From Basel to Saint Petersburg to Basel
Daniel Bernoulli’s father, Johann, wanted his son to become a merchant, but Daniel was more attracted by mathematics. As a compromise he studied medicine but, like his uncle Jakob and his father Johann, wanted to embark on an academic career.
He could not immediately obtain a position in Basel. He travelled in Italy and published his first book in 1724, Exercitationes Quaedam Mathematicae (Mathematical Exercises), a collection of his essays edited with the help of his friend Christian Goldbach, which contains some developments in applied mathematics and physics. It is in this field that he was remarkably inventive, and his fundamental book on hydrodynamics, Hydrodynamica, written as early as 1733 but only published in 1738, is still remembered as a milestone in the discipline. From 1725 onwards, Daniel won a number of scientific prizes, ten of them awarded by the Paris Academie des Sciences. In 1725 he reluctantly accepted a position in the Saint Petersburg Imperial Academy of Sciences, newly established at the instigation of Leibniz. While happy to work there with Leonhard Euler (a fellow countryman from Basel) who arrived in 1727, he was nevertheless relieved to leave in 1733 and, in 1734, started botany lectures in Basel, then switched to physiology in 1743 and finally to physics, and held this latter chair from 1750 to 1776.As regards the moral sciences, Daniel’s best known achievements concern the possible applications of probability theory to individual and collective decision-making: first with his celebrated essay, “Specimen Theoriae Novae de Mensura Sortis” (“Proposal of a new theory of the measure of chance”) - presented in 1731 in Saint Petersburg and published there in 1738 in the Annals of the academy - and, second, with his intervention in the controversy over the desirability or not for the public authority to recommend the inoculation of smallpox to fight against this malady (Bernoulli 1760 [1766]). The theoretical context was a long-standing discussion over the nature and applicability of the calculus of probability, and especially of a central concept: (mathematical) expectation.
Many detailed objections were levelled against this calculus, in particular by one of the most celebrated mathematicians and philosophers of the age, Jean Le Rond d’Alembert (Daston 1979; Paty 1988), who also intervened in the controversy over inoculation and reacted to Bernoulli’s memoir (Daston 1988: 82-9; Paty 1988: 220-25). The Saint Petersburg paper, which will be dealt with here, belongs to an early stage of this controversy. It forms a milestone in utility theory, the apprehension of risk and the formalisation of economic theory. It is also the symbol of a transformation in the notion of rationality and the definition of the conduct of the “reasonable” man: from a question of justice and equity in jurisprudence and games of chance (with, in particular, aleatory contracts and fair stakes) symbolized by the figure of the disinterested judge abstracting from personal and subjective situations, this conduct changed into that of the prudent man, the model of whom is the merchant in a risky environment (Daston 1980, 1989). Daniel Bernoulli stressed this shift of points of view when, in his essay, he referred to a letter Nikolaus sent him in 1732:[H]e [Nikolaus] declared that he was in no way dissatisfied with my proposition on the evaluation of risky propositions when applied to the case of a man who is to evaluate his own prospects. However, he thinks that the case is different if a third person, somewhat in the position of a judge, is to evaluate the prospects of any participant in a game in accord with equity and justice. (Bernoulli 1738 [1954]: 33)