then, Ptolemy introduces another imaginary circle, around which the planet travels with constant velocity: and the center of this is called the “equant,” which is also in empty space. Thus the planet’s motion was circular around one point (the eccentric) and constant around another circle (the equant), neither of which coincide with earth (so much for geocentric astronomy). In addition to all this, the orbit of Venus is not exactly parallel with the sun’s orbit, but tilted, and its tilt wobbles throughout the year. For Ptolemy to account for all this using only the most primitive observational instruments and without the use of calculus or analytic geometry is an extraordinary feat of patience, vision, and drudgery.
Even after writing all this, I am not giving a fair picture of the scope of Ptolemy’s achievement. This book also includes an extensive star catalogue, with the location and brightness of over one thousand stars observable with the naked eye. He argues strongly for earth’s sphericity (so much for a flat earth) and even offers a calculation of earth’s diameter (which was 28% too small). Ptolemy also calculates the distance from the earth to the moon, using the lunar parallax (the difference in the moon’s appearance when seen from different positions on earth), which comes out the quite accurate figure of 59 earth radii. And all of this is set forth in dry, sometimes baffling prose, accompanied by pages of proofs and tables. One can see why later generations of astronomers thought there was little to add to Ptolemy’s achievement, and why Arabic translators dubbed it “the greatest” (from which we get the English name).
A direct acquaintance with Ptolemy belies his popular image as a metaphysical pseudo-scientist, foolishly clinging to a geocentric model, using ad-hoc epicycles to account for deviations in his theories. To the contrary, Ptolemy scarcely ever touches on metaphysical or philosophical arguments, preferring to stay in the precise world of figures and proofs. And if science consists in predicting phenomena, then Ptolemy’s system was clearly the best scientific theory around for its range and accuracy. Indeed, a waggish philosopher might dismiss the whole question of whether the sun or the earth was at the “center” as entirely metaphysical (is it falsifiable?). Certainly it was not mere prejudice that kept Ptolemy’s system alive for so long.
Admittedly, Ptolemy does occasionally include airy metaphysical statements:
We propose to demonstrate that, just as for the sun and moon, all the apparent anomalistic motions of the five planets are produced through uniform, circular motions; these are proper to the nature of what is divine, but foreign to disorder and variability.
Yet notions of perfection seem hard to justify, even within Ptolemy’s own theory. The combined motions of the deferent and the epicycle do not make a circle, but a wavy shape called an epitrochoid. And the complex world of interlocking, overlapping, slanted circles—centered on imaginary points, riddled with deviations and anomalies—hardly fits the stereotypical image of an orderly Ptolemaic world.
It must be said that Ptolemy’s system, however comprehensive, does leave some questions tantalizingly unanswered. For example, why do Mercury and Venus stay within a definite distance from the sun, and travel along at the same average speed as the sun? And why are the anomalies of the “outer planets” (Mars, Jupiter, Saturn) sometimes related to the sun’s motion, and sometimes not? All this is very easy to explain in a heliocentric model, but rather baffling in a geocentric one; and Ptolemy does not even attempt an explanation. Even so, I think any reader of this volume must come to the conclusion that this is a massive achievement—and a lasting testament to the heights of brilliance and obscurity that a single mind can reach.
My rating: 4 of 5 stars
I should think that anyone who considered it more reasonable for the whole universe to move in order to let the earth remain fixed would be more irrational than one who should climb to the top of your cupola just to get a view of the city and its environs, and then demand that the whole countryside should revolve around him so that he would not have to take the trouble to turn his head.
It often seems hard to justify reading old works of science. After all, science continually advances; pioneering works today will be obsolete tomorrow. As a friend of mine said when he saw me reading this, “That shit’s outdated.” And it’s true: this shit is outdated.
Well, for one thing, understanding the history of the development of a theory often aids in the understanding of the theory. Look at any given technical discipline today, and it’s overwhelming; you are presented with such an imposing edifice of knowledge that it seems impossible. Yet even the largest oak was once an acorn, and even the most frightening equation was once an idle speculation. Case in point: Achieving a modern understanding of planetary orbits would require mastery of Einstein’s theories—no mean feat. Flip back the pages in history, however, and you will end up here, at this delightful dialogue by a nettlesome Italian scientist, as accessible a book as ever you could hope for.
This book is rich and rewarding, but for some unexpected reasons. What will strike most moderns readers, I suspect, is how plausible the Ptolemaic worldview appears in this dialogue. To us alive today, who have seen the earth in photographs, the notion that the earth is the center of the universe seems absurd. But back then, it was plain common sense, and for good reason. Galileo’s fictional Aristotelian philosopher, Simplicio, puts forward many arguments for the immobility of the earth, some merely silly, but many very sensible and convincing. Indeed, I often felt like I had to take Simplicio’s side, as Galileo subjects the good Ptolemaic philosopher to much abuse.
I’d like to think that I would have sensed the force of the Copernican system if I were alive back then. But really, I doubt it. If the earth was moving, why wouldn’t things you throw into the air land to the west of you? Wouldn’t we feel ourselves in motion? Wouldn’t canon balls travel much further one way than another? Wouldn’t we be thrown off into space? Galileo’s answer to all of these questions is the principal of inertia: all inertial (non-accelerating) frames of reference are equivalent. That is, an experiment will look the same whether it’s performed on a ship at constant velocity or on dry land.
(In reality, the surface of the earth is non-inertial, since it is undergoing acceleration due to its constant spinning motion. Indeed the only reason we don’t fly off is because of gravity, not because of inertia as Galileo argues. But for practical purposes the earth’s surface can be treated as an inertial reference frame.)
Because this simple principle is the key to so many of Galileo’s arguments, the final section of this book is trebly strange. In the last few pages of this dialogue, Galileo triumphantly puts forward his erroneous theory of the tides as if it were the final nail in Ptolemy’s coffin. Galileo’s theory was that the tides were caused by the movement of the earth, like water sloshing around a bowl on a spinning Lazy Susan. But if this was what really caused the tides, then Galileo’s principle of inertia would fall apart; since if the earth’s movements could move the oceans, couldn’t it also push us humans around? It’s amazing that Galileo didn’t mind this inconsistency. It’s as if Darwin ended On the Origin of Species with an argument that ducks were the direct descendants of daffodils.
Yet for all the many quirks and flaws in this work, for all the many digressions—and there are quite a few—it still shines. Galileo is a strong writer and a superlative thinker; following along the train of his thoughts is an adventure in itself. But of course this work, like all works of science, is not ultimately about the mind of one man; it is about the natural world. And if you are like me, this book will make you think of the sun, the moon, the planets, and the stars in the sky; will remind you that your world is spinning like a top, and that the very ground we stand on is flying through the dark of space, shielded by a wisp of clouds; and that the firmament up above, something we often forget, is a window into the cosmos itself—you will think about all this, and decide that maybe this shit isn’t so outdated after all.