Galton’s 1904 paper in Nature

Nature [28 September] posted an editorial apologizing for publishing Galton’s 1904 speech on Eugenics as part of “material that contributed to bias, exclusion and discrimination in research and society”. Apology that I do not find particularly pertinent from an historical viewpoint, given the massive time, academic, and societal distances we stand from this “paper”, which sounds more than a pamphlet than a scientific paper, by current standards. Reading these 1904 Nature articles show no more connection with a modern scientific journal than considering Isaac Newton’s alchemy notes in the early proceedings of the Royal Society.

“The aim of eugenics is to represent each class or sect by its best specimens; that done, to leave them to work out their common civilization in their own way.” F. Galton

Galton’s speech was published in extenso by the American Journal of Sociology, along with discussions from participants of the Sociological Society meeting. This set of discussions is rather illuminating as the views of the 1904 audience are quite heterogeneous, from complete adherence to a eugenic “golden’ future (see the zealous interventions of K. Pearson or B. Shaw] to misgivings about the ability to define the supposed ranking of members of society by worth or intelligence (H.G. Wells), to rejection that moral traits are genetically inherited (Mercier), to protests against the negation of individual freedom induced by a eugenic state (B. Kidd) and to common sense remarks that improvements in living conditions of the working classes were the key factor in improving society. But, overall, there was no disagreement therein on the very notion of races and on the supposed superiority of the Victorian civilization (with an almost complete exclusion of women from the picture), reflecting on the prejudices of the era and it is quite unlikely that this 1904 paper of Galton had any impact on these prejudices.

What are the chances of that?

What are the chances that I review a book with this title, a few months after reviewing a book called What is luck?! This one is written by Andrew Elliott, whose Is that a big number? I reviewed a wee bit earlier… And that the cover of this book involves a particularly unlucky sequence of die as in my much earlier review of Krysz Burdzy’s book? (About 10⁻⁶ less likely than the likeliest draw!)

The (relative) specificity of this book is to try to convey the notions of chance and uncertainty to the general public, more in demonstrating that our intuition is most often wrong by examples and simulations, than in delving into psychological reasons as in Barbara Blatchley’s book. The author advances five dualities that underly our (dysfunctional) relation to chance: individual vs. collective, randomness vs. meaning, foresight vs. insight, uniformity vs. variability, and disruption vs. opportunity.

“News programmes clearly understand that the testimonies of individuals draw better audiences than the summaries of statisticians.” (p. xvii)

Some of the nice features of the book  are (a) the description of a probabilistic problem at the beginning of each chapter, to be solved at the end, (b) the use of simulation experiments, represented by coloured pixels over a grey band crossing the page, including a section on pseudorandom generators [which is less confusing that the quote below may indicate!], (c) taking full advantage of the quincunx apparatus, and (d) very few apologies for getting into formulas. And even a relevant quote of Taleb’s Black Swan about the ludic fallacy. On the other hand, the author spends quite a large component of the book on chance games, exhibiting a ludic tendency! And contemplates biased coins, while he should know better! The historical sections may prove too much for both informed and uninformed readers. (However, I learned that the UK Government had used a form of lottery to pay interests on premium bonds.) And the later parts are less numerical and quantified, even though the author brings in the micromort measurement [invented by Ronald Howard and] favoured by David Spiegelhalter. Who actually appears to have inspired several other sections, like the one on coincidences (which remains quite light in its investigation!). I finished the book rather quickly by browsing though mostly anecdotes and a lesser feel of a unified discourse. I did not find the attempt to link with the COVID pandemic, which definitely resets our clocks on risk, particularly alluring…

“People go to a lot of trouble to generate truly random numbers—sequences that are impossible to predict.” (p.66)

The apparition of the Normal distribution is somewhat overdone and almost mystical, if the tone gets more reasonable by the end of the corresponding chapter.

“…combining random numbers from distributions that really have no business being added together (…) ends up with a statistic that actually fits the normal distribution quite well.” (p.83)

The part about Bayes and Bayesian reasoning does not include any inference, with a rather duh! criticism of prior modelling.

“If you are tempted to apply a group statistic derived from a broad analysis to a more narrow purpose, you run the risk of making an unfair judgement.” (p.263)

The section about Xenakis’ musical creations as a Markov process was most interesting (and novel to me). I also enjoyed the shared cultural entries, esp. literary ones. Like citing the recent Chernobyl TV drama. Or Philip K. Dick’s Do Androids Dream of Electric Sheep? Or yet Monty Python’s Life of Brian. Overall, there is enough trivia and engagement to keep reading the book till its end!

extinction minus one

The riddle from The Riddler of 19 Feb. is about the Bernoulli Galton-Watson process, where each individual in the population has one or zero descendant with equal probabilities: Starting with a large population os size N, what is the probability that the size of the population on the brink of extinction is equal to one? While it is easy to show that the probability the n-th generation is extinct is

I could not find a way to express the probability to hit one and resorted to brute force simulation, easily coded

for(t in 1:(T<-1e8)){N=Z=1e4 
while(Z>1)Z=rbinom(1,Z,.5)
F=F+Z}
F/T

which produces an approximate probability of 0.7213 or 0.714. The impact of N is quickly vanishing, as expected when the probability to reach 1 in one generation is negligible…

However, when returning to Dauphine after a two-week absence, I presented the problem with my probabilist neighbour François Simenhaus, who immediately pointed out that this probability was more simply seen as the probability that the maximum of N independent geometric rv’s was achieved by a single one among the N. Searching later a reference for that probability, I came across the 1990 paper of Bruss and O’Cinneide, which shows that the probability of uniqueness of the maximum does not converge as N goes to infinity, but rather fluctuates around 0.72135 with logarithmic periodicity. It is only when N=2^n that the sequence converges to 0.721521… This probability actually writes down in closed form as

(which is obvious in retrospect!, albeit containing a typo in the original paper which is missing a ½ factor in equation (17)) and its asymptotic behaviour is not obvious either, as noted by the authors.

On the historical side, and in accordance with Stiegler’s law, the Galton-Watson process should have been called the Bienaymé process! (Bienaymé was a student of Laplace, who successively lost positions for his political idea, before eventually joining Académie des Sciences, and later founding the Société Mathématique de France.)

another book on J.B.S. Haldane [review of a book review]

As I noticed a NYT book review of a most recent book on J.B.S. Haldane, I realised several other books had already been written about him. From an early 1985 biography, “Haldane: the life and work of J.B.S. Haldane with special references to India” followed by a “2016 biography “Popularizing Science” along an  2009 edited book on some Haldane’s essays, “What I require from life“, all by Krishna R. Dronamraju to a 1969 biography with the cryptic title “J.B.S.“, by Richard Clarke, along with a sensational 2018 “Comrade Haldane Is Too Busy to Go on Holiday: The Genius Who Spied for Stalin” by Gavan Tredoux, depicting him as a spy for the Soviet Union during WW II. (The last author is working on a biography of Francis Galton, hopefully exonerating him of spying for the French! But a short text of him comparing Haldane and Darlington appears to support the later’s belief in racial differences in intelligence…) I also discovered that J.B.S. had written a children book, “Mr Friend Mr. Leaky“, illustrated by Quentin Blake, Roald Dahl’s illustrator. (Charlotte Franken Haldane, J.B.S.’s first wife, also wrote a considerable number of books.)

The NYT review is more a summary of Haldane’s life than an analysis of the book itself, hard as it is not to get mesmerised by the larger-than-life stature of J.B.S. It does not dwell very long on the time it took Haldane to break from the Communist Party for its adherence to the pseudo-science Lysenko (while his wife Charlotte had realised the repressive nature of the Soviet regime much earlier, which may have led to their divorce). While the review makes no mention at all of Haldane’s ideological move to the ISI in Kolkata, it concludes with “for all his failings, he was “deeply attractive during a time of shifting, murky moralities.”” [The double quotes being the review quoting the book!]

a conversation about eugenism at JSM

Following the recent debate on Fisher’s involvement in eugenics (and the renaming of the R.A. Fisher Award and Lectureship into the COPSS Distinguished Achievement Award and Lectureship), the ASA is running a JSM round table on Eugenics and its connections with statistics, to which I had been invited, along with Scarlett Bellamy, David Bellhouse, and David Cutler. The discussion is planned on 06 August at 3pm (ET, i.e., 7GMT) and here is the abstract:

The development of eugenics and modern statistical theory are inextricably entwined in history.  Their evolution was guided by the culture and societal values of scholars (and the ruling class) of their time through and including today.  Motivated by current-day societal reckonings of systemic injustice and inequity, this roundtable panel explores the role of prominent statisticians and of statistics more broadly in the development of eugenics at its inception and over the past century.  Leveraging a diverse panel, the discussions seek to shed light on how eugenics and statistics – despite their entangled past — have now severed, continue to have presence in ways that affect our lives and aspirations.

It is actually rather unclear to me why I was invited at the table, apart from my amateur interest in the history of statistics. On a highly personal level, I remember being introduced to Galton’s racial theories during my first course on probability, in 1982, by Prof Ogier, who always used historical anecdotes to enliven his lectures, like Galton trying to measure women mensurations during his South Africa expedition. Lectures that took place in the INSEE building, boulevard Adolphe Pinard in Paris, with said Adolphe Pinard being a founding member of the French Eugenics Society in 1913.