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Infinitesimal tells an interesting story about the genesis of the scientific revolution through the rather esoteric creation of the indefinitely small and indivisible. The idea of infinitesimals had been around for ages: Zeno's paradoxes are based on the idea that space can be sliced smaller and smaller. And for us, they're literally high school math. dx/dy and all that.
In the 16th and 17th century, disorder was at the top of mind for many elites. The Catholic Church had been rocked by the Protestant Reformation, and only belatedly offered theological counters. The elite intellectual shock troops of Catholicism was the new Jesuit order, which combined rigorous philosophical learning with absolute obedience to hierarchy, going up to the Jesuit Governor General and then the Pope. The Jesuits relied on a strict censorship regime to maintain this order, and sought an intellectual underpinning in Euclid's geometry. Geometry was both old (and therefore safe) and promised a perfectly rational and ordered system. In England, Thomas Hobbes, a tutor to aristocratic, political philosopher, and amateur mathematician, pursued a similar vision of absolute order in his Leviathan. Hobbes was also fascinated by the promise of geometry to create a perfect order.
Against absolute order, a few mathematicians postulated another way of thinking. Perhaps lines were made up of an infinite series of points. Planes were made of lines next to each other, like a sheet of paper. Solids were like a book of many sheets. The Italian branch of this school included Galileo, Torricelli, and Bonaventura Francesco Cavalieri, a mathematician of the Jesuat (note the "a") order. In England, Hobbes' main opponent was John Wallis, a member of the nascent Royal Society.
As Alexander discusses, the stability of Euclid's geometry was intellectual tied to political and theological stability. In Italy, the Jesuits had enough authority to have Galileo sentenced to house arrest. Torrecelli died before 40 of a fever. Cavalieri, who wrote the first major book on infinitesimals, was dealt with by having the entire Jesuat order dissolved.
Events in England followed a very different course. Hobbes was successfully baited by Wallis, as Hobbes erroneous claimed he'd "squared the circle", a problem which was later found to be impossible via Euclidian means. Wallis was a decent mathematician and a consummate political operator, who over decades saw Hobbes sidelined and ridiculed.
While it may be much to ascribe single causes (and Alexander is careful not to), Italy stagnated under Jesuit intellectual rigidity, becoming a poor backwater. England birthed the scientific and industrial revolutions, developments which would have been impossible without calculus.
In the 16th and 17th century, disorder was at the top of mind for many elites. The Catholic Church had been rocked by the Protestant Reformation, and only belatedly offered theological counters. The elite intellectual shock troops of Catholicism was the new Jesuit order, which combined rigorous philosophical learning with absolute obedience to hierarchy, going up to the Jesuit Governor General and then the Pope. The Jesuits relied on a strict censorship regime to maintain this order, and sought an intellectual underpinning in Euclid's geometry. Geometry was both old (and therefore safe) and promised a perfectly rational and ordered system. In England, Thomas Hobbes, a tutor to aristocratic, political philosopher, and amateur mathematician, pursued a similar vision of absolute order in his Leviathan. Hobbes was also fascinated by the promise of geometry to create a perfect order.
Against absolute order, a few mathematicians postulated another way of thinking. Perhaps lines were made up of an infinite series of points. Planes were made of lines next to each other, like a sheet of paper. Solids were like a book of many sheets. The Italian branch of this school included Galileo, Torricelli, and Bonaventura Francesco Cavalieri, a mathematician of the Jesuat (note the "a") order. In England, Hobbes' main opponent was John Wallis, a member of the nascent Royal Society.
As Alexander discusses, the stability of Euclid's geometry was intellectual tied to political and theological stability. In Italy, the Jesuits had enough authority to have Galileo sentenced to house arrest. Torrecelli died before 40 of a fever. Cavalieri, who wrote the first major book on infinitesimals, was dealt with by having the entire Jesuat order dissolved.
Events in England followed a very different course. Hobbes was successfully baited by Wallis, as Hobbes erroneous claimed he'd "squared the circle", a problem which was later found to be impossible via Euclidian means. Wallis was a decent mathematician and a consummate political operator, who over decades saw Hobbes sidelined and ridiculed.
While it may be much to ascribe single causes (and Alexander is careful not to), Italy stagnated under Jesuit intellectual rigidity, becoming a poor backwater. England birthed the scientific and industrial revolutions, developments which would have been impossible without calculus.