Les hasards de la variole

Abstract

La nécessité d’un calcul ayant pour fin d’estimer un risque peut être révoquée en doute lorsqu’il s’agit de prendre une décision en situation d’incertitude, a fortiori lorsqu’il s’agit d’une question de vie ou de mort. Dans la controverse engagée sur l’opportunité d’inoculer la variole, la position de D’Alembert constitue un cas exemplaire de scepticisme portant sur l’application des mathématiques, et en l’occurrence du calcul des probabilités, à des décisions relatives à la vie humaine. D’Alembert, en effet, conteste aux mathématiques sociales le pouvoir de rendre compte de phénomènes humains en y cherchant des régularités et des formalisations sans dissocier les dimensions mathématiques et probabilistes des dimensions philosophiques et éthiques. En suivant le débat qui, au milieu du xviiie siècle, se déroule entre le mathématicien français et son homologue suisse Daniel Bernoulli, on assiste à l’un des épisodes de la lente gestation des notions de prise de risque, de décision et de rationalité.

How history of mathematics can help to face a crisis situation: the case of the polemic between Bernoulli and d’Alembert about the smallpox epidemic

“…As for the second hypothesis, he explains that although at first glance the chance to be infected seems to vary highly by age, this can be explained by the fact that most people already got over smallpox in their childhood and are therefore immune when they attain adulthood. He shows that with a choice of n = 8, the result will be that about 1/13 of the entire population dies because of smallpox, a proportion which had been observed in several European cities (Bacaër, 2011;Bernoulli, 1766;Rohrbasser, 2011).…”

“…1 Bernoulli's table (Bernoulli, 1766, p. 44) rest of the population being immunized against smallpox). The risk of inoculation was difficult to estimate, but Bernoulli reasonably supposed that it was less than 1% and with this proportion the inoculation remains highly advantageous in regard to life expectancy (Bacaër, 2011;Rohrbasser, 2011). Bernoulli thus concludes: I simply wish that, in a matter which so closely concerns the wellbeing of the human race, no decision shall be made without all the knowledge which a little analysis and calculation can provide.…”

“…The reading of d'Alembert's polemic text, going through a series of criticisms about Bernoulli's work to arrive finally to the same conclusion as his adversary, namely that inoculation should be promoted, can indeed make a first impression of rivalry instead of a real scientific controversy. There are however thoughtful elements of his criticism, worth close examination (Colombo & Diamanti, 2015;Rohrbasser, 2011;Seth, 2014).…”

“…Inoculation was not however without risks, and could lead to the patient's death. Thus, inoculation meant to submit someone (typically children) to a small but imminent risk of death in order to gain a life-long protection against a fatal disease (Colombo & Diamanti, 2015;Gabriel & de la Harpe, 2010;Rohrbasser, 2011).…”

“…Various French intellectuals, including Voltaire and Diderot among others, engaged in the promotion of inoculation which was the object of debates in the second half of the eighteenth century in newspapers and at the Academy of Sciences, and became one of the important topics of the Enlightenment period. In a lecture presented at the Academy in 1754, La Condamine insisted that inoculation should be publicly promoted and suggested that the question should be seen as a mathematical problem: the decision about inoculation should be based on the comparison of risks (Colombo & Diamanti, 2015;Rohrbasser, 2011;Seth, 2014).…”