Pedagogical Anthropology, Maria Montessori [online e book reader TXT] 📗
- Author: Maria Montessori
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Consequently, the reform which has begun with the introduction of an anthropological movement into the school and the establishment of biographic charts, is nothing less than a reform of science as a whole. Medicine, jurisprudence, and sociology as well as pedagogy, are laying new foundations upon it.
CHAPTER XTHE APPLICATION OF BIOMETRY TO ANTHROPOLOGY FOR THE PURPOSE OF DETERMINING THE MEDIAL MEN
Theory of the Medial Man.—Measurements are used not only in anthropology but in zoology and botany as well; that is, they are applied to all living creatures; therefore anthropometry might to-day be regarded as a branch of biometry. The measurements obtained from living beings, and the statistical and mathematical studies based upon them, tend to determine the normality of characteristics; and when the biometric method is applied to man, it leads to a determination of the normal dimensions, and hence of the normal forms, and to a reconstruction of the medial man that must be regarded as the man of perfect development, from whom all men actually existing must differ to a greater or less extent, through their infinite normal and pathological variations.
This sort of touch-stone is of indisputable scientific utility, since we cannot judge of deviations from the norm, so long as normality is unknown to us. In fact, when we speak of normality and of anomalies, we are using language that is far from exact, and to which there are no clear and positive corresponding ideas.
Whatever has been accomplished in anthropology up to the present time in the study of the morphology of degenerates and abnormals, has served only to illustrate this principle very vaguely—that the form undergoes alteration in the case of pathological individuals. It is only now that we are beginning to give definite meaning to this principle, by seeking to determine what the form is, when it has not undergone any alteration at all. From this fundamental point a new beginning must be made, on more certain and positive bases, of the study of deviations from normality and their etiology.
As far back as 1835, Quétélet, in his great philosophical and statistical work, Social Physics or the Development of the Faculties of Man, for the first time expounded the theory of the "medial man," founded on statistical studies and on the mathematical laws of errors. He reached some very exact concepts of the morphology of the medial man, based upon measurements, and also of the intellectual and moral qualities of the medial man, expounding an interesting theory regarding genius.
But inasmuch as Quétélet's homme moyen was, so to speak, at once a mathematical and philosophical reconstruction of the non-existent perfect man, who furthermore could not possibly exist, this classical and masterly study by the great statistician was strenuously combatted and then forgotten, so far as its fundamental concepts were concerned, and remembered only as a scientific absurdity. The thought of that period was too analytical to linger over the great, the supreme synthesis expounded by Quétélet.
Mankind must needs grow weary of anatomising bodies and tracing back to origins, before returning to an observation of the whole rather than the parts, and to a contemplation of the future. In fact, the thought of the nineteenth century was so imbued with the evolutionary theories as set forth by Charles Darwin, that it believed the reconstruction of the Pithecanthropus erectus from a doubtful bone a more positive achievement than that of the medial man from the study of millions of living men.
But to-day the researches that we have accomplished in the biological field regarding evolution, regarding natural heredity, regarding individual variability, are leading biology as a whole toward eminently synthetic conclusions; and studies which remained neglected or which were combatted in the past, are beginning to be brought into notice and properly appreciated: such studies, for instance, as Mendel's theory and that of Quétélet. Galton, Pearson, Davenport, Dunker, Heinke, Ludwig, and above all others De Vries, are in the advance guard of modern biological thought. But beyond all these scientists, there is one who has an interest for us not only because he is an Italian, but because he has reestablished Quétélet's ancient theory of the medial man, under the present-day guidance of biometry: I mean Prof. Giacinto Viola.
The Importance of Seriation.—Under the statistical method, the basis of biometry is furnished by a regrouping of measurements in the form of series. We have seen that Quétélet's binomial curve represents the symmetrical distribution of subjects in relation to some one central anthropometric measurement.
Let us suppose, for instance, that the curve here described represents the distribution of the stature. If we mark upon the abscissæ the progressive measurements, 1.55; 1.56; 1.57; 1.58; 1.59; 1.60, etc.... 1.75; 1.76; 1.77; 1.78; 1.79; 1.80, and on the axis of the ordinates the number of individuals having a determined stature, the path of the curve will show that there is a majority of individuals possessing a mean central measurement; and that the number of individuals diminishes gradually and symmetrically above and below, becoming extremely few at the extremes (exceptionally tall and low statures). When the total number of individuals is sufficiently large, the curve is perfect (curve of errors): Fig. 156.
Fig. 156.—The highest part of this curve corresponds to the medial centre of density.
In such a case, the general mean coincides with the median, that is, with the number situated at the centre of the basal line, because, since all the other measurements, above and below, are perfectly symmetrical, in calculating the mean average they cancel out. There is still another centre corresponding to the mean: the centre of density of the individuals grouped there, because the maximum number corresponds to that measurement. Accordingly, if, for example, in place of half a million men whose measurements of stature, when placed in seriation, produced a perfect binomial curve, we had selected only ten men or even fewer from those corresponding to the median line; the general mean stature obtained from those half million men and that obtained from the ten individuals would be identical. For we would have selected ten individuals possessing that mean average stature which seems to represent a biological tendency, from which many persons deviate to a greater or less extent, as though they were erroneous, aberrant, for a great variety of causes; but these aberrant statures are still such that by their excess and their deficiency they perfectly compensate for each other; so that the mean average stature precisely reproduces this tendency, this centre actually attained by the maximum number of individuals. Supposing that we could see together all these individuals: those who belong at the centre being numerically most prevalent, will give a definite intonation to the whole mass. Anyone having an eye well trained to distinguish differences of stature could mentally separate those prevalent individuals and estimate them, saying that they are of mean average stature. This curve is the mathematical curve of errors; and it corresponds to that constructed upon the exponents of Newton's binomial theorem and to the calculation of probability. It corresponds to the curve of errors in mathematics: for example, to the errors committed in measuring a line; or in measuring the distance of a star, etc. Whoever takes measurements (we have already seen this in anthropometrical technique and in the calculation of personal error) commits errors, notwithstanding that the object to be measured and the individual making the measurements remain the same. But the most diverse causes; nerves, the weather, weariness, etc., causes not always determinable and perhaps actually more numerous than could be discovered or imagined, all have their share in producing errors of too much and too little, which are distributed in gradations around the real measurement of the object. But since among all these measurements taken in the same identical way we do not know which is the true one; the seriation of errors will reveal it to us, for it causes a maximum number of some one definite measurement (the true one) to fall in the centre of the aberrations that symmetrically grade off from the centre itself.
Viola gives some very enlightening examples in regard to errors. Suppose, for instance, that an artist skilled in modeling wished to reproduce in plaster a number of copies of a leaf, which he has before his eyes as a model.
The well-trained eye and hand will at one time cause him to take exactly the right quantity of plaster needed to reproduce the actual dimensions of the leaf; at another, on the contrary, he will take more and at another less than required.
By measuring or superimposing the real leaf upon the plaster copies, the sculptor will be able to satisfy himself at once which of his copies have proved successful.
But supposing, on the contrary, that the real leaf has disappeared and that a stranger wishes to discover from the plaster copies which ones faithfully reproduce the dimensions of the leaf? They will be those that are numerically most prevalent.
The same thing holds true for any attempt whatever to attain a predetermined object. For example, shooting at a mark. A skilful marksman will place the maximum number of shots in the centre, or at points quite near to the centre; he will often go astray, but the number of errors will steadily decrease in proportion as the shots are more aberrant, i.e., further from the centre. If a marksman wished to practise in like manner against some wall, for example, on which he has chosen a point that is not marked, and hence not recognisable by others, this point thought of by the marksman, may be determined by studying the cluster of shots left upon the wall.
In the same way an observer could determine the hour fixed for a collective appointment, such as a walking trip, by the manner in which the various individuals arrive in groups; some one will come much ahead of time because he has finished some task which he had expected would keep him busy up to the hour of appointment; then in increasing numbers the persons who come a few minutes ahead of time because they are provident and prompt; then a great number of people who have calculated their affairs so well as to arrive precisely on time; a few minutes later come those who are naturally improvident and a little lazy; and lastly come the exceptional procrastinators who at the moment of setting forth were delayed by some unexpected occurrence.
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
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