Tannstetter, also a German, was speaking in part from national pride. But the Epitome of the Almagest turned out to be at least as influential as its source. It was soon a classroom standard, guiding young astronomers into a newly sharp understanding of the Ptolemaic universe. Through the Epitome, the Almagest regained its place as the bible of astronomy.
Within a generation, it would face a fatal challenge.
To read relevant excerpts from the Almagest, visit http://susanwisebauer.com/story-of-science.
PTOLEMY
Almagest
(ca. AD 150)
The Almagest is available in two modern translations. The R. Catesby Taliaferro translation is the first selection in Volume 16 of the “Great Books of the Western World” series, published in 1952 by Encyclopedia Britannica. It is now out of print but widely available used, as well as in most academic and many public libraries.
Robert Maynard Hutchins, ed., Ptolemy, Copernicus, Kepler (Great Books of the Western World, vol. 16), Encyclopedia Britannica (hardcover, 1952, ISBN 978-0852291634).
A more recent, academic but readable, and very expensive translation by G. J. Toomer was published by Princeton University Press with massive footnotes and explanatory text, making the Almagest easier to understand but bulking it up to nearly seven hundred pages (so probably most suitable for the true medieval-astronomy enthusiast).
Ptolemy, Ptolemy’s Almagest, trans. G. J. Toomer, Princeton University Press (paperback, 1998, ISBN 978-0691002606).
* * *
* The presence of ether was necessary because of a prior logical principle: There is no such thing as a space where nothing exists. Every space in the universe is filled with something; therefore, the something was given a name.
† This phenomenon is discussed in detail in Susan Wise Bauer, The History of the Renaissance World (W. W. Norton, 2013), Chapter 6.
SEVEN
The Last Ancient Astronomer
An alternate explanation for the universe, with better mathematics, but no more proof
I often considered whether there could perhaps be found a
more reasonable arrangement of circles.
—Nicolaus Copernicus, Commentariolus, 1514
Nicolaus Copernicus had a problem with the equant.
He had first encountered the Epitome of the Almagest in 1491, as an eighteen-year-old student at the University of Cracow. From the beginning, he had questioned those elaborate and unwieldy orbits. The entire Ptolemaic model had been built on Aristotelian physics—the properties of heavy and light elements, the tendency of the former to fall toward the center of the universe—yet it violated another one of Aristotle’s central principles, which was that heavenly movements were always spherical. The equant and the epicycles, both nominally preserving the spherical orbits of the planets, actually distorted them; the only way to accept Ptolemaic orbits as spheres was to squint, really hard.1
And each planet required its own individual set of movements, its own particular laws. It was as if, Copernicus later wrote, an artist decided to draw the figure of a man, but gathered
the hands, feet, head and other members for his images from diverse models, each part excellently drawn, but not related to a single body . . . the result would be monster rather than man.2
It was not the inaccuracies of the Ptolemaic system that bothered him; it was its inelegance.
Copernicus spent the next decade and a half studying the Almagest and making his own observations. Five years after his matriculation at Cracow, we find him recording the lunar eclipse of Aldebaran. Three years after that, he chronicled the conjunctions of Saturn and the moon. He lectured in Rome on mathematics, taught himself Greek, kept watching the skies.3
By 1514 he had formulated a more graceful theory. He wrote it out in a simple and readable form, eliminating all of the mathematics involved, and circulated it to his friends. This informal proposal, the Commentariolus, began with an admission that the Ptolemaic system worked reasonably well; Copernicus’s primary motivation was to get rid of the mathematical gyrations that it required.
The planetary theories of Ptolemy and most other astronomers, although consistent with the numerical data . . . present no small difficulty. For these theories were not adequate unless certain equants were also conceived. . . . I often considered whether there could perhaps be found a more reasonable arrangement of circles, from which every apparent inequality would be derived and in which everything would move uniformly about its proper center, as the rule of absolute motion requires. After I had addressed myself to this very difficult and almost insoluble problem, the suggestion at length came to me how it could be solved with fewer and much simpler constructions than were formerly used, if some assumptions (which are called axioms) were granted me.4
These assumptions were simple: “All the spheres revolve about the sun as their mid-point, and therefore the sun is the center of the universe.” The earth was merely the center of the “lunar sphere,” and it did not remain motionless. Instead, it sped in a rapid orbit around the sun (like the other spheres), moving at an amazing clip in order to complete its trip within a year, and also performed a “complete rotation on its fixed poles in a daily motion.” This earthly rotation actually caused the apparent movement of the sun and the retrograde motions of the planets. “The motion of the earth alone,” Copernicus concluded, “suffices to explain so many apparent inequalities in the heavens.”5
7.1 THE COPERNICAN UNIVERSE. A SEVENTEENTH-CENTURY SKETCH BY JOHANNES HEVALIUS.
Eighteen hundred years earlier, Aristarchus had proposed a sun-centered universe with a moving earth; Archimedes had used the model for his thought experiment in “The Sand-Reckoner.” The idea had never gained much traction. But Copernicus had an advantage over previous Greek heliocentric thinkers: access to centuries’ worth of observations. The Ptolemaic system had never worked with complete accuracy; there were small slippages and tiny discrepancies in its predictions. And as more and more data were gathered, over greater and greater spans of years, the slippages became more apparent. As Thomas Kuhn has pointed out, the movement of planets around deferents and epicycles is not unlike the movement of a clock’s hands; a clock that loses a second each year will seem to be on time at the end of ten years, or even a hundred, but after a thousand years the error will become obvious.6
The Almagest, in other words, was ripe for a challenge; and Copernicus spent the next quarter century working the ideas of the Commentariolus up into a full-fledged manual, complete with calculations. It was a deliberate counterproposal, equal in length and complexity, and comparable in form, to the revered ancient text.
This manual, On the Revolutions of the Heavenly Spheres, was a masterpiece of mathematics. Like the Greek astronomers before him, Copernicus set out to “save the phenomena”—to produce a series of calculations that would line up with the data. The difference: he manipulated planets in their paths around the sun rather than the earth. And this he did successfully—without making use of Ptolemy’s off-center rotations. He had, as his single private pupil Rheticus put it, “liberated” astronomy from the equant.7
But On the Revolutions, even in its final form, had massive credibility problems.
For one thing, in order to fully save the phenomena, Copernicus had to insert even more interlocking, rotating celestial spheres than his Ptolemaic colleagues had used; he had done away with the equant, but not with the overly elaborate gear system of the heavens. For another, his insistence that the earth was both rotating and hurtling through space at a ridiculously fast pace simply didn’t line up with experience. It was obvious to anyone with eyes that a man who jumped up would come down in exactly the same place; the earth did not rocket out from beneath him while he was suspended in the air. Sixteenth-century physics had absolutely no way to explain this reality, and it was much more reasonable to believe that the earth was doing exactly what it appeared to be doing—standing still.8
On top of all this, the heliocentric theory s
eemed to contradict the literal interpretation of biblical passages such as Joshua 10:12–13, in which the sun and moon “stand still” rather than continuing to move around the earth. The theological problems were actually less troublesome than the scientific ones; but taken together, they cast serious doubt on Copernicus’s new model.
The doubt was so pervasive, in fact, that when On the Revolutions was first printed in 1543, an unsigned introduction was appended to it, explaining that the heliocentric model was merely a tool for calculation, yet another mathematical trick for saving the phenomena: “For these hypotheses need not be true or even probable,” the introduction assured cautious readers. “On the contrary, if they provide a calculus consistent with the observations, that alone is enough. . . . They are not put forward to convince anyone that they are true, but merely to provide a reliable basis for computation.”9
Copernicus may not even have seen this disclaimer; it is generally thought to have been written by his friend Andrew Osiander, whom he had tasked with seeing On the Revolutions through the printing process. Copernicus’s other writings make quite clear that he believed his model to be an accurate reflection of reality. Unlike Hipparchus, he thought that, should he be transported into the heavens, he would see the earth tracking faithfully around the sun.
Yet even in his conviction, Copernicus was aware that there was no proof for his heliocentric model. He was doing exactly the same thing that ancient astronomers had always done: constructing yet another model that gave pretty accurate answers when the calculations were run.
The preface that Copernicus himself wrote—dedicating the work to no less a personage than Pope Paul III—pointed out that the geocentric theory was itself incertitudo mathematicarum traditionum, an uncertain mathematical tradition, and that his model was an alternative mathematical proposal: “Because I knew that others before me had been granted the liberty of constructing whatever circles they pleased in order to demonstrate astral phenomena,” Copernicus explains, “I thought that I too would be readily permitted to test . . . demonstrations less shaky than those of my predecessors.”10
Demonstrations less shaky: Copernicus was consciously refusing to assert that his heliocentrism was reality. Like the Greek atomists, he had actually stumbled onto the truth. And, like the atomists, he had no method that would confirm his conclusions. He knew this perfectly well.
The rhetorical distancing of himself from his own beliefs worked, for a time. Pope Paul III happily accepted the dedication, and On the Revolutions remained on the church’s good side for the next seventy years. But within the work itself, Copernicus’s real beliefs occasionally pop to the surface with suppressed, irresistible energy. Halfway through the first chapter, he lays down the most controversial assertion of his system: that only the mobility of the earth and the sun’s position at “the centre of the world” explain the motions of the stars. “The harmony of the whole world teaches us their truth,” he writes, “if only—as they say—we would look at the thing with both eyes.”11
But human eyes, even both of them, could not prove the heliocentric system.
To read relevant excerpts from the Commentariolus and On the Revolutions of the Heavenly Spheres, visit http://susanwisebauer.com/story-of-science.
If you, like Copernicus’s friends, prefer the conclusions without the math, read the Commentariolus, which is considerably shorter than the full text of On the Revolutions. If you enjoy wrestling with geometric proofs, choose the longer work.
NICOLAUS COPERNICUS
Commentariolus
(1514)
The Commentariolus is included, along with a summary of Copernicus’s work written by his champion Rheticus (the Narratio prima) and a letter written by Copernicus disproving the calculations of the astronomer Johannes Werner (the Letter against Werner), in the paperback Three Copernican Treatises.
Edward Rosen, trans., Three Copernican Treatises, 2nd revised edition, Dover Publications (paperback, 2004, ISBN 978-0486436050).
NICOLAUS COPERNICUS
On the Revolutions of the Heavenly Spheres
(1543)
The early-twentieth-century translation by Charles Glenn Wallis has been reprinted in paperback.
Nicolaus Copernicus, On the Revolutions of the Heavenly Spheres, trans. Charles Glenn Wallis, Prometheus Books (paperback, 1995, ISBN 978-1573920353).
Another edition of the same translation, with introductory essay and notes by Stephen Hawking, can be found in
Nicolaus Copernicus, On the Revolutions of the Heavenly Spheres, trans. Charles Glenn Wallis, ed. Stephen Hawking, Running Press (paperback, 2002, ISBN 0-7624-2021-9).
PART
II
THE BIRTH
OF THE METHOD
Francis Bacon, Novum organum (1620)
William Harvey, De motu cordis (1628)
Galileo Galilei, Dialogue concerning the Two Chief World Systems (1632)
Robert Boyle, The Sceptical Chymist (1661)
Robert Hooke, Micrographia (1665)
Isaac Newton, Philosophiae naturalis principia mathematica (1687/1713/1726)
EIGHT
A New Proposal
A challenge to Aristotle, and the earliest articulation of the scientific method
The logic now in use . . . does more harm than good.
—Francis Bacon, Novum organum, 1620
Copernicus’s scheme was a century old, but nothing had yet changed. His theory remained an outlier. It made no sense, in terms of Aristotelian physics; he hadn’t managed to explain why, if the earth was circling the sun, its motion through the air was imperceptible to people on the earth’s surface.
Thirty years after the publication of On the Revolutions, a possible solution was offered by the Danish astronomer Tycho Brahe, a fan of the Copernican system (“This innovation expertly and completely circumvents all that is superfluous or discordant in the system of Ptolemy,” he wrote). The heliocentric system demanded that the earth, “that hulking lazy body, unfit for motion,” move as quickly “as the aethereal [stars].” What if, instead, the earth remained still with the sun, moon, and stars rotating around it—while the other five planets orbited the sun?1
Tycho is now best known as the first discoverer of a new star, which he called nova stella—a term that survives into modern times as supernova. His ingenious combination system solved the physics problem and explained the motions of the skies. But like Copernicus, Tycho could offer no proof. Without evidence, neither his system nor Copernicus’s was more compelling than the Ptolemaic explanation.
There was still no real reason to rethink Ptolemy, or to challenge Aristotle’s authority.
•
In 1603, Francis Bacon, London born, was forty-three years old: a trained lawyer and amateur philosopher, happily married, politically ambitious, perpetually in debt.
He had served Elizabeth I of England loyally at court, without a great deal of recognition in return. But now Elizabeth was dead at the age of sixty-nine, and her crown would go to her first cousin twice removed: James VI of Scotland, James I of England.
Francis Bacon hoped for better things from the new king, but at the moment he had no particular “in” at the English court. Forced to be patient, he began working on a philosophical project he’d had in mind for some years—a study of human knowledge that he intended to call Of the Proficience and Advancement of Learning, Divine and Human.
Like most of Bacon’s undertakings, the project was ridiculously ambitious. He set out to classify all learning into the proper branches and lay out all of the possible impediments to understanding. Part I condemned what he called the three “distempers” of learning, which included “vain imaginations,” pursuits such as astrology and alchemy that had no basis in actual fact; Part II divided all knowledge into three branches and suggested that natural philosophy should occupy the prime spot. Science, the project of understanding the universe, was the most important pursuit man could undertake. The study of history (“everything that
has happened”) and poesy (imaginative writings) took definite second and third places.2
For a time, Bacon didn’t expand on these ideas. The Advancement of Learning opened with a fulsome dedication to James I (“I have been touched—yea, and possessed—with an extreme wonder at those your virtues and faculties . . . the largeness of your capacity, the faithfulness of your memory, the swiftness of your apprehension, the penetration of your judgment, and the facility and order of your elocution. . . . There hath not been since Christ’s time any king or temporal monarch which hath been so learned in all literature and erudition, divine and human”), and this groveling soon yielded fruit. In 1607 Bacon was appointed as solicitor general, a position he had coveted for years, and over the next decade or so he poured his energies into his government responsibilities.
He did not return to natural philosophy until after his appointment to the even higher post of chancellor in 1618. Now that he had battled his way to the top of the political dirt pile, he announced his intentions to write a work with even greater scope—a new, complete system of philosophy that would shape the minds of men and guide them into new truths. He called this masterwork the Great Instauration: the Great Establishment, a whole new way of thinking, laid out in six parts.
Part I, a survey of the existing “ancient arts” of the mind, repeated the arguments of the Advancement of Learning. But Part II, published in 1620 as a stand-alone work, was something entirely different. It was a wholesale challenge to Aristotelian methods, a brand-new “doctrine of a more perfect use of reason.”3
Aristotelian thinking relies, heavily, on deductive reasoning—for ancient logicians and philosophers, the highest and best road to the truth. Deductive reasoning moves from general statements (premises) to specific conclusions.
The Story of Western Science Page 6