Galileo hurled himself into mathematics with an energy that showed he had finally found a calling, a direction to his life. Even without a degree he was undoubtedly one of the most knowledgeable men in Italy regarding mathematics. But this was of little use unless his talents were recognised. At home in Florence there was no mathematical set. He did a bit of private tutoring and spent one winter in Siena. In order to get on he had to make contacts.
With this in mind, Galileo set out on his first journey to Rome.
The Rome to which the young Florentine mathematician came in the autumn of 1587 was completely different to the Renaissance city where Rafael and Michelangelo had been great heroes earlier in the century. A lot had happened in the intervening period, the essence of which can be summed up in two words: Reformation and Counter-Reformation.
The papacy had strengthened its grip on the Church. Luther's Reformation in northern Europe was a seismic shockwave that demanded a new direction. The Council of Trent (1545-1563) spelt out the basic tenets of the Catholic faith, and at least got rid of some of the blemishes that Luther had pointed to. It was the start of a fight to win back its lost standing - the Counter-Reformation.
The Council of Trent accentuated the splits within Europe by defining the Catholic Church's ideological foundation: absolute monopoly on Christian teaching and interpretation. Every bit as important as the ideology was the inception of two executive organs to carry out the Counter-Reformation: the Jesuit Order (1540) and the reorganised ecclesiastical surveillance apparatus in the area of faith, the Roman Inquisition (1542). At the same time the popes began to view themselves more and more as absolute rulers; not merely as spiritual leaders, but also as princes of the Papal States, just like other sovereigns in autocratic Europe.
When Galileo arrived in Rome, he found himself in the midst of energetic upheaval in the city on various levels. Pope Sixtus V Peretti unrelentingly tore down cramped, old blocks of houses and constructed wide, straight thoroughfares between the main churches. The streets echoed to the constant noise of cobbles being pounded into place - more than a hundred streets were permanently surfaced in a five-year period.
And so Galileo could travel dry-shod over the cobblestones to the powerful, learned and influential organisation he had decided to contact - the Jesuits.
The young Jesuit Order had been founded in Paris by the Spanish nobleman, Ignatius Loyola. With a background in the army and higher education, Loyola built up within a few years an effective, elitist organisation that greatly emphasised teaching and scholarship, and which became the pope's strongest weapon against Luther's doctrines. Not least, the Jesuits achieved startling results in their missionary work, both in Asia and South America.
The two chief seats of the organisation's operations were in Rome and they had just been completed: the II Gesu Church and the large, fortresslike centre of learning, Collegio Romano, which occupied an entire block in the middle of Rome between the Pantheon and the main street, Via del Corso.
In only a few years the Collegio Romano had become a very important institution and was considered to be one of the foremost universities of its age. When Galileo arrived there, 2,100 young men had either taken their degrees, or were still studying for them. There were also large Jesuit colleges in many other places including Köln, Trier and Munich.
Northern Europe was an important area of operations for the Jesuits, and there they undoubtedly helped to stem the tide of Lutheranism and Calvinism. The Jesuits literally conquered higher education. A key college was situated in Leuven (Louvain) in what is now Belgium, on the border between Catholic and Calvinist Europe. One of the Jesuit's keenest intellects, Robert Bellarmine, was at work there, but he would soon be returning to Rome to take up positions of even greater importance.
The Jesuits were famed for their somewhat unorthodox working methods, in which infiltration and undercover work was not unknown. One of Bellarmine's students at Leuven, a Norwegian called Laurits Nilss0n from T0nsberg, was sent to Protestant Stockholm, where - in the guise of a Protestant priest! - he built up an influential school and swayed King Johan III, who had married a Catholic, to such an extent that the King wanted to reintroduce Catholicism into the country, a notion that the clergy and his brothers soon put a stop to.
Galileo had not come to Rome and the college for religious reasons. The Jesuits had realised that if they wanted to wield influence, their scholastic calibre had to be of the very best, and the Collegio Romano could congratulate itself on possessing the greatest contemporary mathematician anywhere in Italy, Father Clavius.
Christopher Clavius was around fifty years of age. Originally German, he had been admitted to the Jesuit order at the age of seventeen and had spent most of his life in Italy. He wrote a number of textbooks on various mathematical and astronomical subjects, books that Galileo knew from his studies. He played a key part in the committee set up by Pope Gregory XIII which, just a fewyears before in 1582, had instigated a great reform. The result was the Gregorian Calendar, which is the foundation of our computation of time to this day. In brief, Father Clavius was a pivotal man to know for anyone wishing to make a career in mathematics on the mainland of Italy.
Totally unknown and unqualified, the 23-year old Tuscan was not overawed by the impressiveness of the Collegio Romano. He immediately sought out Father Clavius. Galileo explained his theories for calculating the centre of gravity of various objects, an area of study the Jesuit mathematicians were already interested in.
Clavius was impressed. He praised the practical work Galileo had done, and discussed the fundamental problems that arose as soon as mathematical models were transferred to the real, physical world: and indeed, whether this was even possible. The ideal, geometrical sphere touches a geometrical plane at just one point. But as soon as one uses a real sphereona real plane, there is acontact surface of greater or lesser extent, between the two. As a result there were those who maintained that mathematics was, in a manner of speaking, self-absorbed; that it might indeed deliver incontrovertible proof, but only when dealing with abstracted mathematical subjects. Father Clavius, on the other hand, argued that mathematics was a necessary bridge between the abstract ("metaphysical") world and the one that actually existed.
Vincenzio Galilei's work on the relationship between string lengths and the perception of pitch reflected a practical attitude to mathematics as a working tool. Galileo's approach was the same, he showed this even as he watched his pendulum in Pisa Cathedral. This basic philosophy, that technical models could be used to reveal definite knowledge of the outside world, was strengthened by the ideas from the Collegio Romano. Presumably he was given lecture notes to take away with him and study at home in Florence.
His visit to Rome was proof of just how high Galileo was aiming. Working as a private tutor in his native city was to waste his time and talents. Nevertheless, Jesuit goodwill was not enough to secure him a permanent position. A professorship was vacant in Bologna, but it went to Giovanni Magini who was nine years older and had good connections with Duke Gonzaga in Mantua.
Galileo had to be content to travel back to Florence, to his family and his private lessons. But there were things happening in his native city: two sudden deaths. They set in motion a train of events that eventually would secure Galileo his first chair in mathematics.
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