Is God a Mathematician? (9 page)

Cicero did not exaggerate in describing Archimedes’ greatness. In fact, I have deliberately put the bar for the title of “magician” so high that progressing from the giant Archimedes, we have to leap forward no fewer than about eighteen centuries before encountering a man of similar stature. Unlike Archimedes, who said he could move the Earth, this magician insisted that the Earth was already moving.

Archimedes’ Best Student

Galileo Galilei (figure 16) was born in Pisa on February 15, 1564. His father, Vincenzo, was a musician, and his mother, Giulia Ammannati, was a witty, if rather ill-disposed woman who couldn’t tolerate stupidity. In 1581, Galileo followed his father’s advice and enrolled in the faculty of arts of the University of Pisa to study medicine. His
interest in medicine, however, withered almost as soon as he got in, in favor of mathematics. Consequently, during the summer vacation of 1583, Galileo persuaded the mathematician of the Tuscan Court, Ostilio Ricci (1540–1603), to meet with his father and to convince the latter that Galileo was destined to become a mathematician. The question was indeed settled soon thereafter—the enthusiastic youth became absolutely bewitched by the works of Archimedes: “Those who read his works,” he wrote, “realize only too clearly how inferior are all other minds compared with Archimedes’, and what small hope is left of ever discovering things similar to the ones he discovered.” At the time, little did Galileo know that he himself possessed one of those few minds that were not inferior to that of the Greek master. Inspired by the legendary story of Archimedes and the king’s wreath, Galileo published in 1586 a small book entitled
The Little Balance,
about a hydrostatic balance he had invented. He later made further reference to Archimedes in a literary lecture at the Florence Academy, in which he discussed a rather unusual topic—the location and size of hell in Dante’s epic poem
Inferno.

Figure 16

In 1589 Galileo was appointed to the chair of mathematics at the University of Pisa, partly because of the strong recommendation of Christopher Clavius (1538–1612), a respected mathematician and astronomer from Rome, whom Galileo visited in 1587. The young
mathematician’s star was now definitely on the rise. Galileo spent the next three years setting forth his first thoughts on the theory of motion. These essays, which were clearly stimulated by Archimedes’ work, contain a fascinating mixture of interesting ideas and false assertions. For instance, together with the pioneering realization that one can test theories about falling bodies using an inclined plane to slow down the motion, Galileo incorrectly states that when bodies are dropped from towers, “wood moves more swiftly than lead at the beginning of its motion.” Galileo’s inclinations and general thought process during this phase of his life have been somewhat misrepresented by his first biographer, Vincenzio Viviani (1622–1703). Viviani created the popular image of a meticulous, hard-nosed experimentalist who gained new insights exclusively from detailed observations of natural phenomena. In fact, until 1592 when he moved to Padua, Galileo’s orientation and methodology were primarily mathematical. He relied mostly on thought experiments and on an Archimedean description of the world in terms of geometrical figures that obeyed mathematical laws. His chief complaint against Aristotle at that time was that the latter “was ignorant not only of the profound and more abstruse discoveries of geometry, but even of the most elementary principles of this science.” Galileo also thought that Aristotle relied too heavily on sensory experiences, “because they offer at first sight some appearance of truth.” Instead, Galileo proposed “to employ reasoning at all times rather than examples (for we seek the causes of effects, and these are not revealed by experience).”

Galileo’s father died in 1591, prompting the young man, who had now to support his family, to take an appointment in Padua, where his salary was tripled. The next eighteen years proved to be the happiest in Galileo’s life. In Padua he also began his long-term relationship with Marina Gamba, whom he never married, but who bore him three children—Virginia, Livia, and Vincenzio.

On August 4, 1597, Galileo wrote a personal letter to the great German astronomer Johannes Kepler in which he admitted that he had been a Copernican “for a long time,” adding that he found in the Copernican heliocentric model a way to explain a number of natural events that could not be explained by the geocentric doctrine. He
lamented the fact, however, that Copernicus “appeared to be ridiculed and hissed off the stage.” This letter marked the widening of the momentous rift between Galileo and the Aristotelian cosmology. Modern astrophysics was starting to take shape.

The Celestial Messenger

On the evening of October 9, 1604, astronomers in Verona, Rome, and Padua were startled to discover a new star that rapidly became brighter than all the stars in the sky. The meteorologist Jan Brunowski, an imperial official in Prague, also saw it on October 10, and in acute agitation he immediately informed Kepler. Clouds prevented Kepler from observing the star until October 17, but once he started, he continued to record his observations for a period of about a year, and he eventually published a book about the “new star” in 1606. Today we know that the 1604 celestial spectacle did not mark the birth of a new star, but rather the explosive death of an old one. This event, now called
Kepler’s supernova,
caused quite a sensation in Padua. Galileo managed to see the new star with his own eyes late in October 1604, and the following December and January he gave three public lectures on the subject to large audiences. Appealing to knowledge over superstition, Galileo showed that the absence of any apparent shift (
parallax
) in the new star’s position (against the background of the fixed stars) demonstrated that the new star had to be located beyond the lunar region. The significance of this observation was enormous. In the Aristotelian world, all changes in the heavens were restricted to this side of the Moon, while the far more distant sphere of the fixed stars was assumed to be inviolable and immune to change.

The shattering of the immutable sphere had started already in 1572, when the Danish astronomer Tycho Brahe (1546–1601) observed another stellar explosion now known as
Tycho’s supernova.
The 1604 event put yet another nail in the coffin of Aristotle’s cosmology. But the true breakthrough in the understanding of the cosmos didn’t descend from either the realm of theoretical speculation or from naked-eye observations. It was rather the outcome of simple experimentation with convex (bulging outward) and concave (curv
ing inward) glass lenses—hold the right two of those some thirteen inches apart and distant objects suddenly appear closer. By 1608, such spyglasses started to appear all over Europe, and one Dutch and two Flemish spectacle makers even applied for patents on them. Rumors of the miraculous instrument reached the Venetian theologian Paolo Sarpi, who informed Galileo around May of 1609. Anxious to confirm the information, Sarpi also wrote to a friend in Paris, Jacques Badovere, to inquire whether the rumors were true. According to his own testimony, Galileo was “seized with a desire for the beautiful thing.” He later described these events in his book
The Sidereal Messenger,
which appeared in March 1610:

Galileo demonstrates here the same type of creatively practical thinking that characterized Archimedes—once he knew that a telescope could be built, it didn’t take him long to figure out how to build one himself. Moreover, between August 1609 and March 1610, Galileo used his inventiveness to improve his telescope from a device that brought objects eight times closer to an instrument with a power of twenty. This was a considerable technical feat in itself, but Galileo’s greatness was about to be revealed not in his practical know-how, but in the use to which he put his vision-enhancing tube (which he called a
perspicillum
). Instead of spying on distant ships from Venice’s harbor, or examining the rooftops of Padua, Galileo pointed his telescope to the heavens. What followed was something unprecedented
in scientific history. As the historian of science Noel Swerdlow puts it: “In about two months, December and January [1609 and 1610, respectively], he made more discoveries that changed the world than anyone has ever made before or since.” In fact, the year 2009 has been named the International Year of Astronomy to mark the four hundredth anniversary of Galileo’s first observations. What did Galileo actually do to become such a larger-than-life scientific hero? Here are only a few of his surprising achievements with the telescope.

Turning his telescope to the Moon and examining in particular the terminator—the line dividing the dark and illuminated parts—Galileo found that this celestial body had a rough surface, with mountains, craters, and vast plains. He watched how bright points of light appeared in the side veiled in darkness, and how these pinpoints widened and spread just like the light of the rising sun catching on mountaintops. He even used the geometry of the illumination to determine the height of one mountain, which turned out to be more than four miles. But this was not all. Galileo saw that the dark part of the Moon (in its crescent phase) is also faintly illuminated, and he concluded that this was due to reflected sunlight from the Earth. Just as the Earth is lit by the full Moon, Galileo asserted, the lunar surface bathes in reflected light from Earth.

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.