Retrograde Motion

Before Newton there was Copernicus, and before Copernicus there was Ptolemy. Living in the second century AD, Ptolemy produced what would become the definitive work in astronomy for the next millennium. It was a geocentric system: the Earth, quite sensibly, set at the center of the solar system. While geocentricism was ultimately to suffer the ignominy of being synonymous with backward thinking, Ptolemy certainly didn’t lack in mathematical sophistication.

Keeping the Earth at the center of the solar system required a great deal creative invention. It was taken as axioms that the planets should travel at constant speeds, and adhere to the perfect forms of geometry (that is to say circles and spheres). But the planets that appeared in the night sky did not conform to these expectation. Unlike the sun and moon, which flattered us earthlings with their regular appearance and disappearance, the planets would sometimes slow down and reverse direction — what they called “retrograde motion”. The solution that Ptolemy and his predecessors developed was a whole Spirograph set of celestial structures called deferents and epicycles. This essentially involved imagining that the other planets were not set upon a wheel revolving about the Earth, but set on a wheel on a wheel in motion about the earth. And, if necessary, perhaps some greater sequence of nested wheels.

Copernicus, the Catholic canon and Polish polymath of the fifteenth and sixteenth century, had, like every other astronomer of his day read Ptolemy. Yet after carefully studying the night sky and much thought, he developed a heliocentric map of the solar system. That is to say, with the Sun at the center. While he managed to free himself from geocentric difficulties, and dramatically simplify the situation in many respects, he still adhered to a belief in constant speed and circular orbits. It would take Keplar and ultimately Newton to settle the matter with elliptic orbit determined by the force of gravity.

The heliocentric theory was controversial for two reasons. The first, and quite reactionary, objection was based on readings of a handful of bible verses. For example, when Joshua led the Israelite in battle against an alliance of five Amorite kings he ordered the sun to halt its motion across the sky, thus prolonging the day, and with it the slaughter of the opposing army. The point is that Joshua ordered the sun to stop, and not the earth. This might seem like pedantry, but that was precisely the point. The Catholic church hoped to hold a monopoly on biblical interpretation, and someone lower down the ecclesiastical hierarchy conducting their own paradigm shift equipped with nothing more than astronomical data and mathematics could set a dangerous precedent. At a time when many such precedents already being set.

The second, and quite serious objection, was that it created a whole new set of scientific questions. Why don’t we feel like we are moving through space? Not only about the sun, but when we make the Earth rotates daily about its own axis? The numbers required to calculate the implied velocity were known. And on top of that, if we were moving at such great speed, they why did we not observe a parallax effect between the stars? As the apparent distance between two buildings appears to change as we move past them, why couldn’t we observe a similar shift in the stars as we moved? Copernicus’ answer was that the stars were much farther away from earth than had ever been imagined before. It was a correct deduction that didn’t do much to convince anyone.

Both Copernicus and Newton were reluctant to publish their ideas. In Newton’s case he was satisfied to have developed his Calculus and did not care to suffer the scrutiny that others would subject his theory of gravity to. His experience justify his thinking to other scientists of his had soured his relationship with the wider scientific community of his day. It was only when it became clear that Leibniz had independently developed the tools of Calculus that he finally set about writing up, formalizing, and getting his hands on data in order to present his Principia.

Copernicus had gathered his data and written his book, yet for many years did not publish it. De revolutionibus orbium coelestium would only arrive in print as he lay on his death bed. While Copernicus had friends who supported his astronomical pursuits, it seems to have been the arrival of a young Lutheran mathematician Georg Joahim Rheticus, who was the key instigator in bringing the manuscript to print.

No one had invited him or even suspected his arrival. Had he sent advance notice of his visit he doubtless would have been advised to stay far away from Varmia. Bishop Dantiscus’ most recent anti-heresy pronouncement, issued in March, reiterated the exclusion of all Lutherans from the province — and twenty-five-year-old Georg Joachim Rheticus was not only Lutheran but a professor at Luther’s own university in Wittenberg. He had lectured there about a new direction for the ancient art of astrology, which he hoped to establish as a respected science. Ruing mundane abuses of astrology, such as selecting a good time for business transactions, Rheticus believed the stars spoke only of the gravest matters: A horoscope signaled an individual’s place in the world and his ultimate fate, not the minutiae of his daily life. If properly understood, heavenly signed would predict the emergence of religious prophets and the rise or fall of secular empires.

A More Perfect Heaven — Dava Sobel

I suspect that we may undervalue the weight that the belief in astrology may have carried in some (but not all) quarters. Many looked back to the Great Conjunction of 1524 as heralding the rise and spread of Lutheranism — an ideological shift with profound and widespread implications that might only be matched by Communism. We live in an age of scientific prediction, taking for granted the reliable weather forecast on our phone in the morning. We (at least most of us) accept the deep implications of the climate data for our future, while also paying heed to the sociology and political science can help us understand our lack of collective action. If we accept the astrology as being a kind of forebear to our own understanding, you can perhaps appreciate why Rheticus might have been willing to take such risks to pursue a better understanding of the stars.

We can only imagine what Rheticus must have said to Copernicus that led him to finally prepare his manuscript for publication. And that is what Dava Sobel has done, writing a biography of Copernicus, A More Perfect Heaven, which contains within it a two act play dramatizing how she imagines the conversation might have gone. It presents a Rheticus shocked to discover that Copernicus literally believes that the Earth orbits about the Sun, a Copernicus perplexed that the young man takes astronomy seriously, but who is won over by the prospect of taking on such a capable young mathematician as his student.

Rheticus’ principal legacy is in the prĂ©cis of Copernicus’ theory that he wrote and had distributed as a means of preparing the way for the ultimate text. His contributions would ultimately be overshadowed by the later accusation, conviction, and banishment for raping the son of a merchant. While Sobel presents Rheticus in her play as pursuing/grooming a fourteen year old boy, it does not feel like she knows exactly where to take this dramatically. By way of contrast, John Banville in his novel Doctor Copernicus gleefully transitions to a Nabokovian narrative upon Rheticus’ arrival.

There is an interesting dramatic irony in the way Copernicus’ ideas were initially received. There was a ruse, by certain parties, to present Copernicus’ heliocentric theory as simply a means of computation. It could be tolerated if it was understood that one was not supposed to actually believe that the Sun was at the center of the solar system. Which struck some as a reasonable compromise. The Catholic church was drawing up what would become the Gregorian calender, and Copernicus’ made important contributions to calculating a more accurate average for the length of a year.

Yet now the situation has been reversed. While Copernicus’ techniques were rendered obsolete with the arrival of calculus, the conceptual understanding carries on in popular understanding. Meanwhile, as Terence Tao and Tanya Klowden have noted Ptolemy’s deferents and epicycles live on in the mathematics of Fourier analysis — a means of approximating arbitrary periodic functions using trigonometry.

Even within a field as definitive as mathematics and science it is interesting how even defunct and obsolete thinking can both be revealing and even persist with strange second lives. Why someone believed something can become more important than the truth of the thing. Eratosthenes deduced an impressive approximation for the Earth’s circumference after hearing a story about a well that would reflect the light of the sun at noon. We posses a more accurate figure now, but technique never grows old.