# Popular Science Monthly/Volume 1/May 1872/Quetelet on the Science of Man

Reprinted from Nature, No. 5, 7 March 1872, pp. 358-363.
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* QUETELET ON THE SCIENCE OF MAN.
By E. B. TYLOR.
TWO lines of research into the Science of Man, of the highest moment as well in theoretical Anthropology as in practical Ethics and Politics, both to be always associated with the name of Quetelet, are now discussed at large in his Social Physics and Anthropometry. The two great generalizations which the veteran Belgian astronomer has brought to bear on physiological and mental science, and which it is proposed to describe popularly here, may be briefly defined: First, he has been for many years the prime mover in introducing the doctrine that human actions, even those usually considered most arbitrary, are in fact subordinate to general laws of human nature; this doctrine, maintained in previous publications, especially in the earlier edition of the first named work some thirty seven years ago, is now put forth in its completest form. Second, he has succeeded in bringing the idea of a biological type or specific form, whether in bodily structure or mental faculty, to a distinct calculable conception, which is likely to impress on future arguments a definiteness not previously approached.
The admission of evidence like this, however, is not always followed by the same philosophical explanation of it. Buckle finds his solution by simply discarding the idea that human action "depends on some capricious and personal principle peculiar to each man, as free will or the like;" on the contrary, he asserts "the great truth that the actions of men, being guided by their antecedents, are in reality never inconsistent, but, however capricious they may appear, only form part of one vast scheme of universal order, of which we, in the present state of knowledge, can barely see the outline." M. Quetelet's argument from the same evidence differs remarkably from this. His expedient for accounting for the regularity of social events, without throwing over the notion of arbitrary action, is to admit the existence of free will, but to confine its effects within very narrow bounds. He holds that arbitrary will does not act beyond the limits at which science begins, and that its effects, though apparently so great, may, if taken collectively, be reckoned as null, experience proving that ​individual wills are neutralized in the midst of general wills (p. 100). Free will, though of sufficient power to prevent our predicting the actions of the individual, disappears in the collective action of large bodies of men, which results from general social laws, which can accordingly be predicted like other results regulated by natural laws. We may perhaps apprehend the meaning of Quetelet's views more clearly from another passage, where, to show how apparently isolated events may be really connected under some wide law, he compares single facts to a number of scattered points, which seem not related to one another till the observer, commanding a view of a series of them from a distance, loses sight of their little accidents of arrangement, and at the same time perceives that they are really arranged along a connecting curve. Then the writer goes on to imagine, still more suggestively, that these points might actually be tiny animated creatures, capable of free action within a very narrow range, while nevertheless their spontaneous movements would not be discernible from a distance (p. 94), where only their laws of mutual relation would appear. M. Quetelet can thus conciliate received opinions by recognizing the doctrine of arbitrary volition, while depriving it of its injurious power. His defence of the existence of free will is perhaps too much like the famous excuse of the personage who was blamed for going out shooting on the day he had received the news of his father's death, and who defended himself on the ground that he only shot very small birds. But it is evident that the statistics of social regularity have driven the popular notion of free will into the narrow space included between Quetelet's restriction and Buckle's abolition of it. In fact, no one who studies the temper of our time will deny the increasing prevalence of the tendency of the scientific world to reject the use of the term free will in its vulgar sense—that of unmotived spontaneous election—and even to discourage its use in any other sense as apt to mislead, while its defenders draw their weapons not so much from observation of facts as from speculative and dogmatic philosophy.
To those who accept the extreme principle that similar men under similar circumstances must necessarily do similar acts; and to those, also, who adopt the notion of free will as a small disturbing cause which disappears in the large result of social law, the regularity of civilized life carries its own explanation. Society is roughly homogeneous from year to year. Individuals are born, pass on through stage after stage of life, and die; but at each move one drops into another's place, and the shifting of individuals only brings change into the social system, so far as those great general causes have been at work which difference one age from another the introduction of different knowledge, different principles, different arts, different industrial materials and outlets. The modern sociologist, whatever his ​metaphysical prepossessions, looks at society as a system amenable to direct cause and effect. To a great extent his accurate reckonings serve to give more force and point to the conclusions of rough experience; to a great extent, also, they correct old ideas and introduce new aspects of social law. What gives to the statistical method its greatest scope and power is, that its evidence and proof of law applies indiscriminately to what we call physical, biological, and ethical products of society, these various effects acting and reacting on one another. A few instances may be given to show the existence of the relations in question, without attempting to show their precise nature, or to trace the operation of other determining causes.
Thus, for instance, the mode of life affects its length. Statistics show that the mortality of the very poor is about half as much again as the mortality of the very rich; while, as to the influence of professions, it appears that, in Germany, only 24 doctors reach the age of 70 as against 32 military men and 42 theologians. The propensity to theft bears a distinct relation to age; thus the French criminal statistics estimate the propensity to theft between the ages of 21 and 25 as being five thirds as much as between the ages of 35 and 40. The amount of criminality in a country bears a relation, indirect and as yet obscure, but unmistakable, to its education, or rather to its want of education. In France, in 1828-'31, the constant percentage of accused persons was about as follows: could not read or write, 61; imperfectly, 27; well, 12. The comparison of this group of numbers with those taken lately in England shows a great change of proportion, evidently resulting from the wider diffusion of education; but the limitation of crime to the less educated classes is even more striking: cannot read or write, 36; imperfectly, 61; well, 3. Again, for an example of connection of physical conditions with moral actions, we may notice a table showing how the hours of the day influence people who hang themselves ("Phys. Soc," ii., 240). The maximum of such cases, 135, occurred between six and eight in the morning; the number decreased slightly till noon, and then suddenly dropped to the minimum; there being 123 cases between ten and twelve o'clock, against only 32 between twelve and two o'clock. The number rose in the afternoon to 104 cases between four and six, dropping to an average of about 70 through the night, the second minimum, 45, being between two and four o'clock in the morning. Here it is impossible to mistake the influences of the periods of the day. We can fancy we see the poor wretches rising in the morning to a life of which the misery is beyond bearing, or can only be borne till evening closes in; while the temporary relief of the midnight sleep and the mid-day meal are marked in holding back the longing to self destruction. Madness varies with the season of the year: the maximum being in summer, and the minimum in winter (p. 187); a state of things which seems intelligible enough. Again, it is well known in ​current opinion that more children are born in the night than in the day; in fact, there are about five night born against four day born, the maximum being about midnight, the minimum a little before noon (i., p. 208). Why this is, no one yet knows; it is a case of unexplained law. But another not less curious law relating to births seems to have been at last successfully unravelled. In Europe about 106 boys are born to every 100 girls. The explanation appears to depend on the husband being older than the wife; which difference again is regulated by prudential considerations, a man not marrying till he can maintain a wife. In connection with this argument, it must be noticed that illegitimate births show a much less excess of male children (p. 168). Here, then (if this explanation may be accepted), it appears that a law, which has been supposed to be due to purely physiological causes, is traceable to an ultimate origin in political economy.
The examples brought forward by Quetelet, which thus show the intimate relation between biological and ethical phenomena, should be pondered by all who take an interest in that great movement of our time the—introduction of scientific evidence into problems over which theologians and moralists have long claimed exclusive jurisdiction. This scientific invasion consists mainly in application of exact evidence in place of inexact evidence, and of proof in place of sentiment and authority. Already the result of the introduction of statistics into inquiries of this kind appears in new adjustments of the frontier line between right and wrong, as measured under our modern social conditions. Take, for instance, the case of foundling hospitals, which provide a "tour," or other means, for the secret reception of infants abandoned by their parents. It has seemed, and still seems, to many estimable persons, an act of benevolence to found and maintain such institutions. But, when their operation comes to be studied by statisticians, they are found to produce an enormous increase in the number of exposed illegitimate children ("Phys. Soc," i., p. 84). In fact, thus to facilitate the safe and secret abandonment of children is to set a powerful engine at work to demoralize society. Here, then, a particular class of charitable actions has been removed, by the statistical study of its effects, from the category of virtuous into that of vicious actions. An even more important transition of the same kind is taking place in the estimation of alms giving from the ethical point of view. Until modern ages, through all the countries of higher civilization, men have been urged by their teachers of morality to give to the poor, worthy or unworthy; the state of public opinion being well exemplified by the narrowing of the word "charity" from its original sense to denote the distribution of doles. Yet, when the statistics of pauperism were collected and studied, it was shown that indiscriminate alms giving is an action rather evil than good, its tendency being not only to maintain, but actually to produce, idle and miserable ​paupers. In our time a large proportion of the public and private funds, distributed among the poor, is spent in actually diminishing their industry, frugality, and self reliance. Yet the evil of indiscriminate alms giving is diminishing under the influence of sounder knowledge of social laws, and genuine charity is more and more directed by careful study of the means by which wealth may be spent for the distinct benefit of society. Such examples as these show clearly the imperfection and untrustworthiness of traditional, or what is called intuitive morality, in deciding on questions of right and wrong, and the necessity of appealing in all cases to the best attainable information of social science to decide what actions are really for or against the general good, and are therefore to be classed as virtuous or vicious.
Moreover, it is not too much to say that the comparatively small advance which moral science has made, since barbaric ages, has been due to the repugnance of moralists to admit, in human action, the regular causality which is the admitted principle of other parts of the action of the universe. The idea of the influence of arbitrary will in the individual man has checked and opposed the calculations which now display the paramount action of society as an organized whole. One point in M. Quetelet's doctrine of society requires a mention for its practical bearing on morals. There has seemed to some to be an immoral tendency in his principle that virtuous and vicious acts are products, not merely of the individual who does them, but of the society in which they take place, as though the tendency of this view were to weaken individual responsibility, and to discourage individual effort. Yet, when properly understood, this principle offers a more strong and definite impulse to the effort of society for good and against evil, than the theory which refers the individual's action more exclusively to himself. M. Quetelet's inference from the regular production of a certain amount of crime year by year, from a society in a certain condition, is embodied in his maxim that society prepares the crime and the criminal executes it. This should be read with a comment of the author's. "If," he says, "I were to take up the pavement before my house, should I be astonished to hear in the morning that people had fallen and hurt themselves, and could I lay the blame on the sufferers, inasmuch as they were free to go there or elsewhere?" Thus every member of society who offers a facility to the commission of crime, or does not endeavor to hinder its commission, is, in a degree, responsible for it. It is absurd to suppose that the crimes in great cities are attributable altogether to the free agency of the poor wretches who are transported or hung for them. The nation which can and does not prevent the existence of a criminal class is responsible collectively for the evil done by this class. This we can see plainly enough, although the exact distribution of the responsibility among the different members of society may be impossible to determine. Such a theory, of course, ​casts aside the revenge theory of criminal law, assimilating the treatment of criminals to the operation of a surgeon healing a diseased part of the body, if possible, or, if not, rendering it harmless or removing it.
The wealthy and educated classes, whose lives seem to themselves as free from moral blame as they are from legal punishment, may at first hear with no pleasant surprise a theory which inculpates them as sharers in the crimes necessarily resulting from the state of society which they are influential in shaping. Yet this consideration is by no means one of mere hopeless regret, for coupled with it is the knowledge that it is in their power, by adopting certain educational and reformatory measures, so to alter the present moral status of society as to reduce the annual budget of crime to a fraction of its present amount. Thus the doctrine that the nation participates in and is responsible for the acts of its individual members is one which widens the range of duty to the utmost. The labors of M. Quetelet, in reducing to absolute calculation this doctrine of the solidarity of human society, entitle him to a place among those great thinkers whose efforts perceptibly raise that society to a higher intellectual and moral level. Here, as everywhere, the larger comprehension of the laws of Nature works for good and not for evil in the history of the world.
Some slight account has now to be given of M. Quetelet's doctrine of typical forms, as displayed in the "homme moyen," or "mean man," of a particular nation or race. This is no new theory; but, since the publication of the "Physique Sociale" in 1835, the author has been at work extending and systematizing it, his last results being shown in the present works. First, it must be pointed out that the term "homme moyen" is not intended to indicate what would be popularly meant by an "average man." An average or arithmetical mean of a number of objects may be a mere imaginary entity, having no real representative. Thus, an average chessman, computed as to height from the different pieces on the board, might not correspond to any one of the actual pieces. But the "homme moyen" or central type of a population really exists; more than this, the class he belongs to exceeds in number any other class, and the less nearly any other class approaches to his standard the less numerous that class is, the decrease in the number of individuals as they depart from the central type conforming to a calculable numerical law. The "mean man" (the term may probably be adopted in future researches, and when technically used its popular meaning will cease to ​interfere with this special one)—the "mean man" thus stands as a representative of the whole population, individuals as they differ from him being considered as forms varying from his specific type.
To realize a conception which even among anthropologists has scarcely yet become familiar, it is desirable to show by what actual observations M. Quetelet was led to the discovery of his principle. When a large number of men of a practically homogeneous population are measured, and arranged in groups accordingly, it becomes evident that the individuals are related to one another by a law of distribution. A central type is represented by the most numerous group, the adjoining groups becoming less and less numerous in both directions. Thus, on classifying the measured heights of some 26,000 American soldiers of the Northern army during the late war, the proportionate number of men to each height was ascertained to be as follows ("Phys. Soc," i., p. 131; "Anthropom.," p. 259):
| Height, inches | .......... | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 |
| No. of men in 1,000 | .......... | 1 | 1 | 2 | 20 | 48 | 75 | 117 | 134 | 157 |
| Height, inches | .......... | 69 | 70 | 71 | 72 | 73 | 74 | 75 | 76 |
| No. of men in 1,000 | .......... | 140 | 121 | 80 | 57 | 26 | 13 | 5 | 2 |
Here it is seen that the mean man is a little under 5 ft. 8 in. in height, the numbers of men shorter and taller diminishing with evident regularity, down to the few representatives of the very short men of 5 ft. and under, and the very tall men of 6 ft. 4 in. and over. The law of relation of height to numerical strength is shown graphically by the binomial curve figured above, where the abscissæ (measured from an origin on the left) represent the heights of the men, and the ordinates the relative numbers of men corresponding to each height. The maximum ordinate, representing the number of mean men, is at $\textstyle {m=}$ about 5 ft. 8 in., the ordinates on both sides diminishing almost to nothing as they reach the dwarfish and gigantic limits $\textstyle {d}$ and $\textstyle {g}$, and vanishing beyond.
Again, measurement around the chest, applied to the soldiers of the Potomac Army, shows a similar law of grouping ("Phys. Soc," ii., 59; "Anthropom.," p. 289):
| Round chest, inches | .......... | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 |
| No. of men in 1,000 | .......... | 1 | 3 | 11 | 36 | 67 | 119 | 160 | 204 |
| Round chest, inches | .......... | 36 | 37 | 38 | 39 | 40 | 41 | 42 | |
| No. of men in 1,000 | .......... | 166 | 119 | 68 | 28 | 13 | 4 | 1 | |
Here the mean man measures about 35 in. round the chest, the numbers diminishing both ways till we reach the few extremely narrow-chested men of 28 in., and the few extremely broad-chested men of 42 in. These two examples may represent the more symmetrical cases of distribution of individuals on both sides of a central type, as worked out by M. Quetelet from various physical measurements applied to large numbers of individuals. Here the tendency to vary is approximately ​equal in both directions. Where the tendency to vary is perceptibly different in the two directions, the curve loses its symmetry, as in the figures representing the weights of women at different ages ("Anthropom.," p. 349), and the number of marriages of men and women at different ages ("Phys. Soc," i., 272). The actual series of numbers given by observation are placed beside series computed according to the law of the expanded binomial, the same which is applied in the theory of probabilities to such calculations as that of the proportionate distribution of less probable events on each side of a most probable maximum term, the distribution of errors of observation of a single object, and of accidental variations in general. It is the closeness of approximation between the observed and calculated series of variations, computed not only as to the dimensions, but the actions of man, which gives to M. Quetelet's theory its remarkable definiteness and precision.
The diagram of statures here figured, which may be looked upon as representing a nation measured in one particular way, at once impresses on the mind a conception of a race type materially differing from the vague notions hitherto current. It is seen that individual men of different statures are required to constitute a nation, but they are required in less and less proportion as they depart in excess or defect from the central type. The nation is not even complete without its dwarfs and giants. In fact, if all the monstrously short and tall men of a particular country were put out of sight, and the census of the population taken according to stature, the national formula thence deduced would enable a statistician to reckon with considerable accuracy how many dwarfs and giants of each size had been removed.
M. Quetelet's investigations further prove, or tend to prove, that similar laws of variation from the central type govern the distribution of individuals classed according to other bodily dimensions, and also according to physical qualities such as weight and strength, it being borne in mind that the particular expressions with their descriptive curves differ for the various qualities or faculties of man, being also in some cases much less symmetrical than in others. An absolute coincidence of the series of observed facts with the numerical law chosen to express them would be too much to expect; it is a great deal to obtain even a rough coincidence. For instance, when the strength of a number of men is estimated by a dynamometer, the maximum number showed 140 to 150 degrees on the scale, the number of weaker and stronger men being both fewer from this point, groups following approximately the proportions of the coefficients of a binomial of the sixth order; the numbers are reduced as follows from the table ("Anthropom.," p. 365):
| Renal force, degrees | 90 | 100-110 | 120-130 | 140-150 | 160-170 |
| No. of men in 64 | 1 | 8 | 14 | 20 | 15 |
| Binom. coeff | 1 | 6 | 15 | 20 | 15 |
| Renal force, degrees | 180-190 | 200 |
| No. of men in 64 | 6 | 1 |
| Binom. coeff | 6 | 1 |
In the various numerical examples here given, the element of age is not introduced, the ages of the individuals being calculated or taken as uniform. The problem of variation of numerical distribution of a population at different ages is treated by M. Quetelet in a comparatively simple case, that of the stature curve. Here a curve approximating to a parabola is laid down, the ages of man from birth onward being measured along its axis; each double ordinate of this curve forms the base on which a binomial curve is erected perpendicularly, the vertices of these curves forming a curve of mean stature, of the nature of a curve of mortality ("Anthropom.," p. 264). How far M. Quetelet may succeed in his contemplated purpose of carrying his method from the physical into the intellectual and moral nature of man, it is premature to judge.
Without entering into the more intricate and difficult problems opened by this theory of central types, it is evident that the bearing of its main conception on the problems of anthropology and biology in general is highly important. Some able anthropologists have accepted the theory of the mean, or central standard, as a basis for the comparison of races, but this line of research is still in its infancy. In M. Quetelet's last volume, a principle is worked out which serves as a bridge between the old and new methods. His experience is that, in a well marked population, no extraordinary number of observations is required for the determination of the mean man. In former ages, one result of the national type being so preponderant in number and so easily recognizable was, that the bodily measurements of any man of ordinary stature and proportions could be trusted to give, with reasonable accuracy, the standard measures of the nation, such as the foot, cubit, fathom, etc. In the same manner M. Quetelet finds a small number of selected individuals sufficient for ascertaining the standard national proportions of the human body, male and female, from year to year of growth; his tables, founded for the most part on Belgian models, are given in an appendix. This method is applicable to the purposes of general anthropology. Thus a traveller, studying some African or American race, has to select by mere inspection a moderate number of typical men and women, by comparison of whose accurately admeasured proportions he may approximate very closely to a central race type. It is not necessary to dwell on the obvious difficulties ​of connecting the standard types of mixed nations with the races composing them. The stature curve of England differs visibly in proportions from that of Italy, the measurements of Scotch and American soldiers show very different mean and extreme terms, and the problems of race underlying these differences are of a most complex character, the more so when the consideration is introduced of the race type varying within itself from century to century. M. Quetelet is naturally apt, when expressing his views in an exordium or a peroration, to draw a good deal on the anticipated future results of his admirable method; but in judging of the value of his doctrine of central types, the best criterion is his actual success in reducing the observed facts of Nature to numerical calculation. The future must show how far it will be possible to apply to the theory of species the definition of central specific forms, from which varieties calculably diminish in numbers as they depart in type.—Nature.
* ↑ Physique Sociale, ou Essai sur le Développement des Facultes de l'Homme. Par Ad. Quetelet. (Brussels, 1869.) Anthropométrie, ou Mesure des differentes Facultés de l'Homme. Par Ad. Quetelet (Brussels, 1870.)
* ↑ In regard to the relation of statistics to the doctrine of fatalism, see Dr. Farre's "Report on the Programme of the Fourth Session of the Statistical Congress."
* ↑ Thus General Lefroy's measurements of thirty three Chippewa Indians ("Journal of the Ethnological Society," vol. ii., p. 44, 1870) are sufficient to determine the stature of the mean man as about 5 ft. 1 in., the number of individuals in this maximum group being 8. It is even possible to guess from this small number of measurements the numerical law of variation in the tribe, the series of groups from five ft. 3 in. to 5 ft. 11 in being as follows: 1, 1½, 2½, 6, 8, 4½, 4½, 3, 1.