Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World Read Online Free Page A

great learning and sound judgment. Little wonder that only the most experienced and trusted teachers at the Collegio Romano were deemed worthy to serve as Revisors.
    But the issue that was brought before the Revisors General that summer day in 1632 appeared far from the great questions that were shaking the intellectual foundations of Europe. While a few short miles away Galileo was being denounced (and would later be condemned) for advocating the motion of the Earth, Father Bidermann and his colleagues were concerning themselves with a technical, even petty question. They had been asked to pronounce on a doctrine, proposed by an unnamed “Professor of Philosophy,” on the subject of “the composition of the continuum by indivisibles.”
    Like all the doctrinal proposals presented to the Revisors, the proposition was cast in the obscure philosophical language of the age. But at its core, it was very simple: any continuous magnitude, it stated, whether a line, a surface, or a length of time, was composed of distinct infinitely small atoms. If the doctrine is true, then what appears to us as a smooth line is in fact made up of a very large number of separate and absolutely indivisible points, ranged together side by side like beads on a string. Similarly, a surface is made up of indivisibly thin lines placed next to each other, a time period is made up of minuscule instants that follow each other in succession, and so on.
    This simple notion is far from implausible. In fact, it seems commonsensical, and fits very well with our daily experience of the world: Aren’t all objects made up of smaller parts? Is not a piece of wood made of fibers; a cloth, of threads; an hour, of minutes? In much the same way, we might expect that a line will be composed of points; a surface, of lines; and even time itself, of separate instants. Nevertheless, the judgment of the black-robed fathers who met at the Collegio Romano that day was swift and decisive: “We consider this proposition to be not only repugnant to the common doctrine of Aristotle, but that it is by itself improbable, and … is disapproved and forbidden in our Society.”
    So ruled the holy fathers, and in the vast network of Jesuit colleges, their word became law: the doctrine that the continuum is composed of infinitely small atoms was ruled out, and could not be pursued or taught. With this, the holy fathers had every reason to believe, the matter was closed. The doctrine of the infinitely small was now forbidden to all Jesuits, and other intellectual centers would no doubt follow the order’s example. Advocates of the banned doctrine would be excluded and marginalized, crushed by the authority and prestige of the Jesuits. Such had been the case with numerous other pronouncements coming out of the Collegio, and Father Bidermann and his colleagues had no reason to think that this time would be any different. As far as they were concerned, the question of the composition of the continuum had been settled.
    Looking back from the vantage point of the twenty-first century, one cannot help but be struck, and perhaps a bit startled, by the Jesuit fathers’ swift and unequivocal condemnation of “the doctrine of indivisibles.” What, after all, is so wrong with the plausible notion that continuous magnitudes, like all smooth objects, are made of tiny atomic particles? And even supposing that the doctrine is in some way incorrect, why would the learned professors of the Collegio Romano go out of their way to condemn it? At a time when the struggle over Copernicus’s theory raged most fiercely; when the fate of Galileo, Copernicus’s ardent advocate and the most famous scientist in Europe, hung in the balance; when novel theories on the heaven and the earth seemed to pop up regularly, didn’t the illustrious Revisors General of the Society of Jesus have greater concerns than whether a line was composed of separate points? To put it bluntly, didn’t they have more important