"In no other way do we find a wonderful commensurability and a sure harmonious connection between the size of the orbit and the planet's period," Copernicus declared in the most soaring cosmological passage in his entire book. What Copernicus had achieved was a linked system in which all the distances were locked into place relative to a common measure, the Earth-Sun distance, which provided the yardstick for the entire system.* But Reinhold and his many followers admired Copernicus for a quite different aesthetic idea, the elimination of the equant. Copernicus devoted the great majority of De revolutionibus to showing how this could be done. While he had eliminated all of Ptolemy's major epicycles, merging them all into the Earth's orbit, he then introduced a series of little epicyclets to replace the equant, one per planet.* Because this made the motion uniform in each Copernican circle, the anti-equant aesthetic was satisfied. My Copernican census eventually helped to establish that the majority of sixteenth-century astronomers thought eliminating the equant was Copernicus' big achievement, because it satisfied the ancient aesthetic principle that eternal celestial motions should be uniform and circular or compounded of uniform and circular parts.
JOHANN STOEFFLER'S Ephemeridum opus of 1532 was one of the first rare books I had bought for my own library. I found it on the shelf of Blackwell's rare book department in Oxford. In the days when a typical scholarly book cost maybe $510, it was quite a plunge to spend 3170 for a book of numbers, but it was exciting to have such an old volume for my very own. Before that I had used a similar volume in Harvard's Houghton Library to help date a poem by the satirical Tudor poet John Skelton, so I had an idea about what I was getting.† Stoeffler's ephemerides were filled with daily positions of the Sun and planets for the years 1532 through 1551.
I was particularly curious about the basis for Stoeffler's numbers because of a popular legend found in many secondary sources. According to that story, a principal reason why Copernicus had sought to create a heliocentric cosmology was that Ptolemy's hoary system had become so encumbered with jury-rigged embroideries that it was at the point of collapse. Astronomers throughout the ages had added one epicycle to another as they attempted to keep up with the observed deficiencies of the system.
Probably the legend had begun soon after the modern recovery around 1880 of Copernicus' Commentariolus, or "Little Commentary." After describing the complexities of planetary motion, Copernicus closed this account with an exclamation: "Behold! Only 34 circles are required to explain the entire structure of the universe and the dance of the planets!" Superficially, the passage looks as if Copernicus were crowing about the great simplification his system afforded. If Copernicus could handle this in only 34 circles, Ptolemy (or at least his medieval successors) must have required many more.
There is a wonderful, very old, but no doubt apocryphal, story that Alfonso the Great, looking over the shoulders of his astronomers who were compiling the Alfonsine Tables, remarked that if he had been around at Creation, he could have given the Good Lord some hints. The obvious interpretation was that King Alfonso's astronomers, in order to take care of the observed discrepancies between the Ptolemaic predictions and where the planets actually were, had been obliged to add more circles, small epicycles on epicycles. It's rather reminiscent of the lines paraphrasing Jonathan Swift:
Great fleas have little fleas
upon their backs to bite 'em
And little fleas have lesser fleas
and so ad infinitum.
The legend reached its apotheosis when the 1969 Encyclopaedia Britannica announced that, by the time of King Alfonso, each planet required 40 to 60 epicycles! The article concluded, "After surviving more than a millennium, the Ptolemaic system failed; its geometrical clockwork had become unbelievably cumbersome and without satisfactory improvements in its effectiveness." When I challenged them, the Britannica editors replied lamely that the author of the article was no longer living, and they hadn't the faintest idea if or where any evidence for the epicycles on epicycles could be found.
Johann Stoeffler from his Ephemeridum opus (Tubingen, 1531). At least a century ago this image became confused as a portrait of Copernicus.
In those early years of the space age, the Smithsonian Observatory's computer spent most of its time tracking satellites. In its spare time, it calculated the flow of photons through the outer layers of stars—that was my specialty—and in my own spare time I had the machine calculate medieval planetary tables. I recomputed the Alfonsine Tables and discovered to my surprise that they were pure Ptolemaic, totally lacking any embroideries at all. Then, using the hundreds of cards the keypunchers had produced for me, I generated a section of the Stoeffler ephemerides. Again a surprise! My pure and simple Alfonsine Tables calculations closely matched the positions that the Tubingen astronomer had published in his book. His were the best ephemerides of the day, and they showed absolutely no evidence of epicycles on epicycles. A much-repeated and well-entrenched myth had just bit the dust, or so I thought.
During 1973, the great quinquecentennial year, I had occasion to mention my conclusions at a symposium in Copernicus' birthplace, Toruh. In the audience was Edward Rosen, the world's foremost Copernican scholar. A professor at City College in New York, he had built his career of fastidious scholarship on finely honed translations and the ability to dig out relevant details from incredibly obscure sources. As part of his doctoral dissertation, Rosen had translated Copernicus' Commentariolus, and he was particularly fond of the line about the entire ballet of the planets being accomplished in just 34 circles; he firmly believed that part of Copernicus' achievement was to simplify an overwrought system. "How can you be so sure there weren't epicycles on epicycles?" he demanded to know. Certainly, I hadn't inspected all the possible medieval manuscripts!
I'm not sure I ever convinced him about epicycles on epicycles, but today I understand the problem a lot better. The entire calculational procedure for the Alfonsine Tables depends on a clever approximation invented by Ptolemy to handle a single epicycle on an eccentric circle. Frankly, there was no mathematician in the Middle Ages ingenious enough to have devised a similarly economical computational scheme for multiple epicycles. It's not even necessary to inspect all the medieval astronomical manuscripts to be sure.
Edward Rosen had simply misread Copernicus' intentions in writing that the entire ballet of the planets was accomplished in only 34 circles. Copernicus must have realized that with his small epicyclets he actually had more circles than the Ptolemaic computational scheme used in the Alfonsine Tables or for the Stoeffler ephemerides. His exuberant conclusion to the Commentariolus surely registered his delight that, although the celestial appearances seem very complicated, a great many phenomena can be modeled with only 34 circles. There was clearly no comparison intended with his predecessors.
THE EPICYCLES-ON-EPICYCLES legend fails in yet another way. There are virtually no records of systematic observations to find possible discrepancies between where the tables predicted the planets to be and where they really were. Yet there is one minor but extraordinarily significant exception that I discovered when Charles Eames and I were photographing the Copernican books in Uppsala.
Bound in the back of his printed copy of the Alfonsine Tables are sixteen extra leaves on which Copernicus added carefully written tables and miscellaneous notes. Below the record of two observations made in Bologna in 1500, there is, in another ink, a cryptic undated remark in abbreviated Latin: "Mars surpasses the numbers by more than two degrees. Saturn is surpassed by the numbers by one and a half degrees" (plate 7a)."
In 1504, soon after Copernicus had returned to Poland from Italy with his newly acquired doctorate, the two slowest-moving naked-eye planets put on a splendid show as faster-moving Jupiter bypassed the slower-moving Saturn. This great conjunction, which takes place only every twenty years, provided a sensitive test of the tables, since it did not require any elaborate instruments to determine on which night the planets actually passed each other. And this time Mars joined t
he ballet. Between October 1503 and March 1504, swifter Mars passed Jupiter and then Saturn, and then, going into retrograde motion, went back past Saturn and Jupiter, and finally in direct motion bypassed Jupiter and Saturn yet again. It was a great celestial display, and surely Copernicus would not have missed it.
With my computer programs I could calculate where the Alfonsine Tables placed these planets not just during this period but for several decades of the sixteenth century, and I could compare these calculations with modern ones showing where the planets really were. To my amazement, the calculations gave a unique error signature for February and March in 1504. During that interval the predictions for Jupiter were excellent, but Saturn lagged behind the tables by a degree and a half while Mars went ahead of the predictions by nearly two degrees. Only during this interval did the errors match Copernicus' notes, so the evidence is firm that he had observed the cosmic dance at this time and was fully aware of the discrepancies in the tables. But what is most astonishing is that Copernicus never mentioned his observation, and his own tables made no improvement in tracking these conjunctions.
It is pretty clear that neither Copernicus nor his predecessors were interested in adding extra circles just to make the predictions work a little better. Nevertheless, the legend of epicycles on epicycles has become so pervasive that barely a year passes without some author in the Physical Review or the AstronomicalJournal remarking, apologetically, "Maybe my theory has too many epicycles." Clearly, I haven't stamped out the myth.
* Surprisingly, Copernicus' planetary system was more compact than the carefully nested pieces of the Ptolemaic arrangement. Yet his cosmos was vastly larger than Ptolemy's because he was obliged to place the stars themselves far enough away so that the motion of the Earth around the Sun would not show any obvious changes in the positions of the stars. "So vast, without any question, is the divine handwork of the Almighty Creator," Copernicus concluded. It was a giant step for humankind, in the right direction, but ultimately that sentence made the Catholic censors very nervous. Probably, they had no objections to the vastness, but they just weren'r convinced that Copernicus could know how God did it. Catholics were ordered to delete that sentence from their copies.
* For the mathematically curious, details of Copernicus' procedure are given in appendix 1. In the Commentariolus Copernicus used a double epicyclet for Venus, Mars, Jupiter, and Saturn, but in De revolutionibus only a single epicyclet with an eccentric orbit. The Earth and Mercury had somewhat more complicated configurations—it remained for Kepler to construct a truly unified Copernican system.
† Skelton's "Garland of Laurel" included the lines
Arectyng my syght to the Zodyake, . . .
When Mars rerrogradanr reversyd his bak . . .
And whan Lucina plenarly did shyne,
Scorpione ascending degrees twyse nyne.
Using the Regiomontanus Ephemerides for 1495,1 could see that on 8 May 1495, the Moon was full in the eighteenth degree of Scorpio and in conjunction with the retrograding Mars.
Chapter 5
"EMBELLISHED BY
A DISTINGUISHED MAN"
THE COUNTDOWN for the Copernican Quinquecentennial built toward a climax in December of 1972. Charles Eames wanted to open his exhibition in the IBM building on Madison Avenue in time for the crowd of Christmas shoppers, so I flew to New York on several occasions to help with the labyrinthine assembly of the panels and artifacts. Edward Rosen came up from City College to lend his critical eye to proofreading the captions. He corrected a few minor errors but overall was quite pleased with the comprehensive presentation.
As the installation reached its final stage, the staff assigned me the task of keeping Charles occupied so that he would no longer make schedule-breaking improvements in the show. To create a dramatic Christmas showpiece on the street side of the exhibition, he had enlarged to mural proportions a page from Julius Schiller's idiosyncratic Coelum stellatum Christianum con-cavum of 1627, which had turned the constellation Pegasus into the angel Gabriel. Charles wanted to color the stars, so I read out the spectral type of each star from the Yale Bright Star Catalogue, and he dutifully used his Magic Markers to give each one its proper color, a characteristic level of sophistication for the Eames office, but entirely lost on the passing shoppers.
While in New York City I took the opportunity to see yet another De revolutionibus, one I hadn't previously recorded, at the Pierpont Morgan Library. It was my hundredth first edition, what collectors call an association copy, in this case a presentation volume from Johannes Petreius, the Nuremberg printer.
The books I had seen fell into four categories. There were a handful of three-star copies—on a Michelin Guide system, "worth the trip." These included the Reinhold copy in Edinburgh, the book that launched the census; Michael Maestlin's fabulously well annotated copy in Schaffhausen, Switzerland; and Harrison Horblit's presentation copy from Rheticus, the ultimate association copy since Copernicus did not himself live long enough to autograph a copy. The two-star copies—"worth a detour"—included one in Copenhagen originally owned and annotated by Matthias Stoy, one of Rheticus' students at Wittenberg who later became professor of mathematics at Konigsberg. Like Horblit's three-star copy, where Rheticus had canceled Osiander's anonymous introduction "To the Reader" with a red crayon, Stoy's copy had the same red cross-out, strongly suggesting that the copy had come directly from Copernicus' only disciple. Another two-star copy was in Toronto, probably the one originally belonging to Philips Lansbergen, a seventeenth-century Dutch astronomer and table calculator. It had an interesting piece of misinformation inscribed at the end of the Os-iander introduction to the effect that the Parisian scholar Petrus Ramus thought that Rheticus had written that introduction!
The angel Gabriel from Julius Schiller's Christian constellations of 1627, a street-side mural in the Eames Copernican exhibition at IBM headquarters in New York December 1972.
The one-star copies—what the Michelin Guide would merely call "interesting"—included the Morgan Library copy and one in Leningrad whose anonymous annotations contained a list of biblical verses that seemed to stand against the mobility of the Earth.
The proper classification or relevance of some of these starred copies was by no means obvious when I first examined them. Often the books became important only in retrospect, when I could make other connections with them. For example, if I had figured out who the first owner was to whom Petreius had presented the Morgan Library copy, and why that first owner had carefully canceled the Osiander introduction, it could well have won another star.
And then there was the fourth category, the large number of also-rans, with only trivial annotations or none at all. Because the books had been sold as stacks of paper that the buyer sent to the binder to be finished according to his tastes and his pocketbook, each copy was different. I carefully measured the height and width of their pages, figuring that someday this physical detail might help track a stolen copy, and I recorded the names of the previous owners whenever possible. Eventually, even these unannotated copies helped to demonstrate the movement of books and showed that the second edition, published in Basel in 1566, had particularly helped supply copies to Italy and England.
THE SPRING OF 1973 found me heading to Cairo, courtesy of American grain surpluses. In the 1960s the granaries of the American Midwest were bulging with corn and wheat, brought about in part by generous farm subsidies. Congress, having got into this particular pickle, found an ingenious way out. With Public Law 480 they arranged to send the grain to needy countries—including Poland, Yugoslavia, Israel, Egypt, and India—with the corn and wheat paid for in soft currencies. In other words, the United States found ways to spend the proceeds within each country rather than demanding hard cash. In turn, Congress allocated these funds to various government agencies including the National Science Foundation and the Smithsonian Institution.
Some of the Smithsonian's PL480 funds proved very useful for my Copernicus census, because they
could be used to buy air tickets from agents within those countries. I helped organize a translation program in Poland to get certain key Polish Copernican scholarship into English, and another program in Egypt to catalog the many unexplored astronomical manuscripts from the Islamic period. Both TWA and PanAm had offices in Warsaw and Cairo, and there was no problem using the tickets they provided to stop off at various points to survey copies of De revolutionibus.
By April of 1973, when I was heading on my annual trip to check up on the Islamic astronomy project in Cairo, my Copernican notes were extensive enough to give a pretty good idea of the way in which the book was used in the sixteenth century, sometimes as an object of intense study, and sometimes as little more than decoration on a library shelf, casually perused at best. Having by then examined more than a hundred copies, surely sufficient for statistical purposes, I was tempted to say that enough was enough. Nevertheless, Rome beckoned, because I knew there were more unexamined Copernicus imprints in that metropolis than in any other single place. Copies were to be found in the Biblioteca Nazionale, in the Accademia dei Lincei, at the Vatican, and in the Biblioteca Casanatense. The latter library, named after Cardinal Casanate, who later became head of the Inquisition that had sentenced Giordano Bruno to the stake in 1600, unexpectedly turned out to have Bruno's De revolutionibus, a second edition. Bruno had been sentenced as a heretic for a plethora of heterodox ideas, including the plurality of worlds, but he seemed at best rather ill informed about Copernicus' ideas. His De revolutionibus contained a bold signature but no evidence that he had actually read the book. In any event, his Copernicanism was not a major factor in his conviction. Bruno's copy was a surprise, but when I arrived in Rome, the really big discovery awaited me at the Biblioteca Apostolica Vaticana.
The Book Nobody Read Page 7