The Venetians: A New History: from Marco Polo to Casanova (30 page)

During Aretino’s later years, Titian would paint another portrait of his beloved friend. This shows the mature Aretino in all his glory – the glory to which he had perhaps always aspired, though
it
took the insight of a great artist to realise this in all its fullness. Titian depicts the considerable bulk of a heavily bearded middle-aged figure dressed up in a resplendent scarlet robe and gold chain – here is Aretino
in excelsis
. The bastard from Arezzo now regards himself as the equal of any man – and with some justification. Yet despite his renown he was never a rich man, and his presence was little better than tolerated by the authorities of the city in which he spent his maturity (or what little of this quality he acquired over the years). In Venice, writers and artists still remained confined to the demimonde. They might on occasion have mixed with the nobility, even have been commissioned by them, but they were not admitted to the social rank of such exalted company. And Aretino was not one to forget this. Indeed, it probably sharpened the quill of the man who claimed that he lived ‘by the sweat of his ink’. At the same time, he was not one to forget those less fortunate than himself. He was renowned for his generosity, and it was said that he never sat down to his Easter dinner without entertaining eighteen street urchins at his table. Aretino finally died in 1556, at the age of sixty-four. According to one report, ‘his death was caused by his falling off his chair when convulsed with laughter at an abominable story’. Even if apocryphal, this would seem to be apt.

*
It has been pointed out that this quote from
The Prince
(Chapter 12) is of course a wild exaggeration where Venice’s mainland territories are concerned. As we have seen, the larger part of these territories constituted a comparatively recent acquisition. It is usually understood that Machiavelli was in fact identifying the European territory as the significant part of the Venetian Empire, whose overall territories had in fact been acquired over the city’s 800-year history.

*
These can be seen to this day at the Topkapi Palace, the former residence of the Ottoman sultans, in Istanbul.

11

Discoveries of the Mind

A
S
WELL AS
being a cultural centre, the Venetian Republic would now also begin to attract attention as one of the great European centres of learning and research. This was largely due to the University of Padua on the nearby mainland. The university here was one of the oldest in Europe, having been founded as early as 1222. Its subsequent list of students and faculty would include a roll call of great scientific figures – ranging from Copernicus to Galileo, from the Englishman William Harvey, who discovered the circulation of the blood, to the Flemish-born Andreas Vesalius, the founder of modern anatomy. The medical school at Padua was particularly renowned, and it was here that the twenty-year-old Polish canon Nicolaus Copernicus came to study in 1501. Copernicus had long been fascinated by the night sky, and had attended extracurricular lectures on mathematical astronomy at the University of Cracow, where he first studied in detail the complex movement of the planets around the Earth as described by the Ptolemaic view of the universe. When he came to Italy as a student, he witnessed a lunar eclipse in Bologna in 1500.

It has been claimed, with some justification, that Copernicus’ first ideas concerning a solar system, with the Earth and the other planets revolving around the sun, crystallised during his medical studies at Padua. As part of his course he was expected to attend lectures on astrology, for it was believed that the movement of the stars had a direct effect on the overall health and ‘humours’ of a patient. The leading authorities on this subject remained the Arabic astrologers, who were among the first in recent history to cast serious doubts on the Ptolemaic system. Copernicus’ interest in humanism also led him to study the ancient Greek philosophers, translations
of whose works were now becoming much more widely available through the printing presses of Venice. In particular, he seems to have learned of the works of Aristarchus of Samos, who used the sun’s shadow to calculate a remarkably accurate figure for the distance of the sun from the Earth. Aristarchus was also known to have speculated that the Earth revolved around the sun. Copernicus would take his ideas back to his homeland when he returned in 1503 to take up his clerical posting in the remote province of Warmia in eastern Poland. Here his misgivings concerning the Ptolemaic system continued to deepen, despite the fact that this was the orthodox teaching of the Church and the questioning of such matters was heresy. In correspondence with former student friends in Italy, he began speaking of ‘defects’ in the Ptolemaic system, admitting, ‘I often considered whether there could perhaps be found a more reasonable arrangement … in which everything would move uniformly about its proper center [sic], as the rule of absolute motion requires.’

But the young canon remained cautious. Only in his later years would he set down his definitive conclusions in a work entitled
De revolutionibus orbium coelestium
(On the Revolution of the Heavenly Spheres), which firmly placed the sun at the centre of its own planetary system. However, not until he was lying on his deathbed in 1543 would Copernicus allow his revolutionary work to be published. This would literally change the world for ever, and would go on to spark great controversy within the Catholic Church. Even the Protestant leader Martin Luther poured scorn on the idea: ‘This fool wishes to overturn the whole science of astronomy. Does not the Holy Bible tell us that Joshua commanded the sun to stand still, and not the earth?’ Just under half a century later Copernicus’ work would be read by Galileo, who would become a convinced advocate of heliocentric astronomy, before being appointed professor of mathematics at Padua, thus bringing Copernicus’ idea full circle.

Just six years after Copernicus left Padua in 1503, the city would be overrun by the forces of the Holy Roman Emperor Maximilian I and the League of Cambrai, causing the university to be shut down. Though the imperial troops only occupied the city for a few weeks, teaching would not resume here until 1517. Amongst the first influx of new students was a young man known as Tartaglia, who would later take up residence in
Venice, where he would make an algebraic discovery that would involve him in the greatest mathematical controversy of his age.

The man known to history as Tartaglia was born Niccolò Fontana in 1500 at Brescia, fifty miles east of Milan (though this was part of Venetian territory at the time). His father was a despatch rider, travelling on horseback across country to neighbouring towns to deliver mail; but in 1506 he was murdered by robbers, plunging his already-poor family into near-destitution. Worse was to follow in 1512 when Brescia was sacked and pillaged by the invading troops of the French king Louis XII, who had arrived in Italy to support the League of Cambrai against Venice. During the sack more than 45,000 citizens of Brescia were put to the sword by the rioting foreign soldiery. In the course of this mayhem the twelve-year-old Tartaglia, along with his mother and brothers, managed to take sanctuary in the local cathedral, but to no avail. A French soldier slashed Tartaglia across the head with his sword, leaving him for dead. In fact, the blow had only severed his jaw and palate. His mother found him alive, and over the coming month nursed him back to health. But the shock and the wound ensured that the young boy would never fully recover the power of speech – hence his nickname Tartaglia, which means ‘the stammerer’. After this he would never shave, growing a beard to camouflage his frightful scars.

As a result of this distressing setback Tartaglia would spend most of his time at home, where he developed an interest in mathematics. Consequently his mother sought out and found a patron for her exceptional son, who took him to study in Padua and then Venice. But as Tartaglia’s talent blossomed, and he began outstripping all those around him, this had a detrimental effect on his character, causing him to overcompensate for his lowly origins and ugly appearance by becoming unbearably proud and arrogant. On his return to Brescia he soon fell out with his patron, and around the age of seventeen he left home to teach mathematics in Verona. He is known to have been desperately poor during the ensuing decade or so; despite this, he seems to have got married and had a family sometime in his early thirties. Then in 1534 he moved to Venice, where he quickly began attracting a reputation for brilliance by defeating a number of renowned mathematicians in the public contests that were becoming so popular. These were a development from the philosophical disputations
held by medieval theologians, the intellectual equivalent of the jousting tournaments between knights. One of the basic rules was that no contestant should submit to his opponent a problem that he could not himself solve. Victory was a means to advancement for the exceptionally skilled in a hierarchical society; even so, the work Tartaglia gained as a mathematics teacher and tutor to the sons of noble families brought him only a modest income.

Tartaglia was soon making significant contributions to his field. One of his first achievements was to translate Euclid’s
Elements
into Italian. Prior to this, Euclid’s work had only been available in Latin translations taken from badly corrupted Arabic sources, rendering parts of the text incomprehensible. Tartaglia’s work revived the study of this formative text, which would prove an inspiring influence on Galileo, leading him to conclude that ‘the book of the world is written in the language of mathematics’. Tartaglia was also the first to understand that cannonballs travel in a trajectory when fired from a gun. (Previously, in accord with Aristotle’s thinking, it had been assumed that the cannonball travelled in a straight line, and then simply dropped straight down out of the sky when its momentum was spent.) This enabled Tartaglia to calculate precisely the angle at which to fire a cannonball, if it was to follow a certain trajectory and hit a particular spot. He would publish a book giving tables of angles and target distances, thus hugely improving the accuracy of cannon fire.

However, his major achievement was to discover a general formula for solving cubic algebraic equations (that is, those that contain an unknown to the power of three, or x
³
as we would write it
*
). The solution of the cubic had become the major mathematical challenge of the age: many sought it, while others simply despaired. When Luca Pacioli had published his masterwork
Summa
in 1494, a work that was said to contain all the mathematical knowledge known to that date, he had offered the opinion that no one would ever find a general solution for cubic equations. Unlike equations involving a simple unknown such as x, or even x
²
, cubic
equations involving x
³
were simply too complex for there to be a general formula that would give a solution. Yet soon after moving to Venice, Tartaglia managed to prove Pacioli wrong and came up with a solution to the cubic. However, news soon reached him that a young mathematician by the name of Antonio Fior had also discovered a method for solving cubic equations. In the prime of his manhood, Fior was even more arrogant than Tartaglia had been, and he reckoned that the uneducated Tartaglia was merely bluffing in an attempt to enhance his reputation. With the aim of achieving an even greater reputation for himself, he challenged Tartaglia to a mathematical duel.

In fact, Fior had not himself discovered a method for solving the cubic. This had been passed on to him sometime earlier by his teacher, Scipione del Ferro, who had decided on his deathbed that he did not wish the secret he had discovered to die with him. During this period mathematicians were not in the habit of publishing their original discoveries. On the contrary, they were in the habit of keeping them to themselves. These were the methods they could use to overcome their opponents at public mathematical contests, thus gaining them prestige, and on occasion leading to academic posts. However, the method passed on by del Ferro to his eager pupil, Fior, did in fact only solve a certain type of cubic equation. As it happens, we now know that Tartaglia too had only discovered a method for solving one type of cubic equation – and this was the very same method that had previously been discovered by del Ferro.

Preparations were soon under way for the great mathematical contest between Tartaglia and Fior. This was to be held on 20 February 1535 at the University of Bologna, where it was expected to attract a large crowd of mathematicians and aficionados to see this great problem resolved once and for all. Each contestant was to submit a list of thirty cubic equations for his opponent to solve using his own method; according to the rules of such competitions, no one could set a problem that he himself was unable to solve.

It was estimated that each contestant would take at least forty days to work his way through the list he had been given, during which time the contest was liable to seesaw either way in an exciting fashion. At the end of the allotted time, the contestant who had correctly solved the most
problems would be declared the winner. The prize for winning the contest was characteristically medieval – the loser would have to pay for a feast to be enjoyed by the winner and thirty of his friends. The real prize would of course be the renown accruing to the winner, who would become famous in universities and courts all over Europe for having discovered the finest solution to this problem, which had defeated all-comers.