Eugenics: Did Fisher Shoot Keynes?

"If you shoot at a king you must kill him." (Ralph Waldo Emerson)

Sir Ronald A. Fisher (1890-1962) is considered one of the 20th century's greatest statisticians. Together with his work in biology ("the greatest biologist since Darwin" in Richard Dawkins' opinion) Fisher's contributions earned him among other honours and awards, "three medals of the Royal Statistical Society, the Darwin Medal (1948) and the Copley Medal (1956). He received honorary degrees from numerous Universities, and was a member in over 20 academies, societies, and institutes".



In 1910, while a student, Fisher joined the Cambridge Eugenics Society, meeting John Maynard Keynes, already a high-profile member (at the time, Keynes and Karl Pearson, Francis Galton's protégé and heir as head of the British Eugenics Society, had a acrimonious spat, Keynes allegedly writing to a friend "the man is a liar"). Like Keynes (7 years his senior), Fisher became a eugenicist.

In the early 1920s, to supplement his income after the birth of his first child, Fisher became a casual book reviewer for the Eugenics Review, the journal of the BES. Fisher (32 at the time) was commissioned to review Keynes' 1921 "A Treatise on Probability". One should imagine it was a sensitive assignment for Fisher, then a humble statistician at the Rothamsted Experimental Station (Hertfordshire): not only was Keynes well-known and respected in eugenic circles, but his previous book, the influential "The Economic Consequences of the Peace" (1919) made of him a celebrity.

The result was Fisher's extraordinary "Mr. Keynes' Treatise on Probability" (1922. Eugenics Review. 14: 46-50: freely available). It's tempting to quote extensively from Fisher's work. For brevity's sake, however, I'll be highly selective and quote verbatim one key comment, only.

After dismissing a more "indulgent account" of Keynes' work, Fisher relates how Keynes, in "Part II of his book (71 pages)", proceeds to prove "all the laws of probability" … when "no definition of probability whatever enters into these proofs. Probability is introduced surreptitiously, not in a definition of probability, but in the definitions of addition and multiplication!" (exclamation point in the original).

In other words: nothing more natural, for Keynes, than to prove theorems already proved and available in any Probability101 textbook, with a revolutionarily undefined concept of probability. You've got to wonder at Keynes' priorities.

----------

For Fisher, Keynes' gratuitous insults to other authors (a constant in Keynes and his fans) were tasteless, but secondary. More important was that his criteria were neither valid nor applicable; he was almost wilfully vague about his ideas, but not even thoroughly acquainted with the basic modern development of statistics: "the fact that the binomial distribution is not in general symmetrical seems to strike him as a novelty" (?!?!). The very idea behind his book was an anachronism; his numerical examples, plagued with errors:

"The author's intention is evidently to contradict Bernoulli's theorem: it is a nice problem, however, to determine how few arithmetical corrections will suffice to bring the above figures into agreement with the binomial distribution."

(I couldn't resist: I enjoyed reading that as much as Fisher evidently enjoyed writing it)

----------

Keynes' fans may feel unpleasantly surprised by Fisher's comments. More critical readers of Keynes will hardly be as surprised: Keynes may have been as brilliant as his admirers claim, but his work often belies such brilliance.

This particular exhibition of ineptitude, however, is especially telling. For one, Keynes' only real academic training was in mathematics and he did not perform well in that, to put it mildly. For another, Keynes' statistical uncertainty is a foundational stone for his economics.

----------

[A]

As far as I know, Lord Keynes, the formidable polemicist, on this precise subject uncharacteristically avoided any polemic. He never replied to Fisher's onslaught and, instead, abstained from pontificating on statistics for nearly two decades. One might say, he preferred to vacate the battlefield. A frank admission of defeat would have been honourable, but Keynes seemed constitutionally averse to that.

At any event, the king, it seems, was dead.

Unfortunately, his subjects did survive: they never read the reviews to "A Treatise on Probability". They are -- and shall remain -- none the wiser.

"A Treatise on Probability" itself has been largely forgotten, to the delight and relief of statisticians.




Image Credits:
[A] Author: New York, Underwood & Underwood, publishers (circa 1906). Image in the public domain. Source: Wikipedia.