Francis Galton
Excerpts from Hereditary genius Macmillan, 2nd edn, 1892,
chapter 3.
I have no patience with the hypothesis occasionally expressed, and often implied, especially in tales written to teach children to be good, that babies are born pretty much alike, and that the sole agencies in creating differences between boy and boy, and man and man, are steady application and moral effort. It is in the most unqualified manner that I object to pretensions of natural equality. The experiences of the nursery, the school, the University, and of professional careers, are a chain of proofs to the contrary. I acknowledge freely the great power of education and social influences in developing the active powers of the mind, just as I acknowledge the effect of use in developing the muscles of a blacksmith's arm, and no further. Let the blacksmith labour as he will, he will find there are certain feats beyond his power that are well within the strength of a man of herculean make, even although the latter may have led a sedentary life. Some years ago, the Highlanders held a grand gathering in Holland Park, where they challenged all England to compete with them in their games of strength. The challenge was accepted, and the well-trained men of the hills were beaten in the foot-race by a youth who was stated to be a pure Cockney, the clerk of a London banker.
Everybody who has trained himself to physical exercises discovers the extent of his muscular powers to a nicety. When he begins to walk, to row, to use the dumb bells, or to run, he finds to his great delight that his thews strengthen, and his endurance of fatigue increases day after day. So long as he is a novice, he perhaps flatters himself there is hardly an assignable limit to the education of his muscles; but the daily gain is soon discovered to diminish, and at last it vanishes altogether. His maximum performance becomes a rigidly determinate quantity. He learns to an inch how high or how far he can jump, when he has attained the highest state of training. He learns to half a pound the force he can exert on the dynamometer, by compressing it. He can strike a blow against the machine used to measure impact, and drive its index to a certain graduation, but no further. So it is in running, in rowing, in walking, and in every other form of physical exertion.
There is a definite limit to the muscular powers of every man, which he cannot by any education or exertion overpass.
This is precisely analogous to the experience that every student has had of the working of his mental powers. The eager boy, when he first goes to school and confronts intellectual difficulties, is astonished at his progress. He glories in his newly developed mental grip and growing capacity for application, and, it may be, fondly believes it to be within his reach to become one of the heroes who have left their mark upon the history of the world. The years go by; he competes in the examinations of school and college, over and over again with his fellows, and soon finds his place among them. He knows he can beat such and such of his competitors; that there are some with whom he runs on equal terms, and others whose intellectual feats he cannot even approach. Probably his vanity still continues to tempt him, by whispering in a new strain. It tells him that classics, mathematics, and other subjects taught in universities, are mere scholastic specialities, and no test of the more valuable intellectual powers. It reminds him of numerous instances of persons who had been unsuccessful in the competitions of youth, but who had shown powers in after-life that made them the foremost men of their age. Accordingly, with newly furbished hopes, and with all the ambition of twenty-two years of age, he leaves his University and enters a larger field of competition. The same kind of experience awaits him here that he has already gone through. Opportunities occur - they occur to every man - and he finds himself incapable of grasping them. He tries, and is tried in many things. In a few years more, unless he is incurably blinded by self-conceit, he learns precisely of what performances he is capable, and what other enterprises lie beyond his compass. When he reaches mature life, he is confident only within certain limits, and knows, or ought to know, himself just as he is probably judged of by the world, with all his unmistakable weakness and all his undeniable strength. He is no longer tormented into hopeless efforts by the fallacious promptings of overweening vanity, but he limits his undertakings to matters below the level of his reach, and finds true moral repose in an honest conviction that he is engaged in as much good work as his nature has rendered him capable of performing.
There can hardly be a surer evidence of the enormous difference between the intellectual capacity of men than the prodigious differences in the numbers of marks obtained by those who gain mathematical honours at Cambridge [....]
The mathematical powers of the last man on the list of honours, which are so low when compared with those of a senior wrangler, are mediocre, or even above mediocrity, when compared with the gifts of Englishmen generally. Though the examination places 100 honour men above him, it puts no less than 300 'poll men' below him. Even if we go so far as to allow that 200 out of the 300 refuse to work hard enough to get honours, there will remain 100 who, even if they worked hard, could not get them. Every tutor knows how difficult it is to drive abstract conceptions, even of the Simplest kind, into the brains of most people - how feeble and hesitating is their mental grasp - how easily their brains are mazed how incapable they are of precision and soundness of knowledge. It often occurs to persons familiar with some scientific subject to hear men and women of mediocre gifts relate to one another what they have picked up about it from some lecture - say at the Royal Institution, where they have sat for an hour listening with delighted attention to an admirably lucid account, illustrated by experiments of the most perfect and beautiful character, in all of which they expressed themselves intensely gratified and highly instructed. It is positively painful to hear what they say. Their recollections seem to be a mere chaos of mist and misapprehension, to which some sort of shape and organisation has been given by the action of their own pure fancy, altogether alien to what the lecturer intended to convey. The average mental grasp even of what is called a well-educated audience will be found to be ludicrously small when rigorously tested.
In stating the differences between man and man, let it not be supposed for a moment that mathematicians are necessarily onesided in their natural gifts. There are numerous instances of the reverse, of whom the following will be found, as instances of hereditary genius, in the appendix to my chapter on SCIENCE. I would especially name Liebnitz, as being universally gifted; but Ampere, Arago, Condorcet, and D'Alembert were all of them very far more than mere mathematicians. Nay, since the range of examination at Cambridge is so extended as to include other subjects besides mathematics, the differences of ability between the highest and the lowest of the successful candidates is yet more glaring than what I have already described. We still find, on the one hand, mediocre men, whose whole energies are absorbed in getting their 237 marks for mathematics; and, on the other hand, some few senior wranglers who are at the same time high classical scholars and much more besides. Cambridge has afforded such - instances. Its list of classical honours is comparatively of recent
date, but other evidence is obtainable from earlier times of their occurrence. Thus, Dr George Butler, the Head Master of Harrow for very many years, including the period when Byron was a schoolboy (father of the present Head Master, and of other sons, two of whom are also head masters of great public schools), must have obtained that classical office on account of his eminent classical ability; but Dr Butler was also senior wrangler in 1794, the year when Lord Chancellor Lyndhurst was second. Both Dr Kaye, the late Bishop of Lincoln, and Sir E. Alderson, the late judge, were the senior wranglers and the first classical prizemen of their respective years. Since 1824, when the classical tripos was first established, the late Mr Goulburn (son of the Right Hen. H. Goulburn, Chancellor of the Exchequer) was second wrangler in 1835, and senior classic of the same year. But in more recent times, the necessary labour of preparation, in order to acquire the highest mathematical places, has become so enormous that there has been a wider differentiation of studies. There is no longer time for a man to acquire the necessary knowledge to succeed to the first place in more than one subject. There are, therefore, no instances of a man being absolutely first in both examinations, but a few can be found of high eminence in both classics and mathematics, as a reference to the lists published in the Cambridge calendar will show. The best of these more recent degrees appear to be that of Dr Barry, late Principal of Cheltenham, and now Principal of King's College, London (the son of the 'eminent architect, Sir Charles Barry, and brother of Mr Edward Barry, who succeeded his father as architect). He was fourth wrangler and seventh classic of his year.
In whatever way we may test ability, we arrive at equally enormous
intellectual differences. Lord Macaulay [....] had one of the
most tenacious of memories. He was able to recall many pages of
hundreds of volumes by various authors, which he had acquired
by simply reading them over. An average man could not certainly
carry in his memory one thirty-second - ay, or one hundredth -
part as much as Lord Macaulay. The father of Seneca had one of
the greatest memories on record in ancient times [. .. .] Person,
the Greek scholar, was remarkable for this gift, and, I may add,
the 'Person memory' was hereditary in that family. In statesmanship,
generalship, literature, science, poetry, art, just the same enormous
differences are found between man and man; and numerous instances
recorded in this book will show in how small degree eminence,
either in these or any other class of intellectual powers, can
be considered as due to purely special powers. They are rather
to be considered in those instances as the result of concentrated
efforts made by men who are widely gifted. People lay too much
stress on apparent specialities, thinking over-rashly that, because
a man is devoted to some particular pursuit, he could not possibly
have succeeded in anything else. They might just as well say that,
because a youth had fallen desperately in love with a brunette,
he could not possibly have fallen in love with a blonde. He may
or may not have more natural liking for the former type of beauty
than the latter, but it is as probable as not that the affair
was mainly or wholly due to a general amorousness of disposition.
It is just the same with special pursuits. A gifted man is often
capricious and fickle before he selects his occupation, but when
it has been chosen, he devotes himself to it with a truly passionate
ardour. After a man of genius has selected his hobby, and so adapted
himself to it as to seem unfitted for any other occupation in
life, and to be possessed of but one special aptitude, I often
notice, with admiration, how well he bears himself when circumstances
suddenly thrust him into a strange position. He will display an
insight into new conditions, and a power of dealing with them,
with which even his most intimate friends were unprepared to accredit
him. Many a presumptuous fool has mistaken indifference and neglect
for incapacity; and in trying to throw a man of genius on ground
where he was unprepared for attack, has himself received a most
severe and unexpected fall. I am sure that no one who has had
the privilege of mixing in the society of the abler men of any
great capital, or who is acquainted with the biographies of the
heroes of history, can doubt the existence of grand human animals,
of nature preeminently noble, of individuals born to be kings
of men. I have been conscious of no slight misgiving that I was
committing a kind of sacrilege whenever, in the preparation of
materials for this book, I had occasion to take the measurement
of modern intellects vastly superior to my own, or to criticise
the genius of the most magnificent historical specimens of our
race. It was a process that constantly recalled to me a once familiar
sentiment in bygone days of African travel, when I used to take
altitudes of the huge cliffs that domineered above me as I travelled
along their bases, or to map the mountainous landmarks of unvisited
tribes, that loomed in faint grandeur beyond my actual horizon.
I have not cared to occupy myself much with people whose gifts are below the average, but they would be an interesting study. The number of idiots and imbeciles among the twenty million inhabitants of England and Wales is approximately estimated at
50,000, or as 1 in 400. Dr Seguin, a great French authority on these matters, states that more than thirty per cent of idiots and imbeciles, put under suitable instruction, have been taught to conform to social and moral law, and rendered capable of order, of good feeling, and of working like the third of an average man. He says that more than forty per cent have become capable of the ordinary transactions of life, under friendly control; of understanding moral and social abstractions, and of working like two-thirds of a man. And, lastly, that from twenty-five to thirty per cent come nearer and nearer to the standard of manhood, till some of them will defy the scrutiny of good judges, when compared with ordinary young men and women. In the order next above idiots and imbeciles are a large number of milder cases scattered among private families and kept out of sight, the existence of whom is, however, well known to relatives and friends; they are too silly to take a part in general society, but are easily amused with some trivial, harmless occupation. Then comes a class of whom the Lord Dundreary of the famous play may be considered a representative; and so, proceeding through successive grades, we gradually ascend to mediocrity. I know two good instances of hereditary silliness short of imbecility, and have reason to believe I could easily obtain a large number of similar facts.
To conclude, the range of mental power between - I will not say the highest Caucasian and the lowest savage - but between the greatest and least of English intellects, is enormous. There is a continuity of natural ability reaching from one knows not what height, and descending to one can hardly say what depth. I propose in this chapter to range men according to their natural abilities, putting them into classes separated by equal degrees of merit, and to show the relative number of individuals included in the several classes. Perhaps some person might be inclined to make an offhand guess that the number of men included in the several classes would be pretty equal. If he thinks so, I can assure him he is most egregiously mistaken.
The method I shall employ for discovering all this is an application
of the very curious theoretical law of 'deviation from an average'.
First, I will explain the law, and then I will show that the production
of natural intellectual gifts comes justly within its scope.
The law is an exceedingly general one. M. Quetelet, the Astronomer-Royal
of Belgium, and the greatest authority on vital and social statistics,
has largely used it in his inquiries. He has also constructed
numerical tables, by which the necessary calculations can be easily
made, whenever it is desired to have recourse to the law. Those
who wish to learn more than I have space to relate should consult
his work, which is a very readable octave volume, and deserves
to be far better known to statisticians than it appears to be.
Its title is Letters on probabilities, translated by Downes, Layton
and Co., London, 1849.
So much has been published in recent years about statistical deductions, that I am sure the reader will be prepared to assent freely to the following hypothetical case: - Suppose a large island inhabited by a single race, who intermarried freely, and who had lived for many generations under constant conditions; then the average height of the male adults of that population would undoubtedly be the same year after year. Also - still arguing from the experience of modern statistics, which are found to give constant results in far less carefully guarded examples - we should undoubtedly find, year after year, the same proportion maintained between the number of men of different heights. I mean, if the average stature was found to be sixty-six inches, and if it was also found in any one year that 100 per million exceeded seventy-eight inches, the same proportion of 100 per million would be closely maintained in all other years. An equal constancy of proportion would be maintained between any other limits of height we pleased to specify, as between seventy-one and seventy-two inches; between seventy-two and seventy-three inches; and so on. Statistical experiences are so invariably confirmatory of what I have stated would probably be the case, as to make it unnecessary to describe analogous instances. Now, at this point, the law of deviation from an average steps in. It shows that the number per million whose heights range between seventy one and seventy-two inches (or between any other limits we please to name) can be predicted from the previous datum of the average, and of any one other fact, such as that of 100 per million exceeding seventy-eight inches.
The diagram on p. 28 will make this more intelligible. Suppose a million of the men to stand in turns, with their backs against a vertical board of sufficient height, and their heights to be dotted off upon it. The board would then present the appearance shown in the diagram. The line of average height is that which divides the dots into two equal parts, and stands, in the case we have assumed, at the height of sixty-six inches. The dots will be found to be ranged so symmetrically on either side of the line of average, that the lower half of the diagram will be almost a
precise reflection of the upper. Next, let a hundred dots be counted from above downwards, and let a line be drawn below them. According to the conditions, this line will stand at the height of seventy-eight inches.
[Picture of distribution]
Using the data afforded by these two lines, it is possible, by the help of the law of deviation from an average, to reproduce, with extraordinary closeness, the entire system of dots on the board.
M. Quetelet gives tables in which the uppermost line, instead of cutting off 100 in a million, cuts off only one in a million. He divides the intervals between that line and the line of average into eighty equal divisions, and gives the number of dots that fall within each of those divisions. It is easy, by the help of his tables, to calculate what would occur under any other system of classification we pleased to adopt.
This law of deviation from an average is perfectly general in its application. Thus, if the marks had been made by bullets fired at a horizontal line stretched in front of the target, they would have been distributed according to the same law. Wherever there is a large number of similar events, each due to the resultant influences of the same variable conditions, two effects will follow. First, the average value of those events will be constant; and, 'secondly, the deviations of the several events from the average will be governed by this- law (which is, in principle, the same as that which governs runs of luck at a gaming-table).
The nature of the conditions affecting the several events must, I say, be the same. It clearly would not be proper to combine the heights of men belonging to two dissimilar races, in the expectation that the compound results would be governed by the same constants. A union of two dissimilar systems of dots would produce the same kind of confusion as if half of the bullets fired at a target have been directed to one mark, and the other half to another mark. Nay, an examination of the dots would show to a person, ignorant of what had occurred, that such had been the case, and it would be possible, by aid of the law, to disentangle two or any moderate number of superimposed series of marks. The law may, therefore, be used as a most trustworthy criterion, whether or no the events of which an average has been taken are due to the same or to dissimilar classes of conditions.
I selected the hypothetical case of a race of men living on an island and freely intermarrying, to ensure the conditions under which they were all supposed to live being uniform in character. It will now be my aim to show there is sufficient uniformity in the inhabitants of the British Isles to bring them fairly within the grasp of this law [. .. .]
I argue from the results obtained from Frenchmen and from Scotchmen, that, if we had measurements of the adult males in the British Isles, we should find those measurements to range in close accordance with the law of deviation from an average, although our population is as much mingled as I described that of Scotland to have been, and although Ireland is mainly peopled with Celts. Now, if this be the case with stature, then it will be true as regards every other physical feature - as circumference of head, size of brain, weight of grey matter, number of brain fibres, &c.; and thence, by a step on which no physiologist will hesitate, as regards mental capacity.
This is what I am driving at - that analogy clearly shows there must be a fairly constant average mental capacity in the inhabitants of the British Isles, and that the deviations from that average - upwards towards genius, and downwards towards stupidity must follow the law that governs deviations from all true averages [....]
The number of grades into which we may divide ability is purely a matter of option. We may consult our convenience by sorting Englishmen into a few large classes, or into many small ones. I will select a system of classification that shall be easily comparable with the numbers of eminent men, as determined in the previous chapter. We have seen that 250 men per million
become eminent; accordingly, I have so contrived the classes in the table opposite that the two highests, F and G, together with X (which includes all cases beyond G, and which are unclassed), shall amount to about that number - namely to 248 per million.
It will, I trust, be clearly understood that the numbers of men in the several classes in my table depend on no uncertain hypothesis. They are determined by the assured law of deviations from an average. It is an absolute fact that if we pick out of each million the one man who is naturally the ablest, and also the one man who is the most stupid, and divide the remaining 999,998 men into fourteen classes, the average ability in each being separated from that of its neighbours by equal grades, then the number in each of those classes will, on the average of many millions, be as it is stated in the table. The table may be applied to special, just as truly as to general ability. It would be true for every examination that brought out natural gifts, whether held in painting, in music, or in statesmanship. The proportions between the different classes would be identical in all these cases, although the classes would be made up of different individuals, according as the examination differed in its purport.
It will be seen that more than half of each million is contained in the two mediocre classes a and A; the four mediocre classes a, b, A, B, contain more than four-fifths, and the six mediocre classes more than nineteen-twentieths of the entire population. Thus, the rarity of commanding ability, and the vast abundance of mediocrity, is no accident, but follows of necessity, from the very nature of these things.
The meaning of the word 'mediocrity' admits of little doubt. It defines the standard of intellectual power found in most provincial gatherings, because the attractions of a more stirring life in the metropolis and elsewhere are apt to draw away the abler classes of men, and the silly and the imbecile do not take a part in the gatherings. Hence, the residuum that forms the bulk of the general society of small provincial places is commonly very pure in its mediocrity.
The class C possesses abilities a trifle higher than those commonly possessed by the foreman of an ordinary jury. D includes the mass of men who obtain the ordinary prizes of life. E is a stage higher. Then we reach F, the lowest of those yet superior classes of intellect, with which this volume is chiefly concerned.
On descending the scale, we find by the time we have reached f, that we are already among the idiots and imbeciles. We have seen [...] that there are 400 idiots and imbeciles to every million of persons living in this country; but that 30 per cent of their number appear to be light cases, to whom the name of idiot is inappropriate. There will remain 280 true idiots and imbeciles to every million of our population. This ratio coincides very closely with the requirements of class f. No doubt a certain proportion of them are idiotic owing to some fortuitous cause, which may interfere with the working of a naturally good brain, much as a bit of dirt may cause a first-rate chronometer to keep worse time than an ordinary watch. But I presume, from the usual smallness of head and absence of disease among these persons, that the proportion of accidental idiots cannot be very large.
Hence we arrive at the undeniable, but unexpected conclusion, that eminently gifted men are raised as much above mediocrity as idiots are depressed below it; a fact that is calculated to considerably enlarge our ideas of the enormous differences of intellectual gifts between man and man.
I presume the class F of dogs, and others of the more intelligent
sort of animals, is nearly commensurate with the f of the human
race, in respect to memory and powers of reason. Certainly the
class G of such animals is far superior to the g of humankind.
Classification of Men According to their Natural Gifts
| Grades of natural ability separated by equal intervals | Numbers of men comprised in the several grades of natural ability, whether in respect to, their general powers, or to special aptitudes | ||||||||
| In total male population of the United Kingdom, say 15 millions of the undermentioned ages | |||||||||
| Below average | Above average | Proportionate viz One in | In each million of the Of the same age | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| a | A | 4 | 256,791 | 641,000 | 495,000 | 391,000 | 268,000 | 171,000 | 77,000 |
| b | B | 6 | 161,279 | 409,000 | 312,000 | 246,000 | 168,000 | 107,000 | 48,000 |
| c | C | 16 | 63,563 | 161,000 | 123,000 | 97,000 | 66,000 | 42,000 | 19,000 |
| d | D | 64 | 15,696 | 39,800 | 30,300 | 23,900 | 16,400 | 10,400 | 4,700 |
| e | E | 413 | 2,423 | 6,100 | 4,700 | 3,700 | 2,520 | 1,600 | 729 |
| f | F | 4,300 | 233 | 590 | 450 | 355 | 243 | 155 | 70 |
| g | G | 79,000 | 14 | 35 | 27 | 21 | 15 | 9 | 4 |
| all grades above g | all grades below G | 1,000,000 | 1 | 3 | 2 | 2 | 2 | - | - |
| On either side of average | 500,000 | 1,268,000 | 964,000 | 761,000 | 521,000 | 332,000 | 149,000 | ||
| Total, both sides | 1,000,000 | 2,536,000 | 1,928,000 | 1,522,000 | 1,042,000 | 664,000 | 298,000 | ||
The proportions of men living at different ages are calculated from the proportions that are true for England and Wales. (Census 1861, Appendix, p. 107.) Example. -The class F contains 1 in every 4,300 men. In other words, there are 233 of that class in each million of men. The same is true of class f. In the whole United Kingdom there are 590 men of class F (and the same number of f) between the ages of 20 and 30; 450 between the ages of 30 and 40; and so on.