The telescope offered a shortcut to stardom for Galileo. We offer some fun cynical twists on the standard story.
Opinionated History of Mathematics
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The year is 1609. What a time to be alive. In London you can go to the theatre and catch the fresh new play Macbeth. In Amsterdam you can make a quick buck trading in stocks—a brand new invention. Science is on fire as well. Kepler’s Astronomia Nova is published this very year—an exquisite masterpiece demonstrating that planets move in elliptical orbits among other things. Quite clearly the single greatest scientific work since the time of Archimedes.
So many exciting things happening. How will you keep up with this whirlwind of innovations and fascinating developments? Perhaps with the aid of another newfangled invention: the newspaper. The first of which comes out right this year, promising in its title to cover for its German readers all “gedenckwürdigen Historien”—thoughtworthy events. Truly it is a time of the new. The winds of change are blowing throughout Europe. Thoughtworthy events are everywhere you look.
What about our friend Galileo? What is he up to at this time? You won’t find him in any of those chronicles of thoughtworthy events. Galileo is already well into his middle age. He is a frail man of 45, not infrequently bedridden with rheumatic or arthritic pains. He is stuck teaching basic geometry for a pittance of a salary in some backwater town. Had Galileo died from his many ailments in this year, 1609, he would have been all but forgotten today. He would have been an insignificant footnote in the history of science, no more memorable than a hundred of his contemporaries. It has often been said that mathematics is a young man’s game. Newton had his annus mirabilis in his early twenties—”the prime of my age for invention,” as he later said. Kepler was the same age when he finished his first masterpiece, the Mysterium Cosmographicum of 1596. Galileo was already nearly twice this age, and he had nothing to show for it but some confused piles of notes of highly dubious value. In short, as a mathematician the ageing Galileo had proved little except his own mediocrity.
It is this middle-aged, run-of-the-mill nobody that first hears of a new invention: the telescope. Now here was his chance at last. He only had to point this contraption to the skies and record what he saw. No need anymore for mathematical talent or painstaking scientific investigations. For twenty years Galileo had tried and failed to gain scientific fame the hard way, but now a bounty of it lay ripe for the plunder. All you needed was eyes and being first.
The mysterious new “optical tube for seeing things close,” as it was called, was the talk of the town at the time. Galileo first hears about it in July 1609. A week or two later a traveller offered one for sale in Padua and Venice at an outrageous price—about twice Galileo’s yearly salary. This enterprising salesman found no takers for his offer. But the sense of opportunity remained in the air. And it was an opportunity tailor-made for Galileo: finally a path to scientific fame that required only handiwork and none of that tiresome thinking in which he was so deficient.
The design of telescopes was still a trade secret among the Dutch spectacle-makers who had stumbled upon the discovery. But acting fast was of the essence. Making a basic telescope is not rocket science. Soon many people figured out how to make their own. “It took no special talent or unique inventiveness to come up with the idea that combining two different lenses … would create a device allowing people to see faraway objects enlarged.” Reading glasses and magnifying glasses were already in common use: they obviously made text and other things appear bigger. They were used for thread count in the cloth business for example. So it was not a far-fetched idea to lenses them to magnify more distant objects as well. And the external shape of the telescopes people reported seeing suggested that at least two lenses were combined in a long cylinder. It didn’t take a genius, therefore, to soon strike upon the simple recipe Galileo found: take one convex and one concave lens and stick them in a tube, and look through the concave end. That’s it. No theoretical knowledge of optics played any part in this; it was purely a matter of hands-on craftsmanship and trial-and-error. As Galileo himself basically admitted.
About a month after first hearing of the telescope, Galileo has managed to build his own, with 8 times magnification. A bit later, maybe 12 times magnification, eventually 16 or so. If you go to a modern toy store or sports good store and but whatever cheapest binoculars they have, that will have the same magnification as a Galilean telescope basically. So if you have an old pair of field binoculars lying around, you basically have a Galilean telescope. So dust it off, why don’t you, and follow along with your own observations as we describe what Galileo found.
In any case, Galileo’s first goal is to leverage the telescope into a more lucrative appointment for himself. He gives demonstrations to various important dignitaries—”to the infinite amazement of all,” according to himself. So on the basis of this Galileo enters multiple negotiations about improved career prospects. Between hands-on optical trials and lens grinding, these showmanship demonstrations, shrewd self-marketing and hyperbole about how “infinitely amazed” everyone is by him, Galileo must have had a busy couple of months indeed. And on top of this marketing campaign and juggling potential job offers, his regular teaching duties were just starting again in the fall.
So we can easily understand why, in these hectic days, the scientific importance of the new instrument for astronomy was not realised right away. At first neither Galileo nor anyone else thought of the telescope as primarily an astronomical instrument. Galileo instead tried to market it as “a thing of inestimable value in all business and every undertaking at sea or on land,” such as spotting a ship early on the horizon. But the moon does make an obvious object of observation, especially at night when there is little else to look at. Perhaps indeed moon observations were part of Galileo’s sales pitch routine more or less from the outset, though as a gimmick rather than science.
But this was soon to change. In the dark of winter, the black night sky is less bashful with its secrets than in summer. It monopolises the visible world from dinner to breakfast; it seems so eager to be seen that it would be rude not to look. In January, Galileo takes up the invitation and spots moons around Jupiter. Yikes! Other planets have moons?! This changes everything. Suddenly it is clear that the telescope is the key to a revolution in astronomy. Eternal scientific fame is there for the taking for whoever is the first to plant his flag on the shores of this terra incognita.
For the next two months Galileo goes on a frenzied race against the clock. He writes during the day and raids of the heavens for one precious secret after another at night. In early March he has cobbled together enough to claim the main pearls of the heavens for himself. He rushes his little booklet into print with the greatest haste: the last observation entry is dated March 2, and only ten days later the book is coming off the presses. Remarkable. It’s a turnaround time modern academic publishers can only dream of, even though they do not have to work with hand-set metal type and copper engravings for the illustrations.
It was a race against the clock and Galileo won. “I thank God from the bottom of my heart that he has pleased to make me the sole initial observer of so many astounding things, concealed for all the ages.” So wrote Galileo, and his palpable relief is fully justified. Little more than dumb luck—or, as he would have it, the grace of God—separated Galileo from numerous other telescopic pioneers who also produced telescopes and made the same discoveries independently of Galileo. For example, Simon Marius in Germany who discovered the moons of Jupiter one single day later than Galileo. As one historian observes, “a delay of only three or four months would have set [Galileo] behind several of his rivals and undercut his claim to priority regarding several key discoveries with the telescope.” Perhaps it was not the grace of God, but Galileo’s desperation, born of decades of impotence as a mathematician, that drove him to publish first. Being incapable of making any contribution to the mathematical side of science and astronomy, Galileo needed and craved this shortcut to stardom more than anyone else.
Accordingly, Galileo greedily sought to milk every last drop of fame he could from the telescope. “I do not wish to show the proper method of making them to anyone”; rather “I hope to win some fame.” Those are Galileo’s own words. His competitors quickly realised that, as one contemporary says, “we must resign ourselves to obtaining the invention without [Galileo’s] help.” Still six years after his booklet of discoveries, people who thought science should be a shared and egalitarian enterprise were rightly upset by Galileo’s selfish quest for personal glory. One writes as follow to Galileo: “How long will you keep us on the tenterhooks? You promised in your Sidereal Message to let us know how to make a telescope so that we could see all the things that are invisible to the naked eye, and you haven’t done it to the present day.”
Meanwhile Galileo never missed a chance to mock stuffy Aristotelian professors for thinking “that truth is to be discovered, not in the world or in nature, but by comparing texts”, Galileo wrote in scorn, adding that “I use their own words.” His opponents themselves had stated that “comparing texts” was their methodology. But if Galileo genuinely wanted them to turn to nature he could have shared his techniques for telescope construction. In truth it served his own interests very well that these people were left with no choice but “comparing texts” while he claimed the novelties of the heavens for himself.
Let’s look at Galileo’s professional situation in a bit more detail. You may have heard that Galileo was a “Professor of Mathematics.” Indeed he was, for twenty years. But we must not let the title fool us. The position had nothing to do with the research frontier in the field. In modern terms Galileo’s position was more comparable to that of high school teacher. Galileo taught very basic and practical courses. His lectures were unoriginal and usually cribbed from standard sources. His mathematical lectures went no further than elementary Euclidean geometry. He also had to teach a basic astronomy course “mainly for medical students, who had to be able to cast horoscopes.” They “needed it to determine when [and when] not to bleed a patient” and the like. Perhaps Galileo didn’t mind, for he seems to have been quite open to astrology judging by the fact that he cast horoscopes for his own family members and friends without renumeration. Alas, he did not enjoy much success as an astrologer. Here’s a quote from The Cambridge Companion to Galileo: “In 1609, Galileo … cast a horoscope for the Grand Duke Ferdinand I, foretelling a long and happy life. The Duke died a few months later.” That’s great, isn’t it? Such a nice bit of deadpan there by The Cambridge Companion.
Galileo was eager to get out of his lowly university post. Now with the telescope he was in a decent negotiating position. After much scheming he resigned from the university and took up a court appointment. You would rather work for some rich guy, a patron, than at a university. That was how it went at the time. Some decades later Leibniz for example did the same thing. He could easily have taken a university job but who wants to be an academic when you can be the resident scholar in the gilded halls of some prince?
So Galileo got his wish. His new appointment freed him from teaching duties and boosted his finances. But Galileo also had an additional demand. Here is what he says:
“I desire that in addition to the title of mathematician His Highness will annex that of philosopher; for I may claim to have studied more years in philosophy than months in pure mathematics.”
This is traditionally taken as a request for a kind of promotion: in addition to being a great mathematician, Galileo also wanted recognition in philosophy, which in some circles was considered more prestigious and in any case included what today is called science (then “natural philosophy”). But I think a more literal reading of Galileo’s request is in order. Galileo is not only declaring himself a philosopher; he is also confessing his ignorance in mathematics. Taken literally, his statement that he has spent “more years in philosophy than months in mathematics” implies that he could not have spent more than two or three years at most on mathematics—which indeed sounds about right considering his documented mediocrity in this field.
Anyway, back to the telescope. So Galileo had some success with it clearly, but not everyone was convinced.
Some believed “the telescope carries spectres to the eyes and deludes the mind with various images … bewitched and deformed.” Perhaps these peculiar “Dutch glasses” were but a cousin of the gypsy soothsayer’s crystal ball? The “transmigration into heaven, even whil’st we remain here upon earth in the flesh,” as Robert Hooke put it, may indeed seem like so much black magic. Add to this the very numerous imperfections of early telescopes, which often made it very difficult even for sympathetic friends to confirm observations, not to mention gave ample ammunition to outright sceptics.
Indeed, we find Galileo on the defensive right from the outset, just a few pages into his first booklet. Seen through the telescope, the moon appeared to have enormous mountains and craters—a big deal, allegedly one of “Galileo’s” monumental discoveries. This was based on shadow effects. Looking at the moon when it’s half full, you see that the surface is uneven because of the shadows cast by mountains and craters. But already there are big problems. The boundary of the moon was still perfectly smooth. A crazy inconsistency. How can there be big mountains in the middle of the moon, but none along the edge? It doesn’t make any sense, yet that’s what it looked like.
Here are Galileo’s own words in the Sidereus Nuncius of 1610, his famous booklet and first claim to fame. “I am told that many have serious reservations on this point”: for if the surface of the moon is “full of … countless bumps and depressions,” then “why is the whole periphery of the full Moon not seen to be uneven, rough and sinuous?” Galileo replies that this is because the Moon has an atmosphere, which “stop[s] our sight from penetrating to the actual body of the Moon” at the edge only, since there “our visual rays cut it obliquely.” So when we look at the edge of the moon our line of sight spends more time passing through the atmosphere of the moon and that’s why it’s blurred. Hence it is “obvious,” says Galileo, that “not only the Earth but the Moon also is surrounded by a vaporous sphere.” This is of course completely wrong.
So already we see that there were serious problems with the telescope. It’s not as simple as saying: the telescope showed everyone new facts. What was a fact and what was an inference or an illusion? Not a trivial question, and as we see Galileo himself got it wrong right off the bat.
And there’s plenty more where that came from. Another puzzling fact was that the planets were magnified by the telescope, but not the stars. The stars remained the same point-sized light spots no matter what the strength the telescope. Some even mistook this for a “law that the enlargement appears less and less the farther away [the observed objects] are removed from the eye.” Galileo tried to explain these things, but once again he gets it completely wrong. A correct explanation was given in 1665, it’s a technical optics thing.
Clearly, then, in light of all these challenges to the reliability and consistency of the telescope, it was important to understand its basis in theoretical optics. That is why, presumably, Galileo felt obliged to swear at the outset, in the Sidereus Nuncius, that “on some other occasion we shall explain the entire theory of this instrument.” To those aware of his mathematical shortcomings, it will come as no surprise that Galileo never delivered on this promise. Kepler—a competent mathematician—took up the task instead, and in the process came up with a fundamentally new telescope design better than that of Galileo. That’s in Kepler’s Dioptrice of 1611. Kepler’s telescope uses two convex lenses instead of Galileo’s pair of one convex and one concave lens. According to Galileo, Kepler’s work was, in his own words, “so obscure that it would seem that the author did not understand it himself.” A modern scholar comments that “this is a curious statement since the Dioptrice, unlike other works by Kepler, is remarkably straightforward.” Apparently still not straightforward enough for a simpleton like Galileo, however. Indeed, Galileo’s naive conception of optics was still mired in the old notion that seeing involved rays of sight spreading outward from the eye rather than conversely. He repeatedly gave statements to this effect.
Regarding the mountains on the moon, let’s look a bit more at the significance of that, which has often been overstated. So Galileo’s famous discovery is, as he puts it, that “The moon is not robed in a smooth and polished surface but is in fact rough and uneven, covered everywhere, just like the earth’s surface, with huge prominences, deep valleys, and chasms.” Now, it is all too easy to cast this report by Galileo as a revolutionary discovery. The “Aristotelian” worldview rested on a sharp division between the sublunar and heavenly realm. Our pedestrian world is one of constant change—a bustling soup of the four elements (earth, water, air, fire) mixing and matching in fleeting configurations. The heavens, by contrast, were a pristine realm of perfection and immutability, governed by its very own fifth element entirely different from the physical stuff of our everyday world. If we are predisposed to view Galileo as the father of modern science, a pleasing narrative readily suggests itself: With his revolutionary discovery of mountains on the moon, Galileo disproved what “everybody” believed. Indeed this is a standard story peddled by many scholars. Let me quote two of them.
“Every educated person in the sixteenth century took as well-established fact … that the Moon was a very different sort of place from the Earth. … The lunar surface, according to the common wisdom, was supposed to be as smooth as the shaven head of a monk.”
Here’s another quote to the same effect. This one is from a Harvard University Press book from 2015, “Galileo’s Telescope”, so this stuff is mainsteam modern scholarship. Here is the quote:
“In those years virtually no one questioned the ontological difference between heaven and earth. … The difference between Earth and the heavenly bodies was an absolute truth for astrologers and astronomers, theologians and philosophers of every ilk and school. … If the Moon turned out to be covered with mountains, just like Earth, a millenary representation of the sky would be shattered.”
So in other words, Galileo sent an entire worldview crashing down by using data and hard facts to expose its prejudices.
The problem with this narrative lies in one word: “everybody.” The Aristotelian worldview is not what “everybody” believed. It is what one particular sect of philosophers believed. As ever, Galileo’s claim to fame rests on conflating the two. If we compare Galileo to this sect of fools—as Galileo wants us to do—then indeed he comes out looking pretty good. Members of this sect did indeed try to deny the mountainous character of the moon in back-pedalling desperation. For instance by arbitrarily postulating that the mountains were not on the surface of the moon at all but rather enclosed in a perfectly round, clear crystal ball. So that way the surface was smooth after all, even though there were shadows and stuff, because the shadows were in the interior of this glass sphere. If we mistake this kind of rubbish for the state of science of the day, then indeed Galileo will appear a great revolutionary hero.
But to anyone outside of that particular sect blinded by dogma, the idea of a mountainous moon had been perfectly natural for thousands of years. It is obvious to anyone who has ever looked at the moon that its surface is far from uniform. Clearly it has dark spots and light spots. If one wanted to maintain the Aristotelian theory one could try to argue, as many people indeed did, that this is perhaps some kind of marbling effect. The moon is still perfectly spherical, only it has some differential colouration like a smooth piece of marble. Or maybe it’s a reflection thing: perhaps the moon is so polished that it is reflective like a mirror. So the light and dark areas are not actual irregularities in the moon itself but just the mirror image of oceans and stuff on earth.
Whatever one thinks of the plausibility of such arguments, they are certainly defensive in nature: the Aristotelian theory is on the back foot trying to explain away even the most rudimentary phenomena that any child is familiar with. The idea of an irregular moon is an obvious and natural alternative explanation. Which is why we find for instance in Plutarch, a millennium and a half before Galileo, the suggestion that “the Moon is very uneven and rugged.” That’s a literal quote, from antiquity.
If we look to actual scientists and mathematically competent people instead of Aristotelian fools, we find that “Galileo’s” discovery of mountains on the moon was already accepted as fact long before. Kepler had already, and I quote him, “deduced that the body of the moon is dense … and with a rough surface,” or in other words the moon is “the kind of body that the earth is, uneven and mountainous.” Those are quotes from a 1604 work by Kepler. Before the telescope.
Kepler also points out that this was also the opinion of his teacher Maestlin before him, who, according to Kepler, “proves by many inferences … that [the moon] also got many of the features of the terrestrial globe, such as continents, seas, mountains, and air, or what somehow corresponds to them.” That’s from the Mysterium Cosmographicum, 1596, long before the telescope.
In a later edition of this work, Kepler added the note that “Galileo has at last throughly confirmed this belief with the Belgian telescope,” thereby vindicating “the consensus of many philosophers on this point throughout the ages, who have dared to be wise above the common herd.” Indeed, Galileo himself says his observations are reason to “revive the old Pythagorean opinion that the moon is like another earth.”
So, altogether, Galileo’s discovery of mountains on the moon was not a revolutionary refutation of what “everybody” thought they knew, but rather a vindication of what everyone with half a brain had seen for thousands of years.
The same goes for other supposed discoveries by Galileo relating to the moon. For instance the discovery of the phenomenon of “Earth shine”: like moon shine, but in the reverse direction. So reflected light from the earth lights up the moon to some extent. Galileo discusses this as one of the novelties made clear by the telescope, but in reality it had been correctly explained previously, by Kepler in 1604.
A similar reality check is in order regarding the idea one sometimes hear that Galileo’s discoveries regarding the moon instigated celestial physics. These people say: By revealing the similarity of heaven and earth, Galileo opened the door to a unification of terrestrial and celestial physics—in other words, he led us to the brink of Newton’s insight that a moon and an apple are governed by the very same gravitational force. In reality, though, a unity between terrestrial and celestial physics had been advocated since antiquity, as we have seen. You don’t need a telescope to realise that this idea makes sense.
Meanwhile, Galileo’s bumbling and superficial attempts to do celestial physics are an embarrassment to all, as we have seen. Remember his erroneous thing about planetary speeds being determined by falling from some faraway point toward the sun, or his completely wrongheaded calculation of how long it would take the moon to fall to the earth.
In fact, Kepler had already written an excellent book on celestial physics before the telescope: the Astronomia Nova of 1609. This is the work where Kepler explains the elliptical orbits of the planets (which Galileo never accepted or even mentioned). Kepler explains the elliptical orbits of the planets as the result of a quasi-magnetic force residing in the sun. So that’s certainly celestial physics in full swing before the telescope.
Ok, so that’s what I had to say about the telescope itself. Next we must turn to the impact of telescopic evidence on the debate between geocentrism and heliocentrism. That’s next time. Thank you.