by Mario Livio
While some of these discoveries were not entirely new, the strength of Galileo’s evidence raised the argument to a whole new level. Until Galileo’s time, there was a clear distinction between the terrestrial and the celestial, the earthly and the heavenly. The difference was not just scientific or philosophical. A rich tapestry of mythology, religion, romantic poetry, and aesthetic sensibility had been woven around the perceived dissimilarity between heaven and Earth. Now Galileo was saying something that was considered quite inconceivable. Contrary to the Aristotelian doctrine, Galileo put the Earth and a heavenly body (the Moon) on very similar footing—both had solid, rugged surfaces, and both reflected light from the Sun.
Moving yet farther from the Moon, Galileo started to observe the planets—the name coined by the Greeks for those “wanderers” in the night sky. Directing his telescope to Jupiter on January 7, 1610, he was astonished to discover three new stars in a straight line crossing the planet, two to its east and one to the west. The new stars appeared to change their positions relative to Jupiter on the following nights. On January 13, he observed a fourth such star. Within about a week from the initial discovery, Galileo reached a startling conclusion—the new stars were actually satellites orbiting Jupiter, just as the Moon was orbiting the Earth.
One of the distinguishing characteristics of the individuals who had a significant impact on the history of science was their ability to grasp immediately which discoveries were truly likely to make a difference. Another trait of many influential scientists was their skill in making the discoveries intelligible to others. Galileo was a master in both of these departments. Concerned that someone else might also discover the Jovian satellites, Galileo rushed to publish his results, and by the spring of 1610 his treatise Sidereus Nuncius (The Sidereal Messenger) appeared in Venice. Still politically astute at that point in his life, Galileo dedicated the book to the grand duke of Tuscany, Cosimo II de Medici, and he named the satellites the “Medicean Stars.” Two years later, following what he referred to as an “Atlantic labor,” Galileo was able to determine the orbital periods—the time it took each of the four satellites to revolve around Jupiter—to within an accuracy of a few minutes. The Sidereal Messenger became an instant best seller—its original five hundred copies quickly sold out—making Galileo famous across the continent.
The importance of the discovery of the Jovian satellites cannot be overemphasized. Not only were these the first bodies to be added to the solar system since the observations of the ancient Greeks, but the mere existence of these satellites removed in a single stroke one of the most serious objections to Copernicanism. The Aristotelians argued that it was impossible for the Earth to orbit the Sun, since the Earth itself had the Moon orbiting it. How could the universe have two separate centers of rotation, the Sun and the Earth? Galileo’s discovery unambiguously demonstrated that a planet could have satellites orbiting it while the planet itself was following its own course around the Sun.
Another important discovery that Galileo made in 1610 was that of the phases of the planet Venus. In the geocentric doctrine, Venus was assumed to move in a small circle (an epicycle) superimposed on its orbit around the Earth. The center of the epicycle was supposed to always lie on the line joining the Earth and the Sun (as in figure 17a; not drawn to scale). In this case, when observed from Earth, one would expect Venus always to appear as a crescent of somewhat varying width. In the Copernican system, on the other hand, Venus’s appearance should change from a small bright disk when the planet is on the other side of the Sun (as seen from Earth), to a large and almost dark disk when Venus is on the same side as Earth (figure 17b). Between those two positions Venus should pass through an entire sequence of phases similar to that of the Moon. Galileo corresponded about this important difference between the predictions of the two doctrines with his former student Benedetto Castelli (1578–1643), and he conducted the crucial observations between October and December of 1610. The verdict was clear. The observations confirmed conclusively the Copernican prediction, proving that Venus indeed orbits the Sun. On December 11, a playful Galileo sent Kepler the obscure anagram “Haec immatura a me iam frustra leguntur oy” (“This was already tried by me in vain too early”). Kepler tried unsuccessfully to decipher the hidden message and eventually gave up. In his following letter, of January 1, 1611, Galileo finally transposed the letters in the anagram to read: “Cynthiae figuras aemulatur mater amorum” (“The mother of love [Venus] emulates the figures of Cynthia [the Moon]”).
Figure 17
All the findings I have described so far concerned either planets in the solar system—celestial bodies that orbit the Sun and reflect its light—or satellites revolving around these planets. Galileo also made two very significant discoveries related to stars—heavenly objects that generate their own light, such as the Sun. First, he performed observations of the Sun itself. In the Aristotelian worldview, the Sun was supposed to symbolize otherworldly perfection and immutability. Imagine the shock caused by the realization that the solar surface is far from perfect. It contains blemishes and dark spots that appear and disappear as the Sun rotates about its axis. Figure 18 shows Galileo’s hand-drawn images of sunspots, about which Galileo’s colleague Federico Cesi (1585–1630) wrote that they “delight both by the wonder of the spectacle and the accuracy of expression.” Actually, Galileo was neither the first to see sunspots nor even the first to write about them. One pamphlet in particular, Three Letters on Sunspots, written by the Jesuit priest and scientist Christopher Scheiner (1573–1650) annoyed Galileo so much that he felt compelled to publish an articulate reply. Scheiner argued that it was impossible for the spots to be right on the Sun’s surface. His claim was based partly on the spots being, in his opinion, too dark (he thought that they were darker than the dark parts of the Moon), and partly on the fact that they did not always appear to return to the same positions. Scheiner consequently believed that these were small planets orbiting the Sun. In his History and Demonstrations Concerning Sunspots, Galileo systematically destroyed Scheiner’s arguments one by one. With a meticulousness, wit, and sarcasm that would have made Oscar Wilde jump to a standing ovation, Galileo showed that the spots were in fact not dark at all, only dark relative to the bright solar surface. In addition, Galileo’s work left no doubt that the spots were right on the Sun’s surface (I shall return to Galileo’s demonstration of this fact later in this chapter).
Figure 18
Galileo’s observations of other stars were truly the first human ventures into the cosmos that lies beyond our solar system. Unlike his experience with the Moon and the planets, Galileo discovered that his telescope hardly enlarged the images of stars at all. The implication was clear—stars were far more distant than planets. This was a surprise in itself, but what was truly eyepopping was the sheer number of new, faint stars that the telescope had revealed. In one small area around the constellation Orion alone, Galileo discovered no fewer than five hundred new stars. When Galileo turned his telescope to traverse the Milky Way—that patch of dim light that crosses the night sky—he was in for the biggest surprise yet. Even the smooth-looking bright splash broke into a countless number of stars no human had ever seen as such before. The universe suddenly got much bigger. In the somewhat dispassionate language of a scientist, Galileo reported:
What was observed by us in the third place is the nature of matter of the Milky Way itself, which, with the aid of the spyglass, may be observed so well that all the disputes that for so many generations have vexed philosophers are destroyed by visible certainty, and we are liberated from worldly arguments. For the Galaxy is nothing else than a congeries of innumerable stars distributed in clusters. To whatever region of it you direct your spyglass, an immense number of stars immediately offer themselves to view. Of which very many appear rather large and very conspicuous but the multitude of small ones is truly unfathomable.
Some of Galileo’s contemporaries reacted enthusiastically. His discoveries ignited the imaginati
on of scientists and non-scientists alike all over Europe. The Scottish poet Thomas Seggett raved:
Columbus gave man lands to conquer by bloodshed,
Galileo new worlds harmful to none.
Which is better?
Sir Henry Wotton, an English diplomat in Venice, managed to get hold of a copy of the Sidereus Nuncius the day that the book appeared. He immediately forwarded it to King James I of England, accompanied by a letter that read in part:
I send herewith unto his Majesty the strangest piece of news (as I may justly call it) that he hath ever yet received from my part of the world; which is the annexed book (come abroad this very day) of the Mathematical Professor of Padua, who by the help of an optical instrument…hath discovered four new planets rolling about the sphere of Jupiter, besides many other unknown fixed stars.
Entire volumes can be written (and indeed have been written) about all of Galileo’s achievements, but these lie beyond the scope of the present book. Here I only want to examine the effect that some of these astounding revelations had on Galileo’s views of the universe. In particular, what relation, if any, did he perceive between mathematics and the vast, unfolding cosmos?
The Grand Book of Nature
The philosopher of science Alexandre Koyré (1892–1964) remarked once that Galileo’s revolution in scientific thinking can be distilled to one essential element: the discovery that mathematics is the grammar of science. While the Aristotelians were happy with a qualitative description of nature, and even for that they appealed to Aristotle’s authority, Galileo insisted that scientists should listen to nature itself, and that the keys to deciphering the universe’s parlance were mathematical relations and geometrical models. The stark differences between the two approaches are exemplified by the writings of prominent members of the two camps. Here is the Aristotelian Giorgio Coresio: “Let us conclude, therefore, that he who does not want to work in darkness must consult Aristotle, the excellent interpreter of nature.” To which another Aristotelian, the Pisan philosopher Vincenzo di Grazia, adds:
Before we consider Galileo’s demonstrations, it seems necessary to prove how far from the truth are those who wish to prove natural facts by means of mathematical reasoning, among whom, if I am not mistaken, is Galileo. All the sciences and all the arts have their own principles and their own causes by means of which they demonstrate the special properties of their own object. It follows that we are not allowed to use the principles of one science to prove the properties of another [the emphasis is mine]. Therefore, anyone who thinks he can prove natural properties with mathematical argument is simply demented, for the two sciences are very different. The natural scientist studies natural bodies that have motion as their natural and proper state, but the mathematician abstracts from all motion.
This idea of hermetic compartmentalization of the branches of science was precisely the type of notion that infuriated Galileo. In the draft of his treatise on hydrostatics, Discourse on Floating Bodies, he introduced mathematics as a powerful engine that enables humans to truly unravel nature’s secrets:
I expect a terrible rebuke from one of my adversaries, and I can almost hear him shouting in my ears that it is one thing to deal with matters physically and quite another to do so mathematically, and that geometers should stick to their fantasies, and not get involved in philosophical matters where the conclusions are different from those in mathematics. As if truth could ever be more than one; as if geometry in our day was an obstacle to the acquisition of true philosophy; as if it were impossible to be a geometer as well as a philosopher, so that we must infer as a necessary consequence that anyone who knows geometry cannot know physics, and cannot reason about and deal with physical matters physically! Consequences no less foolish than that of a certain physician who, moved by a fit of spleen, said that the great doctor Acquapendente [the Italian anatomist Hieronymus Fabricius (1537–1619) of Acquapendente], being a famous anatomist and surgeon, should content himself to remain among his scalpels and ointments without trying to effect cures by medicine, as if knowledge of surgery was opposed to medicine and destroyed it.
A simple example of how these different attitudes toward observational findings could completely alter the interpretation of natural phenomena is provided by the discovery of sunspots. As I noted earlier, the Jesuit astronomer Christopher Scheiner observed these spots competently and carefully. However, he made the mistake of allowing his Aristotelian prejudices of a perfect heaven to color his judgment. Consequently, when he discovered that the spots did not return to the same position and order, he was quick to announce that he could “free the Sun from the injury of spots.” His premise of celestial immutability constrained his imagination and prevented him from considering the possibility that the spots could change, even beyond recognition. He therefore concluded that the spots had to be stars orbiting the Sun. Galileo’s course of attack on the question of the distance of the spots from the Sun’s surface was entirely different. He identified three observations that needed an explanation: First, the spots appeared to be thinner when they were near the edge of the solar disk than when they were near the disk’s center. Second, the separations between the spots appeared to increase as the spots approached the center of the disk. Finally, the spots appeared to travel faster near the center than close to the edge. Galileo was able to show with a single geometrical construction that the hypothesis—that the spots were contiguous to the surface of the Sun and were carried around by it—was consistent with all the observational facts. His detailed explanation was based on the visual phenomenon of foreshortening on a sphere—the fact that shapes appear thinner and closer together near the edge (figure 19 demonstrates the effect for circles drawn on a spherical surface).
The importance of Galileo’s demonstration for the foundations of the scientific process was tremendous. He showed that observational data become meaningful descriptions of reality only when embedded in an appropriate mathematical theory. The same observations could lead to ambiguous interpretations unless understood in a broader theoretical context.
Figure 19
Galileo never gave up an opportunity for a good fight. His most articulate exposition of his thoughts on the nature of mathematics and of its role in science appears in another polemic publication—The Assayer. This brilliant, masterfully written treatise became so popular that Pope Urban VIII had pages from it read to him during his meals. Oddly enough, Galileo’s central thesis in The Assayer was patently wrong. He tried to argue that comets were really phenomena caused by some quirks of optical refraction on this side of the Moon.
The entire story of The Assayer sounds a bit as if it were taken from the libretto of an Italian opera. In the fall of 1618, three comets appeared in succession. The third one, in particular, remained visible for almost three months. In 1619, Horatio Grassi, a mathematician from the Jesuit Collegio Romano, anonymously published a pamphlet about his observations of these comets. Following in the footsteps of the great Danish astronomer Tycho Brahe, Grassi concluded that the comets were somewhere between the Moon and the Sun. The pamphlet might have gone unnoticed, but Galileo decided to respond, having been told that some Jesuits took Grassi’s publication as a blow to Copernicanism. His reply was in the form of lectures (largely written by Galileo himself) that were delivered by Galileo’s disciple Mario Guiducci. In the published version of these lectures, Discourse on the Comets, Galileo directly attacked Grassi and Tycho Brahe. This time it was Grassi’s turn to take offense. Under the pseudonym of Lothario Sarsi, and posing as one of his own students, Grassi published an acrimonious reply, criticizing Galileo in no uncertain terms (the response was entitled The Astronomical and Philosophical Balance, on which the opinions of Galileo Galilei regarding Comets are weighed, as well as those presented in the Florentine Academy by Mario Guiduccio). In defense of his application of Tycho’s methods for determining distances, Grassi (speaking as if he were his student) argued:
Let it be granted that my master followed Tycho. I
s this such a crime? Whom instead should he follow? Ptolemy [the Alexandrian originator of the heliocentric system]? Whose followers’ throats are threatened by the out-thrust sword of Mars now made closer. Copernicus? But he who is pious will rather call everyone away from him and will spurn and reject his recently condemned hypothesis. Therefore, Tycho remains as the only one whom we may approve of as our leader among the unknown courses of the stars.
This text beautifully demonstrates the fine line that Jesuit mathematicians had to walk at the beginning of the seventeenth century. On one hand, Grassi’s criticism of Galileo was entirely justified and penetratingly insightful. On the other, by being forced not to commit to Copernicanism, Grassi had imposed upon himself a straitjacket that impaired his overall reasoning.
Galileo’s friends were so concerned that Grassi’s attack would undermine Galileo’s authority that they urged the master to respond. This led to the publication of The Assayer in 1623 (the full title explained that in the document “are weighed with a fine and accurate balance the contents of the Astronomical and Philosophical Weighing Scales of Lothario Sarsi of Siguenza”).
As I noted above, The Assayer contains Galileo’s clearest and most powerful statement concerning the relation between mathematics and the cosmos. Here is that remarkable text:
I believe Sarsi is firmly convinced that it is essential in philosophy to support oneself by the opinion of some famous author, as if when our minds are not wedded to the reasoning of someone else they ought to remain completely barren and sterile. Perhaps he thinks that philosophy is a book of fiction created by some man, like the Iliad or Orlando Furioso [an epic sixteenth century poem by Ludovico Ariosto]—books in which the least important thing is whether what is written in them is true. Sig. Sarsi, this is not how matters stand. Philosophy is written in that great book which ever lies before our eyes (I mean the universe) but we cannot understand it if we do not first learn the language and grasp the characters in which it is written. It is written in the language of mathematics, and the characters are triangles, circles and other geometrical figures, without which it is humanly impossible to comprehend a single word of it, and without which one wanders in vain through a dark labyrinth. [emphasis added]