Pedagogical Anthropology, Maria Montessori [online e book reader TXT] 📗
- Author: Maria Montessori
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Consequently, this medial stature which still corresponds to the mean average of a very large number of persons, is the stature that is biographically pre-established, the normal stature of the race.
If we select individuals presumably of the same race and in sound health, the serial curve of their statures ought to be very high and with a narrow base, because these individuals are uniform. When a binomial curve has a very wide basis of oscillations in measurements, it evidently contains elements that are not uniform; thus, for example, if we should measure the statures of men and women together, we should of course obtain a curve, but it would be very broad at the base and quite low at the centre of density; and a similar result would follow if we measured the statures of the rich and the poor without distinguishing between them. Since normal stature, including individual variations, has an exceedingly wide limit of oscillation (from 1.25 m. to 1.99 m.), if we should measure all the men on earth, we should obtain a very wide base for our binomial curve, which nevertheless would have a centre of density corresponding to the median line and to the general mean average.
Now this mean stature, according to Quétélet, is the mean stature of the European; and it is that of the medial man. But if we should take the races separately, each one of them would have its own binomial curve, which would reveal the respective mean stature for each race. In the same way, if we took the complex curve of all the individuals of a single race, and separated the men from the women, the two resulting groups would reveal the mean average male stature and the mean average female stature of the race in question. An analogous result would follow if we separated the poor from the rich, etc.
Every time that we draw new distinctions, the base of the curves, or in other words the limits of oscillation of measurements, will contract, and the centre of density will rise; while the intermediate gradations (due, for example, to the intermixture of tall women and short men; or to the overlapping standards of stature of various kindred races, etc.), will diminish. In short, if we construct the binomial curve from individuals who are uniform in sex, race, age, health, etc., it not only remains symmetrical around a centre but the eccentric progression of its groups is steadily determined in closer accordance with the order and progression of the exponents Of Newton's binomial.
However, a symmetrical grading off from the centre is not the same thing as a symmetrical grading off from the centre in a predetermined mode, i.e., that of the binomial exponents. The binomial symmetry is obtained through calculations of mathematical combinations. Now, if the fact of the centrality of a prevailing measurement is to be proved in relation to the predetermination of the measurement itself: for example, in regard to racial heredity, and hence is a fact that reveals normality, the manner of distribution of errors—namely, in accordance with calculations of probability—might very well be explained by Mendel's laws of heredity, which serve precisely to show how the prevailing characteristics are distributed according to the mathematical calculation of probabilities.
Accordingly, the normal characteristic of race would coincide with the dominant characteristic of Mendel's hereditary powers. The characteristic which has been shown as the stronger and more potent is victorious over the recessive characteristics that are latent in the germ. Meanwhile, however, there are various errors which, artificially or pathologically, cause a characteristic, which would naturally have been recessive, to become dominant, or, in other words, most prevalent.
Fig. 157.—The shaded portion represents the eccentricity of the curve, due to the presence of cretins.
Whenever a binomial curve constructed from a large number of individuals is found to be eccentric; and shows, e.g., in the case of stature, a deviation toward the low statures, it reveals (see De Helguero's curves) the presence of a heterogeneous intermixture of subjects, for example, of children among adults, or, as in the case demonstrated by De Helguero, an intermixture of pathological individuals with normal persons (Fig. 157).
The binomial curve obtained by De Helguero from the inhabitants of Piedmont included, as a matter of fact, a great number of cretins; they formed within the great normal mass of men, a little mass of individuals having a stature notably inferior to the normal.
By correcting the eccentric curve on the left of the accompanying figure, and by tracing a dotted line equal and symmetrical to the right side, we obtain a normal binomial curve; well, this curve will actually be reproduced if we subtract all the cretins from the whole mass of individuals.
The section distinguished by parallel lines represents that portion of the curve which departs from the normal toward the low statures, and is due to the cretins; it may be transformed into a small dotted binomial curve at the base, which is constructed from the statures of the cretins alone.
Accordingly, the symmetrical binomial curve gives us a mean average value in relation to a specified measurement.
What has been said regarding stature serves as an example; but it may be repeated for all the anthropometric measurements, as Viola has proved by actual experiment.
The sitting stature, the thoracic perimeter, the dimensions of an entire limb or of each and every segment of it; every particular which it has seemed worth while to take into consideration, comports itself in the same manner; and this is also true of all the measurements of the head and face.
That is to say, if we make a seriation of measurements relating to the sitting stature of an indeterminate number of individuals, we find a numerical prevalence of those corresponding to the medial measurement marked upon the axis of the abscissæ; and the number of individuals will continue to decrease with perceptible symmetry on each side of the centre, i.e., toward the higher and lower statures. If we take into consideration the significance of the sitting stature, this binomial curve relates to individuals who possess a normal physiological mass (the bust; centre of density) and to individuals who fall below or exceed that mass. We have already, in speaking of the types of stature, taken the bust under consideration in relation to the limbs, in order to judge the more or less favourable reciprocal development; but here we obtain an absolute datum of normality, independent of proportional relations to the body as a whole; in other words, there exists a physiological mass for the human body which is normal in itself. The individuals whose sitting stature corresponds to the medial measure of the binomial curve, are precisely those who have the normal development of bust.
The same thing repeats itself in the case of the thoracic perimeter, or the weight, or the length of the leg, or the cranial circumference, etc.
Hence we have a means of obtaining the normal medial measurements by the seriation of a number of measurements actually obtained from living individuals the number of whom should be sufficiently large to enable us to construct a perceptibly symmetrical and regular binomial curve.
Such medial measurements, although they correspond to the true mean average (as we have already seen), are not for this reason unreal, like arithmetical means which represent a synthetic entirety that does not correspond to the single individuals actually existing; the medial measurements obtained by seriation are, on the contrary, measurements that really belong to living individuals; namely, to that group of individuals that possess this particular measurement. Therefore, it is not a combination, or fusion, or abstraction.
But individuals who have one medial measurement, do not necessarily have all the other medial measurements; that is to say, the individuals who find that they belong on the medial abscissæ in relation to stature, do not find themselves similarly placed in relation to the sitting stature, or the thoracic perimeter, or the weight, or the cranial circumference, etc. Indeed, it is impossible that all the bodily measurements of the same individual should be medial measurements: or, to express it better, there has not been found up to the present among living individuals, in the whole wide world, a man so constructed.
Such a man would represent anthropologically the medial man.
It is also very rare to find a man quite lacking in medial measurements: everyone has a few central measurements and certain others that are eccentric.
At the same time it must be admitted that there are men who have many, and even a large majority, of the central measurements; while the rest of their measurements are eccentric or paracentral.
One of the objections which used to be made was that if we should wish to unite all the medial measurements, they would not fit together, or rather, that a man could not be constructed from them; but that the result would be a monstrosity. Nevertheless, this assertion or objection has proved to be absolutely fantastic and contrary to the actual fact.
Professor Viola has observed that men who have a very large number of medial measurements are singularly handsome.
More than that: the medial man reconstructed from medial measurements really gathered from living persons, has the identical proportions of the famous statues of Greek art.
Here, for example, in Figs. 158 and 159, facing page (464), we have the medial man and the Apollo; even to the eye of the observer, they show a marked similarity in proportions. The medial man is very nearly the portrait of an exceedingly handsome young Roman, studied by Viola; this person possessed a great majority of the mean average measurements; but some of his measurements did not correspond to the normal averages, and accordingly Viola had them corrected by an artist under the guidance of anthropological biometry; and the figure thus corrected is represented in the drawing here given. Well, this drawing corresponds perfectly to the proportions of the Apollo.
Consequently, the mean average measurements do not pass unnoticed; it is not alone the anthropological instrument or mathematical reconstruction that reveals them; when presented to the eye of the intelligent man, they notify him that they exist, they arouse in him an æsthetic emotion, they give him the alluring impression of the beautiful.
When the mean average measurements are found accumulated in large numbers in the same person, they render that person the centre of a mysterious fascination, the admiration of all other men.
Now, this coincidence of the beautiful with the average is equivalent to a coincidence of the beautiful with normality. "This unforeseen demonstration," says Viola, "throws a vivid light upon the hitherto obscure problem of the æsthetic sense.... If a man evolves according to normal laws, his proportions arouse an exceptional æsthetic enjoyment."
Anyone having an eye trained to recognise the beautiful, is able through his æsthetic sensations, to pick out normality from the great crowd of biological errors, which is precisely what the scientist does with great weariness of measurements and calculations. In fact, the great artists recognise the beautiful parts of a number of beautiful individuals, and they unite them all together in a single work of art. The Greeks did this, they reconstructed the medial man, on a basis of actual observation, and by extracting all the normalities, all the measurements most prevalent in individuals, and forming from them a single ideal man. The Greek artists were observers; we might call them the positivists in art. Their art is supreme and immortal, because they simultaneously interpreted what is beautiful and what is true in life.
In short, medial measurements are true measurements, actually existing in individuals. No one can acquire a true æsthetic
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