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By Root 492 0

’s orbit called November that the comet was first spotted, and for months afterward it remained an object of intense scrutiny, its path recorded in great detail. In 1687, Isaac Newton would use these data as an example of his inverse square law of gravity at work. And on one clear night in that parcel of land called Basel, Switzerland, another man destined for greatness was also paying attention. He was a young theologian who, gazing at the bright, hazy light of the comet, realized that it was mathematics, not the church, with which he wanted to occupy his life.8 With that realization sprouted not just Jakob Bernoulli’s own career change but also what would become the greatest family tree in the history of mathematics: in the century and a half between Jakob’s birth and 1800 the Bernoulli family produced a great many offspring, about half of whom were gifted, including eight noted mathematicians, and three (Jakob, his younger brother Johann, and Johann’s son Daniel) who are today counted as among the greatest mathematicians of all times.

Comets at the time were considered by theologians and the general public alike as a sign of divine anger, and God must have seemed pretty pissed off to create this one—it occupied more than half the visible sky. One preacher called it a “heavenly warning of the Allpowerful and Holy God written and placed before the powerless and unholy children of men.” It portended, he wrote, “a noteworthy change in spirit or in worldly matters” for their country or town.9 Jakob Bernoulli had another point of view. In 1681 he published a pamphlet titled Newly Discovered Method of How the Path of a Comet or Tailed Star Can Be Reduced to Certain Fundamental Laws, and Its Appearance Predicted.

Bernoulli had scooped Newton on the comet by six years. At least he would have scooped him had his theory been correct. It wasn’t, but claiming publicly that comets follow natural law and not God’s whim was a gutsy thing to do, especially given that the prior year—almost fifty years after Galileo’s condemnation—the professor of mathematics at the University of Basel, Peter Megerlin, had been roundly attacked by theologians for accepting the Copernican system and had been banned from teaching it at the university. A forbidding schism lay between the mathematician-scientists and the theologians in Basel, and Bernoulli was parking himself squarely on the side of the scientists.

Bernoulli’s talent soon brought the embrace of the mathematics community, and when Megerlin died, in late 1686, Bernoulli succeeded him as professor of mathematics. By then Bernoulli was working on problems connected with games of chance. One of his major influences was a Dutch mathematician and scientist, Christiaan Huygens, who in addition to improving the telescope, being the first to understand Saturn’s rings, creating the first pendulum clock (based on Galileo’s ideas), and helping to develop the wave theory of light, had written a mathematical primer on probability inspired by the ideas of Pascal and Fermat.

For Bernoulli, Huygens’s book was an inspiration. And yet he saw in the theory Huygens presented severe limitations. It might be sufficient for games of chance, but what about aspects of life that are more subjective? How can you assign a definite probability to the credibility of legal testimony? Or to who was the better golfer, Charles I of England or Mary, Queen of Scots? (Both were keen golfers.) Bernoulli believed that for rational decision making to be possible, there must be a reliable and mathematical way to determine probabilities. His view reflected the culture of the times, in which to conduct one’s affairs in a manner that was consistent with probabilistic expectation was considered the mark of a reasonable person. But it was not just subjectivity that, in Bernoulli’s opinion, limited the old theory of randomness. He also recognized that the theory was not designed for situations of ignorance, in which the probabilities of various outcomes could be defined in principle but in practice were not known. It is the issue I discussed