Galileo is credited with defeating Ptolemaic earth-centered astronomy, but most mathematical astronomers had already abandoned this theory long before Galileo.
Opinionated History of Mathematics
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Does the earth move around the sun, or is it the other way around? Copernicus worked out the right answer long before Galileo was even born, as did the best Greeks mathematicians thousands of years earlier. Yet somehow Galileo has ended up with much of the credit. Here’s a quote from the Cambridge Companion to Galileo: “If one wonders why the Copernican theory, [which had] almost no adherents at the beginning of the seventeenth century, had pretty much swept the field by the middle [of the century], the answer is above all [Galileo’s] Dialogue.” And here’s another quote from the Very Short Introduction to Copernicus: “Galileo wrote the book that won the war [and] made belief in a moving earth intellectually respectable.”
This standard story from mainstream scholarship may be right in a limited sense: maybe indeed the ignorant masses needed a book like Galileo’s to dumb it down for them before they could finally come to their senses. But mathematically competent people were already convinced long before and had no use for Galileo telling them the ABCs.
When Copernicus made the earth go around the sun, he confidently declared that “I have no doubt that talented and learned mathematicians will agree with me.” Those are his own words. And he was right. In 1600, long before Galileo has published a single word on the matter, there were already at least ten committed Copernicans, besides Copernicus himself. Westman lists them as follows: “Digges and Harriot in England; Giordano Bruno and Galileo in Italy; Diego de Zuniga in Spain; Simon Stevin in the Low Countries; and, in Germany, the largest group—Rheticus, Maestlin, Rothmann, and Kepler.”
That makes eleven in total. Eleven believers in the new astronomy. This is what the Cambridge Companion calls “almost no adherents.” But what do you expect? How many “talented and learned mathematicians” do you think there were in pest-ridden, blood-letting, witch-burning Europe of 1600? And how many of concerned themselves with the Copernican question and formed an opinion on it, even though that was a philosophical question beyond the scope of the official computational task of the astronomer? And, among those in turn, how many were prepared to declare allegiance to a flagrantly heretical opinion in an age where the religious thought-police routinely employed vicious torture and burnt dissenters alive? Including one guy on that very list I just read, in fact: Giordano Bruno, who was burned at the stake by the authorities, as punishment for his heretical views, which included heliocentrism (although it is unclear what weight that carried exactly in relation to his other thought crimes).
At any rate, given this context, I think eleven avowed Copernicans in 1600 is really quite a crowd. Indeed, consider Galileo’s own assessment of the situation in 1597: “I have preferred not to publish, intimidated by the fortune of our teacher Copernicus, who though he will be of immortal fame to some, is yet by an infinite number … laughed at and rejected … for such is the multitude of fools.”
This confirms that social pressures to avoid the issue were very real---enough to “intimidate” Galileo and surely many others. More importantly, Galileo is also making my main point for me: even at this very early stage---long before Galileo has published a single word on the matter, and well before the invention of the telescope---everyone with half a brain has rejected the old astronomy already. By Galileo’s own reckoning, there were only “fools” left to convince. I say that on this point he is exactly right.
Furthermore, there were doubtless many more closet Copernicans who figured “don’t ask, don’t tell” was the best policy to avoid needless conflicts with the intolerant. For example, Harriot had a number of followers in England who were enthusiastic believers in heliocentrism, but “the local political and intellectual milieu … forced them into what we can term preventive self-censorship,” one scholar has observed. Another example is Mersenne, in France. He does not go on the official list of Copernicans because, as one historian puts it, “at no time during his life did he find any proof so overwhelming that he felt like challenging the Church on the matter.” And this despite the fact that he was one of the most enthusiastic readers of Galileo’s Dialogue. He remained uncommitted for political reasons, it would seem.
Another indication that many were silently receptive to Copernicanism is the fact that most of the leading astronomers of the 16th century owned Copernicus’s book, and many of them wrote extensive notes in the margins, as was the habit at the time. Books were printed with enormous margins because everyone was expected to take detailed notes as they read. And indeed they did. Owen Gingerich conducted a thorough census of all surviving copies of Copernicus’s book. He looked at all this marginalia that this large group of serious, competent readers of Copernicus’s book has written. That’s a group far larger than those eleven I mentioned before. Some of them were probably secretly convinced that Copernicus was right; others studied the work because they saw it as they duty to keep up with the best technical mathematical astronomy of the day whether they agreed with it or not. Either way, they took meticulous notes as they painstakingly worked through this long and technical treatise.
But this group did not include Galileo, however. Galileo’s dilettantism is so blatant and shameless that Gingerich could hardly believe his eyes: “I had long supposed that Galileo was not the sort of astronomer who would have read Copernicus’ book to the very end. … Still, when I saw the copy in Florence, my reaction was one of scepticism that it was actually Galileo’s copy, since there were so few annotations in it. … This copy had no technical marginalia, in fact, no penned evidence that Galileo had actually read any substantial part of it. … Eventually, … I realized that my scepticism was unfounded and that it really was Galileo’s copy.” There is no need for surprise, of course. Galileo was a poor mathematician. He had neither the patience nor the ability to understand serious mathematical astronomy, let alone make any contribution to it.
Let’s have a look at what some of these more serious mathematical astronomers were up to. For example, Tycho Brahe, the Danish astronomer in the generation before Galileo. He also considered the question of whether it is the earth or the sun that moves. And he came up with a creative answer that is neither that of Ptolemy nor that of Copernicus.
He saw the strengths in the Copernican system, but he was worried about its drawbacks. Most importantly the problem of parallax, which we discussed before. If the earth moves in a big circle that implies that we are looking at the heavens from different points of view in the course of a year. This should be detectable when we study the positions of the stars. The angles between them should shrink and grow as we move around the sun, because our distance from any particular star configuration would change radically in the course of a year.
But this does not happen. The night sky is immutable. As far as 17th-century astronomers could detect, the constellations all look exactly the same throughout the year, just as if we never move an inch. Tycho Brahe was the most exacting astronomical observer in the pre-telescopic era, but even he, with his very advanced and precise observations, could find no parallactic effect.
To maintain the earth’s motion in spite of this, it is therefore necessary to postulate, as Copernicus does, that “the fixed stars … are at an immense height away.” The diameter of the earth’s orbit is so small in relation to such an astronomical distance that our feeble little motion is all but tantamount to standing still. That is why no parallax can be detected. This is the correct explanation, as we now know, but in the 16th century it didn’t sound too convincing.
Tycho Brahe was one of the sceptics. He calculated that, if Copernicus was right, the stars would have to be at least 700 times further away than Saturn. The universe would not have been designed with so much wasted space, he reasoned.
Tycho therefore devised a system of his own. In this system, the earth remained the center of the universe, while the planets orbit the sun. So it’s a hybrid of Ptolemy and Copernicus. A halfway house that takes the best of both worlds.
This solves the problem of parallax: since the earth is not moving, there shouldn’t be any parallax, so that’s that, problem solved. You can put the “sphere of the fixed stars” just beyond Saturn, like Ptolemy did. That’s how people used to view the stars: as a bunch of specks of shiny glitter glued onto the inside wall of a big ball. We can’t judge depth or distance of heavenly objects by eye anyway, so we might as well imagine everything taking place on a single surface like that. And if you adopt the cosmology of Ptolemy or Tycho, you can imagine this sphere as a natural container of the solar system. Everything fits snugly. Every bit of space has a purpose. Not so in Copernicus’s universe. If there is a glitter sphere of stars at all, it must be enormous. That’s just grotesque, isn’t it? It’s as if someone would make a huge clock face, Big Ben style, many meters across, but then put tiny wristwatch arms in the middle. It’s absurd. So point Tycho for avoiding that problem.
But what about the strengths of the Copernican system? We discussed this before. The advantages have to do with explanatory simplicity. It explains the retrograde motion of the outer planets, and the bounded elongation of the inner planets. But so does Tycho’s system. In fact, Tycho’s system is equivalent to the Copernican one as far as the relative positions of the heavenly bodies are concerned. Tycho and Copernicus describe the same planetary motions, but they choose a different reference point in terms of which to describe them. Kepler illustrates the point with an analogy: the same circle can be traced on a piece of paper by either rotating the pen arm of a compass around the fixed leg, or by keeping the compass fixed while rotating the paper underneath it. So the Copernican and Tychonic systems are by necessity on equal footing as far as the arguments regarding explanatory simplicity are concerned. Although Tycho’s system feels weirder, so to speak, there’s no denying that for all those purposes it is strictly equivalent to heliocentrism. That’s just a geometrical fact.
One might feel that the Tychonic system is less physically plausible than those of Ptolemy or Copernicus. Indeed, traditional conceptions had it that planets were enclosed in translucent crystalline spheres, like the layers of an onion. Both the Ptolemaic and Copernican systems are basically compatible with such an “onion” conception of the cosmos. The Tychonic system clearly is not: planets are crossing each other’s “orbs” all over the place. But Tycho had some good counterarguments to this. By a careful study of the paths of comets, he proved that they evidently passed through the alleged crystalline spheres with ease. Furthermore, he pointed out that these alleged spheres did not refract light, as glass and other materials had been known to do since antiquity. So Tycho has some decent arguments in defence of his system even in the domain of physics.
All in all, Tycho’s system was a serious scientific theory with good arguments to its credit. This is another reason why our headcount of Copernicans above is misleading. The number of people who rejected the Ptolemaic system was certainly greater than the number of outright Copernicans. The middle road put forth by Tycho was by no means blind conservatism but rather a viable system based on the latest mathematical astronomy.
Galileo, however, liked to pretend otherwise. The full title of his famous book reads: Dialogue Concerning the Two Chief World Systems: Ptolemaic and Copernican. Well, that certainly made Galileo’s life a lot easier. It was very convenient for him to frame his fictional debate with fictional opponents in those antiquated terms. That way he could battle two-thousand-year-old ideas instead of having to engage with the latests mathematical astronomy.
More serious and mathematically competent people had a very different view of which were “the two chief world systems.” Around 1600, long before Galileo enters the fray, Kepler considers it obvious that the Ptolemaic system is obsolete. This is Kepler writing before Galileo’s works:
“Today there is practically no one who would doubt what is common to the Copernican and Tychonic hypotheses, namely, that the sun is at the centre of motion of the five planets, and that this is the way things are in the heavens themselves---though in the meantime there is doubt from all sides about the motion or stability of the sun.”
Later, after the telescope has brought its new evidence, not much has changed. Kepler is a bit more assured that “today it is absolutely certain among all astronomers that all the planets revolve around the sun.” That’s Kepler writing in 1619, after the telescope. But even then the battle between Copernicus and Tycho remained far from settled: “either [of those two] hypotheses are today publicly accepted as most true, and the Ptolemaic as outmoded.” “The theologians may decide which of the two hypotheses … ---that of Copernicus or that of Brahe---should henceforth be regarded as valid [for] the old Ptolemaic is surely wrong.” Again, Kepler, writing more than a decade before Galileo’s famous book that dishonestly pretends that the Ptolemaic view is still one of “the two chief world systems.”
Nor was this merely Kepler’s opinion. Historians who study much more minor figures have also concluded that, indeed, “the Ptolemaic system already had been set aside, at least among mathematical astronomers,” well before Galileo wrote his Dialogue. But Galileo, in his great book, like a schoolyard bully secretly too scared to pick on someone his own size, preferred to pretend that the old Ptolemaic system was still the enemy of the day. To be sure, there were still a “multitude of fools” left to convince, and perhaps indeed Galileo did so more effectively than anyone else. But that proves at most that Galileo should be praised as a populariser, not as a scientist. To mathematically competent astronomers he was beating a dead horse.
Some scholars have made too much of the above arguments in favour of the Tychonic system, however. They have concluded that “it is fair to say that, contrary to [the standard view], science backed geocentrism.” That’s a quote from Christopher Graney’s book. Indeed, if you take the petty works of Galileo and his immediate opponents to be the extent of “science” then this conclusion does make some sense. But the conclusion is false if you include genuinely talented scientists like Kepler. Unlike Galileo, Kepler dared to take on the Tychonic system and he gave a long list of compelling arguments against it.
Tycho’s system is equivalent to the Copernican one in terms of relative position of the planets, but “that Copernicus is better able than Brahe to deal with celestial physics is proven in many ways,” says Kepler. And he’s right. He has a range of physics arguments, including the one I discussed before about the implausibility of a heavier body orbiting a lighter one.
Let’s consider in some more detail the relation between Kepler and Galileo. Kepler was the best mathematical astronomer in Galileo’s day. They were contemporaries. Kepler was seven years younger than Galileo. What did they think of each other? What were their relationship? Certainly not as substantive as one might expect.
As one historian says: “One wonders why these two great men, who were both present and actual participants at the very birth of some of the most world-shaking scientific events, and who apparently were very much in accord in their astronomical views, did not engage in a more on-going correspondence over these years.”
This is a puzzle and a paradox if one accepts the standard view of Galileo. But of course it becomes perfectly understandable as soon as one realises that Kepler, who was a brilliant mathematician, had very little to learn from a dilettante such as Galileo.
Their correspondence began when, “in 1597, as a lowly high-school teacher of mathematics and a fledgling author, Kepler … vainly implored Galileo, the established university professor, to give him the benefit of a judgment of his first major work.” Galileo replied briefly, declaring himself in agreement with the Copernican standpoint of Kepler’s book, and then this is where he gives that statement I already quoted, that “I have preferred not to publish, intimidated by the fortune of our teacher Copernicus, who though he will be of immortal fame to some, is yet by an infinite number … laughed at and rejected … for such is the multitude of fools.”
Kepler, in his reply, is happy to hear that Galileo, “like so many learned mathematicians,” has joined in supporting “the Copernican heresy,” as Kepler calls it. Those are Kepler’s words: “like so many learned mathematicians”. Galileo is late to the party. “So many learned mathematicians” got there before him.
Kepler goes on to say, in reply to Galileo’s admission of being “intimidated” by opponents, that Galileo should really grow a backbone. Here is what Kepler says: “For it is not only you Italians who do not believe that they move unless they feel it, but we in Germany, too, in no way make ourselves popular with this idea.” Kepler urges Galileo to focus on compelling mathematics instead of on the number of fools: “Not many good mathematicians in Europe will want to differ from us; such is the power of truth.”
This is very typical and illustrative of the outlooks of Kepler and Galileo. Galileo has his attention turned to “the multitude of fools,” as he calls them. The uneducated masses and their naive beliefs. From that point of view, fighting for heliocentrism is a huge uphill battle. Kepler on the other hand is more concerned with what other mathematicians think, what intelligent people who studied the matter is a serious way believe about the motion of the earth. From that point of view there is every reason to be very optimistic, as Kepler says, because all competent people had rejected Ptolemy’s astronomy already.
At this point, Kepler naively mistook Galileo for a serious scientific interlocutor. In connection with their discussion of Copernicanism, Kepler noted the importance of parallax and asked Galileo if he could help him with observations for this, adding detailed instructions regarding the exact nature and timing of the required measurements. Kepler also sent additional copies of his book, as Galileo had requested, and “asked only for a long letter of response as payment---which was, however, never forthcoming.” Galileo stopped replying, presumably since this kind of actual, substantive mathematical astronomy was beyond his abilities.
Kepler’s was not the only scientific correspondence Galileo shrunk from. He also neglected to reply to all three letters he received from Mersenne, for example, offering only “the rather limp excuse that he found Mersenne’s handwriting too hard to read.” It seems he had a point, for others complained similarly of Mersenne’s letters that “his hande is an Arabicke character to me,” as Cavendish said. Nevertheless those are further instances of Galileo failing to reply to a serious scientific interlocutor.
The tables were turned in 1610. While Galileo had not seen the greatness in Kepler’s book, more mathematically competent people had, and consequently Kepler had succeeded Tycho Brahe as the Imperial Mathematician of the self-declared Holy Roman Emperor in Prague. “In that capacity Kepler’s help was sorely needed by Galileo in 1610, when his momentous telescopic discoveries were being received on all sides with skepticism and hostility.” “To Kepler’s credit … he … swallowed his justifiable resentment” and “ungrundingly gave Galileo the authoritative support he could find nowhere else.” “In spite of Galileo’s earlier silence after his own request in 1597, Kepler quickly and enthusiastically responded to Galileo’s findings, within 11 days.”
Galileo surely had this in mind when, in reply, he praised Kepler for “your uprightness and loftiness of mind”---”you were the first one, and practically the only one, to have complete faith in my assertions” regarding the telescopic discoveries. Kepler’s support was indeed crucial, and Galileo keenly flaunted it to his advantage when promoting his work to others.
Galileo did not take the occasion to revive their scientific discussion or comment on Kepler’s brilliant new book, the Astronomia Nova of 1609, which proved the law of ellipses among other things. Instead Galileo only wanted to make fun of dumb philosophers:
“Oh, my dear Kepler, how I wish that we could have one hearty laugh together! Here at Padua is the principal professor of philosophy, whom I have repeatedly and urgently requested to look at the moon and planets thorough my glass, which he … refuses to do. Why are you not here? What shouts of laughter we should have at this glorious folly!”
Kepler wasn’t there because he was busy doing real science. He ignored idiotic philosophers, as all mathematically competent people had done for thousands of years. Galileo, however, has nothing better to do than to sit around and laugh at idiots, because he is not a serious scientist. He is a salon scientific poseur, to whom the most desirable application of science is a clever put-down and the last laugh.
Kepler eventually grew weary of Galileo’s dilettantism. When, in later years, he found himself having to correct errors in Galileo’s superficial writings, he fully justifiably took a patronising tone. Here is a quote from 1625:
“Galileo rejects Tycho’s argument that there are no celestial orbs with definite surfaces because there are no refractions of the stars. … Rays reach the earth perpendicular to the spheres, says Galileo, and perpendicular rays are not refracted. But oh, Galileo, if there are orbs, it is necessary that they be eccentric. Therefore, no rays perpendicular to the spheres reach to the earth except at apogee and perigee. Hence, Tycho’s argument is a strong one, if you are willing to listen.”
Indeed. So Galileo ignored all the mathematical details as usual and instead only addressed a simplistic straw-man version of Tycho’s actual argument. That’s the way it always goes with Galileo, and by now Kepler has realised as much.
Here’s another example of the same thing. Again Kepler has lost patience with Galileo’s shameless and self-serving rhetoric and sets the record straight as follows. This is a long quote from Kepler:
“Galileo denies that the Ptolemaic hypothesis could be refuted by Tycho, Copernicus, or others, and says that it was refuted only by Galileo [himself] through the use of the telescope for observation of the variation of the discs of Mars and Venus. … Nothing is more valuable than that observation of yours Galileo; nothing is more advantageous for the advancement of astronomy. Yet, with your indulgence, if I may state what I believe, it seems to me that you would be well advised to collect those thoughts of yours that go wandering from the course of reason …. This observation of yours … does not refute the very distinguished system of Ptolemy nor add to it. Indeed, this observation of yours refutes not the Ptolemaic system but rather, I say, it refutes the traditions of the Ptolemaics regarding the least difference of planetary diameters. … Your own observation of the discs confirms the proportion for the eccentric to the epicycle in Ptolemy, as it does the orbit of the sun in Tycho or of the orbis magnus in Copernicus.”
So even though Kepler favours the Copernican conclusions just like Galileo does, he, unlike Galileo, is honest when the evidence is consistent with either of the hypotheses. Kepler thinks it is the obligation of the scientist to consider alternative hypotheses seriously and to engage with them on their own terms, instead of opportunistically twisting everything to confirm one’s own preferred conclusion.
In both of these cases that I quoted, Kepler exposes Galileo’s true colours. Galileo doesn’t treat the matter as a serious mathematical astronomer, but rather as a superficial and unscrupulous rhetorician. Kepler is quite right to scold him as he does.