Galileo Read online

  Galileo made numerous discoveries, but, in four areas, he literally revolutionized the field: astronomy and astrophysics; the laws of motion and mechanics; the astonishing relationship between mathematics and physical reality (dubbed in 1960 by physicist Eugene Wigner “the unreasonable effectiveness of mathematics”); and experimental science. Largely through his unparalleled intuition and partly through his training in chiaroscuro—the art of representing three dimensions in two through a clever use of light and shadows—he was able to transform what would have otherwise been simple visual experiences into intellectual conclusions about the heavens.

  Following Galileo’s numerous observations and the confirmation of his findings by other astronomers, no one could cogently argue anymore that what one saw through the telescope must have been an optical illusion and not a faithful reproduction of reality. The only defense remaining to those obstinately refusing to accept the conclusions implied by the accumulating weight of empirical facts and scientific reasoning was to reject the interpretation of the results almost solely on the basis of religious or political ideology. If such a reaction sounds disturbingly similar to the present-day denial by some people of the reality of climate change, or of the theory of evolution by means of natural selection, it’s because it is!

  CHAPTER 2 A Humanist Scientist

  Galileo Galilei was born in Pisa on February 15 or 16, 1564. His mother, Giulia Ammannati, was an educated, if prickly, difficult, and bitter woman from Pescia, whose family was involved in the wool and clothing business. His father, Vincenzo, was a Florentine musician and music theorist from a family with noble roots, but who had rather unimpressive financial means. Even then, musicians struggled to support themselves and their families on their music alone, so Vincenzo apparently also became a part-time cloth merchant. The couple married in 1563, and, following Galileo, had two more sons and three or, according to some, four daughters. Of these, only Galileo’s younger brother, Michelangelo, and the two sisters Livia and Virginia played significant roles in Galileo’s life.

  Genetics are inescapable. In Galileo’s case, he may have inherited at least some of his rebellious nature, self-righteousness, and distrust of authority from his father, and his selfishness, jealousy, and anxiety from his mother. Vincenzo Galilei objected vehemently to the musical theory promoted by his own teacher, Gioseffo Zarlino. A music theorist from the old school, Zarlino was a strong advocate of a tradition that dated all the way back to the ancient Pythagoreans, according to which all string-generated sounds that are pleasant to our ears (such as the octave or the fifth) are the result of plucking identical strings, with lengths that are in ratios of integer numbers such as 1:2, 2:3, 3:4, and so on. It was the uncompromising clinging to this scheme that produced the old joke that Renaissance musicians spent half their time tuning their instruments and the other half playing out of tune.

  Vincenzo, on the other hand, maintained that adhering to this conservative numerology was arbitrary and that other criteria, equally valid if not better, could be adopted. In simple terms, Galileo’s father argued that musical consonance is determined by the musician’s ear rather than by his or her arithmetical capabilities. By insisting on freeing music from Pythagoras, Vincenzo opened the door for the modern “equally tempered system” popularized later by Johann Sebastian Bach. Through a series of experiments with strings of different materials and of varying tensions, he showed, for example, that strings of different tensions could produce the octave at a length ratio different from the canonical 2:1 (which was used when the tension was held constant). Almost prophetically—or rather, probably having an influence on his son—Vincenzo entitled one of his books on the subject Dialogue on Ancient and Modern Music, and another Discourse Concerning the Work of Messer Gioseffo Zarlino of Chioggia. Years later, two of Galileo’s most important books would be entitled Dialogue Concerning the Two Chief World Systems and Discourses and Mathematical Demonstrations Concerning Two New Sciences. One sentence in particular in Vincenzo’s fictional dialogue on music precisely captured the credo that Galileo was about to espouse later in life. The two interlocutors agree from the outset that they should invariably “set aside… not only authority, but also reasoning that seems plausible but is contradictory to the perception of truth.”

  The young Galileo probably helped his father in the experiments with the strings, and in the process, he might have started to realize the importance of the evidence-based approach to science. This could have been the first step in Galileo becoming a firm believer in the concept that in trying to find descriptions of natural phenomena, one needs, as he later expressed it: “to seek out and clarify the definition that best agrees with that which nature employs.” Having to perform a series of experiments with weights hung on strings (to vary the tension), may have also planted in his mind the seeds of the idea of using pendulums to measure time.

  Vincenzo was not only a talented lutenist, and his interests went beyond his particular objections to contrapuntal polyphony. Besides being an active member of the Florentine Camerata—a group of cultured Florentine intelligentsia interested in music and literature—he was educated in the classical languages and in mathematics. In short, not just in terms of the period of time during which he happened to live, Vincenzo was quite what we would call today a Renaissance man.

  Having grown up in that milieu, Galileo was about to follow in his father’s intellectual footsteps—although not in the direction of music, even though he often played second lute with Vincenzo. At the same time, having also witnessed his father’s idealistic ambitions being frustrated by harsh reality, especially economically, may have instilled in Galileo a stubborn, tenacious will to succeed.

  Galileo’s relationship with his mother was rather more problematic. Even Galileo’s brother Michelangelo described her as an absolutely “terrible” woman. Yet, in spite of numerous unpleasant incidents that included Giulia spying on Galileo and attempting to steal a few of his telescope lenses in order to give them to her son-in-law, he did his best in later years to attend to her ever-growing pecuniary needs.

  Galileo’s father returned from Pisa to Florence when Galileo was about ten. Lack of space in the home of a financially strapped family, in which the number of children was rapidly increasing, may have been one of the reasons for leaving Galileo in Pisa for a while, to live with his mother’s relative Muzio Tedaldi. His primary education at that stage was in what we normally refer to today as the liberal arts: Latin, poetry, and music. Both Galileo’s first biographer, Viviani, and Galileo’s neighbor and second biographer, Niccolò Gherardini, tell us that Galileo rapidly surpassed the level at which his teacher was able to help him and that he continued his schooling through reading classical authors by himself.

  At age eleven, he was sent to the monastery at Vallombrosa, in the serene atmosphere of which he studied logic, rhetoric, and grammar. He was also exposed to the visual arts by virtue of observing the work of artists in residence at the monastery. At that impressionable age, he must have been inspired by the abbot of Vallombrosa, who was apparently a polymath with knowledge in fields ranging from mathematics, to astrology, to theology, as well as in “all the other sound arts and sciences.”

  While there is no doubt that Galileo found the intellectual and spiritual ambience at the monastery appealing, we don’t know with certainty whether he truly intended to become a novice of the order of Camaldolese monks. Be that as it may, however, Vincenzo certainly had different plans for Galileo. Partly wanting perhaps to revive his family’s glorious past, which included a great-grandfather who had been a famous Florentine medical doctor, but at the same time striving to ensure Galileo’s economic future, Vincenzo enrolled his son as a medical student at the University of Pisa in September 1580.

  Unfortunately, medicine, which at the time was being taught based primarily on the teachings of the celebrated anatomist from ancient Greece Galen of Pergamum and which was filled with rigid rules and superstitions, bored Galileo. He did not feel
that he should “give himself up… almost blindly” to the assertions and opinions of archaic writers. However, something good did come out of his first years at Pisa: he met the Tuscan court mathematician Ostilio Ricci. After listening to Ricci’s lectures on Euclidean geometry, Galileo was bewitched. In fact, according to Viviani, even earlier, “the great talent and delight that he had… in painting, perspective, and music, hearing his father frequently say that such things had their origin in geometry, moved in him a desire to try it.” Consequently, he started to devote all of his time to studying Euclid on his own, while totally neglecting medicine.

  More than three centuries later, Einstein would be quoted as saying: “If Euclid failed to kindle your youthful enthusiasm, then you were not born to be a scientific thinker.” Galileo passed this particular “test” with flying colors. Moreover, envisaging mathematics as his vocation, he introduced Ricci to his father in the summer of 1583, hoping that the mathematician would convince Vincenzo that this was the right choice. Ricci explained to Vincenzo that mathematics was the topic Galileo was truly passionate about, and expressed his willingness to be the young man’s instructor. Vincenzo, who was a fairly good mathematician himself, did not object in principle, but he had the legitimate fatherly concern that Galileo would not find a job in mathematics. After all, he himself had already experienced what it meant to have the not particularly remunerative profession of a musician. Therefore, he insisted that Galileo complete his studies of medicine first, threatening that he would close his purse if Galileo refused. Fortunately for the history of science, the father and son eventually reached a compromise: Galileo could continue his studies of mathematics for one more year, with his father’s support, after which he would take on the obligation of sustaining himself.

  Ricci introduced Galileo to the works of Archimedes, whose genius in applying mathematics to physics and to real-life engineering problems was to motivate Galileo and permeate his entire scientific work. Ricci’s own professor, mathematician NiccolÒ Tartaglia, was the scholar who published a few of Archimedes’s works in Latin, and he had also produced an authoritative Italian translation of Euclid’s masterwork The Elements. Not surprisingly, two of Galileo’s very first treatises—one that addressed the problem of finding the center-of-mass of a system of weights, and the other on the conditions under which bodies float in water—were both on topics in which Archimedes had shown great interest. Galileo’s second biographer, Gherardini, cited Galileo as saying: “One could travel securely without hindrance through heaven and earth, if one only did not lose sight of the teachings of Archimedes.” The ironic net result of this entire sequence of events in the young man’s life, however, was that Galileo—one of the greatest scientific minds in history—left the University of Pisa in 1585, after having dropped out of medicine and not having completed any degree.

  Nevertheless, Galileo’s studies with Ricci and the introduction to Archimedes were not in vain. They inculcated in him a strong belief that mathematics can provide the necessary decoding tools for deciphering nature’s secrets. Through mathematics, he saw a way to translate phenomena into precise statements that could then be tested and proven unambiguously. This insight was truly remarkable. About 350 years later, Einstein would still wonder, “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?”

  Viviani tells a fascinating story about Galileo’s time as a student in Pisa: In 1583, the nineteen-year-old watched a lamp suspended on a long chain in the cathedral at Pisa swing from side to side. Galileo realized, through counting his heartbeats, that the time it took the lamp to oscillate a full amplitude was constant (strictly speaking, only as long as the range of the swing was not too large). From this simple observation, Viviani writes admiringly, Galileo went on, and “by very precise experiments, he verified the equality of its [the pendulum’s] vibrations” [the constancy of the period of the swinging]. Viviani recounts further that Galileo used this constancy of the period of a pendulum to construct a medical apparatus to measure the pulse rate. This tale became so widely known in later years that in 1840, painter Luigi Sabatelli created a beautiful fresco depicting young Galileo observing the lamp (see the leftmost panel at the top, in Figure 1 of the color insert).

  There is only one “small” problem with this captivating account. The lamp in question was installed in the cathedral at Pisa only in 1587, four years after Galileo had supposedly watched it swing. It’s possible, of course, that Galileo observed a different lamp that had hung earlier in the same spot. However, since Galileo himself mentions the constancy of the pendulum’s swing for the first time only in 1598, and there is no documented evidence for him having invented any instrument to measure the pulse rate, most historians of science suspect that Viviani’s colorful description of Galileo’s precociousness was the type of embellishment typical for biographies at the time.

  In reality, the Venetian physician Santorio Santorio did publish in 1626 the details of his pulsilogium—a device that could accurately measure the pulse rate based on the constant period of the pendulum. Galileo, who was usually very aggressive about any attempt to deny him credit, never claimed priority. Nevertheless, the fact that Galileo may have experimented in his father’s workshop with weights hung on strings (which effectively constitute pendulums) does leave open the possibility of a grain of truth in Viviani’s account. Galileo definitely did start to use pendulums as time-measuring devices in 1602, and he even had the idea for a pendulum clock in 1637. Galileo’s son, Vincenzo, started constructing a model based on his father’s concept, but, unfortunately, died before finishing, in 1649. Such a working clock was eventually invented in 1656 by the Dutch scientist Christiaan Huygens.

  Having left Pisa without a degree, Galileo had to find some means to make ends meet, so he started to teach mathematics privately, partly in Florence and partly in Siena. In 1586 he also published a small scientific tract entitled La Bilancetta (The Little Balance), which was not particularly original, except for introducing a more accurate way of weighing objects in the air and in water. This was especially useful for jewelers, whose common practice was to weigh precious metals this way.

  At the end of 1586, Galileo started to compose a treatise on motion and free-falling bodies. Following the ancient example of Plato, Galileo wrote in dialogue form. This genre was extremely popular in sixteenth-century Italy as a vehicle for technical exposition, polemic, and miniature dramas of persuasion. This book was never finished, and it addressed mostly problems that seem rather trivial by today’s standards. Yet it constituted an important step along Galileo’s road to a new mechanics. The book did contain, in particular, two interesting points. First, at age twenty-two, Galileo already had the chutzpah to challenge the great Aristotle on topics related to motion, even though the necessary mathematical tools to treat such variables as velocity and acceleration did not exist yet. (Calculus, which allowed for the proper definitions of velocity and acceleration as rates of changes, was formulated by Newton and Gottfried Leibniz only in the mid-seventeenth century.)

  The second interesting point was that Galileo did reach the tentative conclusion that irrespective of their weight, falling bodies made of the same material move with the same speed in a given medium. In later years, this was going to be part of one of his major discoveries in mechanics.

  Given the drama associated with Galileo’s name and his acceptance of Copernicanism, it is also intriguing to discover that in a separate manuscript, Treatise on the Sphere, or Cosmography—probably written in the late 1580s and most likely intended primarily for his private teachings—Galileo fully adopted the old Ptolemaic geocentric system in which the Sun, the Moon, and all the planets revolved around the Earth in circular orbits. This was about to change drastically in the years to come.

  In an attempt to beef up his still unremarkable résumé, Galileo paid a visit in 1587 to the foremost mathematician of the Jesuit order in Rome: C
hristopher Clavius. Clavius, who became a full member of the order in 1575, had been teaching the mathematical subjects at Rome’s prestigious Collegio Romano since 1564. In 1582 he was the senior mathematician on the commission that instituted the Gregorian calendar. Galileo set his eyes on one position in particular: a chair of mathematics had opened up at the University of Bologna, the oldest university in the Western world, and one that boasted distinguished alumni such as Nicolaus Copernicus and humanist and architect Leon Battista Alberti. Hoping to secure Clavius’s recommendation, Galileo left with him a few of his original works on finding the center of gravity of various solids—a popular topic among Jesuit mathematicians at the time.

  At about the same time, Galileo also proved an interesting theorem that generated some buzz. He showed that if you take a series of weights of, say, 1 libra (an ancient unit of weight equal to approximately 11.5 ounces), 2 libras, 3 libras, 4 libras, and 5 libras, and hang them at equal spaces along a balance arm, then the center of gravity (the point around which the arm is in equilibrium) divides the length of the balance arm precisely in a two-to-one ratio. While this little theorem gained Galileo some recognition in places ranging from Padua and Rome to universities in Belgium, the chair at Bologna was still given to Giovanni Antonio Magini, an established astronomer, cartographer (mapmaker), and mathematician from Padua.

  This failure must have been a stinging blow to the young and ambitious Galileo, but its impact was soon softened by a remarkable honor conferred upon him. In 1588 the consul of the Florentine Academy, Baccio Valori, invited Galileo to deliver two lectures to the academy on the geography and architecture of Dante’s Inferno (hell) in his masterpiece The Divine Comedy.