In the seventeenth century the Jesuits placed themselves on the wrong side of history by opposing Galileo’s defense of Copernicus and heliocentrism. Less well known is their stalwart opposition at almost the same time to a much more arcane—but equally seminal—idea. In his book, Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, Amir Alexander describes the Jesuit condemnation of the use of indivisibles in mathematics and portrays it as an additional example of the suffocating effect of dogmatism and obsessive control in any context.
According to Alexander, Italy had led Europe’s emergence from the Dark Ages prior to the clerics’ opposition by reviving the long-dormant commercial economy, nurturing lively political experimentation, producing the first and wealthiest bankers, and leading the way in an artistic and cultural revival that transformed Europe. It had produced leaders in almost every field:
- Humanists from Petrarch to Pico della Mirandola
- Painters from Giotto to Botticelli
- Sculptors from Donatello to Michelangelo
- Architects from Brunelleschi to Bernini
- Scientists from Alberti to Leonardo to Galileo
Prior to the seventeenth century, “As a land of creativity and innovation, it is fair to say, Italy had no peer,” according to Alexander.
But following the disruption and disorder brought about by the Reformation, the Society of Jesus, aka, the Jesuits, was formed to restore order and the authority of the Pope in Europe. In their worldview, no dissent from papal edicts could be permitted, no other sect or belief could be allowed a foothold, and any hint of political opposition needed to be forcefully stifled. They believed it was up to them to “expel the demons of strife and confer the light of truth upon the people,” according to Alexander.
As the Jesuits worked to re-establish the control of the Catholic Church over European society, they mounted a campaign to specifically condemn an increasingly popular mathematical idea promoted by a monk named Bonaventura Cavalieri and a growing number of other mathematicians: “The continuum is composed of a finite number of indivisibles” (i.e., A continuous line is composed of distinct and infinitely tiny parts). Why the insistence that this simple proposition never be taught or even mentioned? Because the Jesuits repeatedly determined that the concept was “dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules.”
According to Alexander:
Where the Jesuits insisted on clear and simple postulates, the new mathematicians relied on a vague intuition of the inner structure of matter; whereas the Jesuits celebrated absolute certainty, the new mathematicians proposed a method rife with paradoxes, and seemed to revel in them; and whereas the Jesuits sought to avoid controversy at all cost, the new method was mired in intractable controversies seemingly from its very inception. It was everything that the Jesuits thought mathematics must never be.
Eventually, the Jesuits found themselves on the wrong side once again as indivisibles, or infinitesimals, became one of the most important tools of modern science. They were a primary source of inspiration for Isaac Newton’s invention of calculus, which transformed the practice of mathematics and the mathematical sciences, and opened up insights into the workings of the natural world, according to Alexander.
As a result of the Jesuits’ victory over the Galileans in Italy in the matter of infinitesimals, Italian thought became characterized by stagnation and decay, in contrast to countries where the idea was embraced. In the years following, for example, “England exhibited a marked and ever-increasing openness to dissent and pluralism. Politically, religiously, and economically, England became a land of many voices, where rival views and interests competed openly, relatively free from state repression. And it was in this relative freedom that England discovered its path to wealth and power” and became the world’s first modern state.
Sometimes insisting on certainty is the most certain way to miss the truth.