Hereditary Genius

We are all prisoners of our backgrounds as well as slaves to our genes, and no field of science is riper for sociological investigation based on this premise than the development of biometry, and hence of much of modern statistics, from 1865 onwards. For did it not grow out of one of the Victorian reform movements, eugenics? Were not its successive leaders drawn from the same class of British society, with its capacity to disguise self-interest behind proposals for social reform, to salve its social conscience by promoting good causes at other people’s expense?

In Statistics in Britain D.A. MacKenzie has harnessed this theory to explain the work of Francis Galton (1822-1911), Karl Pearson (1857-1936) and R.A. Fisher (1890-1962): ‘I argue that eugenics did not merely motivate their statistical work but affected its content.’ That one’s family background and early experiences determine in large measure one’s intellectual motivation is an empty observation (what other determinants could there be?), but that the subsequent development of one’s scientific thought is to an appreciable extent directed by continuing social pressure is a statement of more substance. Sociologists (on account of their family background and early experiences?) seek sociological explanations. Sociology is, after all, either everything or nothing, and we can hardly expect its proponents to accept that it is nothing.

So our first problem is the bias of the observer; we need some relativistic sociologists, capable of interpreting their observations independently of their own frames of reference. But to admit that possibility is to admit it for scientists too. Oddly enough, geneticists encountered a similar problem in their own work in the early years of this century. It arises if one wishes to estimate the proportion of individuals who possess a particular characteristic when the information has been ascertained (the geneticists’ technical word) wholly or partly via persons with the characteristic. The classical example is that of trying to find out the sex-ratio in the general population of school-children by making inquiries at a boys’ school. R.A. Fisher, developing the work of the German physician W. Weinberg, constructed a mathematical theory of ascertainment to compensate for such biases (in the case of the school-children one asks the boys how many brothers and sisters each has, and forms the totals excluding the boys questioned). Francis Galton, in Hereditary Genius, overlooked this point, concluding that since judges were all men, and came from families of average size five, each must have (on average) 2½ sisters and 1½ brothers. The genetical problem has proved tractable, but the sociological problem is fundamentally insoluble. The sociologist asks, What drives the scientist? and the scientist may reasonably reply: What drives the sociologist?

At his best, the sociologist is driven by precisely those forces which he is inclined to deny the scientist. He wants to explain for explanation’s sake, for his own intellectual satisfaction. Of course, his satisfaction is inevitably bound up with how his peers view his explanations, but that is a trite comment which leads nowhere. Man is endowed with curiosity and the power to theorise (attributes which geneticists can explain his possessing without difficulty); scientific man has exploited this endowment with astonishing success, and sociological man wishes to emulate him. Scientific man has developed concepts of ever greater generality from which enormous numbers of verifiable consequences flow – concepts like energy, entropy, gravitation, potential fields. So successful have the physical sciences been that it is part of our culture to think that gravity causes the apple to fall, that momentum causes the bullet to penetrate, that minimising potential energy causes the water to stay in the bath. The idea of a potential field is indeed one of the most powerful of all these concepts, so powerful that it seems to dictate what will happen, and not merely describe it. Many biologists have been intoxicated with the idea that natural selection itself can be described by viewing the changes in gene frequencies in a population as responses to a potential field, the ‘force’ in this case being caused by the differential survival of individuals. Fisher, himself trained in mathematical physics, had to defend his ‘fundamental theorem of natural selection’ against the interpretation that it defined such a potential field. But so strong is the appeal of potential theory that biologists, when off-guard, often express themselves as though they believe that individuals in a population behave so as to maximise their mean fitness (the supposed potential function), whereas in truth a population’s mean fitness is a consequence, and not a determinant, of the behaviour of the individuals. Fisher’s physical analogy was with entropy and the second law of thermodynamics, not potential theory. Some years ago, in collaboration with L.L. Cavalli-Sforza, I introduced the ‘method of minimum evolution’ as a procedure for estimating the structure of evolutionary trees, and it very rapidly found its way into the literature as a method justified by an appeal to the principle that evolution attains its goals by proceeding along some minimum path, like a sentient being going shopping. It is nonsense, of course, but it has proved compelling nonsense.

Now along come the sociologists, attracted to the theories of biology just as the biologists have been attracted to the theories of physics, seeming to want to impose on the generation of ideas a potential field, defined by the social milieu, which in some mysterious way draws the scientist’s thoughts along a predestinate groove. ‘If only,’ they seem to say, ‘we can study the impact of society on science in great enough detail we will find the potential function involved, and all will be clear.’ Were they to succeed, they would be able to predict the path of scientific progress: but in reality the observation that scientists as a class behave in a particular way is no more a clue to the thoughts of an individual scientist than observations on a gas reveal the motion of an individual molecule. It is the penetrating mind of the rare scientist of genius that determines scientific advance, and not the measurable hordes of scientific labourers beavering away from nine to five.

Sir Francis Galton was Charles Darwin’s half-cousin, and (like Darwin) left Cambridge with an ordinary degree. He wrote in his autobiography: ‘I had been immensely impressed by many obvious cases of heredity among the Cambridge men who were at the University about my own time.’ He took his BA in 1844; Darwin’s On the Origin of Species appeared in 1859. It ‘made a marked epoch in my own mental development,’ wrote Galton years later. ‘Its effect was to demolish a multitude of dogmatic barriers by a single stroke, and to arouse a spirit of rebellion against all ancient authorities whose positive and unauthenticated statements were contradicted by modern science.’ In 1869, Galton’s book Hereditary Genius appeared, and during the next twenty years of his long life he developed the concepts of regression and correlation, the cornerstones of biometry in its early days. One of his most profound observations was that the statistical errors which it was the ambition of the physical scientist or astronomer to reduce or even eliminate (as a nuisance which merely clouded the true value sought) ‘were the very things I wanted to preserve and to know about’. Individuals varied, and that very variation was Galton’s raw material, as it had been Darwin’s.

MacKenzie traces Galton’s statistical progress faithfully, stressing the vital importance of his eugenic interests. He ends his chapter on Galton thus: ‘And Galton’s eugenics reflected the social interests of the group of élite professionals to which he belonged. Hence we have here an instance of the effect of social interests on the conceptual development of statistical theory.’ That seems to me to be such a banal conclusion. Galton was Galton: like each one of us, a unique individual, moulded by his background. His thoughts reflected the fact that he was Galton, and it is necessary, in order to understand them, to know something of his life and background. But I do not see anything amounting to a sociological theory in this fact.

Rather, as D.W. Forrest’s readable biography of Galton (1974) shows, Galton was a very gifted man with a splendid imagination and a wealth of experiences from his travels (his Art of Travel is marvellously entertaining). He was very influential, especially through the work of Karl Pearson, who wrote a massive Life of him, published in the years 1914 to 1930. To Pearson Mackenzie now turns his attention.

Karl Pearson was also a Cambridge man, taking his BA from King’s College in 1879, in this case with Honours since he was Third Wrangler in the Mathematical Tripos. In the University lists he is spelt Carl, and it is said that he changed the spelling out of admiration for Germany – of his journal Biometrika, started in 1901, he said: ‘the K was mine (K.P. not C.P.).’ MacKenzie carefully surveys the political development of the young Pearson (‘the poverty and squalor of Victorian England, and the complacent superficiality of Cambridge University, are themes that begin to appear in his thought’), and there is ample evidence that by the time he became seriously involved in the development of biometry, in the 1890s, he possessed a highly-developed political personality, and was actively engaged in the social arguments of the day. Much more so than with Galton, the scene is set for a sociological explanation of Pearson’s statistical work. But suddenly MacKenzie draws back. Pearson was ‘exceptional’; ‘Pearson’s overall intellectual position was unique.’ But ‘if our sociology of knowledge proposes tendencies in belief that need not actually be manifest in the majority of individuals most of the time, then we may actually get more insight by looking at exceptional moments in time and at exceptional individuals rather than at normal periods and average people.’ So MacKenzie studies Pearson, but reaches no more definite conclusion than that, in his case, ‘all we have is an instance of a “match” of beliefs and social interests.’ All is not lost, however, for ‘a sociological approach need not be restricted to relatively large-scale movements but can also be used to analyse the work of unique individuals such as Karl Pearson.’

Pearson, for whom no full biography yet exists, comes across as less gifted than his mentor Galton, but more politically motivated, enormously energetic, a much better mathematician, of course, and increasingly intolerant. From being Professor of Applied Mathematics and Mechanics at University College London (1884) he moved to the Galton Professorship of Eugenics in 1911, founded for him by Galton in his will. Already, with the support of W.F.R. Weldon, the Professor of Zoology, a ‘biometrical’ school had been established: the Galton Professorship confirmed Pearson’s leadership, and gave him immense authority as statistics developed in England.

In the next three chapters MacKenzie reconstructs ‘The Development of Statistical Theory as a Scientific Speciality’, gives an account of ‘Biometrician versus Mendelian’, and examines ‘The Politics of the Contingency Table’. These are good chapters, with a wealth of interesting detail. Though the second covers fairly familiar territory (see, for example, W.B. Provine’s The Origins of Theoretical Population Genetics, 1971), the third breaks new ground. The only participant in these controversies to be severely pigeonholed by MacKenzie is William Bateson, chief Mendelian, whose philosophy MacKenzie describes as one of ‘romantic-conservatism’ founded on Cambridge (his father had been Vice-Chancellor). ‘His defence of traditional Cambridge was in spite of the fact that his personal career in the University was largely unsuccessful. He never reached the prominent position of his father, and for a long time relied on marginal posts (such as the Stewardship of St John’s College) in order not to have to seek employment outside the University.’ Something has gone severely wrong here: it was the father, W.H. Bateson, who never held a University teaching post, and whose one-year stint as Vice-Chancellor occurred in an age when that office rotated amongst the heads of the colleges essentially by seniority (he had also been Orator before being elected Master of St John’s). By contrast, William Bateson, the son, was the subject of a special Report to the University (Cambridge University Reporter, 1907-8, page 213) recommending a Readership for him ‘in view of the distinguished character of his work and the importance of his teaching in University education, and because there seems to be at the present moment no other way in which his services can be secured to the University’. ‘The General Board regret that in view of the state of University finances they cannot propose at the present time to establish a Professorship in Heredity and Variation.’ The following year an anonymous benefactor offered to fund a Professorship of Biology for five years, and the University accepted, the subject to be Genetics. Bateson was elected, and held it until he went to direct the John Innes Horticultural Institution in 1910 (before the five years were up, Arthur Balfour’s benefaction had enabled the University to establish a permanent Professorship of Genetics, held by R.C. Punnett and then R.A. Fisher). MacKenzie is thus wrong in detail, but would in any case have been wrong to regard as necessarily unsuccessful a Cambridge career that did not involve a University post. At the end of the last century the colleges dominated the University, and many a distinguished man never held a University post (John Venn, for example, to name someone MacKenzie’s book also mentions, or – from this century – John Maynard Keynes, son of the University’s Registrary).

And so MacKenzie, having tested his theory on Galton and Pearson, comes to R.A. Fisher. Fisher, I think, defeats him, and he partly admits as much: ‘The explanation of what is novel in Fisher’s statistical theory must, in general, be sought elsewhere’ (and not in Fisher’s commitment to eugenics). But MacKenzie still tries to explain Fisher’s choice of scientific career in terms of his involvement with eugenics. He points out that the work for his degree was in mathematics and mathematical physics (Fisher took the Cambridge Mathematical Tripos, but by 1910 candidates were no longer listed in order of merit: he was a double First), and that ‘there was little in Fisher’s curriculum to turn him in the direction of statistics and genetics.’ Hence it must be eugenics that influenced him.

This is probably false. Fisher’s interests in both mathematics and natural history were much in evidence at school. In a recent Fisher Memorial Lecture, Professor Henry Bennett, of Adelaide, remarked that Fisher used to spend his school prizes for mathematics on books in natural history – not only the works of Charles Darwin in 13 volumes, but also the writings of Bateson and others. Nor does one need any deep hypothesis for this: schoolboys interested in science are often attracted to natural history or to astronomy in the first instance, fields in which the ‘wonders of science’ are most manifest to the youthful observer. Fisher, the talented mathematician, was attracted to natural history, and it is straight forward to postulate that his commitment to eugenics grew out of a thoughtful reading of the work of Darwin and others. There is a story that he was intending to become a biologist until he saw the skull of a codfish laid out in a museum, with each bone carefully labelled, and decided in favour of mathematics! It is a pity that MacKenzie was refused access (he says) to the Fisher papers in Adelaide, which might have helped him fill in the early years: but it is instructive to see how easy it is to jump to the ‘eugenics’ conclusion.

The major difference between the social influences on Galton’s and Pearson’s biometry, on the one hand, and on Fisher’s, on the other, is that the first two came to biometry in middle age, with fully-developed political views, consciously or unconsciously expressed, whilst Fisher’s first major contribution (we now know) was his paper ‘Heredity, comparing the Methods of Biometry and Mendelism’, given as a third-year undergraduate. ‘This paper shows that Fisher had already immersed himself in the academic literature relevant to eugenics.’ Moreover, Fisher published his method of maximum likelihood at the same time, putting his finger precisely on the weak points of Gauss’s method of least squares, Laplace’s method of inverse probability, and Pearson’s method of moments, in the estimation of parameters, and also ‘got out’ Student’s t-distribution – remarkable achievements. Fisher’s eugenics, and indeed the whole of his views on the interaction of genetics and human society manifest in the later chapters of The Genetical Theory of Natural Selection, are rooted in his science, and not the other way round. Fisher is not good material for sociologists.

What, then, drove him? Why was it Fisher, and not someone else, who made these advances? Apart from comments on his professional middle-class associations, MacKenzie tells us that Fisher was absent-minded and unconventional in dress, keen on subsistence farming, kept goats, was eccentric, egocentric and possessed a violent temper. But he never mentions his outstanding characteristic, which explains so much: Fisher was very, very clever.

He understood so much more than most men; his analytical powers were greater than Pearson’s, his scientific imagination was more fertile than Galton’s. He was exceptionally gifted intellectually, and made advances in biometrical thought which were profound, difficult, and often misunderstood. Lesser men criticised his powers of explanation, but in reality the problems that interested him, both in statistics and in population genetics, were simply more difficult than those that Galton and Pearson had grappled with. It is to his credit that MacKenzie has himself understood Fisher’s contribution up to 1930, and his chapter is a fair account of it. But it does not help his social theorising.

There is one facet of the way in which Pearson influenced Fisher which is possibly important, and which has escaped MacKenzie. In 1916, Pearson declined to publish in Biometrika a note by Fisher in which the latter criticised a contributor for using ‘minimum-χ²’ as a method of estimation. Pearson wrote, ‘If you will write me a defence of the Gaussian method, I will certainly consider its publication’: by ‘Gaussian method’ he meant the method of maximising the posterior probability, assuming a uniform prior probability, which Gauss had used in Theoria Motus. Now Fisher had, as mentioned above, already introduced the method of maximum likelihood, but without any justification beyond an appeal to intuition. It is likely that, in response to Pearson’s challenge, Fisher (who had no intention of defending the Gaussian method itself) decided to see if he could defend his method of maximum likelihood in terms which Pearson would understand and accept, by showing that it had sensible properties under ‘repeated-sampling’. The result was his 1922 paper ‘On the mathematical foundations of theoretical statistics’, which introduced so many of the concepts vital to a ‘repeated-sampling’ theory of statistics. Yet in later writings there is ample evidence that to Fisher the maximisation of a likelihood was justified by an appeal to the more primitive notion that likelihood itself was a measure of the acceptability of a hypothesis So perhaps Pearson’s challenge led to most of modern non-Bayesian statistical theory (including the Neyman-Pearson theory, constructed jointly by Neyman and karl Pearson’s son) without Fisher’s whole-hearted commitment to his reply!

Another marked influence on Fisher’s intellect, not mentioned by MacKenzie, was his extreme short-sightedness, which not only encouraged the development of his powers of abstract thought but ensured that he was spared active service in the First World War. Other influences are amply recorded in the biography by one of his daughters, Joan Box (The Life of a Scientist, 1978).

In a closing chapter, MacKenzie contrasts the different possible approaches to the history of science, and defends the sociological. But the best history of science always was ‘sociological’ of necessity, and the only real criticism of MacKenzie’s very thorough and well-written book is that the social theory it contains is unnecessary, for where it is successful it is obvious. In the Introduction the author writes: ‘My intention is not to provide a simple description of the developments in statistical theory of the years from 1865 to 1930.’ In the event, he has succeeded admirably in doing just that.