Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World

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by Alexander, Amir


  To many Europeans in those years, it seemed as if the demons of hell had risen from the underworld to spread misery and confusion upon the land. The old Church that had provided meaning, solace, and certainty to its members since time immemorial was being torn apart by an ever-increasing number of competing creeds. Every day seemed to bring more news of lands in the grip of religious turmoil, with every truth challenged and every certainty gone. The rupture of the Church was followed by political division, as Catholic and Protestant princes faced each other across the religious divide. And beneath the religious and political division lurked the nightmare of a social revolution that would sweep away the entire social order, the only one the people of that time had ever known. It was a time of strife and chaos, and to most Europeans one of debilitating confusion and uncertainty: With all old certainties challenged or discredited, and new ones announcing themselves by the day, how was one to know the difference between Truth and Error? Between the path to heaven and the path to hell?

  The institution that, in the eyes of most Europeans, was charged with providing the answers and resolution to these questions was, inevitably, the Papacy in Rome. As the Pope was vicar of Christ on earth and spiritual leader of Western Christendom, it was his lands and his people that were either lost in confusion or gripped by the alien certainties of sectarians and schismatics. It was therefore the duty of the Pope to step into the breach, arrest the progress of the Protestant heresy, and return unity, order, and certainty to Christendom. Sadly for the Roman Church, however—catastrophically, even—the men who occupied the seat of St. Peter during those years were signally ill equipped to deal with the crisis that confronted them.

  In many respects, the popes of the early sixteenth century were impressive men. Scions of leading Italian families, they were intelligent and highly cultured, and earned a place in history as the greatest patrons of Renaissance art. Popes Julius II (1503–13), Leo X (1513–21), Clement VII (1523–34), and Paul III (1534–49) commissioned paintings, frescoes, and sculptures by Michelangelo, Rafael, and Titian; churches and palaces from architects Sangallo and Bramante. They are responsible for some of the greatest works in the Western tradition, such as St. Peter’s Basilica and Square and the ceiling of the Sistine Chapel. But faced with the greatest crisis in the history of the Church, they found themselves helpless. Competent administrators though they were, they possessed neither the broad vision nor the spiritual authority required to confront the challenge of Protestantism.

  The problem was that the Renaissance popes were not, first and foremost, leaders of Christendom, but rather Italian princelings, whose loyalties were primarily to their families and clans. Julius II belonged to the powerful della Rovere clan of Rome, Leo X and Clement VII were both members of Florence’s ruling Medici family, and Paul III a scion of the ancient Tuscan Farnese family, soon to become the dukes of Parma. For each of these clans, having one of their own elevated to Pope was not only a tremendous honor but also an opportunity to amass wealth and power that might never be repeated. Popes were expected to take care of their own, to lavish their relatives with territories, titles (both secular and ecclesiastical), gifts, and incomes. Fully aware that they would never have obtained their high station without the sponsorship of their families, the popes readily obliged, making the reign of each Pope a race against time to accumulate as many possessions and titles for his family as possible. It was a sorry spectacle of nepotism and greed reminiscent of some of the most corrupt regimes of the developing world in our own day. It hung like a malodorous cloud around the Holy See, and undermined any effort by the Pope to exercise spiritual and moral authority.

  Moreover, in addition to being nominal heads of Christendom and patriarchs of greedy and acquisitive families, Renaissance popes were also the rulers of a substantial territorial state in central Italy. In their efforts to consolidate and expand their possessions, the popes became key players in the cutthroat politics of the Italian peninsula, making use of all the means at their disposal—from diplomacy to warfare to outright treachery—to advance their interests. So notorious were they for their amorality and ruthlessness in Italian politics that it was Cesare Borgia, nephew to Pope Alexander VI (1492–1503) and Alexander’s chief military commander, who served as Machiavelli’s model of a cunning and brutal prince.

  The popes’ active engagement in Italian power struggles not only undercut their spiritual standing, but also hamstrung them politically. In their efforts to protect their domains, the popes had to contend with the rising power of the national states of France and Spain, both of which sought to dominate the Italian peninsula, and each of whom possessed military might and resources on a scale that could never be matched by an Italian prince. The only hope of maintaining the independence of the Papal States was to play the two kingdoms against each other, never allowing either one to gain a permanent victory. The popes managed this delicate dance quite successfully for several decades, albeit at the expense of the people of Italy, who suffered repeated invasions and counterinvasions by their mightier neighbors. But disaster finally struck in 1527, amid one of the periodic wars between Charles V, in his capacity as king of Spain, and Francis I of France. Charles’s troops, who had not been paid in months, mutinied, and sacked the city of Rome; the murder, rape, and looting went on for weeks. Pope Clement VII escaped the Vatican just in time, and holed up in the nearby fortress of Castel Sant’Angelo as the carnage swirled around him. He ultimately surrendered to the emperor, paid a ransom for his own life, and conceded extensive territories to Spain. The humiliated and much-diminished Pope was to remain effectively a client princeling of the emperor for years to come.

  The upshot of all this was that when confronted with the challenge of the Reformation, the Renaissance popes had no answer. Leo X first attempted to use the most tried-and-true weapon in the papal arsenal by excommunicating Martin Luther, but this had little effect. The pleasure-loving Medici prince simply did not possess the moral stature to face down the upright Luther, and his pronouncements carried little weight. The next option for the popes was to rely on the military might of the emperor to bring the schismatics to heel, and Charles was more than willing to take on this role. The popes, however, from Leo X onward, worried that throwing their hat in with the empire meant abandoning the strategy of playing off the Habsburgs against Valois of France. Calling on Charles would effectively end the independence of the Papal States, and reduce the Pope’s temporal power to nothing. So, as Charles V struggled for decades to suppress the Protestant heresy and restore unity to Christendom, he did so with either the grudging support of the Holy See or, just as often, its open enmity. To contemporaries, it seemed that the popes would rather see all Christendom torn to shreds than surrender even a sliver of their power in Italy.

  In 1540 the fires of the Reformation were still spreading unchecked through the domains of the Roman Church, and lands that had been under the sway of Rome for centuries were falling away one by one. The commonality of faith and ritual that had unified Western Christendom was replaced by a cacophony of competing creeds, each denouncing the others as impostors or worse. As chaos, war, and subversion ruled the land, the Pope proved helpless to put out the fire, but was as intent as ever on amassing titles and incomes for his relatives and protecting his territorial interests. With schism on the ground and corrupt leadership at the top, any objective observer of the European scene in 1540 would likely have concluded that the days of the ancient Church of Rome were numbered.

  But on September 27 of that year, at the height of the storm, Pope Paul III took a small administrative step that seemed to bear little relation to the great events of the day: he approved a petition from a group of ten priests to form a religious company dedicated to serving the Pope and the Church. Though hardly noted at the time, it may have been the single most important step taken by the Papacy to save the Roman Church from dissolution. In his bull announcing the new order, Paul also approved the name requested by the group for their new assoc
iation: they called it the Society of Jesus.

  A RAY OF HOPE

  The Society of Jesus, or more commonly, the Jesuit Order, was the creation of one man, the Spanish nobleman Ignatius of Loyola. Born in 1491 to an old aristocratic family in the Basque country, Ignatius spent his early years as a gentleman courtier in the entourage of Ferdinand of Aragon. Though reputedly a good Christian, the handsome Inigo, as he was then called, focused his energies on the arts of courtly refinement and romantic love, rather than religious devotion. Heir to the martial tradition of his ancestors, and an ardent reader of the chivalric literature of his day, he aspired more than anything to live out his dreams of military glory. His opportunity finally came in the spring of 1521 in the Spanish city of Pamplona, just a few short weeks after Luther took his stand at Worms in a different corner of Charles V’s empire. With French forces advancing on the city and the Spanish army in retreat, Ignatius convinced the local commander to stand his ground and refuse the French demand to surrender. According to Jesuit lore, when the besiegers breached Pamplona’s walls, Inigo stood unyielding in their path, but was immediately cut down, and the city was overrun. Close to death, he was treated kindly by the French and delivered to his family’s castle of Loyola.

  The ten months Ignatius spent convalescing at his family seat can rightly be considered a turning point in the history of Christianity. Starved for entertainment, and with no romances of chivalry within reach, Ignatius began reading the lives of the saints, and was affected to his very core. The saints, he realized, were God’s own army in an eternal struggle against the Devil for possession of the human soul. Here was a war truly worth fighting, and Ignatius was determined to join in. As soon as he was physically able, he would make a pilgrimage to Jerusalem and dedicate his life to God’s service. As if to confirm him in his new vocation, he was rewarded one night with a mystical vision of the Virgin Mary.

  In the winter of 1522, Ignatius walked away from his convalescent bed a changed man. Gone was the elegant courtier who had spent his days in pursuit of women and martial glory. In his place was a holy pilgrim, sworn to undertake any hardship and deprivation that would come his way in spreading the word of God. Before setting off on his journey to Jerusalem, he spent a year in the small town of Manresa, where he meditated, begged for his sustenance, and had visions of God the Father, the Son, and the saints. He also wrote the first draft of The Spiritual Exercises, his manual of meditation that would become the cornerstone of the training and formation of Jesuits for centuries to come. When he finally reached the Holy Land, he spent only nineteen days there. The Franciscan friar in charge of the holy sites grew alarmed at this strange pilgrim’s zeal, and unceremoniously sent him home.

  Thwarted, Ignatius returned to Spain and embarked on a systematic course of study in theology at the great Spanish universities of Barcelona, Alcalá, and Salamanca. At thirty-two, he was much older than his classmates, and not a young man by the standards of the time. He struggled in his studies, but nevertheless made a deep impression on his fellow students in his devoutness and self-imposed poverty. He earned a reputation as a mystic and a spiritual counselor, and acquired a band of loyal followers who had undergone the course of meditations in his Spiritual Exercises. His success brought him to the attention of the Spanish Inquisition, which imprisoned him for a spell while investigating him for suspected heresy. Though ultimately released, Ignatius concluded that he could not safely resume his work in Spain, and in 1527 he moved to Paris to continue his studies at the Sorbonne.

  It was at the Sorbonne, among his fellow students, that Ignatius found the men who would form the kernel of the Society of Jesus. Within a few short years he had surrounded himself with a tight-knit group of Spanish, Portuguese, and French theology students, all much younger than he, who viewed him as their undisputed leader in all things, spiritual and worldly. Along with his followers, he once again determined to travel to Jerusalem, with the goal of preaching Christianity to the Muslims of the Holy Land. This time, however, with a touch of realism acquired on his earlier pilgrimage, he included a backup plan: if for some reason it proved impractical for his group to travel to Jerusalem or remain there, they would journey to Rome instead and place themselves at the service of the Pope.

  They never made it to Jerusalem. In 1534 they gathered in Venice to wait for a ship to the Holy Land, but were stranded due to a lack of funds and the war between Charles V and the Ottoman sultan. As they waited, Ignatius’s band spent their time preaching the word of God and serving the poor, sick, and dying in Venice and nearby towns. By 1539, with hopes for the journey fading, they decided to formalize their association by establishing a new religious order, one dedicated to serving the Church and the Pope in any corner of the world. The Society, as Ignatius announced in his petition to the Pope, would be open to “whoever desires to serve as a soldier of God beneath the banner of the cross.” It would be the Pope’s own army.

  THE CHILDREN OF IGNATIUS

  It took almost a year, but Paul III did ultimately approve the Society of Jesus. Showing his doubts, he limited the number of the new order to a mere sixty, but the restriction was soon repealed as the order grew and prospered. Indeed, the early growth of the Society of Jesus was nothing less than spectacular. Only ten men, all close intimates, elected Ignatius as the Society’s first general in 1540. But by the time of the founder’s death in 1556, the ranks of the order had grown a hundredfold, to one thousand. A decade later the Society comprised thirty-five hundred members, and at the death of General Acquaviva in 1615, no fewer than thirteen thousand men had taken Jesuit orders. Thereafter, the Society’s growth was still impressive, if somewhat slower, reaching twenty thousand at the turn of the eighteenth century. Through it all, the Society never compromised on the quality of the new recruits in order to expand its numbers. From the beginning, Ignatius had insisted that all candidates be rigorously screened before being accepted as novices in the Society. For those accepted, the road from novice to full membership was long and arduous, lasting years and sometimes even decades. The Jesuits never relaxed these standards, even though no other religious order required anything remotely as demanding. Despite this, or perhaps because of it, the Jesuits never lacked for volunteers of the highest social and intellectual caliber.

  Many of the Society’s early leaders came from ancient and noble families, as had Ignatius himself and his companion from the Sorbonne Francis Xavier (1506–52). The order’s third general, Francis Borgia (1510–72) had been Duke of Gandia in Castile before taking orders (as well as great-grandson of the notorious “Borgia Pope,” Alexander VI), and Claudio Acquaviva was the son of the Duke of Arti in the Kingdom of Naples. Other Jesuits came from humbler origins, but distinguished themselves as the outstanding intellectuals of the age. Such, for example, were the Spanish theologians Francisco de Toledo (1532–96) and Francisco Suárez (1548–1617), and the Venetian Robert Bellarmine (1542–1621). Christopher Clavius (1538–1612), Gregory St. Vincent (1584–1667), and André Tacquet (1612–60) were leading mathematicians; Christoph Grienberger (1561–1636) and Christoph Scheiner (1573–1650), prominent astronomers; and Athanasius Kircher (1601–80) and Roger Boscovich (1711–87), trendsetting natural philosophers. And no list of prominent Jesuits can leave out the brilliant Matteo Ricci (1552–1610), who traveled to China to spread the word of God and became a leading scholar and exponent of Western learning at the Ming imperial court. This is only a small sample, but it is enough to justify the assessment of the French philosopher and essayist Michel de Montaigne, who visited the Jesuits in their Roman headquarters in 1581. He called the order “a nursery of great men.”

  The Jesuits, however, were far more than an association of impressive individuals. They were a highly trained and disciplined collective, honed into a powerful instrument in a single-minded quest: to spread the teachings of the Catholic Church, expand its reach, and bolster its authority. This was the case from the beginning, when Ignatius and his band of followers first offered to
serve the Pope in any corner of the world, imagining themselves preaching the word of God to Muslims in the Holy Land. Although that mission never materialized, it was not long before the Jesuits distinguished themselves with outstanding missionary work on four continents. Already in 1541, Francis Xavier set out from Portugal on a mission that would take him to Goa in India, Java, the Moluccas, and Japan, preaching the Gospel and setting up missions wherever he went. He died in 1552 while awaiting transport to China, where he hoped to convert the most populous nation in the world to the Roman faith. Other Jesuits, meanwhile, traveled to Mexico, Peru, and Brazil, where they joined with Dominican and Franciscan friars in their efforts to Christianize the New World. They worked zealously and efficiently, established residences and missions, cared for the souls of the new settlers, and worked tirelessly to convert the native people of the Americas.

  Nevertheless, the crucial impact of the Jesuits lay in dealing with heathens much closer to home. For, in the turbulent years of the Reformation, when the very survival of the old Church hung in the balance, the Jesuits became the elite vanguard of Roman Catholicism, dedicated to holding the line against a Protestant tide that appeared to carry all before it. With remarkable skill, dedication, and an energetic, enterprising spirit, they led a stunning Catholic resurgence that not only halted the spread of the Reformation but won back for the Pope many territories that had seemed lost forever. They were just as Ignatius had imagined them: God’s own army battling His enemies, leading a movement of Catholic revival that became known as the Counter-Reformation.

 

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