[2]The Roman family Cosmati (of the thirteenth century), which gave us seven splendid representatives of architecture and mosaic work, hardly comes into consideration, since not one of them is regarded in the history of art as a real genius.
Einstein, however, contradicted this emphatically: "Inherited talent certainly occurs in many cases, where we do not observe it, for genius in itself and the possibility of genius being apprehended are certainly far from always appearing in conjunction. There are only insignificant differences between the genius that expresses itself in remarkable achievements and the genius that is latent. At a certain instant, perhaps, only some impulse was wanting for the latent genius to burst forth with all clearness and brilliance; or, perhaps, it required only an unusual situation in the development of science to call into action his special talents, and thus it remained dormant, whereas a very slight change of circumstances would have caused them to assert themselves in definite results.
"In passing I should like to remark that you just now mentioned the two Humboldts; it seems to me that Alexander von Humboldt, at least, is not to be counted as a genius. It has struck me repeatedly that you pronounced his name with particular reverence——"
"And I have observed equally often, Professor, that you made a sign of disapproval. For this reason slight doubts have gradually been rising in me. But it is difficult to get free from the orders of greatness that one has recognized for decades. In my youth people spoke of 'a Humboldt' just as we speak of 'a Cæsar' or 'a Michelangelo,' to denote some pinnacle of unrivalled height. To me at that time Humboldt's Kosmos was the Bible of Natural Science, and probably such memories have a certain after-effect."
"That is easy to understand," said Einstein. "But we must make it clear to ourselves that for us of the present day Humboldt scarcely comes into consideration when we direct our gaze on to the great seers. Or, let us say more clearly, he does not belong to this category. I certainly grant him his immense knowledge and his admirable faculty of getting into touch with the unity of Nature, which reminds us of Goethe."
"Yes; this feeling for the uniformity of the cosmos had probably persuaded me in his favour," I answered, "and I am glad that you draw a parallel with Goethe in this respect. It reminds me of Heine's story: If God had created the whole world, except the trees and the birds, and had said to Goethe: 'My dear Goethe, I leave it to you to complete this work,' Goethe would have solved the problem correctly and in a god-like manner—that is, he would have painted the trees green and given the birds feathers.
"Humboldt could equally well have been entrusted with this task. But various objections may be raised against such reflections of a playful poetic character ... one objection being that Goethe's own knowledge of ornithology was exceedingly limited. Even when nearly eighty he could not distinguish a lark from a yellow-hammer or a sparrow! Is that a fact?"
"Fully confirmed: Eckermann gives a detailed report of it in a conversation which took place in 1827. As I happened to come across the passage only yesterday, I can quote the exact words if you will allow me: 'Great and good man,' thought Eckermann, 'who hast explored Nature as few have ever done, in ornithology thou seemest still a child!'"
For a speculative philosopher, it may here be interposed, this might well serve as the starting-point of an attractive investigation. Goethe, on the one hand, cannot recognize a lark, but would have been able to grasp the Platonic idea of the feathered species, even if there had been no such things as birds: Humboldt, on the other hand, would perhaps have been able to create the revolving planets, if Heaven had commanded it; but he would never have succeeded in becoming the author of what we call an astronomical achievement, such as that of Copernicus or of Kepler.
And with reference to certain other men I elicited from Einstein utterances that reduced somewhat my estimate of their importance.
We were speaking of Leonardo da Vinci, omitting all reference to his significance in the world of Art—that is, only of Leonardo the Scholar and the Searcher. Einstein is far from disputing his place in the Valhalla of great minds, but it was clear that he wished to recommend a re-numbering of my list, so that the Italian master would not occupy a position in just the first rank.
The problem of Leonardo excited great interest in me, and it deserves the consideration of every one. The further the examination of his writings advances, the more does this problem resolve itself into the question: How much altogether does modern science owe to Leonardo? Nowadays it is declared in all earnestness that he was a painter and a sculptor only by the way, that his chief profession was that of an engineer, and that he was the greatest engineer of all times. This has in turn given rise to the opinion that, as a scientist, he is the light of all ages, and in the abundance of his discoveries he has never been surpassed before or after his own time.
As this question had arisen once before, I had come equipped with a little table of facts, hastily drawn from special works to which I had access. According to my scheme, Leonardo was the true discoverer and author of the following things:
Law of Conservation of Momentum.
Law of Virtual Velocities (before Ubaldi
and Galilei).
Wave Theory (before Newton).
Discovery of the Circulation of the Blood
(before
Harvey).
Laws of Friction (before Coulomb).
Law of Pressure for connected Tubes
containing
Fluid (before Pascal).
Action of Pressure on Fluids (before Stevin
and Galilei).
Laws of Falling Bodies (before Galilei).
True interpretation of the twinkling of
stars (before
Kepler, who, moreover, did not succeed in
finding
the real explanation).
Explanation of the reflected light of the
moon (before
Kepler).
Principle of Least Action (before
Galilei).
Introduction of the plus and the minus
signs into
calculations.
Definition of kinetic energy from mass and
velocity.
Theory of Combustion (before Bacon).
Explanation of the motion of the sea
(before Maury).
Explanation of the ascent of fluids in
plants (before
Hales).
Theory of Fossilization (before
Palissy).
Added to these there are a great number of inventions, in particular those connected with problems of aviation, such as the parachute (before Lenormand), and so forth.
This fist aroused great distrust in Einstein: he regarded it as the outcome of an inquisitive search for sources, excusable historically, but leading to misrepresentation. We are falsely led to regard slightly related beginnings, vague tracks, hazy indications, which are found, as evidences of a real insight, which disposes us to "elevate one above all others." Hence a mythological process results, comparable to that which, in former times, thrust all conceivable feats of strength on to one Hercules.
I learned that recently a strong reaction has asserted itself in scientific circles against this one-sided hero-worship; its purpose is to reduce Leonardo's merits to their proper measure. Einstein made it quite clear that he was certainly not to be found on the side of the ultra-Leonardists.
It cannot be denied that the latter have valuable arguments to support their case, and that these arguments become multiplied in proportion as the publication of Leonardo's writings (in the Codex Atlanticus, etc.), which are so difficult to decipher, proceeds. The partisans of Leonardo derive considerable support in many points from recognized authorities, as in the case of Cantor, the author of the monumental history of mathematics. We there read: "The greatest Italian painter of the fifteenth century was not less great as a scientist. In the history of science his name is famous and his achievements are extolled, particularly those which give him a claim to be regarded as one of the founders of Optics." He is placed on a level with Regiomantus as one of the chief builders of mathematics of that time. Nevertheless, Cantor raises certain doubts by remarking that the results of investigations made up to the present do not prove Leonardo to be a great mathematician. On another page he is proclaimed simultaneously with Archimedes and Pappus as a pioneer of the doctrines of the centre of gravity.
With regard to the main points, Leonardo's priority in the case of the Laws of Falling Bodies, the Theory of Wave-motion, and the other fundamental principles of physics, Einstein has the conviction that the partisans of Leonardo are either mistaken in the facts or that they overlook forerunners. In the case of these principles, above all, there is always some predecessor, and it is almost impossible to trace the line of discoveries back to the first source. Just as writers have wished to deprive Galilei, Kepler, and Newton of their laurels in favour of Leonardo, so the same might be done with Copernicus.
This has actually been attempted. The real Copernicus, so one reads, was Hipparchus of Nicæa, and if we go back still further, a hundred years earlier, two thousand years ago, we find that Aristarchus of Samos taught that the world rotated about its own axis and revolved round the sun.
And we need not even stop there, in Einstein's opinion. For it is open to conjecture that Aristarchus in his turn has drawn on Egyptian sources. This retrogressive investigation may excite the interest of archæologists, and in particular cases perhaps lead to the discovery of a primary claim to authorship, but it cannot fail to excite suspicion against the conscious intention of conferring all the honours of science on an individual discoverer. Leonardo's superlative constructive genius is not attacked in these remarks, and there seems no reason for objecting if anyone wishes to call him the most ingenious engineer of all times.
All the pressures and tensions occurring in Nature seemed to be repeated in him as "inner virtues," an expression borrowed from Helmholtz, who used it with reference to himself. This analogy might be extended by saying that, in the works of both, Man himself with his organic functions and requirements plays an important rôle. For them the abstract was a means of arriving at what was perceptual, physiologically useful, and stimulating in its effect on life. Leonardo started out from Art, and throughout the realm of mechanics and machines he remained an artist in method. Helmholtz set out from the medical side of physiology and transferred the valuations of beauty derived from the senses to his pictures of mechanical relationships. The life-work of each has an æsthetic colouring, Leonardo's being of a gloomy hue, that of Helmholtz exhibiting brighter and happier tints. Common to both is an almost inconceivable versatility and an inexhaustible productivity.
Whenever Einstein talks of Helmholtz he begins in warm terms of appreciation, which tend to become cooler in the course of the conversation. I cannot quote his exact words, and as I cannot thus give a complete account for which full responsibility may be taken, it may be allowable to offer a few important fragments that I have gathered.
Judged by the average of his accomplishments, Helmholtz is regarded by Einstein as an imposing figure whose fame in later times is assured; Helmholtz himself tasted of this immortality while still alive. But when efforts are made to rank him with great thinkers of the calibre of Newton, Einstein considers that this estimate cannot be fully borne out. In spite of all the excellence, subtlety, and effectiveness of Helmholtz's astoundingly varied inspirations, Einstein seems to fail to discover in him the source of a really great intellectual achievement.
At a Science Congress held in Paris in 1867, at which Helmholtz was present, a colleague of his was greeted with unanimous applause when he toasted him with the words: "L'ophthalmologie était dans les ténèbres,—Dieu parla, que Helmholtz naquît—Et la lumière était faite!" It was an almost exact paraphrase of the homage which Pope once addressed to Newton. At that time the words of the toast were re-echoed throughout the world; ophthalmology was enlarged to science generally, and the apotheosis was applied universally. Du Bois-Reymond declared that no other nation had in its scientific literature a book that could be compared with Helmholtz's works on Physiological Optics and on Sensations of Tone. Helmholtz was regarded as a god, and there are not a few to whom he still appears crowned with this divine halo.
A shrill voice pierced the serene atmosphere, attacking one of his main achievements. The dissentient was Eugen Dühring, to whose essay on the Principles of Mechanics a coveted prize was awarded, a fact which seemed to stamp him as being specially authorized to be a judge of pre-eminent achievements in this sphere. Dühring's aim was to dislodge one of the fundamental supports of Helmholtz's reputation by attacking his "Law of the Conservation of Energy." If this assault proved successful, the god would lie shattered at his own pedestal.
Dühring, indeed, used every means to bespatter his fair name in science; and it is hardly necessary to remark that Einstein abhors this kind of polemic. What is more, he regards it as a pathological symptom, and has only a smile of disdain for many of Dühring's pithy sayings. He regards them as documents of unconscious humour to be preserved in the archives of science as warnings against future repetitions of such methods.
Dühring belonged also to those who wished to exalt one above all others. He raised an altar to Robert Mayer, and offered up sanguinary sacrifices. Accustomed to doing his work thoroughly, he did not stop at Helmholtz in choosing his victims. No hecatomb seemed to him too great to do honour to the discoverer of the Mechanical Equivalent of Heat, and so his next prey was Gauss and Riemann.
Gauss and Riemann! Each was a giant in Einstein's opinion. He knew well that this raging Ajax had also made an assault against them, but he had no longer a clear recollection of the detailed circumstances; as the references were near at hand, he allowed me to repeat a few lines of this tragi-comedy.
Helmholtz, according to Dühring (who also calls him "Helmklotz"), has done no more than distort Mayer's fundamental mechanical idea, and interpret it falsely. By "philosophizing" over it, he has completely spoilt it, and rendered it absurd. It was the greatest of all humiliations practised on Mayer that his name had been coupled with that of one whom he had easily out-distanced, and whose clumsy attempts at being a physicist were even worse than those by which he sought to establish himself as a philosopher.
The offences of Gauss and Riemann against Mayer are shrouded in darkness. But there was another would-be scientist, Justus von Liebig, who, being opposed to Mayer, aroused the suspicions of Dühring, particularly as he had used his "brazen-tongue" to defend the two renowned mathematicians. After he, and Clausius too, had been brought to earth, Dühring launched out against the giants of Göttingen. In the chapter on Gauss and "Gauss-worship," we read: "His megalomania rendered it impossible for him to take exception to any tricks that the deficient parts of his own brain played on him, particularly in the realm of geometry. Thus he arrived at a pretentiously mystical denial of Euclid's axioms and theorems, and proceeded to set up the foundations of an apocalyptic geometry not only of nonsense but of absolute stupidity.... They are abortive products of the deranged mind of a mathematical professor, whose mania for greatness proclaims them as new and superhuman truths!... The mathematical delusions and deranged ideas in question are the fruits of a veritable paranoia geometrica."
After Herostratus had burnt to ashes the consecrated temple, the Ionian cities issued a proclamation that his name was to be condemned to perpetual oblivion! The iconoclast Dühring is immortalized, for, apart from the charge of arson, he is notable in himself. In his case we found ourselves confronted with unfathomable problems of a scholar's complex nature, problems which even a searcher like Einstein failed to solve. The simplest solution would be to turn the tables and to apply the term "paranoia" as a criticism to the book on Robert Mayer, and thus demolish it. But this will not do, for if we merely pass over the pages of distorted thought, we are still left with a considerable quantity of valuable material.
Does Dühring, after all, himself deserve a place in our Valhalla? The question seems monstrous, and yet cannot be directly answered in the negative. The individual is to be judged according to his greatest achievement, and not according to his aberrations. The works of Aristotle teem with nonsensical utterances, and Leonardo's Bestiarius is an orgy of abstruse concoctions. If Dühring had written nothing beyond his studies of personalities ranging from Archimedes to Lagrange, the portals would yet have been open to him. Even in his eulogy of Robert Mayer, which is besmirched with unseemly remarks, he displays at least the courage of his convictions.
The attempt at a comparison between Robert Mayer and Helmholtz is doomed to failure even when considered dispassionately, inasmuch as the disturbing factor of priority here intrudes itself. The definite fixing of the Law of Energy is certainly to the credit of Helmholtz, but perhaps he would have gained by laying more stress on the discovery of it five years earlier by the doctor in Heilbronn. And again, this would not have been final, for the invariance of the sum of energy during mechanical actions was known even by Huyghens. The Heilbronn doctor performed one act of genius in his life, whereas Helmholtz during his whole life moved asymptotically to the fine of genius without ever reaching it. If my interpretation of Einstein's opinion is correct, Helmholtz is to be credited with having the splendour of an overpowering gift for research predominant in his nature, but is not necessarily to be given a seat among the most illustrious of his branch of science. Einstein wishes to preserve a certain line of demarcation between this type and not only the Titans of the past, but also those of the present. When he speaks of the latter, his tone becomes warmer. He does not need circuitous expressions, each syllable rings with praise. He has in mind, above all, Hendrik Antoon Lorentz in Leyden, Max Planck, and Niels Bohr; we then see that he feels Valhalla about him.
The reason that I have tried to maintain the metaphor of a Temple of Fame is due to an echo of Einstein's own words at a celebration held in honour of the sixtieth birthday of the physicist Planck in the May of 1918. This speech created the impression of a happy harmony resulting from a fusion of two melodies, one springing from the intellect, the other rising from the heart. We were standing as at the Propylons with a new Heraclitus uttering the cry: Introite, nam et hic dii sunt!
I should like to give the gist of this beautiful address in an extract uninterrupted by commentaries.
"The Temple of Science"—so Einstein began—"is a complex structure of many parts. Not only are the inmates diverse in nature, but so also are the inner forces that they have introduced into the temple. Many a one among them is engaged in Science with a happy feeling of a superior mind, and finds Science the sport which is congenial to him, and which is to give him an outlet for his strong life-forces, and to bring him the realization of his ambitions. There are, indeed, many, too, who offer up their sacrifice of brain-matter only in the cause of useful achievements. If now an angel of heaven were to come and expel all from the temple who belonged to these two categories, a considerable reduction would result, but there would still remain within the temple men of present and former times: among these we count our Planck, and that is why he has our warm affection.
"I know full well that, in doing this, we have light-heartedly caused many to be driven out who contributed much to the building of the temple; in many cases our angel would find a decision difficult.... But let us fix our gaze on those who find full favour with him! Most of them are peculiar, reserved, and lonely men, who, in spite of what they have in common, are really less alike than those who have been expelled. What led them into the temple?... In the first place, I agree with Schopenhauer that one of the most powerful motives that attract people to Science and Art is the longing to escape from everyday life with its painful coarseness and unconsoling barrenness, and to break the fetters of their own ever-changing desires. It drives those of keener sensibility out of their personal existence into the world of objective perception and understanding. This motive force is similar to the longing which makes the city-dweller leave his noisy, confused surroundings and draws him with irresistible force to restful Alpine heights, where his gaze covers the wide expanse lying peacefully before him on all sides, and softly passes over the motionless outlines that seem created for all eternity. Associated with this negative motive is a positive one, by virtue of which Man seeks to form a simplified synoptical view of the world in a manner conformable to his own nature, in order to overcome the world of experience by replacing it, to a certain degree, by this picture. This is what the painter does, as also the poet, the speculative philosopher, and the research scientist, each in his own way. He transfers the centre of his emotional existence into this picture, in order to find a sure haven of peace, one such as is not offered in the narrow limits of turbulent personal experience.
"What position does the world-picture of the theoretical physicist occupy among all those that are possible? He demands the greatest rigour and accuracy in his representation, such as can be gained only by using the language of mathematics. But for this very reason the physicist has to be more modest than others in his choice of material, and must confine himself to the simplest events of the empirical world, since all the more complex events cannot be traced by the human mind with that refined exactness and logical sequence which the physicist demands.... Is the result of such a restricted effort worthy of the proud name 'world-picture'?
"I believe this distinction is well deserved, for the most general laws on which the system of ideas set up by theoretical physics is founded claim to be valid for every kind of natural phenomenon. From them it should be possible by means of pure deduction to find the picture, that is, the theory, of every natural process, including those of living organism, provided that this process of deduction does not exceed the powers of human thought. Thus there is no fundamental reason why the physical picture of the world should fall short of perfection....
"Evolution has shown that among all conceivable theoretical constructions there is at each period one which shows itself to be superior to all others, and that the world of perception determines in practice the theoretical system, although there is no logical road from perception to the axioms of the theory, but rather that we are led towards the latter by our intuition, which establishes contact with experience....
"The longing to discover the pre-established harmony recognized by Leibniz is the source of the inexhaustible patience with which we see Planck devoting himself to the general problems of our science, refusing to allow himself to be distracted by more grateful and more easily attainable objects.... The emotional condition which fits him for his task is akin to that of a devotee or a lover; his daily striving is not the result of a definite purpose or a programme of action, but of a direct need.... May his love for Science grace his future course of life, and lead him to a solution of that all-important problem of the day which he himself propounded, and to an understanding of which he has contributed so much! May he succeed in combining the Quantum Theory with Electrodynamics and Mechanics in a logically complete system!"
"What grips me most in your address," I said, "is that it simultaneously surveys the whole horizon of science in every direction, and traces back the longing for knowledge to its root in emotion. When your speech was concluded, I regretted only one thing—that it had ended so soon. Fortunate is he who may study the text."
"Do you attach any importance to it?" asked Einstein; "then accept this manuscript." It is due to this act of generosity that I have been able to adorn the foregoing description of the excursion into Valhalla with such a valuable supplement.
The conversation had begun with the brilliant constellation Galilei-Newton, and near the end inclined again towards the consideration of a double-star: the names of Faraday and Maxwell presented themselves.
"Both pairs," Einstein declared, "are of the same magnitude. I regard them as fundamentally equal in their services in the onward march of knowledge."
"Should we not have to add Heinrich Hertz as a third in this bond? This assistant of Helmholtz is surely regarded as one of the founders of the Electromagnetic Theory of Light, and we often hear their names coupled, as in the case of the Maxwell-Hertz equations."
"Doubtless," replied Einstein, "Hertz, who is often mentioned together with Maxwell, has an important rank and must be placed very high in the world of experimental physics, yet, as regards the influence of his scientific personality, he cannot be classed with the others we have named. Let us, then, confine ourselves to the twin geniuses Faraday and Maxwell, whose intellectual achievement may be summarized in a few words. Classical mechanics referred all phenomena, electrical as well as mechanical, to the direct action of particles on one another, irrespective of their distances from one another. The simplest law of this kind is Newton's expression: 'Attraction equals Mass times Mass divided by the square of the distance.' In contradistinction to this, Faraday and Maxwell have introduced an entirely new kind of physical realities, namely, fields of force. The introduction of these new realities gives us the enormous advantage that, in the first place, the conception of action at a distance, which is contrary to our everyday experience, is made unnecessary, inasmuch as the fields are superimposed in space from point to point without a break; in the second place, the laws for the field, especially in the case of electricity, assume a much simpler form than if no field be assumed, and only masses and motions be regarded as realities."
He enlarged still further on the subject of fields, and while he was describing the technical details, I saw him metaphorically enveloped in a magnetic field of force. Here, too, an influence, transmitted through space from point to point, made itself felt, and there could be no question of action "at a distance" inasmuch as the effective source was so near at hand. His gaze, as if drawn magnetically, passed along the wall of the room and fixed affectionately on Maxwell and Faraday.
CHAPTER IV
EDUCATION
School Curricula and Reform of Teaching.—Value of Language Study.—Economy of Time.—Practice in Manual Work.—Picturesque Illustrations.—Art of Lecturing.—Selection of Talents by Means of Examinations.—Women Students.—Social Difficulties.—Necessity as Instructress.
OUR conversation turned towards a series of pædagogic questions, in which Einstein is deeply interested. For he himself is actively engaged in teaching, and never disguises the pleasure which he derives from imparting instruction. Without doubt he has a gift of making his spoken words react on wide circles anxious to be instructed, composed not only of University students, but of many others quite outside this category. When, recently, popular lectures on a large scale were instituted, he was one of the first to offer his services in this sound undertaking. He lectured to people of the working class, who could not be assumed to have any preliminary information on the subject, and he succeeded in presenting his lectures so that even the less trained minds could easily follow his argument.
His attitude towards general questions of school education is, of course, conditioned by his own personality and his own work in the past. His first care is that a young person should get an insight into the relationship underlying natural phenomena, that is, that the curricula should be mapped out so that a knowledge of facts is the predominating aim.
"My wish," Einstein declared to me, "is far removed from the desire to eliminate altogether the fundamental features of the old grammar schools, with their preference for Latin, by making over-hasty reforms, but I am just as little inclined to wax enthusiastic about the so-called humanistic schools. Certain recollections of my own school life suffice to prevent this, and still more, a certain presentiment of the educational problems of the future."—"To speak quite candidly," he said, "in my opinion the educative value of languages is, in general, much over-estimated."
I took the liberty of quoting a saying that is still regarded as irrefutable by certain scholars. It was Charles V who said: "Each additional acquired language represents an additional personality"; and to suggest the root of language formation he said it in Latin: "Quot linguas quis callet, tot homines valet." This saying has been handed down through the ages in German in the form: "Soviel Sprachen, soviel Sinnen" (An added language means an added sense).
Einstein replied: "I doubt whether this aphorism is generally valid, for I believe that it would at no time have stood a real test. All experience contradicts it. Otherwise we should be compelled to assign the highest positions among intellectual beings to linguistic athletes like Mithridates, Mezzofanti, and similar persons. The exact opposite, indeed, may be proved, namely, that in the case of the strongest personalities, and of those who have contributed most to progress, the multiplicity of their senses in no wise depended on a comprehensive knowledge of languages, but rather that they avoided burdening their minds with things that made excessive claims on their memories."
"Certainly," said I, "it may be admitted that this gives rise to exaggeration in some cases, and that the linguistic sort of sport practised by many a scholar degenerates to a mere display of knowledge. An intellectual achievement of lasting merit has very rarely or never been the result of a superabundance of acquired linguistic knowledge. An instance occurs to me at this moment. Nietzsche became a philosopher of far-reaching influence only after he had passed the stage of the philologist. As far as our present discussion is concerned, the question is narrowed down considerably: it reduces itself to inquiring whether we do sufficient, too little, or too much Greek and Latin. I must remark at the very outset that, formerly, school requirements went much further in this respect than nowadays, when we scarcely meet with a scholar even in the upper classes who knows Latin and Greek perfectly."
It is just this fact that Einstein regards as a sign of improvement and a result of examining the true aims of a school. He continued: "Man must be educated to 'react delicately'; he is to acquire and develop 'intellectual muscles'! And the methods of language drill are much less suited to this purpose than those of a more general training that gives greatest weight to a sharpening of one's own powers of reflection. Naturally, the inclination of the pupil for a particular profession must not be neglected, especially in view of the circumstance that such inclination usually asserts itself at an early age, being occasioned by personal gifts, by examples of other members of the family, and by various circumstances that affect the choice of his future life-work. That is why I support the introduction into schools, particularly schools devoted to classics, of a division into two branches at, say, the fourth form, so that at this stage the young pupil has to decide in favour of one or other of the courses. The elementary foundation to the fourth form may be made uniform for all, as they are concerned with factors on education that are scarcely open to the danger of being exaggerated in any one direction. If the pupil finds that he has a special interest in what are called humaniora by the educationist, let him by all means continue along the road of Latin and Greek, and, indeed, without being burdened by tasks that, owing to his disposition, oppress or alarm him."
"You are referring," I interposed, "to the distress which pupils feel in the time allotted to mathematics. There are actually people of considerable intelligence who seem to be smitten with absolute stupidity when confronted with mathematics, and whose school-life becomes poisoned owing to the torment caused by this subject. There are many cases of living surgeons, lawyers, historians, and litterateurs, who, till late in life, are visited by dreams of their earlier mathematical ordeals. Their horror has a very real foundation, for, whereas the pupil who is bad at Latin yet manages to get an idea of the language, and he who is weak in history has at least a notion of what is being discussed, the one who is unmathematical by nature has to worry his way through numberless lessons in a subject which is entirely incomprehensible to him, as if belonging to another world and being presented to him in a totally strange tongue. He is expected to answer questions, the sense of which he cannot even guess, and to solve problems, every word and every figure of which glares at him like a sphinx of evil omen. Sitting on each side of him are pupils to whom this is merely play, and some of whom could complete the whole of school mathematics within a few months at express rate. This leads to a contrast between the pupils, which may press with tragical force on the unfortunate member throughout his whole school existence. That is why a reform is to be welcomed that sifts out in time those who should be separated from the rest, and which adapts the school curriculum as closely as possible to individual talents."
Einstein called my attention to the fact that this division had already been made in many schools in foreign countries, as in France and in Denmark, although not so exclusively as suggested by him. "Moreover," he added, "I am by no means decided whether the torments that you mentioned are founded primarily on absence of talent in the pupil. I feel much more inclined to throw the responsibility in most cases on the absence of talent in the teacher. Most teachers waste their time by asking questions which are intended to discover what a pupil does not know, whereas the true art of questioning has for its purpose to discover what the pupil knows or is capable of knowing. Whenever sins of this sort are committed—and they occur in all branches of knowledge—the personality of the teacher is mostly at fault. The results of the class furnish an index for the quality of the preceptor. All things being taken into consideration, the average of ability in the class moves, with only slight fluctuations, about mean values, with which tolerably satisfactory results may be obtained. If the progress of the class is not up to this standard, we must not speak of a bad year but rather of an inefficient instructor. It may be assumed that, as a rule, the teacher understands the subject with which he is entrusted, and has mastered its content, but not that he knows how to impart his information in an interesting manner. This is almost always the source of the trouble. If the teacher generates an atmosphere of boredom, the progress is stunted in the suffocating surroundings. To know how to teach is to be able to make the subject of instruction interesting, to present it, even if it happens to be abstract, so that the soul of the pupil resonates in sympathy with that of his instructor, and so that the curiosity of the pupil is never allowed to wane."
"That is in itself an ideal postulate. If we assume it to be fulfilled, how do you wish to see the subjects distributed in the curriculum?"
"We must leave the detailed discussion of this question for another occasion. One of the main points would be the economy of time; all that is superfluous, vexatious, and only intended as a drill must be dropped. At present the aim of the whole course is the leaving certificate. This test must be given up!"
"Is that serious. Professor? Do you wish to do away with the examination for matriculation?"
"Exactly. For it is like some fearful monster guarding our exit from school, throwing its shadow far ahead, and compelling teacher and pupil to work incessantly towards an artificial show of knowledge. This examination has been elevated by forcible means to a level which the violently drilled candidates can keep only for a few hours, and is then lost to sight for ever. If it is eliminated, it will carry away with it this painful drilling of the memory; it will no longer be necessary to hammer in for years what will be entirely forgotten within a few months, and what deserves to be forgotten. Let us return to Nature, which upholds the principle of getting the maximum amount of effect from the minimum of effort, whereas the matriculation test does exactly the opposite."
"Yes, but who is then to be allowed to enter the university?"
"Every one who has shown himself to be capable not only in a crucial test of an accidental kind, but in his whole behaviour. The teacher will be the judge of this, and if he does not know who is qualified, he again is to be blamed. He will find it so much the easier to decide who is sufficiently advanced to obtain a leaving certificate, in proportion as the curriculum has weighed less on the minds of the young people. Six hours a day should be ample—four at school and two for home-work; that should be the maximum. If this should appear too little to you, I must ask you to bear in mind that a young mind is being subjected to strain even in leisure hours, as it has to receive a whole world of perceptions. And if you ask how the steadily increasing curriculum is to be covered in this very moderate number of hours, my answer is: Throw all that is unnecessary overboard! I count as unnecessary the major part of the subject that is called 'Universal History,' and which is, as a rule, nothing more than a blurred mass of history compressed into dry tables of names and dates. This subject should be brought within the narrowest possible limits, and should be presented only in broad outline, without dates having to be crammed. Leave as many gaps as you like, especially in ancient history; they will not make themselves felt in our ordinary existences. In nowise can I regard it as a misfortune if the pupil learns nothing of Alexander the Great, and of the dozens of other conquerors whose documentary remains burden his memory like so much useless ballast. If he is to get a glimpse of the grey dawn of time, let him be spared from Cyrus, Artaxerxes, and Vercingetorix, but rather tell him something of the pioneers of civilization, Archimedes, Ptolemy, Hero, Appolonius, and of inventors and discoverers, so that the course does not resolve into a series of adventures and massacres."
"Would it not be expedient," I interrupted, "to take some of the history time to branch off into an elementary treatment of the real evolution of the state, including sociology and the legal code?"
Einstein does not consider this desirable, although he himself is deeply interested in all manifestations of public life. He does not favour an elementary political training received at school, presumably above all owing to the fact that in this branch the instruction cannot be removed from official influences, and because political questions require the attention of a mature mind. His picture of how a youth is to meet the requirements of modern life is something quite different, far removed from all theories. His whole efforts are directed at finding a means of counteracting the tendency to overburden one side of the youthful mind. "I should demand the introduction of compulsory practical work. Every pupil must learn some handicraft. He should be able to choose for himself which it is to be, but I should allow no one to grow up without having gained some technique, either as a joiner, bookbinder, locksmith, or member of any other trade, and without having delivered some useful product of his trade."
"Do you attach greater importance to the technique itself or to the feeling of social relationship with the broad masses of the people which it engenders?"
"Both factors are equally important to me," said Einstein, "and others become added to these which help to justify my wish in this respect. The handiwork need not be used as a means of earning money by the pupil of the secondary school, but it will enlarge and make more solid the foundation on which he will rest as an ethical being. In the first place, the school is not to produce future officials, scholars, lecturers, barristers, and authors, but human beings, not merely mental machines. Prometheus did not begin his education of mankind with astronomy, but by teaching the properties of fire and its practical uses...."
"This brings to my mind another analogy," I continued, "namely, that of the old Meistersinger, who were, all of them, expert smiths, tinkers, or shoemakers, and yet succeeded in building a bridge to the arts. And at bottom, the sciences, too, belong to the category of free arts. Yet, a difficulty seems to me to arise. In demanding a compulsory handicraft, you lay stress on practical use, whereas in your other remarks you declared science in itself as being utterly independent of practice."
"I do this," replied Einstein, "only when I speak of the ultimate aims of pure research, that is, of aims that are visible to only a vanishing minority. It would be a complete misconception of life to uphold this point of view and to expect its regulative effectiveness in cases in which we are dealing only with the preliminaries of science. On the contrary, I maintain that science can be taught much more practically at schools than it is at present when bookwork has the upper hand. For example, to return to the question of mathematical teaching: it seems to me to be almost universally at fault, if only for the reason that it is not built up on what is practically interesting, what appeals directly to the senses, and what can be seized intuitively. Child-minds are fed with definitions instead of being presented with what they can grasp, and they are expected to be able to understand purely conceptual things, although they have had no opportunity given them of arriving at the abstract by way of concrete things. It is very easy to do the latter. The first beginnings should not be taught in the schoolroom at all, but in open Nature. A boy should be shown how a meadow is measured and compared with another. His attention must be directed to the height of a tower, to the length of his shadow at various times, to the corresponding altitude of the sun; by this means he will grasp the mathematical relationships much more rapidly, more surely, and with greater zeal, than if words and chalk-marks are used to instil into him the conceptions of dimensions, of angles, or perchance of some trigonometrical function. What is the actual origin of such branches of science? They are derived from practice, as, for example, when Thales first measured the height of the pyramids with the help of a short rod, which he set up at the ultimate point of the pyramid's shadow. Place a stick in the boy's hand and lead him on to make experiments with it by way of a game, and if he is not quite devoid of sense, he will discover the thing for himself. It will please him to have discovered the height of the tower without having climbed it, and this is the first thrill of the pleasure which he feels later when he learns the geometry of similar triangles and the proportionality of their sides."
"In the matter of physics," pursued Einstein, "the first lessons should contain nothing but what is experimental and interesting to see. A pretty experiment is in itself often more valuable than twenty formulæ extracted from our minds; it is particularly important that a young mind that has yet to find its way about in the world of phenomena should be spared from formulæ altogether. In his physics they play exactly the same weird and fearful part as the figures of dates in Universal History. If the experimenter is ingenious and expert, this subject may be begun as early as in the middle forms, and one may then count on a responsiveness that is rarely observable during the hours of exercise in Latin grammar."
"This leads me," said Einstein, "to speak in this connexion of a means of education that has so far been used only by way of trial in class-teaching, but from an improved application of which I expect fruitful results later. I mean the school cinema. The triumphal march of the cinematograph will be continued into pedagogic regions, and here it will have a chance to make good its wrongs in thousands of picture shows in showing absurd, immoral, and melodramatic subjects. By means of the school-film, supplemented by a simple apparatus for projection, it would be possible firstly to infuse into certain subjects, such as geography, which is at present wound off organ-like in the form of dead descriptions, the pulsating life of a metropolis. And the lines on a map will gain an entirely new complexion in the eyes of the pupil, if he learns, as if during a voyage, what they actually include, and what is to be read between them. An abundance of information is imparted by the film, too, if it gives an accelerated or retarded view of such things as a plant growing, an animal's heart beating, or the wing of an insect moving. The cinema seems to me to have a still more important function in giving pupils an insight into the most important branches of technical industry, a knowledge of which should become common property. Very few hours would suffice to impress permanently on the schoolboy's mind how a power-station, a locomotive, a newspaper, a book, or a coloured illustration is produced, or what takes place in an electrical plant, a glass factory, or a gasworks. And, to return to natural science, many of the rather difficult experiments that cannot be shown by means of school apparatus may be shown with almost as great clearness on a film. Taken all in all, the redeeming word in school-teaching is, for me: an increased appeal to the senses. Wherever it is possible, learning must become living, and this principle will predominate in future reforms of school-teaching."