Pedagogical Anthropology

by Maria Montessori

Causes of error in the individual and in the environment interfere in like manner with the astronomer who wishes to estimate the distance of the stars and it is necessary for him to repeat his measurements and calculations on the basis of those which show the greatest probability of being exact.

Accordingly, such distribution of errors is independent of the causes which produce them and which, whatever they are, remain practically the same at any given time, and consequently produce constant effects and symmetrical errors; but it is dependent upon the fact of the existence of some pre-established thing (a measurement, the dimensions of an object to be copied, an appointed hour, the centre of a target, etc.). In short, whenever a tendency is established the errors group themselves around the objective point of this tendency.

In the case of anthropometry, as for instance, in the curve of stature given above, we find that the resulting medial stature was predetermined, e.g., for a given race; but many individuals, for various causes, either failed to attain it or surpassed it to a greater or less extent; and therefore in the course of their development they have acquired an erroneous stature.

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.