Francis Galton delivered “Probability, the Foundation of Eugenics” as the Herbert Spencer Lecture at Oxford in 1907, and the Clarendon Press printed it that same year. It is a short expository work—part memorial tribute, part scientific manifesto—in which the aging founder of eugenics explains how the mathematics of variation and correlation can be turned into a program for improving the human stock. The lecture moves from personal recollection to the history of a movement, then through five imagined “object lessons” in probability, and closes on the psychology of public opinion and the law.
Remembering Spencer at the Athenaeum
Galton opens by confessing that the invitation to give the Spencer lecture stirred vivid memories. He recalls Spencer’s forceful personality, his devotion to a self-imposed lifelong task, and the rare gleams of tenderness that broke through his abstract thought. Galton will not presume to lecture on Spencer’s writings; instead he acknowledges a large personal debt. Spencer would discuss ideas with quick sympathy and keen criticism through afternoons of rest in the old smoking room of the Athenaeum Club, strolling afterward to an adjoining compartment for billiards. Age, Galton observes, has stripped him of contemporaries. As a diffident young man he deferred to his seniors; now, an old man himself, he sees younger friends treating him with the same deference, and he regrets the loss of outspoken criticism that investigators need.
He notes with surprise that “Eugenics” appears in the titles of both the Boyle lecture given at Oxford a fortnight earlier and his own. The coincidence was accidental, but he accepts it as a happy omen. The field is wide enough that he need not overlap with the earlier lecturer, and he gladly defers to Professor Karl Pearson, a far higher authority on the subjects Pearson treated.
The History of a Word and an Idea
Galton admits he must be egotistical here, since he kindled the feeble flame that grew into a brisk fire. He coined “Eugenics” in Human Faculty (1883), a book long out of print and soon to be reissued cheaply. Its themes: the essential brotherhood of mankind, the reality of heredity, and the duty to act rather than wait for help like able-bodied idlers whining for doles. Individuals, he wrote, are finite detachments from an infinite ocean of being, temporarily endowed with executive powers—his only answer to the question “Why? whence? and whither?” The immediate “whither” is not wholly dark: Nature moves toward the evolution of mind, body, and character in increasing energy and co-adaptation.
He wonders why Keats’s Hyperion has not been ranked foremost among past speculations on evolution, since Keats makes the very divinities its product: Coelus, born of Chaos, engenders Saturn, Oceanus, Hyperion and the Titans, who are in turn superseded by the Olympian gods, with notable advance at each stage. Galton quotes Coelus’s whispered comfort to the prostrate Hyperion—”yet do thou strive for thou art capable”—and ten lines from Oceanus’s speech summarizing evolution, ending “this is the truth, and let it be your balm.”
From this Galton draws his creed. Men may be the chief, perhaps the only, executives on earth, detached on active service with possibly illusory free will, accountable for success or failure in furthering obscure ends. They are justified in interfering with the pitiless course of Nature by gentler, kindlier ways when possible. True piety, he holds, resides in action rather than submissive acquiescence—as with lightning conductors on churches, once thought impious, now their absence would draw contempt.
Direct pursuit of eugenics did not at first attract investigators; the idea ran too far ahead of popular imagination. So Galton waited, occupying himself with collateral problems, especially the measurable treatment of faculties distributed across a large population, published in Natural Inheritance (1889). That book proved more timely. Its methods were greatly elaborated by Karl Pearson and applied to biometry, powerfully aided by Professor Weldon of Oxford, whose untimely death Galton deplores. A new science was created primarily for biometry but equally applicable to eugenics, their provinces overlapping. Biometrika appeared in 1901, in which Galton took little more than a nominal part.
Appointed Huxley Lecturer before the Anthropological Institute in 1901, he took the title “The possible improvement of the Human Breed under the existing conditions of Law and Sentiment.” The next important step was Pearson’s Huxley lecture of 1903, “The Laws of Inheritance in Man,” a valuable compendium containing a passage Galton treats as central: “We are ceasing as a nation to breed intelligence as we did fifty to a hundred years ago. The mentally better stock in the nation is not reproducing itself at the same rate as it did of old; the less able, and the less energetic are more fertile than the better stocks. No scheme of wider or more thorough education will bring up, in the scale of intelligence, hereditary weakness to the level of hereditary strength. The only remedy, if one be possible at all, is to alter the relative fertility of the good and the bad stocks in the community.” In 1904 the newly formed Sociological Society asked him for a memoir, “Eugenics, its definition, aim, and scope,” followed in 1905 by three more: “Restrictions in Marriage,” “Studies in National Eugenics,” and a third the notes leave unfinished.
How Much Mischief? The Case for Quantifying Degeneracy
With the history told, Galton turns to application. Eugenics seeks quantitative results—”how much” or “how little” in precise figures, not vague words like “much” or “little.” Suppose a class A afflicted with a specified form and degree of degeneracy, inferred from personal observation and family history, and class B consisting of A’s offspring. When A’s grade is very low, the average B will fall below par and do mischief to the community; how much mischief is a familiar question, answerable once enough facts are collected. A second, stranger question is the trustworthiness of forecasts from averages when applied to individuals. The average mischief done by each B individual he calls M; individual mischiefs deviate from M by amounts whose average is D, the measure of untrustworthiness. The smaller D, the more precise the forecast and the stronger the case for drastic measures against propagation of class B. A large D means uncertainty—a risk akin to the maxim that it is better many guilty escape than one innocent suffer. But that maxim is not the sentiment guiding natural selection, and Galton warns it is dangerous to yield far to it. A thorough investigation, even of a single grade of degeneracy, would be serious work, requiring masses of trustworthy material and skilled treatment by methods few can employ; extended investigation implies huge labor for eugenics laboratories indefinitely.
Five Object Lessons in Probability
Most ordinary persons, Galton complains, know nothing of the fundamental principles of probability involved in the newer methods of biometry and eugenics, and this ignorance obstructs the cause. He is conscious of the study required to handle those mathematical methods adequately, but he holds that the fundamental ideas of abstruse probability problems can be presented to any intelligent person ignorant of mathematics—provided the lessons are “object lessons,” handling real objects as in the Kindergarten system. He hopes teachers of science will elaborate the course, which he divides into five lessons of one hour each, leading to a notion of correlation, which in turn requires knowledge of variation. Variability, seemingly indefinite, can like Proteus be seized, bound, defined, and measured. Old statistics concerned itself solely with averages, treating a population as a structureless atom; the newer methods treat it as a compound unit.
The first lesson explains the variability of size, weight, number and the like by specimens marshalled at random or arrayed in order of magnitude—chestnuts, acorns, hazel-nuts, stones of wall fruit strung as beads. An array of variates falls into a continuous series; variates differ little from their neighbors about the middle, but the differences increase toward the extremities. Arrays of the same class laid side by side have their middlemost variates, or medians, compared, and medians become very similar when numbers are large. Double accuracy usually accompanies a four-fold number, treble accuracy a nine-fold number. The words learned: variability, variate, array, median.
The second lesson gives precision to the array. Variates strung on a cord are disposed at equal distances before equal compartments, like horses before stalls, their tops joined; there is always one more side to the row than objects. Position is indicated by serial number or by degrees like a thermometer, counting the first side as 0°, which makes one more graduation than objects. The serial position of the median is always the same in any two arrays whatever the number of variates, but the serial positions of subdivisions cannot be the same, since the ignored half interval at either end varies with the number and becomes considerable when the number is small. Lines of proportionate length are drawn on a blackboard, limits drawn at a half interval from either end, the base divided centesimally, the tops joined by a smooth curve; then everything is wiped out except the curve, the limits, and the centesimally divided base. This is a scheme of distribution of variates, whose shape is independent of number so long as the number is large enough for statistical constancy. Numerous schemes show a family likeness between their bounding curves. The words learned: schemes of distribution, centesimal graduation of base.
The third lesson passes from variates measured upward from the base to deviates measured upward or downward from the median as positive or negative values. A scheme of variates consists of the median, a constant, and the curve, the variations from it; a horizontal line through the top of the median serves as axis, divided centesimally, and everything is wiped out except curve, axis, and limits—a scheme of distribution of deviates. Ordinates at the 25th and 75th divisions are the “quartile” deviates. The genesis of the theoretical normal curve might be briefly explained, along with its generality and its property of reproduction; diagrams show the prevalence of approximately normal distributions, and strongly marked skew curves are exhibited with their genesis explained. The ordinate at any centesimal division in two normal curves measures relative variability, but the quartile is commonly the unit of variability, under the “almost grotesque” name “probable error”—signifying that a deviate is as likely as not to exceed or fall short of it, which by construction is the case of either quartile. New words: scheme of distribution of deviates, axis, normal, skew, quartile, probable error.
The fourth lesson explains that the curve of normal distribution is not the direct result of calculation, nor does its formula lend itself as freely to further calculation as that of frequency; their shapes differ—the first an ogive, the second bell-shaped. In the curve of frequency, deviations are reckoned from the mean of all variates, not the median; mean and median coincide in normal curves but may differ much in others. Either curve can be transformed into the other, best exemplified using a polygon of rectangles differing in height by the same amounts but with widths representing frequencies. The curve of frequency lacks a readily perceived unit of variability comparable to the quartile; its unit is the “standard deviation,” whose genesis admits of illustration, though the calculations for finding its value lie beyond these lessons. The learner must accept the calculated ordinates of the normal curve as he accepts the time of day from his watch, ignorant of its construction; the formulae for quasi-normal and skew curves are further beyond his reach, requiring advanced mathematics. New words and ideas: curve of frequency, standard deviation, mean, binomial series.
Correlation, and the Pulley Demonstration
The fifth and last lesson concerns the measurement of correlation—the closeness of relation between two systems whose variations arise partly from common causes and partly from causes special to each. It applies to nearly every social relation: environment and health, social position and fertility, kinship of parent to child, of uncle to nephew. Galton illustrates it mechanically with two pulleys and weights suspended from a cord held by three persons. No. 2 holds the middle; one half of the cord passes round one pulley to No. 1’s hand, the other half round the other pulley to No. 3’s hand. The hands move independently, but since both weights are partly controlled by No. 2, their movements become “correlated.”
A table of correlations on squared paper is then explained on the blackboard. Pairs of correlated values A and B are expressed in units of their respective variabilities and sorted into squares—vertically by magnitude of A, horizontally by magnitude of B—and the mean of each partial array of B values for each grade of A is determined. Theoretically, where variability is normal, the means of B lie practically in a straight line; observation shows this in most other cases too. Thus the average deviation of a B value bears a constant ratio to the deviation of the corresponding A value—the “index of correlation,” expressed by a single figure. If thigh-bones deviate “very much” from the usual length of their race, the average corresponding arm-bones will differ “much,” but not “very much,” and the ratio between “very much” and “much” is constant and in the same direction whatever numerical value is attached to “very much.” The trustworthiness of the index for individual cases is readily calculable; absolute correlation is expressed by 1.0, nil correlation by 0.0. With this, Galton closes the object lessons, trusting they show that a brief illustrated course would give an acceptable introduction to the newer methods in biometry and eugenics, and that experts reading the printed form at leisure would find sufficient guidance for elaborating the details.
Assurance, Public Opinion, and the Levers of Reform
The lecture’s final movement turns from probability to the influence of collective truths upon individual conduct. Probability, determined by methods cognizant of variations, yields exact results and affords a solid foundation for action. But human action is a superstructure into which emotion enters; we are guided less by certainty and probability than by “assurance” to a greater or lesser degree. The word derives from “sure,” an abbreviation of “secure” (se-cura, without misgiving); it names a contented attitude of mind largely dependent on custom, prejudice, or other unreasonable influences which reformers must overcome—and some of which they are apt to exploit on their own behalf. Human nature rarely finds its way by pure reason; it peers through spectacles with colored and distorting glasses.
Locke, Galton suggests, seems to confound certainty with assurance when he describes how men are guided in daily affairs: a man would be at a great loss with nothing to direct him but the certainty of true knowledge, which is very short and scanty; he who will not eat till it is demonstrated that food will nourish him, nor stir till he infallibly knows his business will succeed, will have little else to do but sit still and perish.
A society, Galton proposes, may be considered a highly complex organism with a consciousness of its own, caring only for itself, establishing regulations and customs for its collective advantage and creating a code of opinions to serve that end. Its power over the individual is hard to overrate regarding any obvious particular on which it emphatically insists; Galton trusts that in future the practice of eugenics will be one such particular. Otherwise the influence of collective truths on individual conduct is deplorably weak, as the quoted verses put it: others’ follies teach us not, nor much their wisdom teaches, but chief of solid worth is what our own experience preaches.
Professor Westermark, among many remarks Galton fully endorses, has aptly stated the obstacle that keeps individuals from perceiving the importance of eugenics: “the prevalent opinion that almost anybody is good enough to marry is chiefly due to the fact that in this case, cause and effect, marriage and the feebleness of the offspring, are so distant from each other that the near-sighted eye does not distinctly perceive the connexion between them.” Enlightenment of individuals is a necessary preamble to practical eugenics, but social opinion is the tyrant by whose praise or blame the principles of eugenics may hereafter influence individual conduct—and public opinion, Galton concludes, may easily be directed.
What the Lecture Bequeathed
The lecture is a strange and revealing document: a founding text of eugenics that spends most of its length on chestnuts, thermometers, and pulleys. Galton’s wager is that a statistical education in variation and correlation will make the case for selective breeding feel like common sense, and that the machinery of public opinion can then be steered toward it. The confidence in measured heredity, the fear of differential fertility among the “better” and “less able” stocks, and the frank ambition to shape law and sentiment all reappear in the twentieth-century eugenics movements that followed—movements whose consequences made the lecture’s calm arithmetic notorious. Read historically, it shows how a Victorian statistician’s faith in numbers became a program for intervening in human reproduction.
