Part 32

Shall we, then, in our gymnasiums fill out the hours of study which stand at our disposal, or are still to be wrested from the classicists, with as great and as varied a quantity of mathematical and scientific matter as possible? Expect no such proposition from me. No one will suggest such a course who has himself been actively engaged in scientific thought. Thoughts can be awakened and fructified as a field is fructified by sunshine and rain. But thoughts cannot be juggled out and worried out by heaping up materials and the hours of instruction, nor by any sort of precepts: they must grow naturally of their own free accord. Furthermore, thoughts cannot be accumulated beyond a certain limit in a single head, any more than the produce of a field can be increased beyond certain limits.

I believe that the amount of matter necessary for a useful education, such as should be offered to all the pupils of a preparatory school, is very small. If I had the requisite influence, I should, in all composure, and fully convinced that I was doing what was best, first greatly curtail in the lower classes the amount of matter in both the classical and the scientific courses; I should cut down considerably the number of the school hours and the work done outside the school. I am not with many teachers of opinion that ten hours work a day for a child is not too much. I am convinced that the mature men who offer this advice so lightly are themselves unable to give their attention successfully for as long a time to any subject that is new to them, (for example, to elementary mathematics or physics,) and I would ask every one who thinks the contrary to make the experiment upon himself. Learning and teaching are not routine office-work that can be kept up mechanically for long periods. But even such work tires in the end. If our young men are not to enter the universities with blunted and impoverished minds, if they are not to leave in the preparatory schools their vital energy, which they should there gather, great changes must be made. Waiving the injurious effects of overwork upon the body, the consequences of it for the mind seem to me positively dreadful.

I know of nothing more terrible than the poor creatures who have learned too much. Instead of that sound powerful judgment which would probably have grown up if they had learned nothing, their thoughts creep timidly and hypnotically after words, principles, and formulæ, constantly by the same paths. What they have acquired is a spider's web of thoughts too weak to furnish sure supports, but complicated enough to produce confusion.

But how shall better methods of mathematical and scientific education be combined with the decrease of the subject-matter of instruction? I think, by abandoning systematic instruction altogether, at least in so far as that is required of all young pupils. I see no necessity whatever that the graduates of our high schools and preparatory schools should be little philologists, and at the same time little mathematicians, physicists, and botanists; in fact, I do not see the possibility of such a result. I see in the endeavor to attain this result, in which every instructor seeks for his own branch a place apart from the others, the main mistake of our whole system. I should be satisfied if every young student could come into living contact with and pursue to their ultimate logical consequences merely a few mathematical or scientific discoveries. Such instruction would be mainly and naturally associated with selections from the great scientific classics. A few powerful and lucid ideas could thus be made to take root in the mind and receive thorough elaboration. This accomplished, our youth would make a different showing from what they do to-day.

What need is there, for example, of burdening the head of a young student with all the details of botany? The student who has botanised under the guidance of a teacher finds on all hands, not indifferent things, but known or unknown things, by which he is stimulated, and his gain made permanent. I express here, not my own, but the opinion of a friend, a practical teacher. Again, it is not at all necessary that all the matter that is offered in the schools should be learned. The best that we have learned, that which has remained with us for life, outlived the test of examination. How can the mind thrive when matter is heaped on matter, and new materials piled constantly on old, undigested materials? The question here is not so much that of the accumulation of positive knowledge as of intellectual discipline. It seems also unnecessary that all branches should be treated at school, and that exactly the same studies should be pursued in all schools. A single philological, a single historical, a single mathematical, a single scientific branch, pursued as common subjects of instruction for all pupils, are sufficient to accomplish all that is necessary for the intellectual development. On the other hand, a wholesome mutual stimulus would be produced by this greater variety in the positive culture of men. Uniforms are excellent for soldiers, but they will not fit heads. Charles V. learned this, and it should never be forgotten. On the contrary, teachers and pupils both need considerable latitude, if they are to yield good results.

With John Karl Becker I am of the opinion that the utility and amount for individuals of every study should be precisely determined. All that exceeds this amount should be unconditionally banished from the lower classes. With respect to mathematics, Becker, in my judgment, has admirably solved this question.

With respect to the upper classes the demand assumes a different form. Here also the amount of matter obligatory on all pupils ought not to exceed a certain limit. But in the great mass of knowledge that a young man must acquire to-day for his profession it is no longer just that ten years of his youth should be wasted with mere preludes. The upper classes should supply a truly useful preparation for the professions, and should not be modelled upon the wants merely of future lawyers, ministers, and philologists. Again, it would be both foolish and impossible to attempt to prepare the same person properly for all the different professions. In such case the function of the schools would be, as Lichtenberg feared, simply to select the persons best fitted for being drilled, whilst precisely the finest special talents, which do not submit to indiscriminate discipline, would be excluded from the contest. Hence, a certain amount of liberty in the choice of studies must be introduced in the upper classes, by means of which it will be free for every one who is clear about the choice of his profession to devote his chief attention either to the study of the philologico-historical or to that of the mathematico-scientific branches. Then the matter now treated could be retained, and in some branches, perhaps, judiciously extended, without burdening the scholar with many branches or increasing the number of the hours of study. With more homogeneous work the student's capacity for work increases, one part of his labor supporting the other instead of obstructing it. If, however, a young man should subsequently choose a different profession, then it is his business to make up what he has lost. No harm certainly will come to society from this change, nor could it be regarded as a misfortune if philologists and lawyers with mathematical educations or physical scientists with classical educations should now and then appear.

* * * * *

The view is now wide-spread that a Latin and Greek education no longer meets the general wants of the times, that a more opportune, a more "liberal" education exists. The phrase, "a liberal education," has been greatly misused. A truly liberal education is unquestionably very rare. The schools can hardly offer such; at best they can only bring home to the student the necessity of it. It is, then, his business to acquire, as best he can, a more or less liberal education. It would be very difficult, too, at any one time to give a definition of a "liberal" education which would satisfy every one, still more difficult to give one which would hold good for a hundred years. The educational ideal, in fact, varies much. To one, a knowledge of classical antiquity appears not too dearly bought "with early death." We have no objection to this person, or to those who think like him, pursuing their ideal after their own fashion. But we may certainly protest strongly against the realisation of such ideals on our own children. Another,--Plato, for example,--puts men ignorant of geometry on a level with animals. If such narrow views had the magical powers of the sorceress Circe, many a man who perhaps justly thought himself well educated would become conscious of a not very flattering transformation of himself. Let us seek, therefore, in our educational system to meet the wants of the present, and not establish prejudices for the future.

But how does it come, we must ask, that institutions so antiquated as the German gymnasiums could subsist so long in opposition to public opinion? The answer is simple. The schools were first organised by the Church; since the Reformation they have been in the hands of the State. On so large a scale, the plan presents many advantages. Means can be placed at the disposal of education such as no private source, at least in Europe, could furnish. Work can be conducted upon the same plan in many schools, and so experiments made of extensive scope which would be otherwise impossible. A single man with influence and ideas can under such circumstances do great things for the promotion of education.

But the matter has also its reverse aspect. The party in power works for its own interests, uses the schools for its special purposes. Educational competition is excluded, for all successful attempts at improvement are impossible unless undertaken or permitted by the State. By the uniformity of the people's education, a prejudice once in vogue is permanently established. The highest intelligences, the strongest wills cannot overthrow it suddenly. In fact, as everything is adapted to the view in question, a sudden change would be physically impossible. The two classes which virtually hold the reins of power in the State, the jurists and theologians, know only the one-sided, predominantly classical culture which they have acquired in the State schools, and would have this culture alone valued. Others accept this opinion from credulity; others, underestimating their true worth for society, bow before the power of the prevalent opinion; others, again, affect the opinion of the ruling classes even against their better judgment, so as to abide on the same plane of respect with the latter. I will make no charges, but I must confess that the deportment of medical men with respect to the question of the qualification of graduates of your Realschulen has frequently made that impression upon me. Let us remember, finally, that an influential statesman, even within the boundaries which the law and public opinion set him, can do serious harm to the cause of education by considering his own one-sided views infallible, and in enforcing them recklessly and inconsiderately--which not only can happen, but has, repeatedly, happened. The monopoly of education by the State thus assumes in our eyes a somewhat different aspect. And to revert to the question above asked, there is not the slightest doubt that the German gymnasiums in their present form would have ceased to exist long ago if the State had not supported them.

All this must be changed. But the change will not be made of itself, nor without our energetic interference, and it will be made slowly. But the path is marked out for us, the will of the people must acquire and exert upon our school legislation a greater and more powerful influence. Furthermore, the questions at issue must be publicly and candidly discussed that the views of the people may be clarified. All who feel the insufficiency of the existing régime must combine into a powerful organisation that their views may acquire impressiveness and the opinions of the individual not die away unheard.

I recently read, gentlemen, in an excellent book of travels, that the Chinese speak with unwillingness of politics. Conversations of this sort are usually cut short with the remark that they may bother about such things whose business it is and who are paid for it. Now it seems to me that it is not only the business of the State, but a very serious concern of all of us, how our children shall be educated in the public schools at our cost.

FOOTNOTES:

Although substantially contained in an address which I was to have made at the meeting of Natural Scientists at Salzburg in 1881 (deferred on account of the Paris Exposition), and in the Introduction to a course of lectures on "Physical Instruction in Preparatory Schools," which I delivered in 1883, the invitation of the German Realschulmännerverein afforded me the first opportunity of putting my views upon this subject before a large circle of readers. Owing to the place and circumstances of delivery, my remarks apply of course, primarily, only to German schools, but, with slight modifications, made in this translation, are not without force for the institutions of other countries. In giving here expression to a strong personal conviction formed long ago, it is a matter of deep satisfaction to me to find that they agree in many points with the views recently advanced in independent form by Paulsen (Geschichte des gelehrten Unterrichts, Leipsic, 1885) and Frary (La question du latin, Paris, Cerf, 1885). It is not my desire nor effort here to say much that is new, but merely to contribute my mite towards bringing about the inevitable revolution now preparing in the world of elementary instruction. In the opinion of experienced educationists the first result of that revolution will be to make Greek and mathematics alternately optional subjects in the higher classes of the German Gymnasium and in the corresponding institutions of other countries, as has been done in the splendid system of instruction in Denmark. The gap between the German classical Gymnasium and the German Realgymnasium, or between classical and scientific schools generally, can thus be bridged over, and the remaining inevitable transformations will then be accomplished in relative peace and quiet. (Prague, May, 1886.)]

"A host of words exist which are out and out Latin or Greek, yet are employed with perfect correctness by people of good education who never had the good luck to be taught the ancient languages. For example, words like 'dynasty.' ... The child learns such words as parts of the common stock of speech, or even as parts of his mother-tongue, just as he does the words 'father,' 'mother,' 'bread,' 'milk.' Does the ordinary mortal know the etymology of these Saxon words? Did it not require the almost incredible industry of the Grimms and other Teutonic philologists to throw the merest glimmerings of light upon the origin and growth of our own mother-tongue? Besides, do not thousands of people of so-called classical education use every moment hosts of words of foreign origin whose derivation they do not know? Very few of them think it worth while to look up such words in the dictionaries, although they love to maintain that people should study the ancient languages for the sake of etymology alone."]

APPENDIX.

A CONTRIBUTION TO THE HISTORY OF ACOUSTICS.

While searching for papers by Amontons, several volumes of the Memoirs of the Paris Academy for the first years of the eighteenth century, fell into my hands. It is difficult to portray the delight which one experiences in running over the leaves of these volumes. One sees as an actual spectator almost the rise of the most important discoveries and witnesses the progress of many fields of knowledge from almost total ignorance to relatively perfect clearness.

I propose to discuss here the fundamental researches of Sauveur in Acoustics. It is astonishing how extraordinarily near Sauveur was to the view which Helmholtz was the first to adopt in its full extent a hundred and fifty years later.

The Histoire de l'Académie for 1700, p. 131, tells us that Sauveur had succeeded in making music an object of scientific research, and that he had invested the new science with the name of "acoustics." On five successive pages a number of discoveries are recorded which are more fully discussed in the volume for the year following.

Sauveur regards the simplicity of the ratios obtaining between the rates of vibration of consonances as something universally known. He is in hope, by further research, of determining the chief rules of musical composition and of fathoming the "metaphysics of the agreeable," the main law of which he asserts to be the union of "simplicity with multiplicity." Precisely as Euler did a number of years later, he regards a consonance as more perfect according as the ratio of its vibrational rates is expressed in smaller whole numbers, because the smaller these whole numbers are the oftener the vibrations of the two tones coincide, and hence the more readily they are apprehended. As the limit of consonance, he takes the ratio 5:6, although he does not conceal the fact that practice, sharpened attention, habit, taste, and even prejudice play collateral rôles in the matter, and that consequently the question is not a purely scientific one.

Sauveur's ideas took their development from his having instituted at all points more exact quantitative investigations than his predecessors. He is first desirous of determining as the foundation of musical tuning a fixed note of one hundred vibrations which can be reproduced at any time; the fixing of the notes of musical instruments by the common tuning pipes then in use with rates of vibration unknown, appearing to him inadequate. According to Mersenne (Harmonie Universelle, 1636), a given cord seventeen feet long and weighted with eight pounds executes eight visible vibrations in a second. By diminishing its length then in a given proportion we obtain a proportionately augmented rate of vibration. But this procedure appears too uncertain to Sauveur, and he employs for his purpose the beats (battemens), which were known to the organ-makers of his day, and which he correctly explains as due to the alternate coincidence and non-coincidence of the same vibrational phases of differently pitched notes. At every coincidence there is a swelling of the sound, and hence the number of beats per second will be equal to the difference of the rates of vibration. If we tune two of three organ-pipes to the remaining one in the ratio of the minor and major third, the mutual ratio of the rates of vibration of the first two will be as 24: 25, that is to say, for every 24 vibrations to the lower note there will be 25 to the higher, and one beat. If the two pipes give together four beats in a second, then the higher has the fixed tone of 100 vibrations. The open pipe in question will consequently be five feet in length. We also determine by this procedure the absolute rates of vibration of all the other notes.

It follows at once that a pipe eight times as long or 40 feet in length will yield a vibrational rate of 12½, which Sauveur ascribes to the lowest audible tone, and further also that a pipe 64 times as small will execute 6,400 vibrations, which Sauveur took for the highest audible limit. The author's delight at his successful enumeration of the "imperceptible vibrations" is unmistakably asserted here, and it is justified when we reflect that to-day even Sauveur's principle, slightly modified, constitutes the simplest and most delicate means we have for exactly determining rates of vibration. Far more important still, however, is a second observation which Sauveur made while studying beats, and to which we shall revert later.

Strings whose lengths can be altered by movable bridges are much easier to handle than pipes in such investigations, and it was natural that Sauveur should soon resort to their use.

One of his bridges accidentally not having been brought into full and hard contact with the string, and consequently only imperfectly impeding the vibrations, Sauveur discovered the harmonic overtones of the string, at first by the unaided ear, and concluded from this fact that the string was divided into aliquot parts. The string when plucked, and when the bridge stood at the third division for example, yielded the twelfth of its fundamental note. At the suggestion of some academician probably, variously colored paper riders were placed at the nodes (noeuds) and ventral segments (ventres), and the division of the string due to the excitation of the overtones (sons harmoniques) belonging to its fundamental note (son fondamental) thus rendered visible. For the clumsy bridge the more convenient feather or brush was soon substituted. . While engaged in these investigations Sauveur also observed the sympathetic vibration of a string induced by the excitation of a second one in unison with it. He also discovered that the overtone of a string can respond to another string tuned to its note. He even went further and discovered that on exciting one string the overtone which it has in common with another, differently pitched string can be produced on that other; for example, on strings having for their vibrational ratio 3:4, the fourth of the lower and the third of the higher may be made to respond. It follows indisputably from this that the excited string yields overtones simultaneously with its fundamental tone. Previously to this Sauveur's attention had been drawn by other observers to the fact that the overtones of musical instruments can be picked out by attentive listening, particularly in the night. He himself mentions the simultaneous sounding of the overtones and the fundamental tone. That he did not give the proper consideration to this circumstance was, as will afterwards be seen, fatal to his theory.

While studying beats Sauveur makes the remark that they are displeasing to the ear. He held the beats were distinctly audible only when less than six occurred in a second. Larger numbers were not distinctly perceptible and gave rise accordingly to no disturbance. He then attempts to reduce the difference between consonance and dissonance to a question of beats. Let us hear his own words.

"Beats are unpleasing to the ear because of the unevenness of the sound, and it may be held with much plausibility that the reason why octaves are so pleasing is that we never hear their beats.