Vainglorious Sycophant, Eerily Insightful Scientist

May 17, 2011

Book Review
Ernest Davis

Galileo. By J.L. Heilbron, Oxford University Press, New York and Oxford, UK, 2010, xiv + 508 pages, $34.95.

J.L. Heilbron's masterly new biography paints a rich portrait of Galileo, placing his manifold and revolutionary accomplishments within the intellectual ferment of his tempestuous times. The trajectory of Galileo's career begins with literature---he is, in addition to everything else, one of the great masters of Italian prose. He writes a comparison of Tasso and Ariosto, strongly favoring Ariosto; according to Heilbron, this is still required reading for students of Tasso and Ariosto. Like all Italian intellectuals of his day, Galileo writes his own poetry, best forgotten. He engages in a debate about the geography of Hell, as described in Dante's Inferno.

In 1609, at the age of 45, he hears a vague report from Holland of a device with two lenses for magnifying distant objects. He constructs it, points it at the sky, and over the next two years discovers the craters and mountains of the moon, the composition of the Milky Way, the moons of Jupiter, and the phases of Venus. The latter two decisively demolish the Ptolemaic model and, almost as decisively, establish the Copernican model. These discoveries make him the leading scientist in Europe, and ensure his fame over the centuries and as far into the future as we now can imagine; they also set him on a collision course with the repressive Catholic church of the counter-reformation.

During the next twenty years, he carries out an amazing sequence of scientific research and theorizing. He revolutionizes the theory of motion, and thus lays the foundations for Newton's definitive formulation sixty years later. He proposes the constant acceleration of gravity and calculates its consequences. He discovers the isochrony of the pendulum. He posits the principle of Galilean relativity. And on and on.

In the background, the opposition of the church to Copernicanism is a constant threat; Galileo is formally warned as to what he may say and how. The crisis comes in 1633; he is prosecuted and forced to recant. And for all the complexities of this affair, laid out by Heilbron clearly and at great length---for all that Galileo foolishly baited and infuriated his enemies with his arrogance and insults, and generally played with fire (Heilbron's chapter on these events is titled "Vainglory"), for all that can be said in extenuation of his adversaries (not actually very much, when all is said and done)---the scene of the great scientist, 69 years old, begging forgiveness on his knees for the crime of telling the truth remains, deservedly, one of the iconic images of the persecution of free minds by bigots in power.

He remains under house arrest until his death in 1642, closely watched and highly restricted in what he may write and to whom he may speak, broken in spirit and gravely ill. But despite all that, he manages in those final years to produce what is arguably his greatest work, Two New Sciences.


It is impossible not to admire Galileo. It is also very difficult to like him, and some of his biographers, particularly Arthur Koestler, have loathed him. His vanity was limitless; his sycophancy toward powerful people whose help he wanted was nauseating, though probably unavoidable in his circumstances; and his nastiness toward his fellow scientists was inexcusable. If they had been wrong, he held them up to ridicule as fools. If they had been right where he had been wrong, or if they had beaten him to a discovery, his fury and contempt knew no bounds. Christoph Scheiner was "an animal, a pig, an ass" because he had observed that sunspots rotate at an angle of 7 to the ecliptic before Galileo saw it. Orazio Grassi was an idiot who knew nothing about optics for having correctly stated that the telescope made dim stars brighter because the objective lens collected more light, as against Galileo's wrong theory that the telescope magnified the disk of the star. Such repeated attacks alienated many who could have been his allies; he paid dearly when the crisis came.

A biography of Galileo must guide the 21st-century reader through the complex, foreign thickets of Galileo's social, political, and intellectual milieux; the muddles of Aristotelian physics that he contended with; and the intricate development of Galileo's own thought and writing. Heilbron meets this challenge triumphantly; his book is thorough, clear, patient, and engaging. One reason for his success is that he adopts the standpoint of the modern reader, rather than trying to force the reader into a 17th-century mindset. When Galileo has presented a good correct argument, Heilbron explains it clearly, with a well-drawn diagram. When Galileo has presented a correct but unnecessarily convoluted geometric argument, he fixes it. When Galileo has presented a fallacious argument, he explains where the argument goes wrong. When Galileo was boring, Heilbron moves on to the next thing. When Galileo was being unfair to an opponent, Heilbron calls him on it.

One passage in Two World Systems, which Galileo himself called a "bizzarria," presents greater difficulties of interpretation. Galileo presented a fallacious proof that an object released at rest from a tower moves at constant speed along a semi-circular arc whose other end is the center of the earth. It is not true, it does not make any sense, it is not consistent with any of Galileo's other theories of motion, and it does not serve any purpose. Heilbron's explanation is as follows:

"Galileo as stage manager is the creator of ingenious fancies, mathematical caprices, an epic poem, a set of stories. Sagredo asks Salviati to describe the curve of a freely falling body in space; the masked Galileo replies with the clever nonsensical bizzarria; nature too is part of the masquerade."

Perhaps, but I do not see that Heilbron makes a sufficient case for such a reading. Something that does not make sense can always be passed off as a joke, but as a joke this is unamusing and pointless. Galileo did not make mathematical jokes anywhere else, though he made plenty of errors, and Heilbron presents no evidence that any of Galileo's contemporaries read it as a joke.

The most important philosophical and historical problem that arises in connection with Galileo's work is the relation of experiment and theory: To what extent did Galileo base his theory on his experimentation, and to what extent did he use experimentation merely to confirm theoretical conclusions he had already decided on? Heilbron's view is that the question cannot be resolved from the historical evidence that we have, and that probably, during Galileo's most active period, he jumped freely back and forth between theory and experiment as the spirit moved him.

Galileo left a large number of manuscripts tracing his work, but they are difficult to date and often to interpret, despite massive scholarly labors. Heilbron writes, "No single ordering [of the manuscripts] uniquely makes chronological and logical sense." The manuscripts describe many experiments involving such devices as pendulums, inclined planes, water clocks, and free drops. Modern historians have successfully reproduced many of the experiments from the manuscripts, and have confirmed Galileo's measurements. Some of the "experiments" described in his writings were not carried out but rather were rhetorical devices. (No deception is implied; they were understood as such.) Sometimes he stuck to a beloved theory in the teeth of overwhelming experimental evidence to the contrary. Looking for a consistent and coherent methodology is probably misdirected effort.

For most of his career, Galileo was a professor of mathematics, but neither his interest nor his abilities seem to have been particularly strong. Though he idolized Archimedes, few of the mathematical expositions in his writings require anything beyond the first six books of Euclid. "Galileo's paradox"---that there are as many square numbers as natural numbers---was his one major contribution to mathematics, but it did not bear fruit until Cantor's work more than two centuries later.

Like many other great scientists, Galileo at times moved beyond the amazingly great to a level that seems almost eerily miraculous. When Kepler first confirmed Galileo's account of the moons of Jupiter, he predicted that it would never be possible to determine their period. Within a couple of years, Galileo had accomplished that feat, to an accuracy of five minutes; Heilbron writes that this "amazes modern connoisseurs as it did Galileo's contemporaries."

Heilbron paraphrases Galileo's statement of Galilean relativity, in his "Letter to Francesco Ingoli," as follows:

"Enclose yourself, a friend, a jar dripping water vertically into a pot, a tank of fish, and a flock of small winged creatures in the cabin of a docked ship. Play catch, jump back and forth, and observe that the fish and flying things move easily in all directions. Now suppose the ship under sail at constant speed. Everything will remain as before: the jumping, ball throwing, flying, and swimming still take place as easily toward the prow as toward the stern and the water continues to drip vertically."

To find such a pellucid exposition, clearly an influence on Einstein, in a 1624 scientific text is extraordinary enough in itself. But how on earth did Galileo arrive at this amazing insight?

Ernest Davis is a professor of computer science at the Courant Institute of Mathematical Sciences, New York University.

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