Galileo
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One of the impressions one might get from the immense efforts invested in his investigations of motion and the writing of De Motu is that Galileo had neglected his polymath roots and started to devote all his time to purely mathematical or experimental matters. This was definitely not the case. Even though Galileo spent much of his time in Pisa on empirical studies, his interest in philosophy and his love for poetry remained intact. In his writings, Galileo reveals an extraordinary grasp of Aristotle’s teachings, notwithstanding the fact that sometimes he uses that very expertise to attack Aristotle’s conclusions, as when he says: “How ridiculous is this opinion [Aristotle’s] is clearer than daylight… if from a high tower two stones, one stone twice the size of the other, were flung simultaneously that when the smaller was halfway down the tower, the larger would have already reached the ground?” It is clear that Galileo did not absorb the knowledge and deep understanding of Aristotle just from drinking the Pisan water—he had to work hard to acquire it. In fact, as late as sixteen months before his death, Galileo still stated that he had consistently continued to follow Aristotle’s logical methodology. In his own philosophy, however, Galileo stressed repeatedly the central role of mathematics. To him, true philosophy had to be a judicious mixture of observation, reasoning, and mathematics, with all three ingredients being absolutely necessary.
There was another amusing incident that happened at Pisa, in which Galileo demonstrated on one hand his admiration for the witty sixteenth-century poet Ludovico Ariosto (as well as for the parodic spirit of poet Francesco Berni), and on the other, his deep-seated aversion to authority and pompous formalism. It all started with a decree by the rector of the university requiring all professors to wear their academic gowns whenever they appeared in public. On top of the inconvenience imposed by this ridiculous order, Galileo was apparently further annoyed by the fact that he had been stiffly fined several times for breaking this rule. To express his disdain, he composed a 301-line satirical poem entitled “Capitolo Contro Il Portar la Toga” (“Against the Donning of the Gown”). In this rather risqué poem, Galileo reveals for the first time his contemptuous and provocative side and his inventive verbal humor—qualities he would make repeated use of in his later writings. In a few of the verses, he even advocates for people to walk naked because that would allow them to better appreciate one another’s virtues. It is very likely that Galileo did not object just to the gown itself. Rather, he probably used the rule about the gown as a symbol for the dogmatic acceptance of Aristotle’s authority by many of the scientists of his time. Alas, Galileo’s mocking attitude most likely did not endear him to his Pisan colleagues. Here are a few lines from the controversial poem:
I shan’t waste words but move out of my tower:
Such fashion I will follow as is now in town,
But how it pains and takes all my willpower!
And pray don’t think I’ll ever don a gown
As if I were a Pharisaic professor:
I couldn’t be convinced, not for a golden crown.
Overall, Galileo managed to survive economically at Pisa, although his salary was a meager 60 scudi per year. This reflected the rather unglamorous status of mathematics at the time. By comparison, philosopher Jacopo Mazzoni was making more than ten times that amount at the same university. The death of Galileo’s father in 1591 put an enormous financial burden on him, since he was the eldest son. He therefore sought, and fortunately obtained, an appointment at the University of Padua in 1592, where his salary was tripled. That prestigious chair had been vacant since the death of renowned mathematician Giuseppe Moletti in 1588, and university officials were rather picky in choosing a successor. Galileo’s winning the position was aided greatly by the strong support of Neapolitan humanist Giovanni Vincenzo Pinelli, whose library in Padua—at the time the largest in Italy—functioned as an intellectual center, and whose strong recommendation carried enormous weight. Pinelli opened his library for Galileo, and it was there that he gained access to unpublished manuscripts and lecture notes on optics, all of which were to become helpful in Galileo’s later work with the telescope.
Galileo would later describe his years in Padua—the city about which Shakespeare wrote: “fair Padua, nursery of the arts”—as the best time of his life. This was no doubt due largely to the freedom of thought and lively exchanges of information enjoyed by all scholars in the Venetian Republic, of which Padua was a part. These were also the years in which Galileo “converted” to Copernicanism.
PADUAN MECHANICS
Every researcher today knows that one cannot expect experimental results to demonstrate precisely any quantitative prediction. Statistical and systematic uncertainties (a range of values likely to enclose the real value)—creep into every measurement, making it sometimes difficult to even discern existing patterns at first glance. This concept runs contrary to the ancient Greeks’ emphasis on very precise pronouncements. Living in a period in which no accurate measurements of time were possible, Galileo found the study of motion quite challenging and frustrating in his early attempts. In addition, his research was often interrupted by the fact that starting at about 1603, Galileo began to suffer from serious arthritic and rheumatic pains, which sometimes became so bad that they confined him to bed. These debilitating medical problems persisted, according to Galileo’s son, “from about the fortieth year of his life to its end.”
Nevertheless, from 1603 to 1609, Galileo developed a number of his ingenious methods for investigating motion, and a few of his groundbreaking results in mechanics had their roots in those years, too. Much later, in his book Discorsi, Galileo described both the problems he had faced in probing and analyzing the free fall of bodies, and his brilliant solutions. In particular, he had to overcome the seemingly insurmountable experimental difficulty of having to determine whether the speeds of objects of different weights were really equal or different after having been in free fall for relatively short time intervals. Galileo wrote:
In a small height [from which the different bodies are dropped], it may be doubtful whether there is really no difference [in the speeds of the bodies or the precise times they hit the ground], or whether there is a difference, but it is unobservable. So I fell to thinking how one might many times repeat descents from small heights and accumulate many of those minimal differences of time that might intervene between the arrival of the heavy body at the terminus and that of the light one, so that added together in this way they would make up a time not only observable but easily observable.
This was already a remarkable insight. In an age that preceded the formulation of statistical methods, Galileo understood that if the same experiment is performed multiple times, the results can tease out and make credible even small differences. But his genius idea for these experiments was still to come. Galileo was seeking a way to literally slow down free fall, or to “dilute” gravity, so that the times of fall would be longer and more easily measurable, thereby making differences believable. Then it hit him: “I also thought of making moveables [objects] descend along an inclined plane not much raised above the horizontal. On this, no less than in the vertical, one may observe what is done by bodies differing in weight.” In other words, a free-falling ball could be regarded as an extreme case of a ball rolling down an inclined plane when the plane is vertical. As Galileo’s calculations show, by letting bodies slide (or roll) down an inclined plane tilted only by 1.7 degrees, he was able to considerably slow down the motion, to the point where he could make more reliable measurements.
In terms of his method for acquiring new knowledge, there is one interesting point that we should realize about Galileo’s experiments in mechanics: his explorations were largely driven by theory or reasoning, rather than the other way around. In his words, from De Motu, one must “employ reasoning at all times rather than examples (for what we seek are causes of effects, and these causes are not given to us by experience).” About 350 years later, the great theoretical astrophysicist Arthur Eddington would ec
ho a similar viewpoint: “Clearly a statement cannot be tested by observation unless it is an assertion about the results of the observation. Every item of physical knowledge must therefore be an assertion of what has been or would be the result of carrying out a specified observational procedure.”
In Galileo’s astronomical discoveries, on the other hand, observations were leading the way. Science progresses sometimes by experimental results preceding theoretical explanations, and sometimes by theories making predictions that are later confirmed (or falsified) experimentally or observationally. For example, it was known since 1859 that the orbit of the planet Mercury around the Sun did not quite agree with predictions based on Newton’s theory of gravity. Einstein’s theory of general relativity, which was published in 1915, explained the anomaly. At the same time, however, general relativity predicted that the path of the light from distant stars would be bent or deflected around the Sun to a certain degree. This prediction was first confirmed by observations made during a total solar eclipse in 1919, and it has since been reconfirmed by many subsequent observations. Arthur Eddington, by the way, led one of the teams that performed the observations in 1919.
The research concerning climate change today is progressing along similar steps. First, there has been an observed century-scale rise in the average temperature in the Earth’s climate system. This was followed by studies aimed at identifying the main causes for this change, resulting in detailed climate models that have by now made predictions regarding the anticipated effects in the twenty-first century.
In spite of the fact that Galileo was happy in Padua on a personal level, this period marked a time of dire financial straits. His two sisters Virginia and Livia married in 1591 and 1601, respectively, and the obligation to pay the exorbitant dowries fell on Galileo. Worse yet, Virginia’s husband even threatened that he would have Galileo arrested if he didn’t pay the agreed-upon sum. While Galileo’s brother Michelangelo also signed the dowry contract, he failed to make the payments, even though at the time he did succeed in securing two reasonable employments in succession as a musician. One of those was in Poland for which Galileo covered the travel expenses, and the other in Bavaria. As if to add insult to injury, while in Bavaria, Michelangelo married Anna Chiara Bandinelli and spent all of his money on an extravagant wedding banquet. Consequently, despite the fact that Galileo’s salary at Padua climbed from its initial 180 scudi per year to 1,000 scudi by 1609, he constantly had to rely on giving private tutoring, accommodating about a dozen students for rent at his home, and selling instruments he manufactured at his workshop, to avoid becoming mired in serious debt. Casting occasional horoscopes for students and various socialites provided another source of much-needed income.
The fact that Galileo engaged in astrology is hardly surprising. One of the traditional functions of mathematicians at the time was to draw astrological charts. In addition, they were supposed to teach medical students how to use horoscopes to indicate the appropriate treatment. More than two dozen astrological charts drawn by Galileo have survived. Those include two charts for his own birth and charts for his daughters Virginia and Livia. However, we do know from a letter written by Ascanio Piccolomini, in whose house Galileo spent the first six months of his house arrest in 1633, that by that time the scientist derided astrology entirely and made fun of it “as a profession founded on the most uncertain, if not false, foundations.”
The proximity of Padua to Venice allowed Galileo to forge new friendships and alliances with intellectuals and other influential figures there. One in particular, Gianfrancesco Sagredo, who owned a palace on Venice’s Grand Canal, was to become almost like a brother to Galileo, and he was later immortalized in Galileo’s Dialogo, playing the role of an intelligent and curious layperson. That depiction was apparently accurate, since in one of his letters, Sagredo gave the following self-evaluation of his own characteristics: “If I sometimes speculate about science, I do not presume to compete with the professors let alone criticize them, but only to refresh my mind by searching freely, without any obligation or attachment, the truth of any proposition that appeals to me.” Another friend and close advisor, Fra Paolo Sarpi, in addition to being a prelate, a historian, and a theologian, was also a scientist and a superb mathematician with great interest in topics ranging from astronomy to anatomy. Galileo would later say in admiration: “No one in Europe comes before him [Sarpi] in knowledge of the [mathematical] sciences.”
In 1608 Sarpi, who himself had an excellent command of optics and of the processes involved in vision, provided Galileo with the first reliable information about the invention of the telescope, after rumors of a Dutch device had spread throughout Europe. Even the polymath and playwright Giambattista della Porta confessed that he “never knew any man more learned” than Sarpi. This was the kind of praise reserved previously only for people such as Leonardo da Vinci, about whom King François I of France said that “he did not believe that a man had ever been born who knew as much as Leonardo.”
Venice offered another important attraction to Galileo. Its celebrated arsenal—a complex of armories and shipyards—overflowed with instrumentation in which he showed great interest. It was said that at its peak, the thousands of men working at the arsenal could build a ship in one day. We shouldn’t be surprised, therefore, that Galileo opened his book on the Two New Sciences with: “It seems to me that frequent visits to your famous Venetian arsenal open a large field of philosophizing on the part of speculative minds, especially in regard to the field in which mechanics is required. For every sort of instrument and machine is continually in use there by a large number of artisans.” The fact that the space of the arsenal is used today for the Venice art Biennale acts as a symbolic reminder of the connection between art and science in Renaissance Italy.
All of these frenzied scientific and engineering activities in Venice’s arsenal inspired Galileo to establish his own workshop, where he permanently employed an instrumentalist named Marcantonio Mazzoleni, who lived with his family in Galileo’s house. The workshop (in some sense, a seventeenth-century equivalent of a start-up company today) served Galileo both in his own experimental investigations and in producing an income through the manufacturing of various measuring, surveying, and mathematical devices, some for military purposes. In particular, one such instrument, the geometric and military compass, was a type of calculator that aided in rapid computations of useful battlefield quantities such as the distance and height of a target. Galileo even published a small book in Italian (with only sixty copies distributed, to limit unauthorized access) demonstrating and explaining the operation of this calculator. Another scientist, Baldessar Capra, later published a book about the same apparatus, but in Latin, claiming falsely to have invented it—when in reality he had received lessons in its use from Galileo! Galileo’s reaction was swift and aggressive. He collected affidavits from several people to whom he had demonstrated the instrument a few years earlier and accused Capra of plagiarism. After winning the case in front of university authorities, he followed up with a vicious article against Capra entitled “Defense Against the Calumnies and Impostures of Baldessar Capra.”
Why did Galileo react so vehemently? There is little doubt that due to his economic struggles, he felt compelled to vigorously defend himself against any attack that could in any way tarnish his reputation and thereby diminish his chances of attaining a higher income or better employment opportunities. There was, however, probably an additional, personal honor element to Galileo’s somewhat disproportionate reaction toward Capra. When a new star appeared in the sky in October 1604, Capra gloated in public that he had seen it five days before Galileo. This must have struck a nerve.
Galileo found more than mere intellectual and artistic stimulation in Venice. Through his friend Sagredo, he was introduced to the temptations that the Venetian night life had to offer—mainly fine wine and women. He formed a romantic association with Marina di Andrea Gamba, who consequently moved to Padua. The couple never
married, but they stayed together for more than a decade and had two daughters, Virginia (later Sister Maria Celeste) and Livia (later Sister Arcangela), and a son, Vincenzo. One could speculate that Galileo’s reluctance to enter into a formal marriage arrangement was influenced by the fact that the marriages in his immediate family were far from encouraging, but it is also possible that he gave up on a conventional relationship to be able to financially accommodate his sisters. At least, that’s what his brother Michelangelo thought.
With regard to his scientific work, the most impressive results produced during his eighteen years in Padua came out of Galileo’s experiments with inclined planes. Even though these results were not published until the 1630s, most of the experimental work was carried out in the period from 1602 to 1609. On October 16, 1604, Galileo wrote a letter to his friend Fra Paolo Sarpi in which he announced the discovery of the first mathematical law of motion—the law of free fall:
Reconsidering the phenomena of motion… I can demonstrate… that the spaces passed over in natural motion [free fall] are in proportion to the squares of the times [emphasis added], and consequently the spaces passed over in equal times are as the odd numbers beginning from one.… Now the principle is this: that the body in natural motion increases its speed in the same proportion as its departure from the origin of its motion.