VALHALLA
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.
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; Faraday, 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.
* * * * * * * *
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 lower
than the sixth order of magnitude in Einstein's list. Nevertheless, the
number of selection of constellations is no mean one, 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, ἄνδρα μοῐ ἔννεπη!
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 Galilei or Newton 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
rectilinear 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 Aristoteles. 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 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.
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.
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.
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 a mixed 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, not
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 modern 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.
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 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 naïve faith on to 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."
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.[2]
"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."
[Footnote 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.