To understand Galileo, do what Galileo did, says Mark A. Peterson: Remain alert to insights from across the arts and sciences.
In Galileo’s Muse: Renaissance Mathematics and the Arts (Harvard University Press), Peterson, a professor of mathematics and physics at Mount Holyoke College, argues that the intellectual formation and reach of the great Renaissance thinker has not been fully understood.
And, he adds, an inadequate view of Galileo makes for an incomplete picture of the great scientific ferment of the 17th century—a new understanding of the physical world—to which Galileo crucially contributed.
Among scientists, the best-known Galileo is the one who formulated laws of freely falling bodies and the parabolic path of projectiles—findings that would be critical half a century later for Isaac Newton’s framing of universal principles of motion. To almost everyone else, the familiar Galileo is the one the Inquisition sentenced to permanent house arrest for advocating a Copernican, Sun-centered worldview, deemed blasphemous.
Galileo waded into that fraught issue with observations he had made of the heavens—with improved telescopes he had designed—as well as of such terrestrial phenomena as tides. Oddly, church-imposed detention may have done Galileo a favor; while under sentence he contentedly wrote Two New Sciences (1638), his last book and the culmination of his life’s work.
Two New Sciences mingled the arts, including poetry, music, painting, and architecture, with ideas more recognizably scientific by today’s standards. Peterson claims that by ignoring the nature of that mingling, historians of science have missed the extent to which the mathematics of Renaissance arts, as much as of Renaissance sciences, drove the emergence of modern science. “The Copernican controversy crowds out important elements of Galileo’s story,” the scholar says.
He notes that simultaneous consideration of artistic and scientific facets of physical reality was a practice that Galileo developed early in his studies, long before the dramatic censure by Rome that would unduly influence how he was viewed throughout history.
Peterson noticed that aspect of Galileo’s work early in his own academic career. It was the scientist’s skill as a prose stylist that attracted Peterson’s attention. Riveted, he read on, and he came to the same puzzle that some other scholars had scratched their heads over: “Renaissance mathematics didn’t seem to be leading up to Galileo, at all,” he says by phone from his Mount Holyoke office. “There was something discontinuous.”
Galileo had seemed to ignore writings from his time and recent centuries, having concluded that Hellenistic Greek mathematics was of better use in solving the problems that concerned him. For example, Galileo credited not medieval “impetus theory” for his discoveries about parabolic motion, but the findings of Hellenistic Greeks of 2,000 years earlier, Peterson says.
Archimedes, Pythagoras, Euclid, and other classical Greek mathematicians became crucial to Galileo’s thinking. He “really did regard himself as the direct heir of the Greeks,” Peterson writes.
That makes sense, Peterson says. As a child, Galileo studied the arts and humanities at a monastic boarding school, then began university studies in medicine. For lack of funds, he returned home. Proudly self-educated, he drew extremely well and studied poetry attentively, to the great benefit of his later, much-admired prose style.
He also learned from his father to play the lute, expertly. That entailed studying not just technique, but also the mathematics of music, the counterpart of astronomical mathematics. At that time, astronomical mathematics lay closer to theology and moral philosophy than to physics. That was thanks to the Romans, who had reformulated Greek learning in search of a mathematics of abstractions to explain perfection, the eternal, the heavens. By contrast, Galileo’s passion was the earthier mathematics he found in music and other arts.
Coming to see this, Peterson began to explore Galileo’s involvement in his era’s revival of classical learning. He also looked for other thinkers who had shared the scientist’s view of the continuing utility of Greek mathematics. Dante, for example.
Galileo had commented on Dante’s conception of the Inferno in his Divine Comedy. When Peterson first began looking at that question, in the late 1970s, he found that Dante had deployed “unexpected mathematical sophistication.” For example, three centuries before Galileo, the poet had hinted at the calculus that Newton and Leibniz would develop 350 years later. To construct his Paradise, Dante had made poetic use of ideas about space that foreshadowed a 20th-century concept in theoretical physics: He had, specifically, created a four-dimensional, curved-space “hypersphere.”
A good deal of Peterson’s book examines the classical mathematical legacy in Renaissance painting, music, and architecture, as well as in the earlier poetics of Dante. The author sets the influence of Archimedes, Pythagoras, and company apart from the everyday applications of numbers—in commerce, construction, business, surveying. Those uses, too, were reformed in the late-medieval and early-Renaissance eras, thanks in good part to the influence of Arabic science.
If the interplay among the arts and sciences has become a history-of-science commonplace, it has rarely been presented by someone as historically and scientifically well versed as Peterson. He explains such developments as the emergence of perspective in Western art clearly enough for nonspecialists in science or history.
A scientist’s eyes can be helpful when analyzing scientific history, Peterson notes. Long in contention, for example, has been whether Galileo was religious. Peterson thinks not, or not exactly. If Galileo thought little about God, and more about making good use of God-given intellect, that is something scientists can understand, he says. “Scientists very often satisfy their religious impulses with something scientific, and nonscientists don’t realize how perfectly that works, so that might look like irreligion to them.”
No doubt such disputes will be stoked by Peterson’s book, which has already raised one eyebrow, a bibliographic one. On the basis of his study of a 1627 manuscript, Oratione de Mathematicae Laudibus, a lecture attributed to Galileo’s protégé Niccolo Aggiunti, Peterson argues that the lecture’s author was more likely Galileo himself.
In a review in New Scientist, the Galileo authority William R. Shea (he holds the “Galileo Chair” of History of Science at the University of Padua) says he doubts that: “Aggiunti may have talked with Galileo about his lecture, but it cannot be said to evoke Galileo’s style.”
As other Galileo scholars study the arguments, at least Peterson will not be at risk of house arrest. He will be on sabbatical, probably spending more time on the strictly physics-related end of his broad array of interests. There, he studies the fluid dynamics of cell motility, a phenomenon that even looking through Galileo’s telescopes the wrong way wouldn’t help explain.
