On bad anecdotes and good fun

My initial topic is the attractions of scandal, and an oft-told story: Diderot, humiliated at the court of Catherine by his inability to answer Euler’s supposed mathematical proof of the existence of God, limps back home to Paris.

The moral generally drawn from the story is: Learn your algebra! My moral will be an admonition to historians (but not only to historians).

I’ve read the Diderot anecdote many times—mathematicians seem to like it—and I’ve long been suspicious. Inspired by a colleague’s use of it in a talk last semester, I did some checking. Here’s what I found.

First of all, Diderot knew the calculus, and I’m quite sure Euler knew he knew it. So the story was unlikely to be true. I had little trouble tracking down its source (also here), which I translate:

The empress [Catherine], struck by the usefulness, the necessity even, of imposing silence on Diderot in these matters [i.e. of religion], yet wishing nevertheless to appear to have no part in the means employed [to silence him], did not invoke her authority, but instead agreed that the French philosophe was to be told that a Russian philosophe [Euler, who was not Russian, of course], a learned mathematician and a distinguished member of the Academy, was offering to demonstrate to him the existence of God algebraically, before the entire Court. Once Diderot had given notice that he would be quite ready to listen to such a demonstration—whose reality he very much doubted—the date and time was set. When the appointed moment arrived, the Russian philosopher, in the presence of the entire Court—the men, that is, and especially the young people—advanced in a grave manner toward his adversary, and with a tone of conviction, said to him:

“Monsieur,
(a + bn)/n = x; therefore God exists: your response?”

Diderot, indignant, wanted to exhibit the nullity and ineptitude of this supposed proof; but he felt despite himself the embarrassment {or: frustration] that is necessarily produced in us by an obvious mystification that has been prepared in advance by people acting in concert: he was not, moreover, going to escape the pleasantries to which this scene was going to bring forth; nor in the end, would he escape being damaged by this venture which Catherine could not have been unaware of. He therefore gave notice that he wished to return to France.

—Thiébault Souvenirs (1860) 2:9; also (1804) 3:158–159 (in the 1804–1805 edition the denominator in the supposed proof is z, not n, but this makes no difference—it’s still nonsense)

The queen paid Diderot’s way home to the extent of fifty thousand francs, and when his carriage broke down, the governor of Riga paid for its repair. Thiébault concludes with a disclaimer: “Je n’assure la vérité d’aucun de ces faits; je dis seulement que, dans le temps, ils ont été débités et reçus comme vrais par les habitans du Nord”. Nevertheless those facts suited the Russians and many story-tellers to come.

The anecdote is not in the English translation of Thiébault’s memoirs published in 1806. Its source in English is later than that. Before I tell you where it came from, here’s a sampling of how it gets mangled: Marcus Du Sautoy, Music of the primes, 42; Arthur Zajonc, Catching the light, 113; Arild Stubhaug, Niels Henrik Abel and his times, 204. (Not dupes: Ian Stewart, Richard Dawkins—neither of whom can resist telling it anyway, with disclaimers; and the historian Dirk Struik, about whom more below.)

The culprit seems to be Augustus de Morgan (Budget of paradoxes, 1872). De Morgan was using, or rather misusing, the 1860 edition of Thiebault.

Diderot paid a visit to the Russian Court at the invitation of the Empress. He conversed very freely, and gave the younger members of the Court circle a good deal of lively atheism. The Empress was much amused, but some of her councillors suggested that it might be desirable to check these expositions of doctrine. The Empress did not like to put a direct muzzle on her guest's tongue, so the following plot was contrived. Diderot was informed that a learned mathematician was in possession of an algebraical demonstration of the existence of God, and would give it him before all the Court, if he desired to hear it. Diderot gladly consented: though the name of the mathematician is not given, it was Euler. He advanced towards Diderot, and said gravely, and in a tone of perfect conviction: Monsieur, (a + bn)/n = x, donc Dieu existe; répondez! Diderot, to whom algebra was Hebrew[, though this is expressed in a very roundabout way by Thiébault—and whom we may supposed to have expected some verbal argument of alleged algebraical closeness,] was embarrassed and disconcerted; while peals of laughter rose on all sides. He asked permission to return to France at once, which was granted.

—Augustus de Morgan, Budget of paradoxes 2:4, 339 (Chicago, London: Open Court, 1915) ed. David Eugene Smith (the passage in brackets is from the second telling of the anecdote)

I list three succinct debunkings of the usual versions of the anecdote:

Lester Gilbert Krakeur, Raymond Leslie Krueger, “The Mathematical Writings of Diderot”. Isis 33.2 (June 1941);

R. J. Gillings, “The so-called Euler-Diderot incident”. American Mathematical Monthly 61.2 (1954);

A. Brown, “The Euler-Diderot anecdote", American Mathematical Monthly, 49.5 (May 1942).

Among other things they note, as I have, Diderot’s well-attested expertise in mathematics; they also observe that no Russian source for the story has turned up. It originated, perhaps, from the court of Frederick, no friend of the philosophes. Diderot’s nineteenth-century biographer Tourneux cites a letter in which the Swedish ambassador to Sweden, Nolcken, writes of having been delegated by Catherine to persuade Diderot to stay; but Diderot, exhibiting (to Nolcken’s surprise) the virtues of a père de famille, would speak of nothing but “his wife, his daughter, his grandson, and his friends” whom he dearly wished to see. It was Diderot, in short, and not the Queen, who instigated his departure.

As a historian I find it depressing that historians of the calibre of Cajori have recounted the falsified version without bothering to check the original. But Cajori at least had no Internet to assist him. Marcus du Sautoy, on the other hand, should have had no trouble checking, or having someone check for him. It took me all of five minutes. Google and Google Books are going to turn a lot of people into liars…

There is something a sloppy or tendentious writer will sometimes do which is not quite lying, because one can at least claim to be in good faith, but which is akin to lying. You recount an anecdote which is convenient for your purpose, an anecdote you may even think is fishy, as Du Sautoy gives evidence of doing; you could check it but you don’t, since its falsehood would deprive you of a telling illustration of your point. That’s not lying, but it’s close.

Morals

First: when a story looks too good to be true, it may well be; and now one can check many of them easily and quickly. When the story is to someone’s detriment, it is at least a venial sin to repeat it without doing so.

Second: it is often the case that the truth is more interesting than the falsehood. In Thiébault’s version, we don’t have the simple-minded slapstick humiliation of a non-mathematician by algebra; instead we find a careful calculation, or so it would seem, on Diderot’s part, of the intentions of Catherine in having him made to look silly before the court—in effect a day in the life of a courtier. It is the difference between a comfortable caricature and the unsettling, messy truth.

Third: even so, people like to tell the corrupt version, with or without disclaimers. I emphasize tell. Thiébault’s anecdote exists not as an abstract object of the sort sometimes postulated in æsthetics to represent the work of art itself, in contrast to its many performances, but as an imitable act, performed within a larger narrative which supplies to it the moral it is used to illustrate. Dirk Struik calls it a “good example of a bad historical anecdote”. Bad because it obscures rather than reveals the character of Euler and Diderot. The bad anecdote survives nevertheless by virtue of being useful in other ways—useful and pleasant to retell‚ pleasant to hear.

Mercier and Sperber have recently argued (Behavorial and brain sciences 34(2011); doi:10.1017/S0140525X10000968) that the function of what they call reasoning is not to “to improve knowledge and make better decisions” but to persuade. It is a conclusion that would not have surprised Cicero, though instead of ‘reasoning’ he would have used ‘rhetoric’. Bad anecdotes persuade no less efficiently, and perhaps more, than good ones. The telling of one (here I think of Kant’s characterization of rhetoric) mimics the offering of evidence without doing so, in appearance better evidence, perhaps, than the uncorrupted version, because the corrupt version can be tailored to its purpose.

Mercier and Sperber claim that people are “skilled arguers”, performing much better when the material they are tested on has been placed in an argumentative context (rather than presented in isolation). It would be interesting to know whether people are likewise better at estimating the plausibility of stories when they are told in a context of persuasion. Anecdotes lend themselves not only to being adduced as evidence—of character, for example—, but also to being told in isolation, like jokes, and the damage done by a bad anecdote is no doubt amplified when it is an entertaining fragment.