Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World Read Online Free
Author: Amir Alexander
a half centuries ago it had the power to shake the foundations of the early modern world. And so it did: the ultimate victory of the infinitely small helped open the way to a new and dynamic science, to religious toleration, and to political freedoms on a scale unknown in human history.
Part I
The War Against Disorder
THE JESUITS AGAINST THE INFINITELY SMALL
A unity among many cannot be maintained without order, nor order without the due bond of obedience between inferiors and superiors.
— IGNATIUS OF LOYOLA
1
The Children of Ignatius
A MEETING IN ROME
On August 10, 1632, five men in flowing black robes came together in a somber Roman palazzo on the left bank of the Tiber River. Their dress marked them as members of the Society of Jesus, the leading religious order of the day, as did their place of meeting—the Collegio Romano, headquarters of the Jesuits’ far-flung empire of learning. The leader of the five was the elderly German father Jacob Bidermann, who had made a name for himself as the producer of elaborate theatrical performances on religious themes. The others are unknown to us, but their names—Rodriguez, Rosco, Alvarado, and (possibly) Fordinus—mark them as Spaniards and Italians, like many of the men who filled the ranks of the Society. In their day these men were nearly as anonymous as they are today, but their high office was not: they were the “Revisors General” of the Society of Jesus, appointed by the general of the order from among the faculty of the Collegio. Their mission: to pass judgment upon the latest scientific and philosophical ideas of the age.
The task was a challenging one. First appointed at the turn of the seventeenth century by General Claudio Acquaviva, the Revisors arrived on the scene just in time to confront the intellectual turmoil that we know as the scientific revolution. It had been over half a century since Nicolaus Copernicus published his treatise proclaiming the novel theory that the Earth revolved around the sun, and the debate on the structure of the heavens had raged ever since. Could it be possible that, contrary to our daily experience, common sense, and established opinion, the Earth was moving? Nor were things simpler in other fields, where new ideas seemed to be cropping up daily—on the structure of matter, on the nature of magnetism, on transforming base metals into gold, on the circulation of the blood. From across the Catholic world, wherever there was a Jesuit school, mission, or residence, a steady stream of questions came flowing to the Revisors General in Rome: Are these new ideas scientifically sound? Can they be squared with what we know of the world, and with the teachings of the great philosophers of antiquity? And most crucially, do they conflict with the sacred doctrines of the Catholic Church? The Revisors took in these questions, considered them in light of the accepted doctrines of the Church and the Society, and pronounced their judgment. Some ideas were found acceptable, but others were rejected, banned, and could no longer be held or taught by any member of the Jesuit order.
In fact, the impact of the Revisors’ decisions was far greater. Given the Society’s prestige as the intellectual leader of the Catholic world, the views held by Jesuits and the doctrines taught in the Society’s institutions carried great weight far beyond the confines of the order. The pronouncements coming from the Society were widely viewed as authoritative, and few Catholic scholars would have dared champion an idea condemned by the Revisors General. As a result, Father Bidermann and his associates could effectively determine the ultimate fate of the novel proposals brought before them. With the stroke of a pen, they could decide which ideas would thrive and be taught in the four corners of the world and which would be consigned to oblivion, forgotten as if they had never been proposed. It was a heavy responsibility, requiring both
Part I
The War Against Disorder
THE JESUITS AGAINST THE INFINITELY SMALL
A unity among many cannot be maintained without order, nor order without the due bond of obedience between inferiors and superiors.
— IGNATIUS OF LOYOLA
1
The Children of Ignatius
A MEETING IN ROME
On August 10, 1632, five men in flowing black robes came together in a somber Roman palazzo on the left bank of the Tiber River. Their dress marked them as members of the Society of Jesus, the leading religious order of the day, as did their place of meeting—the Collegio Romano, headquarters of the Jesuits’ far-flung empire of learning. The leader of the five was the elderly German father Jacob Bidermann, who had made a name for himself as the producer of elaborate theatrical performances on religious themes. The others are unknown to us, but their names—Rodriguez, Rosco, Alvarado, and (possibly) Fordinus—mark them as Spaniards and Italians, like many of the men who filled the ranks of the Society. In their day these men were nearly as anonymous as they are today, but their high office was not: they were the “Revisors General” of the Society of Jesus, appointed by the general of the order from among the faculty of the Collegio. Their mission: to pass judgment upon the latest scientific and philosophical ideas of the age.
The task was a challenging one. First appointed at the turn of the seventeenth century by General Claudio Acquaviva, the Revisors arrived on the scene just in time to confront the intellectual turmoil that we know as the scientific revolution. It had been over half a century since Nicolaus Copernicus published his treatise proclaiming the novel theory that the Earth revolved around the sun, and the debate on the structure of the heavens had raged ever since. Could it be possible that, contrary to our daily experience, common sense, and established opinion, the Earth was moving? Nor were things simpler in other fields, where new ideas seemed to be cropping up daily—on the structure of matter, on the nature of magnetism, on transforming base metals into gold, on the circulation of the blood. From across the Catholic world, wherever there was a Jesuit school, mission, or residence, a steady stream of questions came flowing to the Revisors General in Rome: Are these new ideas scientifically sound? Can they be squared with what we know of the world, and with the teachings of the great philosophers of antiquity? And most crucially, do they conflict with the sacred doctrines of the Catholic Church? The Revisors took in these questions, considered them in light of the accepted doctrines of the Church and the Society, and pronounced their judgment. Some ideas were found acceptable, but others were rejected, banned, and could no longer be held or taught by any member of the Jesuit order.
In fact, the impact of the Revisors’ decisions was far greater. Given the Society’s prestige as the intellectual leader of the Catholic world, the views held by Jesuits and the doctrines taught in the Society’s institutions carried great weight far beyond the confines of the order. The pronouncements coming from the Society were widely viewed as authoritative, and few Catholic scholars would have dared champion an idea condemned by the Revisors General. As a result, Father Bidermann and his associates could effectively determine the ultimate fate of the novel proposals brought before them. With the stroke of a pen, they could decide which ideas would thrive and be taught in the four corners of the world and which would be consigned to oblivion, forgotten as if they had never been proposed. It was a heavy responsibility, requiring both
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