Galileo’s father had opposed the idea of his becoming a mathematician and tried, arguing from long personal experience with mathematics and patrician poverty, to dissuade his son from choosing such a poorly paid career.
Vincenzio made a minimal living giving music lessons in the rented Pisan house where Galileo was born and partly raised. He also dabbled in the business dealings of his wife’s family, the Ammannati cloth merchants, to supplement his small teaching income, but he was at heart a composer and musical theorist in the days when musical theory was considered a special branch of mathematics. Vincenzio taught Galileo to sing and to play the organ and other instruments, including the recently remodelled lute, which became their favourite. In the course of this instruction he introduced the boy to the Pythagorean rule of musical ratios, which required strict obedience in tuning and composition to numerical properties of notes in a scale. But Vincenzio subjected these prevailing rules to his own studies on the physics of sound. Music, after all, arose from vibrations in the air, not abstract concepts regarding whole numbers. Using this philosophy, Vincenzio established an ideal tuning formula for the lute by fractionally shortening the intervals between successive frets.
After Vincenzio moved to Florence with his wife in 1572, temporarily leaving Galileo behind in the care of relatives, he joined other virtuoso performers, scholars and poets bent on reviving classic Greek tragedy with music.* Vincenzio later wrote a book defending the new trend in tuning that favoured the sweetness of the instrument’s sound over the ancient adherence to strict numerical relationships between notes. This book openly challenged Vincenzio’s own former music teacher, who prevented its publication in Venice in 1578. Vincenzio persevered, however, until he saw the work printed in Florence three years later. None of these lessons in determination or challenge to authority was lost on the young Galileo.
‘It appears to me’, Vincenzio stated in his Dialogue of Ancient and Modern Music, ‘that they who in proof of any assertion rely simply on the weight of authority, without adducing any argument in support of it, act very absurdly. I, on the contrary, wish to be allowed freely to question and freely to answer you without any sort of adulation, as well becomes those who are in search of truth.’
When Galileo was ten, he journeyed across Tuscany to join his parents and his infant sister, Virginia, in Florence. He attended grammar school near his new home until his thirteenth year, then moved into the Benedictine monastery at Vallombrosa to take instruction in Greek, Latin and logic. Once there, he joined the order as a novice, hoping to become a monk himself, but his father wouldn’t let him. Vincenzio withdrew Galileo and took him home, blaming an inflammation in the youth’s eyes that required medical attention. Money more likely decided the issue, for Vincenzio could ill afford the down payment and regular upkeep required to support his son in a religious vocation that generated no income. A girl was different. Vincenzio would have to pay dowries for his daughters, either to the Church or to a husband, and he could expect no return on either investment. Thus Vincenzio needed Galileo to grow up gainfully employed, preferably as a doctor, so he could help support his younger sisters, now four in number, and two brothers.
Vincenzio planned to send Galileo back to Pisa, to the College of the Sapienza, as one of forty Tuscan boys awarded free tuition and board, but couldn’t obtain the necessary scholarship. A good friend of Vincenzio’s in Pisa offered to take Galileo into his own home, to reduce the cost of the boy’s education. Vincenzio, however, hearing that this friend was romancing one of Galileo’s Ammannati cousins, held off for three years until the love affair ended in marriage and made the house a respectable residence for his son.
In September of 1581, Galileo matriculated at the University of Pisa, where medicine and mathematics both fitted into the Faculty of Arts. Although he applied himself to the medical curriculum to please his father, he much preferred mathematics from the moment he encountered the geometry of Euclid in 1583. After four years of formal study, Galileo left Pisa in 1585, at the age of twenty-one, without completing the course requirements for a degree.
Galileo returned to his father’s house in Florence. There he began behaving like a professional mathematician – writing proofs and papers in geometry, going out to give occasional public lectures, including two to the Florentine Academy on the conic configuration of Dante’s Inferno, and tutoring private students. Between 1588 and 1589, when Vincenzio filled a room with weighted strings of varying lengths, diameters and tensions to test certain harmonic ideas, Galileo joined him as his assistant. It seems safe to say that Galileo, who gets credit for being the father of experimental physics, may have learned the rudiments and value of experimentation from his own father’s efforts.
Having impressed several established mathematicians with his talent, Galileo procured a teaching post at the University of Pisa in 1589 and returned once more to the city of his birth at the mouth of the River Arno. The flooding of the river in fact delayed Galileo’s arrival on campus, so that he missed his first six lectures and found himself fined for these absences. By the end of the year, the university authorities were docking his pay for a different sort of infraction: his refusal to wear the regulation academic regalia at all times.
Galileo deemed official doctoral dress a pretentious nuisance, and he derided the toga in a three-hundred-line verse spoof that enjoyed wide readership in that college town. Any kind of clothing got in the way of men’s and women’s frank appraisals of each other’s attributes, he argued in ribald rhyme, while professional uniforms hid the true merits of character under a cloak of social standing. Worse, the dignity of the professor’s gown barred him from the brothel, denying him the evil pleasures of whoring while resigning him to the equally sinful solace of his own hands. The gown even impeded walking, to say nothing of working.
A long black robe would surely have hindered Galileo’s progress up the Leaning Tower’s eight-storey spiral staircase, laden, as legend has it, with cannonballs to demonstrate a scientific principle. In that infamous episode, the weight of iron on the twenty-five-year-old professor’s shoulders was as nothing compared to the burden of Aristotelian thought on his students’ perceptions of reality. Not only Galileo’s classes at Pisa, but university communities all over Europe, honoured the dictum of Aristotelian physics that objects of different weights fall at different speeds. A cannonball of ten pounds, for example, would be expected to fall ten times faster than a musket ball of only one pound, so that if both were released together from some summit, the cannonball would land before the musket ball had got more than one-tenth of the way to the ground. This made perfect sense to most philosophical minds, though the thought struck Galileo as preposterous. ‘Try, if you can,’ Galileo exhorted one of his many opponents, ‘to picture in your mind the large ball striking the ground while the small one is less than a yard from the top of the tower.’
‘Imagine them joining together while falling,’ he appealed to another debater. ‘Why should they double their speed as Aristotle claimed?’ If the incongruity of these mid-air scenarios didn’t deflate Aristotle’s ideas, it was a simple enough matter to test his assertions with real props in a public setting.
Galileo never recorded the date or details of the actual demonstration himself but recounted the story in his old age to a young disciple, who included it in a posthumous biographical sketch. However dramatically Galileo may have executed the event, he did not succeed in swaying popular opinion down at the base of the Leaning Tower. The larger ball, being less susceptible to the effects of what Galileo recognised as air resistance, fell faster, to the great relief of the Pisan philosophy department. The fact that it fell only fractionally faster gave Galileo scant advantage.
‘Aristotle says that a hundred-pound ball falling from a height of a hundred braccia [arm lengths] hits the ground before a one-pound ball has fallen one braccio. I say they arrive at the same time,’ Galileo resummarised the dispute in its aftermath. ‘You find, on making the test, that the larger ball beats the smaller one by two inches. Now, behind those two inches you want to hide Aristotle’s ninety-nine braccia and, speaking only of my tiny error, remain silent about his enormous mistake.’
Indeed this was the case. Many philosophers of the sixteenth century, unaccustomed to experimental proof, much preferred the wisdom of Aristotle to the antics