Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World

by Alexander, Amir

  What was it about the indivisibles that was so abhorrent to the Jesuit Revisors in the seventeenth century? The Jesuits, after all, were a religious order—the greatest one of the day—whose purpose was saving souls, not resolving abstract, technical philosophical questions. Why, then, would they bother to proclaim their opinion on so inconsequential a matter, pursue it and its advocates decade after decade, and with the sanction of the highest authorities of the order, make every effort to stamp it out? Clearly the Black Robes, as the Jesuits were popularly known, saw something in this apparently innocuous thesis that is completely invisible to the modern reader—something dangerous, perhaps even subversive, that could threaten an article of faith or core belief the Society held dear. To understand what this was, and why the largest and most powerful religious order in Europe took it upon itself to eradicate the doctrine of indivisibles, we need to go back a century, to the founding days of the order in the early sixteenth century. It was during that time that the seeds of the Jesuit “war on indivisibles” were sown.

  THE EMPEROR AND THE MONK

  In the year 1521 the young emperor Charles V convened a meeting of the estates of the Holy Roman Empire in the west German city of Worms. Only two years past his election to his high office, Charles was titular head of the Holy Roman Empire, commanding the allegiance of its princes and vast populace. In fact, he was both less and more than that: less because the so-called “empire” was in reality a patchwork of dozens of principalities and cities, each fiercely protective of its independence and as likely to oppose as to aid its imperial lord in time of need; and more because Charles was no ordinary prince; he was a Habsburg, a member of the greatest noble family the West has ever known, with possessions extending from the coast of Castile to the plains of Hungary. Consequently, Charles was not only the elected emperor of Germany, but also, by birthright, the king of Spain and the duke of portions of Austria, Italy, and the Low Countries. Moreover, in those very years, Castile was fast acquiring new territories in the Americas and the Far East, making Charles, in a phrase from the time, “the emperor in whose lands the Sun never sets.” And though Francis I of France and Henry VIII of England might have bridled at the suggestion, to his contemporaries as well as to himself, Charles V was the leader of Western Christendom.

  In the winter of 1521, however, it was his fractured German empire, not his vast overseas possessions, that were chiefly on the emperor’s mind. It had been three and a half years since Martin Luther, an unknown Augustinian monk and professor of theology, nailed a copy of his Ninety-Five Theses to the door of the Castle Church in Wittenberg. The theses themselves were narrowly focused, confronting what Luther saw as an unconscionable abuse practiced by the Church: the sale of “indulgences,” which were guarantees of divine grace, absolving the purchasers of their sins and sparing them the torments of purgatory. Luther was far from alone in denouncing the sale of indulgences, which was one among many Church practices that were routinely condemned as abuses by both clerics and laypeople. Nevertheless, Luther’s open challenge to Church authorities struck a nerve with both scholars and the common people like nothing before it. Over the following months, with the aid of the newly invented printing press, the theses were disseminated all across the Holy Roman Empire, and were enthusiastically received nearly everywhere.

  If this had been where things ended, then the affair would have been of no concern to Charles V. Like many in his day, Charles, too, was distressed by the more egregious practices of the Church, and he may even have felt some sympathy toward the audacious monk. But events soon acquired a momentum of their own. Alarmed by Luther’s success, his Augustinian superiors called him to account at a meeting in Heidelberg, but by the time he left, he had converted many of them to his position. When he was then summoned to Rome, he sheltered under the protection of his prince, the elector Frederick the Wise of Saxony, who arranged for a hearing for him in Germany instead. In an effort to discredit this irksome critic, Church authorities sent the Dominican professor Johann Eck of Ingolstadt, a professional debater and theologian, to confront Luther. The two met for a public debate in 1519, in which Eck skillfully maneuvered his opponent into admitting to clear heresies: that divine grace is granted to believers through faith alone, not through the sacraments of the Church; that the Church is a purely human construct and holds no special power to mediate between men and God; and that its supreme head, the Pope, is fundamentally an impostor. Luther made no apologies for his beliefs; Eck denounced him as a heretic.

  Unfortunately for Church leaders, this designation did nothing to slow down the zealous Luther. In 1520 he published three treatises that outlined his basic doctrines in deliberate defiance of established teachings. No longer a critic, he was now a rebel, openly calling for the overthrow of the Church hierarchy and institutions. His influence continued to spread, first in Wittenberg, then in Saxony, and soon clear across Germany and beyond. Everywhere, it seemed, Luther was acquiring followers in all classes and stations of life—men and women, nobles and peasants, country people and city dwellers—all of whom saw him as a leader of a religious awakening that would displace the ossified and corrupt Church of Rome. At long last growing alarmed at the fast-deteriorating situation, Pope Leo X excommunicated Luther, but by this time the drastic action had little effect. Luther’s teachings were spreading like wildfire throughout German lands.

  It was at this time, spurred by the threat of religious schism, that Charles V entered the fray. Two centuries later the French philosophe Voltaire would mock the empire as “neither Holy, nor Roman, nor an Empire,” but to Charles, his realm was holy indeed. As the secular leader of Christendom, and a devout Christian himself, he saw it as his sacred duty to preserve the Church and the spiritual unity of his people. Though Holy Roman emperors have for centuries vied with popes for supremacy in Europe, their squabbles on occasion resolved only by open warfare, it was clear to Charles that the former could not do without the latter. After all, it was the Pope who, since the days of Charlemagne, crowned emperors, and the Church that gave legitimacy and purpose to the office of emperor. The notion of an empire without a Roman Church, or an emperor without a pope, was unthinkable to Charles. To put his domains in order, and stop the spread of the Lutheran heresy once and for all, he called for a “diet”—a meeting of the estates of the empire.

  When the diet convened in the city of Worms in January of 1521, Charles sent Luther a summons to appear before the emperor and the estates and account for his actions. Despite Charles’s guarantee of his safety, many of Luther’s friends cautioned him against placing himself in his enemies’ power and advised him not to go. Nevertheless, in April, Luther arrived in the city and was promptly called before the assembled notables. There he was immediately presented with a list of his heretical doctrines and asked to acknowledge them and recant. Luther was surprised; he had expected to be allowed to argue his case, and was unprepared for the swiftness of the attack. He managed only to ask for a day’s reprieve to consider the matter, and Charles, the chivalrous Christian emperor, granted the request. But the next day, Luther was ready. He willingly acknowledged his beliefs, even in the face of hostile questioning and fierce denunciations. When pressed to recant, he answered calmly, “Here I stand; I can do no other; God help me; amen.”

  With these words Luther ensured the failure of Charles’s mission to stamp out heresy in his German lands, but he also did much more: he sealed the fate of Western Christendom. For over a thousand years the Roman Church had reigned supreme in western Europe. It had witnessed the rise and fall of empires, invasion and occupation by infidels, heresies large and small, plague and pestilence, and ruinous wars of king against king and emperor against pope. Through it all, the Church had survived, thrived, and expanded its reach until, by the sixteenth century, its dominion stretched from Sicily to Scandinavia and from Poland to Portugal, and to beachheads in the New World. From baptism to last rites, the Roman Church oversaw the lives of Europeans, giving order, meaning,
and purpose to their existence, and ruling on everything from the date of Easter to the motion of the Earth and the structure of the heavens. To the people of western Europe, regardless of nation, language, or political allegiance, the fabric of life itself was inextricably bound to the Roman Church.

  But when Luther took his stand at the Diet of Worms, this spiritual and cultural unity came to an abrupt end. By proudly proclaiming his heretical beliefs, he renounced the authority of the Roman Church and led his followers along a new religious path. By openly defying both Pope and emperor before a public gathering of the great men of the empire, he burned his bridges, and eliminated any chance of reconciliation. What up to that point could have been viewed as an internal rebellion within the Church now became a schism in which two rival faiths confronted each other in open hostility. On the one side stood the followers of the old Church; the Pope; and his secular sword, the emperor. On the other, the adherents of the new “Protestant” Church, which claimed direct descent from the ancient apostolic church and rejected the Roman faith as a monstrous aberration. The spiritual unity of the West was shattered with one blow, and any realistic hope of healing the rift through conciliation or threats was at an end. Luther and his followers refused to concede their errors or surrender to the might of the empire. Consequently, they had to be subdued by force of arms.

  DECLINE INTO CHAOS

  For the next thirty-four years of his reign, Charles V tried to accomplish precisely that. Though all too often distracted by threats from his European rivals and the Ottoman sultan, he nevertheless carried on a consistent campaign to suppress the cancer of Protestantism that was spreading through his lands. But it was too late. Not only was the new faith gaining adherents by the day among the populace, but great princes of the empire were also rallying to Luther, and establishing his church in their territories. First were the electors of Saxony, Frederick the Wise and his successors, who had been Luther’s protectors from the beginning. Next was Albrecht of Hohenzollern, grand master of the Teutonic knights, who refashioned himself as the first duke of Prussia and laid the foundations of what would become the greatest Protestant power in Germany. The elector Philip of Hesse followed suit, as did the margrave of Brandenburg, the dukes of Schleswig and Brunswick, and many smaller potentates of the empire. The great imperial cities (Nuremberg, Strassburg, Augsburg) also sided with Luther, broke with the Pope, and established their own reformed churches. By the mid 1520s it seemed nothing could resist the rising tide of Lutheranism.

  If the rupture of the empire wasn’t bad enough, it soon became clear the dissolution of Christendom would not stop there. In the early 1520s a cleric at Zurich Cathedral named Huldrych Zwingli began preaching fiery sermons denouncing the wickedness of Rome and advocating doctrines even more radical than Luther’s. Within a few years he rallied Zurich, and then the neighboring Swiss cities of Bern and Basel, to his cause. Zwingli’s death in a battle against the Catholic forest cantons of the Swiss Confederacy in 1531 brought a temporary halt to the spread of his radical vision, but by the late 1530s a new beacon of reform had emerged in Geneva. In 1536, John Calvin launched his long campaign to make Geneva into a shining example of the purest Protestant faith, and of upright public and personal morality. Over the following twenty years, Calvin managed to transform Geneva into a strict theocracy in which no individual action was beyond the scope of religious oversight or censure. And though the example of Geneva might appear unattractive to us, reminiscent as it is of some of the darker theocratic regimes of our own day, contemporaries judged it differently. Calvin’s city was glorified as the “city on the hill,” a shining example of what could be achieved through religious fervor, moral rectitude, and hard work. Aspiring reformers from across Europe flocked to the city to learn from Calvin how it was done, and to spread his teachings to their native lands. Thanks to the example of Geneva, Calvin’s brand of Protestantism, set down in his Institutes of the Christian Religion, became the most dynamic and influential movement of the Reformation from the 1540s onward. Even without the princely support that had institutionalized Luther’s reforms, Calvin captured millions of converts, from France and England in the west to Poland and Hungary in the east.

  Meanwhile, disasters kept piling up for the Roman Church, as not only cities and territories but entire kingdoms were lost to Protestantism. In 1527 the Swedish king Gustavus Vasa adopted Lutheranism and, over the following years, established it as a national church. Less than a decade later, Frederick I, a north German prince who had become king of Denmark, drove out the bishops, abolished the monasteries, and installed Lutheranism as the state religion. Since Norway was at the time under Danish suzerainty, and Finland was a province of Sweden, this made all Scandinavia into the Protestant stronghold it remains to this day.

  In England, welcoming the Reformation was initially more of a pragmatic than a spiritual choice. Henry VIII had stood faithfully by the Roman Curia in the early years of the Reformation and even authored an anti-Lutheran treatise that earned him the title Defender of the Faith from Pope Leo X. But as the years went by, Henry grew restless as his wife, the Spanish princess Catherine of Aragon, failed to provide him with a male heir. Resolved to replace Catherine with her charismatic lady-in-waiting Anne Boleyn, he appealed to Pope Clement VII to annul his marriage. Clement, eager to maintain close relations with his royal champions, would likely have granted Henry’s request, had it not been for the fact that the queen was Charles V’s maternal aunt. Charles made it clear that any attempt to cast Catherine aside would be a personal affront to his honor, and Pope Clement VII could not defy his chief protector. He denied the petition, prompting Henry to sever ties with Rome, marry Anne, and declare himself the head of an independent “Church of England” in 1534.

  Henry had no interest in the teachings of the continental reformers, and he intended only to replace the authority of the Pope with his own. Nevertheless, once the English church broke with Rome, the trend toward Protestantism proved irreversible. Under Henry’s son, the boy king Edward VI (1547–53), the English reformation veered toward radical Protestantism, only to reverse course under Edward’s half-sister (and Catherine’s daughter) Mary I (1553–58), who restored Catholicism in her tumultuous five-year reign. It was only when Anne’s daughter, Elizabeth I (1558–1603), ascended the throne that Protestantism was established as the state religion once and for all. Under the Thirty-Nine Articles of 1563, the Church of England retained many of the outward forms of the Roman Church that were favored by Henry, including the office of bishop, the sacraments, and the worship in grand and lavishly decorated churches and cathedrals. Doctrinally, however, the Church of England looked not to Rome but to Geneva, adopting the core teachings of John Calvin. To the Holy See, England was irretrievably lost.

  As the Reformation spread, it soon became clear that religious truth was far from the only thing at stake. With the Pope denounced, the emperor ignored, and all the established authorities questioned and ridiculed, the entire social order came under scrutiny, and the threat of revolution hung in the air. Respectable reformers such as Luther and Calvin, and the conservative kings and princes who backed them, struggled mightily to contain the revolutionary passions set loose by the Reformation, but not always successfully. As early as 1524 the peasants of southern Germany rose in revolt against their princes, demanding greater freedoms and a greater say in the rule of the land. They declared themselves followers of Luther, believing that his overthrow of the spiritual authority of the Roman Church was but a prelude to the overthrow of the social and political order it supported. The socially conservative Luther, however, was horrified at what he saw as a profound misunderstanding and misuse of his doctrines and fiercely denounced the uprising in a tract, Against the Murderous, Thieving Hordes of the Peasants. Though the uprising was crushed within the year by the combined forces of Catholic and Protestant princes, the fear that religious reformation might spell social revolution had already taken root.

  The dread of social up
heaval continued to haunt the Reformation as more and more reformers and would-be prophets openly questioned the established truths and challenged the authority of the powers that be. Many were peaceful, such as the reformer of Strasbourg Martin Bucer, or the saintly wanderers Caspar von Schwenckfeld and Sébastian Franck. But others were not. Thomas Müntzer was an early follower of Luther, until he broke with him over Luther’s embrace of the princes’ power and the existing social order. In 1524, Müntzer joined the peasants’ uprising, preaching to his followers that the end of days was at hand and calling for the blood of princes. He was captured in 1525, tortured, and killed, but his legacy was still at work ten years later, when a group of radical Anabaptists took control of the city of Münster in northwestern Germany. Unlike the mainstream reformers, whose churches included all members of a community, the Anabaptists insisted that only they were the elect, the true church of God, to the exclusion of all others. At Münster they showed just how dangerous such a doctrine can be when it gains possession of earthly power. Under the leadership of Jan Bockelson of Leyden, the Anabaptists imposed a reign of terror in the city, killing or driving out anyone who stood in their way. When Münster’s former Catholic bishop, backed by the Lutheran elector of Hesse, laid siege to the city, Bockelson declared himself the Messiah, abolished private property, and instituted polygamy. In 1535 the forces of the bishop and the prince finally overcame the fierce resistance of Bockelson’s fanatical followers, and exacted a bloody revenge on the Anabaptists and anyone remotely suspected of association with them. But across Europe, fear of an impending collapse of all social hierarchy and order only deepened.