The Net Advance of Physics RETRO:
Alexander Moszkowski:

Chapter Three


2014 March 17

The 1842 Walhalla Ruhmes- und Ehrenhalle in Regensburg. [Photo by Michael J. Zirbes]

SOURCE: Einstein: Einblicke in seine Gedankenwelt -- Gemeinverständliche Betrachtegung über die Relativitätstheorie und ein neues Weltsystem entwickelt aus Gesprächen mit Einstein von Alexander Moszkowski [Hamburg: Hoffmann und Campe, 1921]
English translation: Einstein the Searcher translated by Henry L. Brose [New York: E. P. Dutton, 1922], with a few additions and modifications.

Moszkowski's words are in bold.


Order of Distinction and Characteristics of Great Discoverers. --- Galilei and Newton. --- Forerunners and Priority. --- Science and Religion. --- Inheritance of Talent. --- A Dynasty of Scholars. --- Alexander von Humboldt and Goethe. --- Leonardo da Vinci. --- Helmholtz. --- Robert Mayer and Dühring. --- Gauss and Riemann. --- Max Planck. --- Maxwell and Faraday.

I HAD made up my mind to question Einstein about a number of famous men, not concerning mere facts of their lives and works, for these details were also procurable elsewhere, and, moreover, I was not ignorant of them, but what attracted me particularly was to try to discover how the greatness of one might be compared with that of another. This sometimes helps us to see a personality in a different light and from a new perspective, which leads us to assign to him a new position in the series of orders of merit.

Interior of the Regensburg Walhalla. [Photo by Christian Horvat]

I had really sketched out a list for this purpose, including a great number of glorious names from the annals of physics and regions just beyond : a table, as it were, from which one might set up a directory for Valhalla ! It seemed to me a pleasing thought to roam through this hall of celebrities in company with Einstein, and to pause at the pedestal of the busts of the great, who, in spite of their number, are still too few, far too few, in comparison with the far too many who populate the earth like so many factory-produced articles. If we set to work to draw up a list of this sort, we soon find that there is no end to these heroes of Valhalla, and we are reminded of the hall of fame of the Northern Saga, of the mythological Valhalla, whose ceiling was so high that the gable was invisible, and whose extent was so great that anyone wishing to enter could choose from five hundred and forty entrances.

In reality our little excursion was far from taking these dimensions, the chief reason being probably that we had begun at Newton. However attractive it may be to hear Einstein talk of Newton, a disadvantage arises in that we find it hard to take leave of his bust situated at the main portal, and that we continually revert to it even when we call to mind the remaining paths free for our choice and stretching out of sight.

Reality, even figuratively, offered a picture which differed considerably from the measures of greatness apportioned by legendary accounts. In Einstein's workroom, certainly, a visitor encounters portraits, not busts, and it would be rash to speak of this little collection of portraits as of a miniature museum. No, it is certainly not that, for its catalogue numbers only to three. But here they act as a trinity with a special significance under the gaze of Einstein, who looks up to them with reverence. To him their contribution of thought is immeasurable :


MAXWELL with his rich coils of hair ;

and between them, NEWTON with his flowing wig, represented in an excellent English engraving, whose border consists of symbolic insignias encircling his distinguished-looking countenance. [I have been thus far unable to locate any widely-circulated engraving of Newton which exactly matches this description ; those with borders of symbolic insignias for some reason usually omit Newton's wig, and vice versa ! The nearest I have found is a 1740 Dutch engraving by Houbraken which may be viewed at the Royal Society's web-site, subject to excessively legalistic "terms of use"; it shows the famous Kneller portrait of Newton (bewigged) on an ornate pedestal in front of what seems to be a pyramid. ]

According to Schopenhauer, the measure of reverence that one can feel is a measure of one's own intrinsic value. Tell me how much respect you can feel, and I shall tell you what is your worth. It is certainly not necessary to emphasize this quality specially in the case of Einstein, for there are other points of vantage from which we may form an estimate of his excellence. Nevertheless, I make special mention of the circumstance to give an indication of the difference between a revolutionary discoverer and revolutionary pioneers in other fields.

It is particularly noticeable that inborn respect is seldom found in modernists of Art. The only means of propaganda known to them consists in a passionate denunciation of what has been developed historically by gradual and patient effort ; their retrospect consists of unmitigated contempt ; they profess to be disciples only of what is most recent, remaining confined within the narrow circle surrounding their own ego. The horizon of the discoverer has a different radius. He takes over responsibility for the future by never ceasing his offerings at the altar of the Past.

There is probably no discoverer who is devoid of this characteristic, but I should like to emphasize that, among all the scientists with whom I am acquainted, no one recognizes the merit of others so warmly as Einstein. He becomes carried away with enthusiasm when he talks of great men, or of such as appear great to him. His Valhalla is not, of course, the same as that favoured by Encyclopædias, and many a one whom we rank as a Sirius among men is to be found dimmer than the sixth order of magnitude in Einstein's list. Nevertheless, his scientific heaven is richly stocked, and the reverence that was originally inspired by reasoned thought has become infused in his temperament and become a part of his emotional self.

One need only mention the name of Newton --- and even this is scarcely necessary, for Newton seems always near at hand ; if I happen to start with Descartes or Pascal, it does not take long before we arrive at Newton. ANΔPA MOI ENNEΠH !

Galileo's Tomb. Photo by Ricardo André Frantz.

Once we began with Laplace ; and it seemed almost as if the Traité de la méchanique céleste was to become the subject of discussion. But Einstein left his seat, and, taking up a position in front of his series of portraits on the wall, he meditatively passed his hand through his hair, and declared :

"In my opinion the greatest creative geniuses are Galilei and Newton, whom I regard in a certain sense as forming a unity. And in this unity Newton is he who has achieved the most imposing feat in the realm of science. These two were the first to create a system of mechanics founded on a few laws and giving a general theory of motions, the totality of which represents the events of our world."

Interrupting his remarks, I asked : "Can Galilei's fundamental law of inertia (Newton's First Law of Motion) be said to be a law deduced from experience ? My reason for asking is that the whole of natural science is a science of experience, and not merely something based on speculation. It might easily suggest itself to one that an elementary law like that of linear motion could be derived from our everyday experience. But, if this is the case, how is it that science had to wait so long before this simple fact was discovered ? Experience is as old as the hills ; why did the law of inertia not make its appearance at the very beginning, when Nature was first subjected to inquiry ? "

"By no means ! " replied Einstein. "The discovery of the law of rectihnear motion of a body under no external influences is not at all a result of experience. On the contrary ! A circle, too, is a simple line of motion, and has often been proclaimed as such by predecessors of Newton, for example, by Aristotle. It required the enormous power of abstraction possessed only by a giant of reason to stabilize rectilinear motion as the fundamental form."

To this may be added that before and even after the time of Galilei, not only the circle but also other non-rectilinear lines have been regarded even by serious thinkers (and pseudo-thinkers) as the primary lines given by Nature ; these thinkers even dared to apply their curvilinear views to explaining world phenomena that could be made clear only after Galilei's abstraction had been accepted.

Painting by Rita Greer.

I asked whether the theory of gravitation was already implicitly contained in Galilei's Laws of Falling Bodies. Einstein's answer was in the negative : the gravitational theory falls entirely to the credit of Newton, and the greatness of this intellectual achievement remains unimpaired even if the efforts of certain forerunners are recognized. He mentioned Robert Hooke, whom, among others, Schopenhauer sets up against Newton, with absolute injustice and from petty feelings of antipathy, which takes its origin from Schopenhauer's unmathematical type of mind. The vast difference between Hooke's preliminary attempts at explaining gravitation, and Newton's monumental structure, was beyond his power of discernment.


Schopenhauer ( vol. ii. of the Parerga) uses two arguments to discredit Newton. Firstly, he refers to two original works, both of which he misinterprets ; secondly, he undertakes a psychological analysis of Newton. He uses psychological means, which would be about equally reasonable as applying the Integral Calculus to proving facts of Ethical Psychology, and he arrives at the conclusion that priority in discovering the law of gravitation is due to some one else ; Hooke is pictured as having been treated like Columbus : we now hear of "America," and likewise "Newton's Gravitational System " !

Schopenhauer has, however, quite forgotten that he himself, some pages earlier, trumpeted forth Newton's imperishable fame with the words : "To form an estimate of the great value of the gravitational system which was at least completed and firmly established by Newton, we must remind ourselves how entirely nonplussed about the origin of the motion of celestial bodies thinkers had previously been for thousands of years."

That bears the ring of truth. Newton's greatness can be grasped only if thousands of years are used as a measure. Whereas Schopenhauer argued from grounds drawn from psychology and the principle of universal knowledge, his antagonist Hegel, who was still more vague in these fields, sought to dispense with both Newton and Kepler by calling to his aid the so-called pure intuition of the curved line. In an exposition of truly comical prolixity, such as would have delighted the hearts of scholiasts, he proves that the ellipse must represent the fundamental type of planetary motion, this being quite independent of Newton's laws, Kepler's observations, and resulting mathematical relationships. And Hegel actually succeeds, with a nebulous verbosity almost stultifying in its unmeaningness, in paraphrasing Kepler's second law in his own fashion. It reads like an extract from some carnival publication issued by scientists in a bibulous mood to make fun of themselves.

Figure from Newton's Principia, I.ii: "The areas, which revolving bodies describe by radii drawn to an imovable centre of force ... are proportional to the times in which they are described."

But these extravagances, too, serve to add lustre to Newton, for his genius shines out most brilliantly when it is a question of expressing clearly, and without assumptions, a phenomenon of cosmic motion. Here there are no forerunners, not even with regard to his own law of gravitation. Newton showed with truly triumphant logic that Kepler's second law belongs to those things that are really self-evident.

This law, taken alone, offers considerable difficulties to anyone who learns of it for the first time. Every planet describes an ellipse ; that is accepted without demur. But the uninitiated will possibly or even probably deduce from this that the planet will pass over equal lengths of arc in equal times. By no means, says Kepler ; the arcs traversed in equal times are unequal. But if we connect every point of the elliptic path with a definite point within the curve (the focus of the ellipse) by means of straight lines, each of which is called a radius vector, we get that the areas swept out by the radius vector in equal times (and not the arcs) are equally great.

Why is this so ? This cannot be understood a priori. But one might argue that since the attraction of the sun is the governing force, this will probably have something to do with Newton's law of gravitation, in particular with the inverse square of the distance. And one might further infer that, if a different principle of gravitation existed, Kepler's law would assume a new form.

A fact amazing in its simplicity here comes to light. Newton states the proposition : "According to whatever law an accelerating force acts from a centre on a body moving freely, the radius vector will always sweep out equal areas in equal lengths of time."

Nothing is assumed except the law of inertia and a little elementary mathematics, namely, the theorem that triangles on the same base and of the same altitude are equal in area. The form in which this theorem occurs in Newton's simple drawing is certainly astonishing. One feels that there in a few strokes a cosmic problem is solved ; the impression is ineffaceable.

This theorem together with its proof is contained in Newton's chief work, Philosophiæ naturalis principia mathematica. The interfusion of philosophy and mathematics furnished him with the natural principles of knowledge.


Einstein made some illuminating remarks about Newton's famous phrase : "Hypotheses non fingo." I had said that Newton must have been aware that it is impossible to build up a science entirely free from hypotheses. Even geometry itself has arrived at that critical stage at which Gauss and Riemann discovered its hypothetical foundations.

Einstein replied : "Accentuate the words correctly and the true sense will reveal itself ! " It is the last word that is to be stressed and not the first. Newton did not want to feel himself free from hypotheses, but rather from the assumption that he invented them, except when this was absolutely necessary. Newton, then, wished to express that he did not go further back in his analysis of causes than was absolutely inevitable.

Perhaps, I allowed myself to interject, a more violent suspicion against the word "hypotheses" was prevalent with scholars in Newton's time than now. Newton's emphatic defence would then appear a shade more intelligible Or did he cherish the belief that his world-law was the only possible one in Nature ?

Einstein again referred to the universality of Newton's genius, saying that Newton was doubtless aware of the range within which his law was valid : this law applies to the realm of observation and experience, but is not given a priori, no more than Galilei's Law of Inertia. It is certainly conceivable that beyond the domain of human experience there may be an undiscoverable universe in which a different fundamental law holds, and one which, nevertheless, does not contradict the principle of sufficient reason.

Bullet in flight. Photo by Ernst Mach, 1888.

The antithesis : Simplicity --- Complexity, led the conversation into a short bypath ; it arose out of an example which I quoted and that I shall repeat here even if it may seem irrelevant.

One might well expect that just as for attraction there must be a general law for resistance or repulsion. And if attraction occurs according to the inverse square of the distance, then it would be an extremely interesting parallel if a similar law were to hold for repulsion except that the proportionality were direct instead of inverse. There have actually been physicists who have proclaimed a direct square law of repulsion ; I have heard it in lectures myself. The action of a resisting medium, as, for example, the resistance of the air to the flight of a cannon-ball, is stated to be proportional to the square of the velocity of the projectile.

This theorem is wrong. If it were correct, and verified by experiment, we should have to regard it as being presumably the only possible and directly evident form of the law of repulsion or resistance. There would, at least, be no logical reason for contradicting it.

But here we have "an impure relationship," as Einstein calls it --- that is, we are unable to express an exact connexion between the velocity of a body in flight and the air resistance.

This fallacious assumption by no means proceeded from illogical reasoning, and it seemed to rest on a sound physical basis. For, so it was argued, if the velocity is doubled, there is twice as much air to be displaced, so that the resistance will be four times as great. But this was contradicted outright by experimental evidence. One cannot even call it an approximate law, except for very low speeds. For greater speeds we find, instead of a quadratic relation, a cubical one, or one of a more complex nature.

Photographs have demonstrated that the resistance experienced by a projectile in flight is due to the excitation of a powerful central wave, to the friction between the air and the surface of the projectile, and to eddies produced behind the projectile --- that is, to various conjoined factors, each of which follows a different law, and such that the combined effect cannot be expressed by a simple formula at all. This phenomenon is thus very complicated and offers almost insuperable difficulties to analysis. A beautiful remark was once made, which characterizes such events in Nature.

During a conversation with Laplace, Fresnel said that Nature does not worry about analytical difficulties. There is nothing simpler than Newton's Law in spite of the complicated nature of planetary motions. "Nature here despises our analytical difficulties," said Fresnel ; "she applies simple means, and then by combining them produces an almost inextricable net of confusion. Simplicity lies concealed in this chaos, and it is only for us to discover it ! " But this simplicity when it is discovered is not always found to be expressible in simple formulae, nor must it be forgotten that even the ultimate discoverable simplicity points to certain hypothetical assumptions.

"Hypotheses non fingo ! " This phrase of Newton's remains true, if we maintain Einstein's interpretation : "He did not wish to go further back in his analysis of causes than was absolutely inevitable." It interested me to pursue this line of thought suggested by Einstein still further, and I discovered that these words of Newton had actually been falsely accentuated and hence misinterpreted by many authorities on science. Even Mill and the great scholar, William Whewell, succumbed to this misunderstanding. Credit must be given to a more modem scholar, Professor Vaihinger of Halle, for being sufficiently keen of hearing to detect the true accentuation ; and now that Einstein has corroborated fully this explanation, doubts as to the true sense of the words are no longer to be feared. [See Die Philosophie des Als Ob by Hans Vaihinger (1922), page 57.]

The trend of our talk brought us to a discussion of the conception, "law of nature." Einstein recalled Mach's remarks, and indicated that the point was to determine how much we read out of Nature ; and these observations made at least one thing clear, namely, that every law signifies some limitation ; in the case of human laws, expressed in the civil and penal code, the limitation affects the will, and possible actions, whereas natural laws signify the limitations which we, taught by experience, prescribe to our expectations.

Nevertheless, the conception remains elastic, for the question will always intrude itself : What does prescription mean ? Who prescribes ? Kant has assigned to Man the foremost position inasmuch as it is he who is regarded by Kant as prescribing laws to Nature. Bacon of Verulam [ Novum Organum: Aphorisms I.3] emphasizes the ambiguous point of view by asserting : "Natura non vincitur nisi parendo," Man conquers Nature only by obeying her, that is, by conforming to her immanent norms. Thus the laws exist without us, and we have only to discover them. When they have been found, Man can react by applying them to subdue Nature. Man becomes the dictator and dictates to Nature the laws according to which she for her part has to subjugate mankind. Whether we adopt the one view or the other, there is a vicious circle, from which there is no escape. A law is a creation of intellect, and Mephisto's words remain true : "In the end we depend on the creatures of our own making ! "

In Newton's soul, obedience and the wish to obey must have been pre-eminent traits. Is he not reputed to have been pious and strong of faith ?

Einstein confirmed this, and, raising his voice, he generalized from it, saying : "In every true searcher of Nature there is a kind of religious reverence ; for he finds it impossible to imagine that he is the first to have thought out the exceedingly delicate threads that connect his perceptions. The aspect of knowledge which has not yet been laid bare gives the investigator a feeling akin to that experienced by a child who seeks to grasp the masterly way in which elders manipulate things."

This explanation implied a personal confession. For he had spoken of the childlike longing felt by all, and had interpreted the subtle intricacies of the scientist's ideas in particular as springing from a religious source. Not all have confessed this ; we know, indeed, that the convictions of many a one were not so. Let us cling to the fact that the greatest in the realm of science --- Newton, Descartes, Gauss, and Helmholtz --- were pious, although their faith varied in degree. And let us not forget that the most bitter opponent of this attitude of mind, the originator of "Ecrasez l'infame," finally had a temple built bearing the inscription : "Deo erexit Voltaire."

In Newton positivism found its most faithful disciple, and his research was directly affected by his religious attitude. He, himself, was the author of that beautiful thought : "A limited measure of knowledge takes us away from God ; an increased measure of knowledge takes us back to Him." It was he who considered that the world-machine that he had disclosed was not sufficiently stabilized by his mathematical law, and so he enlisted the intermittent help of an assistant for the Creator, Concursus Dei, to attend to the functioning of the machine. Finally, he slipped from the path of naive faith onto theological bypaths and wrote devout essays on apocalyptic matters.

On the other hand, Descartes' piety, which was genuine at root, exhibited suspicious offshoots, and one cannot shake off the feeling that he was smiling up his sleeve when he was making some of his solemn declarations. He was a master of compromise, and gave due expression to its spirit, which F. A. Lange bluntly stated was merely a veil for "Cowardice towards the Church." Voltaire, an apostle of Newton's system of natural philosophy, went so far in his condemnation of Descartes' confession of faith that he affirmed: "The Cartesian doctrine has been mainly instrumental in persuading many not to recognize a God."

As Einstein had called special attention to the childlike nature of the scientist's root-impulse, I quoted a remark of Newton that seemed to me at the moment to be a confirmation of Einstein's attitude : "I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me." Are we not to regard this analogy of Newton's as being intended to convey a religious meaning ?

"There is no objection to this," said Einstein, "although it seems to me more probable that, in saying this, Newton set down the view only of the pure investigator. The essential purpose of his remarks was to express how small is the range of the attainable compared with the infinite expanse offered for research."

Chart by Cutler.

Through some unexpected phrase that was dropped, the conversation took a new turn at this point, which I should not like to withhold, inasmuch as it gave rise to a noteworthy observation of Einstein about the nature of genius. We were talking about the "possibility of genius for science being inherited" and about the comparative rareness with which it occurs. There seems to have been only one case of a real dynasty of great minds, that of the ten Bernoullis who were descended of a line of mathematicians, and all of them achieved important results, some of them making extraordinary discoveries. Why is this exception unique ? In other examples we do not get beyond three or four names in the same family, even if we take Science and Art conjointly. There were two Plinys, two Galileis, two Herschels, two Humboldts, two Lippis, two Dumas, several Bachs, Pisanos, Robbias, and Holbeins --- the net result is very poor, even if we count similar names, disregarding the fact of relationship ; there is no recognizable dynasty except in the case of the ten Bernoullis. (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.) "And so," I continued, "the conclusion seems justified that Nature has nothing to do with a genealogy of talents, and that, if we happen to notice manifestations of talent in one and the same family, this is a mere play of chance."

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 --- "

Humboldt und Bonpland in der Urwaldhütte by Edouard Ender, ca. 1850. [Berlin-Brandenburgische Akademie der Wissenschaften]

"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.

[This discussion of an anecdote by Heine that would have been familiar to most German readers is perhaps meant by Moszkowski, Einstein's personal Eckermann, as some kind of self-deprecating joke. In Chapter 26 of his Italian Travel Sketches, Heine ridicules Eckermann as Goethe's "parrot", attributing to him the story about Goethe completing God's creation and adding, "Some truth lies in these words, and I am indeed of opinion that Goethe would occasionally have managed his part better than the good God himself ; for instance, he would have created Herr Eckermann much more completely --- that is to say, with feathers ..." The anecdote about God is in fact a very loose paraphrase -- or rather parody -- of some remarks on Goethe's genius in Eckermann's early philosophical work Beiträge zur Poesie [Stuttgart: Cotta, 1824].]

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 :

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 list 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 onto 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.

Schadow's bust of Copernicus in the Regensburg Walhalla. [Photo by "Matthead"]

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 role. 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 naquit --- 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.

Eugen Dühring

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 [Kritische Geschichte der allgemeinen Principien der Mechanik, Leipzig, 1877] 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 [an arsonist motivated by the desire to go down in history] 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 [Tempel-Attentäter] 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 blind philosopher and social scientist Eugen Dühring, little remembered today, was a towering, wrathful figure looming large in his era's intellectual life. Irascible and combative, a fervent nationalist, a convinced materialist, equally virulent in his antisemitism, his anti-Christianity, his anti-Darwinism, his anti-capitalism, and his anti-Marxism, the archenemy of Friedrich Engels was one of those regrettably numerous Nineteenth Century German thinkers who in retrospect are hard to see as anything but forerunners of Nazism ; certainly his remarks quoted above anticipate what the "Aryan Physicists" of the 1930s would say about Einstein ! However Dühring's political theory, a kind of Romantic socialism, was more anarchist than fascist. Physics was one of his (numerous) major interests. He was still alive in 1919, but died around the time Moszkowski's book was published.]

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 line 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 hie dii sunt!

I should like to give the gist of this beautiful address in an extract uninterrupted by commentaries.

The Regensburg Valhalla. [Photo by Michael J. Zirbes]

"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.

Alexander Stoddart's new (2008) statue of Maxwell on George Street in Edinburgh. [Photo by Kim Traynor]


  1. Phenomena of the Heavens
  2. Beyond our Power
  3. Valhalla
  4. Education
  5. The Discoverer
  6. Of Different Worlds
  7. Problems
  8. Highways and By-ways
  9. An Experimental Analogy
  10. Disconnected Suggestions
  11. Einstein's Life and Personality