Infinitesimal #4

A intellectual war involving math and politics also occurred between Thomas Hobbes and John Willis. Near the end of the English Civil War (1642-1651) Hobbes wrote Leviathan. In it Hobbes argued for a social contract and rule by an absolute sovereign. He wrote that civil war and a brutal state of nature ("the war of all against all") could only be avoided by strong, undivided government.

Hobbes also was a geometer of some repute. Similar to the Jesuits, he believed that the answer to uncertaity and chaos was absolute certainty and eternal order. They believed the key to both was Euclidean geometry. He set about trying to "square the circle" and solve two other long-standing geometry problems. "Square the circle", or "quadrature the circle," means construct a square with area exactly equal to the area of a given circle. (It can be done with great, but not perfect, precision.) Under the traditional restrictions of using only a compass and straight edge, this had been proven impossible. Hobbes tried anyway. Mathematician John Willis was well prepared to discredit any solution Hobbes proposed. Willis' political attitudes also reflected the chaotic years in England, but he believed in a state that would allow for a plurality of views and wide scope for dissent. Willis also sided with those who supported the use of infinitesimals.

Hobbes was also a sharp critic of the mathematical works of Willis. For Hobbes the infinitely small was an unwelcome intruder in mathematics. In contrast Willis considered practically all the features of the infinitely small to be clear advantages. His math was for investigating the world as it is. The world could be a little mysterious, unexplored, and ambiguous, but it invited new investigation and new discovery (p. 287).