Galileo thought comets were an atmospheric phenomenon, not physical bodies in outer space. How could he be so wrong when all his colleagues got it right? Perhaps because his theory was a convenient excuse for not doing any mathematical astronomy of comets. We also discuss his unsavoury ways of dealing with data in the case of double stars and the rings of Saturn.
Opinionated History of Mathematics
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“Have you seen the fleeting comet with its terrifying tail?” That was the question on everyone’s lips in 1618. In that year a comet appeared that was “of such brightness that all eyes and minds were immediately turned toward it.” “Suddenly, men had no greater concern than that of observing the sky. Great throngs gathered on mountains and other very high places, with no thought for sleep and no fear of the cold.” “That stellar body with its menacing rays was considered a monstrous thing.” According to some prophets, the comet was a cosmic omen foretelling imminent disaster.
I quoted these vivid descriptions from Orazio Grassi: a contemporary of Galileo. These two had a big fight about comets. Grassi was a fine scientist. He was basically right about comets. Galileo, on the other hand, was way wrong on this. His theory of comets is extremely poor. However, Galileo managed to spin this somehow and still come out on top, in the eyes of many modern readers, despite being absolutely wrong as a matter of scientific fact.
This is quintessential Galileo: wrong on science, but a rhetorical master. Galileo could write a self-help book called “How to appear to win any debate even when you’re wrong from start to finish on every single point of substance.” If Galileo is the father of anything it is this art form. So you’re looking to pick up some tricks from that playbook then Galileo is your guy, and the comets dispute is the place to start.
Galileo skilfully caricatures his opponent as an obstinate enemy of science who relies on books and the words of authorities instead of using facts and reason and observation. People eat this up, this propaganda. Galileo is like a populist politician. He’s giving people a pleasing narrative that flatters and validates their worldview. Truth has little to do with anything.
That’s an overview of the story. Now let’s look at the details.
The science of comets. Like Grassi says, “the single role of the mathematician” is merely to “explain the position, motion, and magnitude of those fires,” that is to say the comets. So none of that superstition nonsense, just calculate the paths and distances and speeds and so on. Indeed, this is what mathematicians had been doing for generations. Tycho Brahe, for instance, worked extensively on comets in the generation before Galileo. He gave thorough mathematical analyses of their motions, as a mathematician should.
Now, of course, it would be difficult for Galileo to enter this game, since he was such a poor mathematician, as I have argued before. If Galileo had been honest he would have said: frankly, all those detailed calculations that Tycho Brahe and the other big-boy mathematicians are doing, that’s all too technical for me to follow.
But of course he doesn’t want to say that. He needs to save face. He needs an excuse for ignoring what all serious mathematical astronomers were saying about comets. Sure enough, he is quick to offer such excuses. First he claims that mathematical accounts of comets are hopelessly inconsistent. Here are his own words:
“Observations made by Tycho and many other reputable astronomers upon the comet’s parallax vary among themselves. If complete faith be placed in them, one must conclude that the comet was simultaneously below the sun and above it,” for example.
So the mathematical astronomy of comets is just a bunch of useless nonsense, you see. In fact Galileo has an even more fundamental argument for this. Namely that comets are not physical bodies travelling through space at all. Rather comets are nothing but a chimerical atmospheric phenomena. “In my opinion,” says Galileo, comets have “no other origin than that a part of the vapour-laden air surrounding the earth is for some reason unusually rarefied, and … is struck by the sun, and made to reflect its splendour.” A comet is like the northern lights. Galileo specifically makes this comparison.
So that’s Galileo’s very convenient excuse for why he doesn’t engage with the best mathematicians working on comets. This way he is able to pretend that: well, you see, it’s not that I can’t do these calculations, it’s just that I don’t want to, because they all just contradict themselves anyway, and it’s all nonsense in the first place because you can’t do mathematical astronomy of some vapour-cloud optical illusion thing. That’s a futile as chasing a rainbow.
That’s textbook Galileo. If you don’t believe my thesis that Galileo was a poor mathematician, the you tell me a better explanation for this. Why did Galileo propose such an idiotic theory of comets, that is dead wrong and obviously way worse than the common-sense standard opinion among all mathematical astronomers at the time? I gave you one explanation. I don’t think you can come up with a better one. Nobody has so far.
Galileo’s claim that the mathematical astronomy of comets was incoherent and self-contradictory did not convince anybody. Kepler was flabbergasted that someone who calls himself a geometer could write such drivel. Here are Kepler’s words:
“Galileo, if anyone, is a skilled contributor of geometrical demonstrations and he knows what a difference there is between the incredible observational diligence of Tycho and the indolence common to many others in this most difficult of all activities. Therefore, it is incredible that he would criticize as false the observations of all mathematicians in such a way that even those of Tycho would be included.”
Indeed. It is “incredible” that a “skilled geometer” could make such ludicrous claims. But of course the paradox disappears if one recognises that Galileo is not a skilled geometer after all.
Galileo also offered another very poorly considered argument against the correct view of comets as orbiting bodies. The orbits of comets are clearly much bigger than that of the planets in our solar system. Galileo tries to argue that this is unrealistic. Here is what he says: “How many times would the world have to be expanded to make enough room for an entire revolution [of a comet] when one four-hundredth part of its orbit takes up half of our universe?” This is a poor argument, because the universe must indeed be very big and then some according to Copernican theory. This is because of the absence of stellar parallax, as we have discussed before. Since the earth’s motion is observationally undetectable, the orbit of the earth must be minuscule in relation to the distance to the stars. That means there is plenty of room for comets. But Galileo conveniently pretends otherwise in his argument against comets. Evidently Galileo “was so intent on refusing Tycho[’s treatment of comets] that he failed to notice that he was pleading for a universe in which there would be no room for the heliocentric theory” either.
Galileo’s vapour theory of comets, meanwhile, is inconsistent with basic observations, as he himself admits. If comets are nothing but “rarefied vapour”---that is to say, some kind of pocket of thin gas---then you’d imagine that their natural motion would be straight up, like a helium balloon. Indeed Galileo does propose that comets have such paths. But then he at once admits that this doesn’t fit the facts: “I shall not pretend to ignore that if the material in which the comets takes form had only a straight motion perpendicular to the surface of the earth …, the comet should have seemed to be directed precisely toward the zenith, whereas, in fact, it did not appear so. … This compels us either to alter what was stated, … or else to retain what has been said, adding some other cause for this apparent deviation. I cannot do the one, nor should I like to do the other.” Bummer, it doesn’t work. But Galileo sees no way out, so he just leaves it at that.
Galileo’s contemporaries were not impressed. “[Grassi’s] criticism of Galileo is on the whole penetrating and to the point. He was quick to spot Galileo’s inconsistencies. Grassi produced an impressive array of arguments to show that vapours could not explain the appearance and the motion of the comets [as Galileo had claimed].” For instance, the speeds of comets do not fit Galileo’s theory. According to Galileo’s theory, the vapours causing the appearance of comets rise uniformly from the surface of the earth straight upwards. Therefore the comet should appear to be moving fast when it is close to the horizon, and then much slower when it is higher in the sky. Just imagine a red helium balloon released by a child at a carnival: it first it shoots off quickly, but soon you can barely tell if it’s rising anymore, even though it keep going up at more or less the same speed, because your distance and angle of sight is so different. But comets do not behave like that. Detailed observations of the comet of 1618 showed a much more constant speed than Galileo’s hypothesis requires.
Now let’s see how Galileo responded to this. Not by improving the scientific quality of his arguments, mind you. But with some clever rhetorical tricks that has many readers fooled to this day. Many find Galileo’s rousing mockery of his opponent so satisfying that they are seduced into celebrating it as proof of Galileo’s philosophical acumen. You can read Galileo’s triumphant put-downs of his opponent and go “yeah, crush him!” It’s the same kind of pleasure as watching the villain get punched in the face in an action movie. But a little reflection shows that this hero-versus-villain dynamic that Galileo tries to cultivate is a dishonest fiction that has very little to do with reality.
One of Galileo’s most celebrated passages concerns eggs. The context is this. Grassi makes the absolutely correct point that comets, if they entered the earth’s atmosphere, would quickly heat up to very great temperatures due to the friction of the air. In support of this point, Grassi quotes a 10th-century Byzantine author, Suidas, who claimed that “The Babylonians whirl[ed] about eggs placed in slings … [and] by that force they also cooked the raw eggs.” Grassi also quotes passages describing similar phenomena in Ovid, Lucan, Lucretius, Virgil, and Seneca. And then he says: “For who believes that men who were the flower of erudition and speak here of things which were in daily use in military affairs would wish egregiously and impudently to lie? I am not one to cast this stone at those learned men.”
Galileo is unable to answer the substantive point. Indeed, he thinks comets entering the atmosphere would cool down because of the wind rather than heat up because of friction. Galileo is wrong and Grassi is right about the actual scientific issue about comets. But that’s nothing Galileo’s trademarked sophistry can’t work around. Galileo finds a way to “win” the debate anyway, without actually offering any correct scientific claim regarding the actual subject of comets. He does this by gloatingly attacking Grassi for relying on books rather than experimental evidence:
“If [Grassi] wants me to believe that the Babylonians cooked their eggs by whirling them in slings, … I reason as follows: If we do not achieve an effect which others formerly achieved, then it must be that in our operations we lack something that produced their success. And if there is just one single thing we lack, then that alone can be the true cause. Now we do not lack eggs, nor slings, nor sturdy fellows to whirl them; yet our eggs do not cook, but merely cool down faster if they happen to be hot. And since nothing is lacking to us except being Babylonians, then being Babylonians is the cause of the hardening of eggs, and not friction of the air. … Is it possible that [Grassi] has never observed the coolness produced on his face by the continual change of air when he is riding post? If he has, then how can he prefer to believe things related by other men as having happened two thousand years ago in Babylon rather than present events which he himself experiences?”
Like I said, not a few modern philosophers blindly and uncritically fall for Galileo’s rhetoric. Here’s a typical quote on this. It’s from the Wiley-Blackwell book “Philosophy of Science: An Historical Anthology.” Here’s what the editors of this popular textbook say about Galileo’s argument: “Galileo shot back with a blistering critique in which he pillories [Grassi] and articulates a tough-minded empiricism as an alternative to the mere citation of venerable authority.”
Galileo would no doubt be very pleased that so many readers still to this day come away with the impression that “tough-minded empiricism” is what sets him apart from his opponents. That is precisely the intended effect of his ploy. It has very little basis in reality, however. Just a few pages earlier in the same treatise, Grassi describes extensively various laboratory experiments he has carried out himself with regard to another point. “I decided that no industry or labor ought to be spared in order to prove this by many and very careful experiments,” says this supposed obstinate enemy of empirical science. So the notion that Galileo is the only one “tough-minded” enough to reject authority in favour of experiment is very far off the mark.
Even in the passage criticised, Grassi is clearly not engaged in “the mere citation of venerable authority.” Rather he honestly and openly cites sources purporting to truthfully report empirical information, just like any scientist today cites previous works without re-checking all the experiments personally. Grassi does not believe that these authors are automatically right because they are “venerable authorities.” Rather he explicitly considers the possibility that they are wrong, but estimates, quite reasonably, that they are probably right.
For that matter, Galileo himself was not above believing falsehoods on the basis of “venerable authorities.” We have seen him make an error of this type in his theory of tides. He had heard somewhere that high and low tide in Lisbon occurred twelve hours apart rather than six, and jumped at the chance to cite this false information as “evidence” for his erroneous theory. To take another example, Galileo also believed the ancient myth of Archimedes setting fire to enemy ships by means of mirrors focussing the rays of the sun. This myth is “credible,” Galileo says. Descartes sensibly took the opposite view.
Altogether, the simplistic contrast between Grassi the credulous believer in authority and Galileo the experimenter has little basis in fact. Galileo is scoring easy points with his taunts about the eggs, by dishonestly pretending that a simplistic point about empiricism was the crux of the matter.
It is worth keeping the context of the passage in mind. Indeed, the pro-Galileo interpretation I quoted above from the Wiley-Blackwell textbook comes with its own origin story:
“In the course of his career [Galileo] engaged in many controversies and made powerful enemies. One of those enemies was the Jesuit Grassi, who published an attack on some of Galileo’s works.”
This framing goes well with the notion of the “tough” Galileo bravely defending himself against “attacks” from the “powerful” establishment. But the reality is quite different. Grassi was not a “powerful enemy”: he was a middling college professor just like Galileo. And the conflict did not start with Grassi “attacking” Galileo, but precisely the other way around. Grassi published a fine lecture on comets in which he argued, correctly, that the absence of parallax shows that comets are beyond the moon. Galileo is not mentioned in this work. Galileo read Grassi’s lecture and filled the margins, as one scholar has observed, with an entire vocabulary’s worth of savage expletives. Buffoon, bumbling idiot, piece of utter stupidity, and so on.
Galileo then published an attack on Grassi which was not much more restrained than these marginal notes. Grassi replied to it. It is this reply that is called “an attack on some of Galileo’s works” in the pro-Galilean quotation above.
So, to sum up, Galileo’s celebrated “pillorying” of Grassi was not a “tough” defence against an “attack” on “some of his works” by “powerful enemies.” The “enemy” was not a “powerful” arm of “authority,” but a conscientious scholar who was right about comets based on good scientific arguments that Galileo rejected. And the enemy was not a cruel aggressor going after “some works” by Galileo unprovoked; rather, the “some works” in question was an aggressive attack initiated by Galileo in the first place. Furthermore, Galileo’s enemy did not favour venerable authority over empiricism, but rather based his analysis of comets on much more thorough empirical work than Galileo did.
Ok, that’s what I had to say about comets.
Let me tell you another story: Double stars. The telescope revealed the existence of “double stars,” meaning stars that had appeared as just a single point of light to the naked eye but then when you looked at them with good magnification in a telescope they turned out to consist of two separate stars.
Double stars had the potential to prove Copernicus right. This was pointed out to Galileo by his friend Castelli. Castelli was excited about double stars, because he hoped they could be used to prove that the earth moves around the sun because of how the double star would change appearance in the course of a year.
The idea is the following. You look at the double star in your telescope. You see that it is not one star but two: one bigger and one smaller. Now you make the assumption that probably all stars are pretty much the same. They are all just so many suns, as it were. So the smaller-looking one is probably about the same size, in reality. It’s just further away.
Now let’s see what happens when the earth moves. Let’s try to picture this. You can use your index fingers. Hold up one finger in front of you. Now put your other index finger further away from you but aligned with the first one in a single line of sight. Now if you move your head slightly to one side, you will see the two fingers “move apart,” so to speak. And if you move your head to the other side, they will move apart in the other direction. So the closer finger, which corresponds to the bigger star, is sometimes to the left and sometimes to the right of the other one. Moving your head means moving the earth. If the earth is truly moving like Copernicus said then we should be able to observe this kind of thing: stars “switching places” in this way. This would certainly not happen if the earth was stationary, so we have striking and undeniable evidence for the motion of the earth.
This is a parallax effect. We spoke about parallax before. Astronomers had failed to detect parallax in the past, even though Copernican theory predicts that parallax must be a thing. The traditional method to look for parallax was based on trying to detect subtle shifts in the relative position of stars using tricky precision measurements of angles. The double star case would prove the matter in a much more striking and immediate way, without the need for technical measurements: anyone would be able to see with their own eyes the undeniable fact the the two stars switched places in the course of a year. And since with this method everything takes place within the field of view of the telescope, there was reason to hope that this new technology could enable success where conventional naked-eye astronomy had failed.
Castelli urged Galileo to make observations of double stars for this purpose, as indeed Galileo did in 1617, when he made detailed observations of the double star Mizar. Galileo used the above principle that however many times smaller a star is, it is that many times further away. With this method Galileo estimated that Mizar A and B were 300 and 450 times further away than the sun, respectively. This means the above effect should easily be noticeable: “Mizar A and Mizar B should have swung around each other dramatically as Galileo observed them over time.” But that didn’t happen. They didn’t change position at all. Everything remained exactly stationary, as if the earth did not move.
Today we know that all the stars in the night sky are much further away than Galileo estimated, and much too far away for any effects of this sort to be detectable with the telescopes of Galileo’s time. Galileo’s distance estimates were way off because of certain optical effects that make it impossible to judge the distances of stars in the manner outlined above. It would be anachronistic to blame Galileo for not knowing these things, which were only understood much later.
But Galileo’s way of discussing the matter in the Dialogue is not above reproach. He describes the above procedure but frames it hypothetically: “if some tiny star were found by the telescope quite close to some of the larger ones,” they would, if the above effect could be observed, “appear in court to give witness to such motion … of the earth.” “This is the very idea that later won Galileo renown and for which he was to be remembered by parallax hunters in the centuries that followed. While it is generally thought that Galileo never tried to detect stellar parallax himself, he is credited with this legacy to future generations.” In reality he deserves no renown, because the idea was not his own. It had already been explained to him in detail not only by Castelli, who discovered the double star Mizar and explained its importance for parallax to Galileo, but also even earlier by Ramponi in 1611. There is no indication that Galileo had though of any of this before his friends explained it to him.
Furthermore, Galileo’s discussion in the Dialogue is deceitful. He didn’t want to state the truth, of course, which is that he tried the experiment and it came out the wrong way; the data said that the earth did not move. But that’s only important if you are an honest scientist concerned with objectively evaluating the evidence. Galileo instead finds it more convenient to pretend that this falsifying data doesn’t exists. Instead he presents the double star idea as a suggestion for further research, and pretends that he hasn’t already carried it out. That way he doesn’t have to explain actual data or engage seriously with actual current astronomy like the system of Tycho for instance which agreed better with this data. It was much easier for Galileo to suppress his data and disingenuously insinuate that the outcome of the observation would be the opposite of what he knew it to be.
Now I will turn to another topic. The rings of Saturn. We all know that iconic cartoon-planet look. But that image only became clear some twenty years after Galileo’s death. Christiaan Huygens published a book on Saturn in 1659 where the rings are depicted with perfect clarity just as we are used to seeing it.
But the telescopes of Galileo’s day were not good enough to show the rings of Saturn with any clarity. Instead Galileo thinks the rings are actually two moons. Saturn is “made of three stars,” says Galileo. The planet has two “ears,” as it were. We can’t blame Galileo for limitations that were inherent to his time. It was no fault of his that he didn’t discern the rings of Saturn. Neither did any of his contemporaries.
However, we can blame Galileo for his lack of balance in evaluating the evidence. He does not say, as an honest scientist might, that his theory about Saturn’s “companion stars” is the best guess on the available evidence and that we can’t know for sure until we have better telescopes. Instead he boldly proclaims it as certainty that Saturn is “accompanied by two stars on its sides,” “as perfect instruments reveal to perfect eyes.” Those are Galileo’s words. And they are of course very hubristic. But that’s Galileo for you, always overstating his case, not least when he is wrong.
In the same vein, Galileo overconfidently declared that the appearance of Saturn’s companions would never change:
“I, who have examined [Saturn] a thousand times at different times, with an excellent instrument, can assure you that no change at all is perceived in him: and the same reason … can render us certain that, likewise, there will be none.”
Bombastic certainty as usual. All the more embarrassing then when in fact the appearances did change radically soon thereafter. Here’s Galileo again, just a few months later:
“I found [Saturn] solitary without the assistance of the supporting stars. … Now what is to be said about such a strange metamorphosis? Perhaps the two smaller stars … have vanished and fled suddenly? Perhaps Saturn has devoured his own children?”
This is a reference to classical mythology. Saturn the god “devoured his newborn children to forestall a prophecy that he would be overthrown by one of his sons.”
In any case, one moment Galileo says that “thousands” of observations prove that Saturn’s companion stars will never change, and then just months later he has to admit that, whoops, it turns out that that exact thing he said would never happen actually took place almost right away. That was some bad publicity, especially at a time when many doubted the reliability of his telescope.
The so-called disappearance of Saturn’s ring was due to the earth passing through the plane of the ring, so that a line of sight from earth was parallel to the plane of the ring. This made the ring invisible, just like a sheet of paper becomes vanishingly thin if you look at it exactly sideways.
But Galileo did not interpret it that way. Instead, he proposed what he considered to be some “probable conjectures” about the future appearance of Saturn’s companion stars. This theory was based on attributing to them a slow revolution, like very slow-moving moons. Later he praised himself for “thinking in my own special way” and marvelled at how “I took the courage” to make such brave conjectures. Those are Galileo’s own words, praising himself.
Indeed, Galileo liked his model so much that he also “took the courage” to lie about having made an observation verifying it. He claims that he “saw Saturn triple-bodied this year , at about the time of the summer solstice.” But modern calculations show that the ring of Saturn would have been vanishingly thin at this time. There was a paper on this in the Journal for History of Astronomy not long ago. Here is the conclusion from the paper: “Clearly [Galileo] could not have observed the ring at the summer solstice of 1612. … Yet the picture of the Saturnian system that was accepted by Galileo implied that the ring should have been visible, so much so that he made a claim to this effect that we know must have been untrue.” Oh well. That’s business as usual in Galileo land.
This concludes our discussion of Galileo’s work with the telescope. Next time I believe we shall have to get to the real hot potato: Galileo and the church.