The Theory of Heliocentrism

Even more so than Claudius Ptolemy’s Almagest, Nicolaus Copernicus’s On the Revolutions of the Heavenly Spheres reads today like a strange mishmash of brilliant innovation and obstinate pedantry. The parts of it that seem most obviously important to us are the earliest pages. Ironically, though, it was the later chapters, which appear far less impressive to the modern eye, that caused the biggest initial stir back in the sixteenth century.

In the book’s first twenty pages — just the first five percent or so of its imposing total length — Copernicus lays out the core tenets of his heliocentric cosmos. What humanity thought it saw above it for thousands of years, he says, was just an optical illusion caused by the relativity of motion, which makes it impossible for an observer to determine from visual evidence alone whether it is the observer or the observed that is actually moving when an object changes position in his line of sight. By way of anachronistic example, think of a first-person videogame or a 3D flight simulator. It is the images drawn on the screen that are really moving as we manipulate the controls, but our minds are tricked into believing that we are the ones moving through space. Likewise, it is impossible to tell whether a Sun that seems to rise and set each day is moving in relation to us, or whether we are moving in relation to the Sun. Yet our minds seem to come pre-wired to assume the former; one might go so far as to say that this quirk in our psychological wiring is the original wellspring from which all of our confusion about geocentrism versus heliocentrism arose.

Having explained all of this (albeit without recourse to videogames or flight simulators, naturally), Copernicus then unleashes an astonishing series of claims that combine together to form a solar system if not a universe — for Copernicus, the solar system still was the universe — that will be very, very familiar to any modern schoolchild. The Sun sits in the middle of it all, and around this body orbit six planets: in order from innermost to outermost, these are Mercury, Venus, Earth, Mars, Jupiter, and Saturn. (Copernicus was unaware of the existence of Uranus and Neptune because they cannot be seen from Earth with the naked eye, and the telescope had not yet been invented.) The Moon orbits the Earth even as the latter pursues its own orbit around the Sun. Each of these revolutions of the Earth around the Sun takes 8766 hours. Meanwhile the Earth is also rotating on its axis, once every 24 hours. These two circular motions create the two repeating cycles that define life on Earth, the year and the day. What we have here is the first description of our local cosmos to be broadly accurate. (Copernicus went so far as to suspect — correctly — that the Earth wobbles slightly as it rotates on its axis, although he incorrectly suggested that this is the cause of the changing seasons rather than a more subtle and slow-moving effect that modern astronomers know as the precession of the equinoxes.) “We find under this orderly arrangement,” he writes, “a wonderful symmetry of the universe, and a definite relation of harmony in the motion and magnitude of the orbs, of a kind that it is not possible to obtain in any other way.”

Alas, after he deployed his paradigm-shifting stroke of brilliance, Copernicus then proceeded to muck it all up over the course of the remaining 95 percent of his book, until he ended up with a nonsensical mess that might have made even Ptolemy shudder, that is in reality the farthest thing from a “wonderful symmetry” and “definite relation of harmony.” This desecration was committed in the name of making the math work without abandoning certain principles that were as fixed and inviolate for Copernicus as a geocentric universe had been for Ptolemy. By the time he gets to the end of hundreds of pages of some of the gnarliest mathematics ever committed to paper, you can almost feel his exhaustion and disillusionment radiating off the page. The bright-eyed and bushy-tailed idealist who wrote those first twenty pages has been well and truly beaten into submission. We stand in the background no less exhausted, wondering how on earth — or rather how in space — it all could have gone so wrong.

The fact that Copernicus stumbled upon something true and revolutionary and worked it out to the best of his ability using logic and mathematics tempts us to see him as a more modern thinker than he actually was. In truth, there is a reason that the “scientists” of his age were still more commonly referred to as “natural philosophers.” A modern scientist looks at individual data points, at what is objectively, physically the case, then employs inductive reasoning to attempt to draw broader conclusions about the universe. A natural philosopher works in the opposite direction, deciding what may be or ought to be true in his opinion, then looks to see if he can make his empirical observations square with his theories. Such an approach brings with it a host of dangers, of which massive intellectual blind spots, such as the failure of so many minds over so many centuries to even consider that the Earth might not be the center of the universe, are only one example.

By some quirk of personality, Copernicus cleared the last-mentioned hurdle over which so many thousands before him had stumbled, but for all that he remained a natural philosopher rather than a scientist at bottom, taking as his spirit guide Aristotle, the most famed of all practitioners of the tradition. For Aristotle, it wasn’t sufficient that a system of the world conform to empirical observation, wasn’t even sufficient that it could be worked out mathematically. It also had to be beautiful, in keeping with a universe that was possessed of a divine and perfect First Mover.  Aristotle wasn’t as specific on the nature of that deity as the Christians would later be, but he was quite convinced of his existence, which made it rather easy to transport his ideas into a Christian framework when the time came. Inevitably, of course, the beauty that Aristotle saw as universal was actually culturally specific, emphasizing the “wonderful symmetry” and “definite relation of harmony” that the ancient Greeks so loved, and that an optimistic Copernicus describes at the beginning of his magnum opus. For, like almost all of his Renaissance peers, he worshiped Aristotle and his ilk as demigods in their own right, and had no beef with arguments from their intrinsic authority. Very much the contrary, in fact.

It is fitting for us to follow the methods of the ancients strictly and to hold fast to their observations which have been handed down to us like a testament. And to him who thinks that they are not to be entirely trusted in this respect, the gate of our science is certainly closed. He will lie before that gate and spin the dreams of the deranged, and he will get what he deserves for believing that he can lend support to his own hallucinations by slandering the ancients.

We have to remember that Ptolemy was himself one of the revered heirs to Aristotle. In light of this, the most remarkable thing about Copernicus’s story is that such an intensely conservative scholar ever dared to break with Ptolemy on anything at all.

Copernicus’s core problem with his initial version of his own heliocentric system — the one that he seems to be describing in those optimistic first twenty pages of his book — was that it conformed to empirical astronomical observation only marginally better than the rudimentary geocentrism of Pythagoras. It was the same old story: the individual bodies that you could see in the sky from Earth were never quite where they ought to be if Copernicus’s theory was correct. The principal reason for this is, we now know, jaw-droppingly simple: because the orbits of the planets and the Moon are not perfect circles, but rather ellipses. Yet this was a solution to his difficulties that Copernicus seems never to have even considered, so alien was it to the intellectual milieu in which he had been raised and still lived. He was as sure that the planets were all pursuing perfectly circular orbits as he was that water is wet.

To understand why, we have to go slightly further back than Aristotle, to that philosopher’s own mentor Plato and his ideas about the nature of forms. To Plato and to all those who followed in his footsteps, up to Copernicus and beyond, the circle and the sphere were the most perfect forms of all, because they were the only ones that were infinite: you could trace a line around them forever, trace a line that had no beginning and no end and never needed to change direction. What better symbols of ineffable, infinite divinity than these could there possibly be? Nothing else would do for a divinely created cosmos but perfect spheres pursuing perfect orbits. Natural philosophers went to the most extreme lengths to preserve this perfection, even if it meant mucking up the rest of their system of the cosmos to a well-nigh absurd degree. Ptolemy had done so — and now, his heliocentrism notwithstanding, Copernicus was prepared to do so as well.

In the end, then, Copernicus came this far only to fall back on Ptolemy’s all too familiar bag of tricks, all in the name of forcing physical reality to conform with a metaphysical philosophy that had become so ingrained in him that he didn’t even know he was practicing it. Once again, his all-purpose kludge was epicycles, those strange little orbits around nothing. Once again, yet another epicycle was the sledgehammer to use on every inconvenient wrinkle that popped up on the surface of his heliocentrism, until it was epicycles within epicycles within epicycles. As we read further into On the Revolutions, we learn to our dismay that Copernicus’s planets do not actually orbit the Sun at all, but rather a point in space that is itself orbiting the Sun. (This would lead Arthur Koestler to refer to the Copernican system as really a “vacuo-centric system” — a cheeky but not technically inaccurate formulation. For what it’s worth, though, the same thing could be said about Ptolemy’s system, which has the other heavenly bodies orbiting a point that is itself circling the Earth.) By the time he was done, Copernicus was describing his universe in terms of 48 recurring circular motions, eight more than Ptolemy.

He did his ancient forefather one better in another respect as well. Ptolemy’s epicycles had finally failed him when it came to explaining why his five planets seemed to speed up and slow down as they cross the terrestrial sky. He had to resort to a novel kludge called the equant to deal with that. The equant was yet another point arbitrarily suspended in space, around which a planet maintained a constant angular velocity, adjusting its linear velocity as need be to achieve that end. Needless to say, Ptolemy proposed no physical reason why an equant should function in this way. It was merely the only way he could come up with to make the math work — nothing more, nothing less.

For some, however, Ptolemy’s equants were one kludge too many; the notion of a planet that was forever speeding up and slowing down, even if in a predictable way, was a blemish on the music of the spheres. Copernicus was among these naysayers, finding equants to conflict with an overriding “principle of regularity. [It seems] altogether absurd that a heavenly body should not always move with a uniform velocity in a perfect circle. Having become aware of these defects, I often considered whether there could perhaps be found a more reasonable arrangement of circles, in which everything would move uniformly about its proper center.” Although some might quibble over whether his system was really more “reasonable,” Copernicus did indeed succeed in using his heliocentricism to explain all of the motions of the heavenly bodies overhead without resorting to equants. He found he could do the trick just by piling on some more epicycles. He considered this a triumph — maybe his biggest triumph of all. His cosmos, unlike Ptolemy’s, was one of perfect spheres pursuing perfect orbits at perfectly uniform speeds.

If what has emerged from all of this is not quite the Copernicus of grade-school textbooks — not quite the visionary scientist challenging dogma and demolishing norms left and right — it is more in line with the typical pattern of scientific progress. We are all prisoners of our times, our cultures, our circumstances. Copernicus laid the necessary groundwork for a great leap forward in our understanding of our place in the universe, but by no means did he do all of the work in one fell swoop. That is too much to expect of anyone.

Still, this portrait of Copernicus as a somewhat less original thinker than he is often believed to be does lead to another question: was the heliocentric model in the abstract really his own conception, or was he merely cribbing from Aristarchus? Arthur Koestler, whose book The Sleepwalkers: A History of Man’s Changing Vision of the Universe was something of a popular sensation upon its publication in 1959, has no doubt that he was. In fact, he goes so far as to accuse Copernicus of deliberately obfuscating the intellectual trail he followed, pointing to a mention of Aristarchus that is crossed out in the manuscript copy of On the Revolutions and thus never made it into the printed version. (Yes, remarkably enough, Georg Joachim Rheticus’s handwritten manuscript has survived across half a millennium; it is housed today at Jagiellonian University in Kraków.) Before he began to write science history, Koestler was a novelist, and he perhaps retained a novelist’s reliance on heroes and villains to drive his plot along. Copernicus was unfortunate enough to be given the latter role; Koestler’s portrayal of the man may just be the most unsympathetic ever committed to the page. The true story is more nuanced.

Aristarchus’s original treatise on his theory of heliocentrism was of course as lost to Copernicus as it remains to us. The treatise by Archimedes about the size of the universe, which provides us with our best description of Aristarchus’s theory, first appeared in print in Europe in 1544, the year after Copernicus’s death. It is just possible that Copernicus may have seen it in manuscript form during his time in Italy, but this seems unlikely. Copernicus — or Rheticus — does mention Aristarchus no fewer than six times in the course of the manuscript copy of On the Revolutions, but these mentions are less significant than one might be tempted to assume. Five are blatant mistakes, crediting Aristarchus with discoveries that should have been attributed to other ancient Alexandrian astronomers. Only one of these mistakes was corrected before publication, leaving the printed book with four references to Aristarchus, all of them crediting him for work he didn’t actually do.

The last reference to Aristarchus in the manuscript of On the Revolutions is the one that Arthur Koestler cites as evidence of Copernicus’s dishonesty. It notes that “Aristarchus of Samos” was “of that opinion” that the Earth orbits the Sun: “But since such things could not be comprehended except by a keen intellect and continuing diligence, there were very few philosophers in that time who mastered the study of celestial motions.” This statement isn’t nothing, but it isn’t quite the smoking gun Koestler would have it be either.

Since Koestler’s book, the academic historian of astronomy Owen Gingerich has examined in great detail the contents of the cathedral library in Frombork upon which Copernicus relied. Based on this inventory, he believes that the only reference to Aristarchus’s theory of heliocentrism that Copernicus could have seen stemmed from a Roman text called Opinions of the Philosophers, written by an obscure figure named Aetius Amidenus but attributed in the sixteenth century to the vastly more prominent essayist and biographer Plutarch. The reference consists of only two sentences: “Aristarchus counts the Sun among the fixed stars. He has the Earth moving around the ecliptic and therefore by its inclinations he wants the Sun to be shadowed.” As I noted in my introduction, a text that can be accurately attributed to Plutarch describes Aristarchus and his theory at slightly greater length, noting that “an action for impiety” was laid against him as a result of it in Alexandria. But Gingerich at least does not believe that Copernicus was aware of this text. It seems reasonable to argue, then, that Nicolaus Copernicus — or, even more likely, Georg Joachim Rheticus — chose to eliminate the passage in question from On the Revolutions not in an effort to cover any intellectual tracks but as an unnecessary digression in an already lengthy manuscript.

By way of summing up, we can conclude that Copernicus was vaguely aware that there had been some discussion about the prospect of a peripatetic Earth among the ancient astronomers who preceded Claudius Ptolemy, and that he could even connect the name of Aristarchus to those discussions, but that he knew none of the details (which is not to say that we know all that many of them even today). The heliocentric system he provided was, in both everything that it got right and in everything that it got wrong, his own creation from top to bottom.

That said, he did wind up coming to many of the same conclusions as the ancients. In addition to the love of epicycles that he shared with Ptolemy, there is his resolution of the issue of stellar parallax — or rather the lack thereof. Here he deployed the same reasoning that Archimedes and probably Aristarchus had, that the stars must simply be so far away that their parallax cannot be seen from the Earth as our planet moves along on its orbit of the Sun.

Copernicus had left worldly concerns behind by the time the fruits of his lifetime’s labor reached the book dealers of Europe, but Rheticus awaited the book’s reception with a combination of excitement and worry. What he got was arguably worse than either widespread commendation or condemnation would have been. This exhaustive working-out of a heliocentric cosmos garnered considerably less attention than Copernicus’s earlier Brief Sketch of same had attracted. A goodly chunk of the 1000 copies that were printed by the press of Johannes Petreius languished unsold for years. Rheticus was convinced that the blame for the underwhelming reception lay principally at the feet of Andreas Osiander and his decision to position the theory of heliocentrism as nothing more than another way of calculating the positions of the heavenly bodies in the sky of Earth, with no more intrinsic claim to physical truth than the system of Ptolemy. In a fit of pique, Rheticus drew a red line through the words of the Heavenly Spheres on the title page of his copy, then crossed out the entirety of Osiander’s preface with a big red X. He mused about going to Nuremberg himself in order to “so maul the fellow that he would mind his own business and not dare to mutilate astronomers anymore in the future.” He even levied a legal complaint against the printer Petreius for accepting Osiander’s “unauthorized” changes; like his threats of physical violence, it ultimately went nowhere.

The fact that On the Revolutions of the Heavenly Spheres did not create an immediate sensation in line with the revolutionary nature of its central tenet caused Arthur Koestler to famously dub it “the book that nobody read,” “an all-time worst-seller” with “a remarkable negative record, quite unique among books which made history,” all of it thanks not so much to Osiander’s meddling as to its “supreme unreadability.” Once again, it was left to Owen Gingerich to come along and restore a measure of balance and context to his claims. Over the course of 30 years, stretching from 1970 to 2000, Gingerich conducted an exhaustive (and doubtless exhausting) census of the surviving copies of the first two editions of Copernicus’s book, uncovering 600 of them in all. “I found copies owned by saints, heretics, and scalawags, by musicians, movie stars, medicine men, and bibliomaniacs,” he writes. “But most interesting are the exemplars once owned and annotated by astronomers.”

The annotations by sixteenth-century astronomers which Gingerich discovered reveal that these men did seriously engage with Copernicus’s book, but that most of them seem to have missed the forest for the trees. Apparently taking to heart Osiander’s statement in the preface that heliocentrism was just another hypothesis among many, with no unusual claim to physical truth, they wrestled with the twisted mathematics that constitute the last 95 percent of the book as an end unto itself. As far as they were concerned, the preponderance of the empirical evidence was still heavily on the side of geocentrism. The idea that the stars could be so far away that their parallax effectively disappeared, as Copernicus claimed, struck most astronomers as far less likely than the more straightforward explanation of a stationary Earth. Then, too, lacking our modern understanding of the nature of gravity and atmosphere, they wondered why people, animals, and things weren’t continually being thrown off of Copernicus’s rotating, wandering Earth, wondered why they themselves didn’t feel like they were spinning around and rushing through space at breakneck speed as they sat in their cozy libraries perusing his book.

Most astronomers who read the book did so to see if they could adapt some of Copernicus’s mathematical innovations to a more traditional geocentric model. In some quarters, he was even hailed as a genius — not for the extraordinary revelation that the Earth travels around the Sun rather than vice versa, but for devising an alternative to Ptolemy’s ugly equants, thus creating at least the possibility of a more perfect cosmos in the Aristotelian sense. On the Revolutions was treated as an important step on the path to that noble goal. The race was soon on to describe the equant-less cosmos that had eluded Ptolemy by using some of Copernicus’s approaches in a geocentric setting. In the end, though, no one could pull it off. If it had been possible, it is likely that Copernicus would already have done so, what with him being such a traditionalist by disposition.

So, even if most of its early audience was in some sense missing the point, On the Revolutions was read and discussed, albeit initially haltingly, over a period of decades. Demand for the book was sufficient that a printer in Basel by the name of Heinrich Petri, a cousin of Johannes Petreius, prepared and published a second edition in 1566. This volume also included Rheticus’s First Account of the theory of heliocentrism, thus finally putting his name on a book that would almost certainly have languished forever in a desk drawer in Fombork without him. On the Revolutions was a slow burner, yes, but Rheticus need not have fretted and raged so: it really would change the world in the due course of time. Even its most stubbornly pedantic readers wouldn’t be able to bury the lede forever.

In the meantime, Rheticus went on with his life, neither celebrated nor reviled for the services he had rendered to Nicolaus Copernicus and to the cause of science. He remained just a respected professor at the University of Leipzig, one who divided his study time between astrology and mathematics, two fields far more closely related then than they are today. His downfall, when it came, had nothing to do with the theory of heliocentrism he had promoted.

By 1551, it had long been an open secret at the university that Rheticus often engaged in physical dalliances with his young male students. That year, however, he was publicly accused by the father of one of these students of “a sudden, outrageous, and unchristian act”: he had allegedly “plied [the young man] with strong drink, until he was inebriated, and finally did with violence overcome him and practice upon him the shameful and cruel vice of sodomy.” While Rheticus’s teacher-student relationships were hardly in keeping with our modern ideas of proper sexual ethics, it does seem as probable as not that the charge of forcible rape in this particular case was fabricated by the embarrassed or jilted youth. Nonetheless, the damage was done. Rheticus  ran away from Leipzig rather than face a humiliating criminal trial that might very well have ended with a sentence of death. A shadow hung over him thereafter, but he did find less prestigious university postings in Prague, in Kraków, and finally in the Slavic town of Košice. All the while, he was struggling to complete his own magnum opus, a book on the philosophy, mathematics, and occult significance of triangles that he believed would prove every bit as important as the great work of Nicolaus Copernicus.

One day in 1574, a young German scholar named Valentin Otto came to visit Rheticus in Košice. A parallel occurred to his aging host. “You come to see me at the same age as I was when I visited Copernicus,” he said to a doubtless rather bemused Otto. “If it had not been for my journey, his work would never have seen the light of day.” The implication was plain: Otto was expected to complete the circle — or perhaps the triangle — by performing the same service for Rheticus.

But sadly, young Otto was no young Rheticus, even as the aged version of the latter was no Copernicus. Rheticus died barely six months after their first meeting at age 60, leaving Otto as the steward of his legacy in his will. Twenty years later, Otto did manage to shepherd the book on triangles to publication — 1500 pages on triangles, in fact, which may have been more than anyone really needed to know about them even if the book had been worthwhile. It was not; it was a confused and confusing mess, although it is an open question whether the blame for that should rest more with the mentor or the mentee. Georg Joachim Rheticus was thus doomed to go down in history as a Boswell rather than a man who became a Johnson in his own right.

Even as Rheticus was approaching his end of all ends, though, men at scattered locations all around Europe were continuing to read Copernicus’s book, his most important contribution to his posterity. Some of them were now beginning to see the real reason that it was so important, even as the political and religious climate around them continued to change. These factors together would produce the first martyr for the cause of heliocentrism within a few more decades. Rheticus plainly had a taste for drama and controversy. In time, On the Revolutions of the Heavenly Spheres would deliver just that. They would just come a little bit too late for him to witness.

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(A full listing of print and online sources used will follow the final article in this series.)