Tag: Copernicus

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 précis 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.


As an undergraduate, I was prone to wandering the university library, looking to some kind of literary distraction from whatever math assignment I was suffering to complete. One day pulled a worn paperback copy of Sexual Politics by Kate Millett off the shelf. It was not a book I had ever been assigned or recommended. I had no understanding or conception of what it might contain, aside from the vague possibility of feminism. But the title seemed provocative enough, so I read a few pages to get a sense. It was polemical and read like a response to an ongoing conversation that I was not party to. There was an account of the notorious and horrifying evening when Norman Mailer stabbed his then wife with a penknife. But as horrifying as that was to read, I had no idea who Norman Mailer was. (I later discovered that I had read maybe fifty pages of his biography of Lee Harvey Oswald while in high school before discarding it; I had been hoping for conspiratorial speculation).

What did capture my imagination, was the marginalia on the opening page of the text. As I recall, someone had taken issue with the author’s use of the default male pronoun, as if that was enough to discredit and undermine the integrity of all that followed. I did not get the impression that this was done from a viewpoint sympathetic to feminism, and was a very bold assertion to make so early on in the reading. This is what scholars term “hostile” marginalia.

From this initial salvo followed a whole chain of pencilled and biro-ed interjections and objections from subsequent readers, although who knows how much further than the opening paragraphs any of them made it through the text. In content alone, this was little better than the below-the-line comments that have become ubiquitous online. And to be fair, much worse than most of what in the tech space is called user generated content. But it felt fun and exciting to read for a few obvious reasons. The first being the irreverence of writing in the book itself. The second being the simple aesthetic appeal of seeing the back and forth written out in people’s own hand.

Much has been written about marginalia and its virtues. The rise of the e-reader was occasion for much thinking about what might be lost in a transition to digital. Sam Anderson, who has written much on the subject, writes here from the point of view of a practitioner (as opposed to my own as the voyeur):

One day in college I was trawling the library for a good book to read when I found a book called “How to Read a Book.” I tried to read it, but must have been doing something wrong, because it struck me as old-fashioned and dull, and I could get through only a tiny chunk of it. That chunk, however, contained a statement that changed my reading life forever. The author argued that you didn’t truly own a book (spiritually, intellectually) until you had marked it up.

This hit home for me — it spoke to the little scribal monk who lives deep in the scriptorium of my soul — and I quickly adopted the habit of marginalia: underlining memorable lines, writing keywords in blank spaces, jotting important page numbers inside of back covers.

[…] Soon my little habit progressed into a full-on dependency. My markings grew more elaborate — I made stars, circles, checks, brackets, parentheses, boxes, dots and lines (straight, curved and jagged). I noted intra- and extratextual references; I measured cadences with stress marks. Texts that really grabbed me got full-blown essays (sideways, upside-down, diagonal) in the margins. I basically destroyed my favorite books with the pure logorrheic force of my excitement, spraying them so densely with scribbled insight that the markings almost ceased to have meaning. Today I rarely read anything — book, magazine, newspaper — without a writing instrument in hand. Books have become my journals, my critical notebooks, my creative outlets. Writing in them is the closest I come to regular meditation; marginalia is — no exaggeration — possibly the most pleasurable thing I do on a daily basis.

This belongs to a genre of advocacy for marginalia: looking to transforming passive readers into pencil wielding intellectuals deploying their critical judgements, droll asides, and tasteful underlinings. A closely related genre is more in my own voyeuristic camp, inspecting the great marginalia of the past. To my mind, the most significant marginalia lies in scientific discourse. An example: the journalist Arthur Koestler once dismissively referred to Copernicus’ On The Revolution as “the book that nobody read”, in his history of cosmology. In response Owen Gingrich titled a book with the offending quote as the title, in which he described his efforts to examine all surviving copies of On The Revolution from the 16th century. In the margins of these copies he found copious evidence that Copernicus’ opus was read very carefully indeed. Indeed, if you were to break into the offices of likely any practicing mathematician you will find preprints, with very wide margins, covered in scribbles testifying to the continuing engagement with tricky mathematical texts.

Back in the literary sphere the current king of marginalia has to be David Foster Wallace. While his posthumous reputation as a secular saint has been shattered, Infinite Jest continues to attract devoted readers. His personal library has entered the collection of the Ransom Center, and we’ve all been able to peer at the scans of the paperbacks he extensively and idiosyncratically annotated. More than anything else, these particular images illustrate else the purely aesthetic and textural appeal of marginalia.

But all of this commentary, to my mind, hasn’t acknowledged a more obvious truth about reader engagement with the printed word. Engagement is not always welcome, wanted, or virtuous. We do not tickled by the puerile and often hateful graffiti to be found in any high school textbook in the same way we are when we discover DFW added galsses, fangs, and a mustache to DeLillo’s author photo. Nor do we treat the posts of an unmasked sock puppet account as being worthy of the same respect as the abuse that the “great artist” leaves in the margins of their private library.

The digital age has transformed marginalia into a public performance, and if you abandon the fixation on the codex itself (to my money, still a robust and preferable reading technology) you can find much engagement and innovation, but frequently not among the artists we admire, valorize, and maybe aspire to.

“Fisking” is the practice of taking a text that you find particularly egregious and writing a rebuttal by quoting the text, likely in its entirety interspersed in-line with your debunking, criticism, and abuse. It takes its name from the British journalist whose reports from the Middle East were an early and frequent target of the conservative bloggers who pioneered this innovation. Whatever its roots, it is the logical digital evolution of hostile marginalia. What shifted the paradigm was the ability to instantly copy, paste, and then start writing the commentary. It’s the kind of thing that happens when there are no editors around and your audience seems to appreciate open insults.

The term still gets used, but mostly in conservative circles. There used to be a Wikipedia page that subsequently got removed. Fisk’s Wikipedia page used to mention it, but no longer. There is a dictionary definition, at least. Fisking does not have the same champions as marginalia. Nor the same caliber of practitioner. It also has to be said that the people who coined the term may not have appreciated all the possible associations the term might conjure.

Pile ons, ratios, and dunkings are nothing more than hostile marginalia done in public, en mass. It is possible to have too much of a good thing, and certain things are better done in the privacy of one’s own home. Editors offer a valuable service, and writing is often the process of working out what you think, rather than just responding in the moment. What can be an exciting insight into someones inner life — their unfiltered response as they read a novel — maybe shouldn’t become a model for public discourse. What made those glimpses so interesting, was how fleeting and how precious they could be. And let’s not over-think the thrill of seeing what a writer’s actual handwriting was like.