THE DISCOVERER
Relation of Discovery and Philosophy in History.--The Absolute and the
Relative.--The Creative Act.--Value of Intuition.--Constructive
Activity.--Invention.--The Artist as Discoverer.--Theory and
Proof.--Classical Experiments.--Physics in Primitive Ages.--_Experimentum
Crucis_.--Spectral Analysis and Periodic System.--The Rôle of
Chance.--Disappointed Expectations.--The Michelson-Morley Experiment
and the New Conception of Time.
NEXT time--so one of our talks ended--next time, as you insist on it, we
shall talk of discovery in general. This, was a promise of special
import for me, for it meant that I was to draw near to a fountain-head
of instruction, and to have an opportunity of hearing the pronouncements
of one whose authority could scarcely be transcended.
We are precluded from questioning Galilei personally about the
foundations of Mechanics, or Columbus about the inner feelings of a
navigator who discovers new lands, or Sebastian Bach about the merits of
Counterpoint, but a great discoverer lives among our contemporaries who
is to give us a clue to the nature of discovery. Was it not natural that
I should feel the importance of his acceptance of my proposal?
Before meeting him again I was overwhelmed with ideas that arose in me
at the slightest echo of the word "discovery" in my mind. Nothing, it
seemed to me, could be higher: man's position in the sphere of creation
and the sum of his knowledge can be deduced from the sum of his
discoveries which find their climax in the conceptions civilization and
philosophy, just as they are partly conditioned by the philosophy of the
time. We might be tempted to ask: which of these two precedes, and which
follows? And perhaps the ambiguous nature of this question would furnish
us with the key to the answer. For, ultimately, these two elements
cannot at all be resolved into the relationship of cause and effect,
antecedent and consequent.
Neither is primary, and neither secondary: they are intimately
interwoven with one another, and are only different aspects of one and
the same process. At the root of this process is our axiomatic belief
that the world can be comprehended, and the indomitable will of all
thinking men, acting as an elementary instinct, to bring the perceptual
events in the universe into harmony with the inner processes of thought.
This impulse is eternal; it is only the form of these attempts to make
the world fully intelligible that alters and is subject to the change of
time. This form finds expression in the current philosophy which brings
each discovery to fruition, just as philosophy bears in itself
constituents of the ripe discovery.
It seemed to me that even at this stage of my reflections I was
somewhere near interpreting Einstein's intellectual achievement. For his
principle of relativity is tantamount to a regulative world-principle
that has left a mighty mark in the thought of our times. We have lived
to see the death of absolutism; the relativity of the constituents of
political power, and their mutability according to view-point and
current tendencies, become manifest to us with a clearness unapproached
by any experience of earlier historical epochs. The world was far enough
advanced in its views for a final achievement of thought which would
demolish the absolute also from the mathematico-physical aspect. This is
how Einstein's discovery appeared as inevitable.
Yet a shadow of doubt crossed my mind. Einstein's discoveries came to
light in the year 1905--that is, at a time when hardly a cloud was
visible to forewarn us of the storms which were to uproot absolutism in
the world. But what if a different kind of necessity had imposed itself
on world-history, and hence on the world-view? Nowadays we know from
authentic accounts, which no one doubts, that all that we have
experienced during the war and the revolution has hung upon the
activities of one frail human being of quite insignificant exterior, a
bureaucrat of the Wilhelm-Strasse, a choleric eccentric who succeeded in
frustrating the Anglo-German alliance which was unceasingly being
pressed upon us for six long years after the beginning of the century.
Amid the noisy progress of universal evolution the secret and
insignificant nibbling of a mole cannot be regarded as of momentous
importance for history, and yet if we eliminate it from the complete
picture of events we find as a result that all our experiences have been
inverted. Absolutism would not have been thrown overboard, but would
probably have kept the helm with greater mastery than ever as the
exponent of an Anglo-German hegemony of the world, and a political
outlook fundamentally different in tendency would now have been
prevailing on the earth.
But Einstein's Theory of Relativity would not have taken the slightest
heed of this. It would have arisen independently of the current forms of
political conceptions, simply because we had reached that point in our
intellectual development and because Einstein was living and spinning
his webs of thought. And the question whether his theory will also have
crushed absolutism for the non-physicist cannot be answered.
It may indeed be doubted whether its time had already come. In the case
of many important events in the history of thought their moment of birth
can be fixed to within about ten years, as for example the Theory of
Evolution, which had been conceived in several minds at the same time
and had of necessity to come to life in one of them, even if it had
failed in the case of the others. I venture to say that without
Einstein, the Theory of Relativity in its widest sense, that is,
including the new doctrine of gravitation, would perhaps have had to
wait another two hundred years before being born.
This contradiction is cleared up if we use sufficiently great time
intervals. History does not adapt itself to the time measures of
politics and of journalism, and philosophies are not to be calculated in
terms of days. The philosophy of Aristotle held sway right through the
Middle Ages, and that of Epicurus will gain its full force only in the
coming generation. But if we make our unit a hundred years the connexion
between philosophies and great discoveries remains true.
Whoever undertakes to explore the necessity of this connexion cannot
evade the fact that the lines of the result had been marked out in the
region of pure thought, as can be proved, before even the great
discovery or invention was able to present it in a fully intelligible
form. Even the achievement of Copernicus would follow this general rule
of development: it was the last consequence of the belief in the Sun
Myth which had never been forsaken by man in spite of the violent
efforts of the Church and of man himself to force the geocentric view.
Copernicus concentrated what had survived of the wisdom of the earliest
priests--which includes also the germ of our modern ideas of energy and
electricity--of the teachings of Anaxagoras and the Eleatics which had
remained latent in our consciousness: his discovery was the
transformation of a myth into science. Mankind, whose wandering fancy
first feels presentiments, then thinks and wishes to know, is a large
edition of the individual thinker. The latter sees further only because
he, so to speak, stands on the shoulders of a sum-total of beings with a
world-view.
Let us turn our attention to an example from the most recent history of
philosophy and discovery. The absolute continuity of events was one of
the generally accepted canons of thought, and is even nowadays taught by
serious philosophers as an incontrovertible element in our knowledge.
The old quotation _Natura non facit saltus_, popularized by Linné, is
one of the formulae of this apparently invincible truth. But deep down
in the consciousness of man there has always been an opposition to it,
and when the French philosopher Henri Bergson set out to break up this
line of continuity by metaphysical means in ascribing to human knowledge
an intermittent, cinematographic character, he was proclaiming in an
audible and eloquent form only what had lain latent in a new but as yet
incomplete philosophy. Bergson made no new "discovery," he felt his way
intuitively into a new field of knowledge and recognized that the time
was ripe for the real discovery. This was actually presented to us in
our day by the eminent physicist Max Planck, the winner of the Nobel
Prize for Physics in 1919, in the form of his "Quantum Theory." This is
not to be taken as meaning that a revolutionary philosophy and a triumph
of scientific research now become coincident, but only that a
discontinuous, intermittent sequence, an atomistic structure, was proved
by means of the weapons of exact science, to be true of energies which,
according to current belief, were expected to be radiated regularly and
connectedly. This was probably not a case of the accidental coincidence
of a new philosophical view with the results of reasoning from physical
grounds, but a demand of time, exacting that the claims of a new
principle of thought be recognized.
As above suggested, it is more difficult to find a link between
Einstein's discoveries and antecedent presentiments of relativity. For a
mere reference to the downfall of absolutism in the world of human
events will not suffice. In the case of Einstein, we see such a
tremendous rush of thought in one being that we almost feel compelled to
recognize an analogy with the Quantum Theory and believe in a
discontinuity in the course of intellectual history. Yet there are
certainly threads that connect Einstein's achievement with a prophetic
insight. In this case, however, we must spread out over centuries what
in the case of other discoveries extends, in comparison, only over
decades. That doubt of Faust, which troubles the spirit of every
thinker: "whether in yonder spheres there is also an Above and a Below,"
and which goes back as far as Pyrrhon and Protagoras, is itself
relativistic; it expresses doubt whether the co-ordinate system passing
through our own lifes as centres is valid. It is ultimately a matter of
point of view, and the mathematico-physical consequences of the endless
series of questions, and the relation, which arises from the couple,
Above-Below, probably leads to a new mode of comprehending the
constitution of the world, for which Einstein's creative work found the
adequate expression in abstract terms. And from this point onwards, in
accordance with the principle of reciprocal action, a new stream of
knowledge will pour itself into the hazy stretches of philosophy. A
fundamental and radical reform of our philosophy seems inevitable,
particularly with respect to our conceptions of Space and Time, perhaps,
too, even with respect to Infinity and Causality. Much dross will have
to be sifted out of our old categories of thought and out of our world
wisdom, which once served as material for fine structures. What will the
finer ones look like that are to take their places in obedience to the
command of physics? Who would care to take it upon himself to form an
estimate?
Much will be uprooted, and it is possible that even the defiant
"ignorabimus," the antipole of the search for truth from Pyrrhon to
Dubois, will again take up the cudgel. For in the face of despairing
uncertainty there is the one certainty: what cannot be comprehended is
being encircled more and more by the great discoverers! And even if the
absolute point of convergence can never be reached, there is within our
reach at least another point which is a haven of rest in the passing
stream of philosophies, namely, a moral centre around which eddies of
happiness circle. At the heart of this world-view there is the uplifting
belief in an advance of knowledge in spite of all, and a belief in the
vanishing of age-long problems and difficulties under the flood of
discoveries. And even if afterwards and concurrently ever new problems
and difficulties arise, these do not suppress our feeling of triumph.
Every achievement in this field gives us a sense of enfranchisement from
prejudices, not the least of which is narrowness of national outlook.
Not only do discoverers construct bridges of thought that stretch to
astronomical distances, but, what is more difficult, they build bridges
for our feelings, that surmount political obstacles. Every thinking
being who plays a part in the making of some great discovery and who,
with deepened vision, bows before a new achievement of mind, gradually
becomes a disciple of the religion of universal politics, the creed of
which is faith in the brotherhood of thought. The nucleus of a
philosophy that belongs to the future is the recognition that differing
national view must be compounded into a unity, and that every great
discovery means a step towards attaining this end.
Even if we accept Pascal's wonderful dictum that human knowledge is
represented by a sphere which is continually growing and increasing its
points of contact with the unknown, we must not interpret it as a sign
of despair. It is not the enlargement of the unknown, but only that of
knowledge that stirs our feelings with ethical forces. The positive
calls up in us a living force by inspiring in us the feeling that the
sphere of knowledge is destined to grow, and that there can be no higher
duty for all the energies of mind than to obey the call for combined
action towards this growth which will bring the world into harmony.
Full of such reflections I entered the home of the great discoverer,
whose activities unceasingly hovered before my vision as ideal examples
of creative effort. I discovered him, as almost always, seated before
loose sheets of paper which his hand had covered with mathematical
symbols, with hieroglyphics of that universal language in which,
according to Galilei, the great book of Nature is written.
What a very different picture many an outsider draws of the manner in
which a seeker in the heavens works! He is imagined like Tycho Brahe to
be surrounded by unusual pieces of apparatus, spying through the ocular
of a long range refractor into the universe, seeking to unravel its
ultimate secrets. The true picture does not correspond to this fancy in
the slightest. Nothing in the make-up of the room reminds one of
super-earthly sublimity, no abundance of instruments or books is to be
seen, and one soon becomes aware that here a thinker reigns whose only
requirement for his work, which encompasses the world, is his own mind,
plus a sheet of paper and a pencil. All that acts on the observatories
outside, that gives rise to great scientific expeditions, that, indeed,
ultimately regulates the relationship of mankind to the constitution of
the universe, the revolution in the knowledge of things connecting
heaven and earth, all this is here concentrated in the simple figure of
a still youthful scholar, who spins out endless threads from the fabric
of his mind: the words of a poet are recalled to our memory, which,
addressed to all of us, have been fulfilled to the last degree by one
living among us:--
"Whereso thou roamest in space, thy Zenith and Nadir unite thee--
This to the heavenly height, that to the pole of the world,--
Whatsoever thou do, let thy will mount up into Heaven--
But let the pole of the world still o'er thine actions preside."
(Schiller: _Translation by Merivale_.)
And this one helped to fulfil this aim and I must break off his thread
of thought to put the question: What is Discovery, and what does it
signify?
It is a purely abstract question that may appear to many to be devoid of
content. Such will repeat to themselves, as best they can, the list of
discoveries and think a man makes a discovery when he finds out
something important, such as the Laws of Falling Bodies, the formation
of Rainbows, or the Origin of Species: a general denomination may be
found for it perhaps only by ascribing to Discovery something requiring
a powerful mind, a creative genius.
At first it staggered me to hear Einstein say: "The use of the word
'Discovery' in itself is to be deprecated. For discovery is equivalent
to becoming aware of a thing which is already formed; this links up with
proof, which no longer bears the character of 'discovery' but, in the
last instance, of the means that leads to discovery." He then stated at
first in blunt terms, which he afterwards elaborated by giving detailed
illustrations: "Discovery is really not a creative act!"
Arguments for and against this view flashed through my mind, and I
thought involuntarily of a great master of music who, when he was asked:
"What is Genius?" answered: "A genius is one to whom ideas occur." This
parallel might be carried still further, for I have repeatedly heard
Einstein call "ideas" what we would regard as wonderful thoughts. Does
not the philosopher Fritz Mauthner speak of the discovery of gravitation
as being an "aperçu" of Newton; yes, in the sense of _aperçus_ as
applied in ancient Greek philosophy, and which included almost
everything that was left by Pythagoras, Heraclitus, etc., as a token of
their genius. On the other hand, we are all possessed of the desire to
differentiate clearly between an idea and a creative act of thought, as
occurs in Grillparzer's aphorism: "An idea is not a thought; a thought
knows its bounds, whereas the idea leaps over them and succeeds in
accomplishing nothing!"
Here, then, we must revise our view. We know, for example, how much
Einstein's "ideas," felt by him to be such and named so accordingly,
accomplished. Let us hear how he characterizes in a few words his own
"idea" which shook the world:
"The underlying thought of relativity," he said, in connexion with this
question, "is that there is physically no unique (specially favoured)
state of motion. Or, more exactly, among all states of motion there is
none that is favoured in the sense that, in contradistinction to the
others, it may be said to be a state of rest. Rest and Motion are not
only by formal definition but also by their intrinsic physical meaning
_relative conceptions_."
"Well, then," I interposed, "surely this was a creative act! This first
flashed across _your_ mind, Professor; it represents your discovery, so
that we may well let the word retain the meaning usually associated with
it!"
"By no means," answered Einstein, "for it is not true that this
fundamental principle occurred to me as the primary thought. If this had
been so perhaps it would be justifiable to call it a "discovery." But
the suddenness with which you assume it to have occurred to me must be
denied. Actually, I was lead to it by _steps_ arising from the
_individual_ laws derived from experience."
Einstein supplemented this by emphasizing the conception "invention,"
and ascribed a considerable importance to it: "Invention occurs here as
a constructive act. This does not, therefore, constitute what is
essentially original in the matter, but the creation of a method of
thought to arrive at a logically coherent system ... the really valuable
factor is _intuition_!"
I had thought, long and intently, about these theses to discover as
nearly as possible what distinguished their content from the usual view.
The fundamental differences suggest an abundance of ideas whose
importance grows in value as we apply them to various cases as
illustrations. And I feel convinced that we shall yet have to occupy
ourselves with these words of Einstein, which present themselves as a
confession, as with the famous "hypotheses non fingo" that Newton set up
as the idea underlying his work.
The latter as well as the former implies something negative: it denies
something. In Einstein's words there is apparently a repudiation of the
really creative act in discovery; he lays stress on the gradual,
methodical constructive factors, not omitting to emphasize intuition.
There is no other course open to us but to seek indirectly a synthesis
of these conceptions, and to eliminate what is apparently contradictory
in them.
I consider this possible if we decide to subdivide the discovery into a
series of individual acts in which succession takes the place of
instantaneous suddenness The creative factor may then remain intact;
indeed, it attains a still higher degree of importance if we imagine to
ourselves that a series of creative ideas must be finked together to
make possible a single important discovery.
The original idea never springs fully equipped and armed like Minerva
out of the head of its creator. And it is wise to bear in mind that even
Jupiter had to suffer in his head a period of pregnancy accompanied with
great pain. It is only in the after-picture that Pallas Athene appears
with the attribute of suddenness. It is the nature of our myth-building
imagination to leap over the actual act of birth so as to give a more
brilliant form to the finished creation.
We feel great satisfaction when we learn that Gauss, the Prince of
Mathematicians, declared in one of his valuable flashes of insight: "I
have the result, only I do not yet know how to get to it." For in this
utterance we see above all that he emphasizes a lightning-like
intuition. He has possession of a thing, which is, however, not yet his
own, and which can only become his own when he has found the way to it.
Is this contradictory? From the point of view of elementary logic,
certainly; but methodologically, by no means. Here it is a question of:
_Erwirb es um es zu besitzen_! This makes necessary a series of further
intuitions along the road of invention, and of construction.
This is, then, where that phase commences, which Einstein denotes by the
word "gradual," or "by steps." The first intuition must be present; its
presence as a rule usually guarantees that further intuition will follow
in logical sequence.
This does not always happen. In passing, we discussed several special
cases from which particular inferences may be drawn. The powerful
mathematician Pierre Fermat has presented the world with a theorem of
extremely simple form which he discovered, a proof of which is being
sought even nowadays, two and a half centuries after he stated it. In
easy language, it is this: the sum of two squares may again be a square,
for example, 5^2 + 12^2 = 13^2, since 25 + 144 = 169; but the sum of two
cubes can _never_ be a cube, and, more generally, as soon as the exponent,
the power index _n_, is greater than 2, the equation _x_^_n_ + _y_^_n_ =
_z_^_n_ can never be satisfied by whole number values for _x_, _y_, and
_z_; it is impossible to find three whole numbers for _x_, _y_, and _z_,
which, when substituted in the equation, give a correct result.
This is certainly true; it is an intuitive discovery. But Fermat's
assertion that he possessed a "wonderful proof," is for very good
reasons open to contradiction. No one doubts the absolute truth of the
theorem. But the later inspiration, the next step after the intuition,
has occurred neither to Fermat nor to anyone else. It cannot be
established whether his remark about the proof was due to a subjective
error, or was baseless. In any case it seems probable that Fermat had
arrived at the result _per intuitionem_ without knowing the way to it.
His creative act stopped short; it was only a first flare of a
conflagration, and did not fulfil the condition that Einstein associates
with the conception of a logically complete method.
We may, indeed, pursue this case of Fermat still further. He had
enunciated another theorem, again _per intuitionem_, namely, that it was
possible to construct prime numbers of any magnitude by a formula he
gave. Euler later showed by a definite example that the theorem was
false. It was stated in a letter to Pascal written in 1654 in the words:
the result of squaring 2 continuously and then adding 1 must in each
case be a prime number, that is, 2^(2^_k_) + 1 must always be a prime no
matter what value _k_ may have. Fermat added: "This is a property for
the truth of which I answer." Euler chanced to try _k_ = 5, and found
that 2^32 + 1 = 4,294,967,297, which may be represented as the product
of 641 and 6,700,417, and hence is not a prime.
It is conceivable that no Euler might have lived, and that no one else
might have discovered this contradiction. What would then have been the
position of this "discovery" of Fermat?
We should certainly not have disputed its creative character, for we
should have said that it corresponds to a fact which is fully formed,
but cannot be proved. But now that we know that the fact does not exist
at all, the tiling assumes a different colour. It was not a discovery at
all, but an erroneous conjecture. But one would never be able to arrive
at an erroneous conclusion of this sort without being a mathematical
genius, and having the inspiration of the moment. And from this again it
follows that to make a discovery in the full sense of the word the
intuition of the moment does not suffice, but must be supported by a
series of intuitions, and this is the condition that it become a
permanent component of universal truth.
The fact that Einstein refers to the action of "inventing" in his
explanation, gives support, it seems to me, to the view that, strictly
speaking, discovering and inventing are never to be regarded as being
separable. In discovering, what has to be constructed persists, and in
inventing, it is a question of finding the path along which there is the
promise of success, be it by a method, a proof, or by some general work.
We spoke of works of art, and I was delighted to see that Einstein was
by no means disinclined to claim certain works of pure thought, which
are usually placed in the category of scientific discovery, as works of
art. In the latter, however, the pure process of invention plays the
prominent part, for in them something is represented that did not exist
at all before; this has repeatedly led to the artist's achievement being
given the higher rank, as being properly and exclusively creative. The
argument runs somewhat along these lines: the infinitesimal calculus
would certainly have been discovered even if there had been no Newton
and no Leibniz, but without Beethoven we should never have had a C Minor
Symphony, and never in the future would it have appeared, for it was a
subjective, absolutely personal, and unique product of its creator.
I believe this may be admitted, and that we may nevertheless retain the
view that in the work of art, too, the act of discovering is to be
found. Let us consider for a moment the elementary substance of the
first movement of this fifth symphony, a colossal movement of 500 bars,
which expresses itself quite definitely in four notes, of which one is
repeated three times. "Thus Destiny thunders at the gates" is
Beethoven's motto for this section; it is expressed tonally in a
succession of notes which through all eternity existed among the
possible permutative arrangements of these sounds.
Beethoven, so it is expressed, invented it. But it is just as correct to
say--in Einstein's words--"he became aware of what was already
formed"--that is, he "discovered" the fundamental theme, and afterwards
"proved it" in terms of musical logic unheard-of beauty in a methodical
elaboration. We may, indeed, go further still. This _motif_ of four
tones was not only extant as an abstractum, as a possible mathematical
arrangement, but also as something natural. Czerny, a pupil of
Beethoven, to whom the master confided many a remark about the origin of
his compositions, reports that a bird, the yellow-hammer, had sung this
theme to Beethoven in the woods. But neither the bird nor any other
living creature had invented it; rather what could not be created,
because it had always been in existence, became objectified in the
medium of sound. Beethoven found it; it was _res nullius_ when he found
it and when he discovered simultaneously with the succession of tones
that they were appropriate for a powerful musical representation of
sombre Destiny. Every theme, be it of Beethoven, Bach, Wagner, or anyone
else, may be represented graphically by a curve (in the case of Bach's
fugal themes this has, in fact, been done for special purposes), and
just as it is certain that every elliptic-arc existed before all
geometry, so it may be affirmed with equal certainty that everything
musical was in existence before the advent of composition, and was
merely waiting for a discoverer whom we designate the inventor, the
creative organ.
But may not some of this glory be reflected on to scientific discovery?
When we are in an ecstasy of admiration, we talk of a creative act as of
something divine; may we not also grant to the scientist this tribute
which, owing to a slight confusion of conceptions, we shower on the
artists? And I believe that Einstein's definition does not set up an
insuperable barrier in this respect to our admiration, which exerts
every effort to pass beyond, refuses to come to a standstill before the
rigid fact that the discoverer reveals only what is preformed; our
emotions prove to be stronger than our minds with their objective
valuation. In the last instance, we opine, the scientific discoverer,
too, creates something new, namely, a piece of knowledge that was
previously not in existence. And we obey the impulse of hero-worship,
when we call a definite first discoverer a creator.
This silences opposition certainly only for a time, without vanquishing
it. For this knowledge, too, lay ready before the first discoverer
appeared: he did not create it, but merely drew back the veil that
enveloped it. So that, ultimately, we get back to "intuition" in its
literal sense, a becoming aware of things, an exact consideration of
things, states, and relationships; and this intensive consideration,
full of wonderment, has always been a privilege of a very few chosen
men.
It might be asked: Was there any knowledge of Pythagoras' Theorems
before Pythagoras gave us his proof? We should have to answer: It was in
existence at least in the still dark field of vision of Pythagoras,
which became illumined one day when he took such a view of the
number-ratios 3--4--5 that an exact intuition could actually come about.
It is erroneous to assume that a creative act suddenly called up before
his soul as if by magic the figure with the three squares drawn
externally on the sides of a triangle. Rather, he "took his stride" (as
we know from Vitruvius) by considering a triangle whose sides were of a
definite length; and the well-known proof, which is linked indissolubly
in our minds with his work, is not his at all, but Euclid's. Yet our
annals grow musty, centuries pass by, and the credit of being the
creator rests with the man who first succeeded in getting a clear
picture of such a triangle.
It seems natural to test discoveries by experiments. The first result of
doing this is a very remarkable increase in the rate at which the
intuitive process has developed. In ancient times, intuition, it seems,
scarcely felt the need of proving things by experiment; all that was
discovered by Archimedes in mechanics, by the Pythagoreans in acoustics,
by Euclid in optics, may be reduced practically to the formula
"heureka," and it is probably scarcely an exaggeration to say that more
and more fruitful experiments are performed in one week nowadays than in
the whole of the classical age taken together.[3]
[Footnote 3: Recently certain precisians in definition have been seeking
to establish a fundamental difference between physicists of reality,
experimental physicists, and "blackboard-physicists." The last term is
given jeeringly to theoretical physicists because they, in the opinion
of these critics, wish to found Nature entirely on formulæ argued out
on the blackboard. The history of science does recognize this
distinction, although it is, of course, quite possible for a physicist
to arrive at important discoveries without making any experiments.
One might be more justified in asserting that the great theorist need
not necessarily be a great experimenter and vice versa. But I can quote
no example of a physicist who confined himself obstinately to blackboard
discussion, and on principle disowned all experimental work.
I must add that Einstein himself is fond of experimenting, and has had
much success in experimental work. The amount of advice and
encouragement that he has given, and still gives, to many workers in
this field is very considerable. But he does not practise experimental
work regularly, and remarked that he is obliged to appeal to outside
help for certain practical tests. There are specific experimental
geniuses, whose activity assumes the happiest and most fruitful form
when it supplements that of the theorist and fertilizes it.]
Experiments have become, if not the sole, yet the most definite, test of
intuition. I need only recall the observations of the solar eclipse of
1919, which were of an experimental character inasmuch as they used
apparatus to question Nature. To the world generally, they gave the
irrefutable confirmation of Einstein's Theory of Gravitation, but not to
Einstein himself, whose intuition felt itself so certain that the
confirmation was a mere matter of course.
But this is not the average case; in many cases the intuition of the
discoverer appeals to experiment as a judge of great authority, who is
to confirm, reject, or correct.
Let us take some examples of cases in which the intensity and the value
of intuition were measured by the experimental results. Benjamin
Franklin's Kite Experiment may be taken as a classical instance. Here is
a man in whose head the idea takes root that lightning and electricity
are one and the same thing. Innumerable persons before and after his
time might have hit on the same idea, which is now the common knowledge
of children. Yet, a single man had to appear who became aware of this
pre-formed fact and who simultaneously thought out a method of putting
it to proof. In 1752 he constructed a kite, sent it up into the clouds
during a storm, and caught up sparks on the ground by a metallic
contrivance, and, as d'Alembert so aptly described it to the French
Academy:
"Eripuit coelo fulmen ..."
He wrested the lightning from the heavens. Jupiter Tonans illuminated a
great discovery, a mighty intuition which had entered like a lightning
stroke into the brain of a discoverer.
This case would be classical, were it not that nine-tenths of it is
based on legend. Franklin was by no means the first who had this
intuition, and his experimental test was so full of faults that it was
within an ace of failing. Franklin used a dry thread of hemp, which he
thought to be a conductor, but which became a conductor only after it
had been made wet by rain. Till that moment the exhibition of sparks on
the ground had been poor enough, and little was wanting for Franklin to
give up his attempt and confess that he had been inspired, not with an
intuition, but with a hallucination.
But to whom then is the glory of this discovery due? This is a difficult
point to decide. As early as 1746, that is, six years before Franklin's
kite made its ascent in Philadelphia, Professor Winkler of Leipzig had
asserted in a dissertation that the two phenomena were identical, and
had proved this theoretically; and three years earlier still Abbé
Nollet had declared the storm clouds to be the conductors of an
electrical induction machine. Almost simultaneously with Franklin,
Dalibard, Delor, Buffon, Le Monnier, Canton, Bevis, and Wilson made
experiments on an elaborate scale, which far exceeded that of Franklin
in their results. To this must be added that the experiment was
conducted with evident success only in 1753, when de Romas of Nerac in
South France wove a real conductor of thin annealed wire into the
kite-string, and succeeded in bringing down a regular thunderstorm with
flashes of lightning ten feet long, accompanied by a deafening uproar.
It was only then that the track of the inspiration was traced back
through time to the Roman Kings, Numa Pompilius and Tullus Hostilius, as
the first experimenters with lightning. And then the physicist
Lichtenberg sought to furnish a proof that the old Hebrew ark of the
Covenant, together with the tabernacle, were nothing other than great
pieces of electrical apparatus highly charged with electricity derived
from the air; thus the first intuition, and the priority of discovery,
would have to be ascribed to Moses or Aaron! And connected with this was
the fact, supported by substantial proof, that the Temple of Solomon was
protected by lightning-conductors.
I must not omit to mention that Einstein regards this whole chain of
proofs stretching back to early times as by no means established,
although besides Lichtenberg, other important scholars, such as Bendavid
in Berlin and Michaelis in Göttingen, have vouched for their truth. And
as it is a matter of electrical relationships, Einstein's doubts cannot
be passed over. As far as I recollect, they were not directed against
the rough facts in themselves, but against the sense that is construed
into them--that is to say, in the case of both the ancient Roman and the
Biblical data, the conception of discovery must be excluded, and must be
awarded rather to those intellectual efforts which have led to the
creation of a method of thought. None the less, we may uphold our
statement that in this case, presumed to be classical, neither Franklin
nor anyone else is to be claimed as the discoverer or as the central
figure in a creative act.
The experimental case of spectral analysis is incomparably simpler and
less open to dispute. It is without doubt a discovery of fundamental
importance bearing all the characteristics of originality, for no
predecessors are discernible. I have always felt a little dissatisfied
with the fact that it required two men to think it out, that a duo of
minds was necessary for one act of thought which appears quite uniform,
elementary and inseparable from the intuition of a single mind. But it
seems possible that tradition has not handed the facts down to us
faithfully, and that the two men, with a unanimity arising from their
partnership in work, combined their results, which were not, at the
beginning, of a dual character. This possibility became clear to me from
a remark of Einstein which made it plain to me that the conjunction
Kirchhoff and Bunsen is to be taken as denoting Kirchhoff and then,
after a pause, Bunsen in the next breath! But if we discard this
question of unity or duality, we are left with the fact that the idea of
a spectral analysis occurred to some one (as a result of preceding
optical experiments with Fraunhofer lines), and was fully confirmed by
later experiments. Only fully confirmed? No, the classic rank of this
case manifested itself in a much more triumphant manner, for it is
impossible that the intuition of Kirchhoff and Bunsen could have grasped
the whole significance and range of their discovery even after they had
made it their own.
Every discovery encloses a germ of hope. However great this may have
been in the case of Kirchhoff, it could not by any stretch of
imagination approach the degree of its fulfilment. The fundamental
theoretical idea that "a vapour absorbs from the ray-complex of white
light only those wave-lengths which it can emit" gave rise to a process,
the ingenuity, delicacy, and certainty of which is almost inconceivable.
When rays of light emitted by incandescent vapour were separated by a
prism, there were discovered fine coloured lines that betrayed some
unknown mystery. The spectroscopic experiments proved, in a succession
of results, that the author of the above idea had made not only one
discovery, but a whole host of them. For example, it was observed that,
in burning minute residues obtained by evaporating certain mineral
waters, a red line and a blue line that had never been seen before
appeared in the spectrum. One knew immediately that an element, hitherto
undiscovered, was proclaiming its presence. In this way in quick
succession the element Cæsium was discovered, then Rubidium, Thallium,
Indium, Argon, Helium, Neon, Krypton, Xenon--certainly things that were
already pre-formed in Nature, just as the idea of a bridge from Optics
to Chemistry lay all ready in the heart of Nature; but no blame can be
given to the astonished contemporaries who regarded this fundamental
discovery of spectroscopic analysis as a creative achievement of the
intellect.
This ray of hope gave a glimpse of the degree of accuracy attainable. In
this connexion the experiment confirmed infinitely more than the boldest
imagination could ever have dreamed. A yellow line was detected in the
spectrum of sodium. And it was found experimentally that the
three-millionth part of a thousandth of a gramme of a sodium salt is
sufficient to produce this sodium line in the spectrum of a Bunsen
burner. There commenced a dizzying passage in the Calculus of
Probabilities for, since it was found that in the sun's atmosphere
hydrogen, carbon, iron, aluminium, calcium, sodium, nickel, chromium,
zinc, and copper were present, the question arose as to how great was
the possibility of an error in this observation. Kirchhoff calculated it
as a chance of a trillion to one that these substances are actually
present in the sun!
Never before had an experiment verified to such an extreme degree a
discoverer's idea. It seems appropriate at this stage to deal with a
doctrine which seeks to shed light into the deepest recesses of the
connexion between experiment and discovery. It teaches that an
_experimentum crucis_, an experiment that verifies absolutely, is
_impossible_ in physics. That is to say, every idea of a discoverer
involves a hypothesis, and, however the experiment that follows may turn
out, there still remains the possibility that this hypothesis was false,
and may later have to make way for another essentially contradictory
hypothesis which will be valid again only for a limited time.
The chief exponent of this theory is the eminent scholar, Pierre Duhem,
Membre de l'Institut. He draws a parallel between experiment and
mathematical proof, particularly with the indirect, apagogic form which
has been so successfully applied in Euclidean geometry. In this method
it is assumed that a certain statement is erroneous; it is then shown
that it leads to an obvious contradiction; consequently the statement
was correct provided that a certain doubt be excluded. Thus in the
domain of mathematics we have a real _experimentum crucis_.
In accordance with this, Duhem tests the validity of two physical
theories, both of which were put forward and claimed as discoveries.
Newton had discovered the nature of light to consist in "emission"; to
him, as well as to Laplace and Biot, light consists of projectiles that
are emitted with very great velocity. The discovery of Huyghens,
supported by Young and Fresnel, substitutes wave-motion in place of
corpuscular emission. Hence, according to Duhem, we have, or we had,
here two hypotheses which appear to be the only ones possible.
Experiment was to pronounce a judgment, and at first it decided
irrefutably in favour of the wave-theory. Therefore, the discovery of
Huyghens is alone true, and that of Newton is shown to be an error;
there is no third outlet, and so we have quite certainly an
_experimentum_ crucis before us.
The term itself originates in Bacon's _Novum Organum_. Contrary to
Duhem's assumption, it does not refer to a signpost at cross-roads
giving various routes, nor is it connected with _croix ou pile_, heads
or tails. _Experimentum crucis_ denotes rather a divine judgment at the
cross, that is a test that is absolutely decisive and beyond further
appeal. But no! adds Duhem, there is no room for a third judgment in the
case of two contradictory statements in geometry, but there is between
two contradictory statements in physics. And, in fact, this third
possibility has manifested itself in the discovery of Maxwell, who has
shown that the nature of light is founded on a process of periodic
electromagnetic disturbances. Hence, so concludes Duhem, experiment can
never decide whether a certain theory is alone valid. The physicist is
never certain that he has exhausted all conceivable possibilities, of
thought. The truth of a physical statement, the validity of a discovery,
cannot be confirmed by any _experimentum crucis_.
According to this argument, therefore, it is also possible that the
scientific grounds of spectral analysis do not conform to truth. A
contradictory hypothesis may, indeed, be set up, with the result that
the same experiments that had led Kirchhoff's discovery from one triumph
to another would have to be interpreted in a totally different sense.
I must frankly confess that I cannot subscribe to such an extreme
eventuality, since, in my opinion, Duhem's analogy with mathematics
excludes this possibility. For if a certain probability is expressed by
a trillion to one, then I venture to state that even in the case of
mathematical truths certainty reaches no higher degree of probability.
From the history of mathematics we know of theorems which were
enunciated and provided with complete proofs, and yet did not succeed in
establishing themselves; hence we see that, however evident a
mathematical theorem may be, it is still only a matter of very great
probability.
If, following our usual habits of thought, we take this for absolute
certainty, then we may also consider the sum-total of experiments in the
realm of spectral analysis to be a great _experimentum crucis_ for the
correctness of the theory itself.
Far removed from it, and yet connected with it, there is the "Periodic
System of the Elements," the discovery of Mendelejew and Lothar Meyer.
It, too, offered prophetic glances into the future, foretold the
unknown, hinted at things that were present only in imagination in a
scheme of thought that assigned definite places of existence to
undiscovered things. The Periodic System is represented by a table
containing vertical and horizontal rows, in the squares of which the
elements are entered according to certain rules depending on their
atomic weights. The discovery consisted theoretically in stating that
the physical and chemical properties of each element is the arithmetic
mean between the properties of its horizontal and vertical neighbours.
This gave rise to predictions concerning the unoccupied squares. These
gaps, these blank spaces in the table, seem to say prophetically: There
are elements missing here that must be discoverable. The neighbours will
betray them, and the empty space itself shows by what means they are to
be found. With the shrewdness of a detective, Mendelejew was able to
say: There must be elements of the atomic weights 44, 70, and 72; we do
not know them yet, but we are in a position to determine the properties
of these foundlings of the future, and, what is more, the properties of
their compounds with other elements. Later researches, which led to the
discovery of the elements. Scandium, Gallium, and Germanium, have
actually confirmed all these predicted properties.
The metal Gallium was discovered in 1875 by spectroscopic means. Its
properties are the mean of those of Aluminium and Indium, and this
places it in a position which had already been assigned to it in the
periodic table before its discovery; for, owing to a gap in the system,
Mendelejew had asserted its existence five years previously, although he
then knew nothing of its characteristic spectral signs, namely, two
beautiful violet lines. Radium, too, which was discovered in 1900 and
was found to have the atomic weight 226, completely satisfied this test
and fitted exactly into the place which this number reserved for it in
the table. Thus prediction and confirmatory discovery were fully
congruent in this case; the experiment followed on the visionary insight
just as a Euclidean proof follows on a mathematical assertion, and we
have every reason to say that the system of Mendelejew and Lothar Meyer
has stood the crucial test. Future hypotheses will perhaps supplement
the system or enlarge our knowledge of it, but will certainly not reduce
it _ad absurdum_.
* * * * * * * *
Apart from these cases, there are achievements by men who may be called
_lucky_ discoverers, although they displayed no genius for finding nor
for creating. The philosopher-physicist, Ernst Mach, has devoted a
lecture to such intellects, which seems to me very valuable, if only for
the reason that he traces back the conceptions of discovery and
invention to one common root of knowledge, and explains their difference
as being due only to a difference in the application of this discovery.
But when Ernst Mach in this lecture, "On the Influence of Accidental
Circumstances on the Development of Inventions and Discoveries," extends
the influence of chance to include accidental circumstances that can
only enter when the discoverer is closely attentive, it seems to me that
certain limitations are advisable. Otherwise, if we pursue Mach's line
of thought to its extreme, we could declare every discovery to be due to
chance, and this would be the end of the intuitive-creative idea. This
assertion would ultimately mean that genius owes its achievements to the
accidental arrangement of the molecules in the brain-cells of its
associated body. This would be just as wrong as saying that chess is a
game of chance because we lose a game when, by chance, we come up
against a better player.
Huyghens, the great discoverer and inventor, says, in his _Dioptrica_,
that he would have to consider anyone who invented the telescope without
the favourable intervention of chance to be a superhuman genius. Why
should he choose just the telescope? To many the invention of the
Differential Calculus will appear grander and due to a higher degree of
ingenuity. And since it was produced quite methodically, and since
chance was excluded, we may follow Huyghens and with good reason
proclaim its authors superhuman geniuses.
* * * * * * * *
Many a true inspiration is dependent on some impulse from without. Who
discovered Electromagnetism? The world-echo answers, "Oersted," with the
same confidence that it couples together the names America and Columbus.
This shows how enormously important was the achievement. Next to
steam-power nothing has exerted such a revolutionary influence in all
branches as electromagnetism. Without it, the world of to-day would
present a totally different aspect. Without it, we should have no
dynamos, no electric trams, no telegraphy, no electric-power stations,
all of which are due to the work of Arago, Gay-Lussac, Ampère, Faraday,
Gramme, and Siemens. Without it, there would be none of the abundance of
brilliant discoveries that are associated with the names of Maxwell,
Hertz, and Einstein. The fact that physics used to be divided into three
parts--Mechanics, Optics, Electrodynamics--and that, since then, the
coherent unity of the physical picture of the world has been developed,
shows us a picture in the background of which we see the illuminating
figure of Hans Christian Oersted. It must not be overlooked, however,
that in the case of his great discovery, too, chance played a definite
part. It occurred one day when Oersted was holding a lecture in the
winter of 1819-20; a magnetic needle situated near his Volta-battery
began to vibrate irregularly. This apparently unimportant trembling of
the metal points contained the key to a fact, the whole consequences of
which could in no conceivable way have entered the mind of this observer
of a hundred years ago, in spite of the genius of the Danish scientist,
which is documented in the classical and far-famed dissertation,
"Experimenta circa effectum conflictus electrici in Acum magneticam,"
which appeared in July 1820. It cleared the way for intuitions that were
equally as fruitful for theory as for practice. Thirteen years after
this initial discovery the world saw the first very important
consequence in Gauss' and Weber's electric telegraph, and a little later
the eminent discoverer Fechner, in Leipzig, proclaimed it as his
conviction that, within two years, electromagnetism would entirely
reform the world of machines, and would entirely supersede steam- and
water-power. Of course, his time estimate fell far short of the mark. It
has been reserved for the present generation to realize that we live in
an electromagnetic world, and that we have, theoretically and
practically, to spend our life electromagnetically. The first indication
of this knowledge hung upon the quivering point of a magnetic needle,
and from it there evolved the electromagnetic ideas that we are so fond
of picturing as our handmaids, but which, in reality, are sovereign over
us all.
* * * * * * * *
A great deal of the history of discovery must be revised and corrected.
The Spiral of Archimedes is not due to Archimedes, nor Marriotte's Law
to Marriotte, nor Cardan's formula to Cardan, nor Crookes' Tube to
Crookes, and Galvanism is only related to Galvani by the following
anecdote. It arose from an accidental experience of Madame Galvani in
the kitchen: a half-skinned frog that was to be fried for the evening
meal happened to rest between a scalpel and a tin plate, which brought
it into metallic contact with an accidental discharge of electricity;
the frog twitched; the head of the house gave a very naïve
interpretation to the phenomenon; and it was under such auspices that
Galvanism made its entry into the world. It would be a futile task to
endeavour to trace the connexion between experiment and the underlying
idea, which, in this case, first came to life in Alexander Volta. What
would have remained a mere frog-dance if left to Galvani now acquired
the rank of a discovery through the work of a thinking physicist, who
set up a "Voltaic series"; this discovery then assumed power and dignity
in the hands of Nicholson, Davy, Thomson, Helmholtz, and Nernst. The
words Galvanic Electricity should be made to give way entirely to
Voltaic Electricity,[4] as in the case of many another expression for
which chance and insufficient thought have stood sponsor.
[Footnote 4: The usual term in England is Voltaic Electricity, or,
simply, Current Electricity.--H. L. B.]
It often happens that experiment acts as a corrective of the underlying
idea, neither confirming nor contradicting, but nursing it, as it were,
strengthening, and purging it of errors. Such experiments, partly in
conjunction with chance, play an important, sometimes a decisive, rôle
in the works of Dufay, Bradley, Foucault, Fresnel, Fraunhofer, and
Röntgen. Faraday, who was incapable of observing otherwise than
intensively, found himself compelled, whilst studying induction
phenomena, to alter his initial view, and it is just this correction by
experiment that constitutes Faraday's real discovery. In many cases the
initial idea is corrected, nay surpassed, by the result. Columbus worked
methodically when he set out to reach the East Indies by travelling
westwards; but what he discovered was not a confirmation of his nautical
idea only, but something much greater, which certainly did not lie in
his calculation. Thus he became the archetype of all searchers, who had
thought out and anticipated essentially different conditions from those
that were afterwards discovered to be prevalent. Among these are to be
counted Priestley and Cavendish, who clung to the erroneous notion of
phlogiston, even when they had the evidence to the contrary in the
elements they had themselves discovered, namely, oxygen and hydrogen.
Graham Bell, the inventor, was seeking something quite different from
what he later hit on: as a teacher of the deaf and dumb he was trying to
give a visual picture of sounds, in order to make clear the formation of
sounds to his pupils; this led him to construct an electrical apparatus,
which finally led to the discovery of the telephone.
The truest and sharpest contrast with the _experimentum crucis_ is
furnished by experiment when it shows the exact opposite of what the
explorer was expecting. But since an absolute No entails a very decisive
Yes--namely, in this case, the affirmation of a relationship that was
previously held to be impossible--a negative experiment of this kind,
when it occurs, will be followed by momentous consequences; these will
be the more important in proportion as the question, the affirmation of
which was expected by the physicist, is of a fundamental character.
The experiments of Michelson and Morley, directed at proving the
existence of the ether, are to be regarded as the true classical
instances of these experiments answering with an overwhelming negative.
Their first effect was to produce a sense of helplessness, a check to
thought, a void in the chamber of ideas. And to fill this void there
arose new views of the world in which we nowadays recognize the true
thought-pictures of the universe. The great names--Lorentz, Minkowski,
Albert Einstein--shone out!
As there are forerunners for almost every Important event, so also in
the case of the _experimentum crucis_ of Michelson and Morley. Henri
Poincaré, the famous mathematician, whilst still a student of the
École Polytechnique, had initiated experiments with his fellow-student
Favé, which followed the same object. The Michelson-Morley experiment
was at least a hundred times more accurate. In each case the conclusion
was that the laws of optics are not disturbed by a motion of
translation, such as that of the earth through space this is, however,
contrary to what the old physical ideas lead us to expect.
If we assume the existence of a space-filling ether, the earth, owing to
its own velocity of nineteen miles per second, would have to pass
through a hurricane just as in the case of travellers sitting in an open
train rushing along at very great speed. If we send out light rays in
all directions simultaneously from any point on the earth's surface,
some will travel in the teeth of the ether-storm, others will experience
only a part of the storm's power; so that of two light-rays travelling
in exactly opposite directions the retardation of the one should be
equal to the acceleration of the other; and yet they are not quite
equal, for a simple calculation shows that in every case the retardation
is slightly more than the acceleration.
This may be made clear by means of a model of easy construction, or,
better still, by considering a ship that is subject to a constant
current and, simultaneously, to a pressure of the wind. The time taken
by the boat in making a trip up and down stream can never be the same
for the cases when the wind is in the direction of the current, and vice
versa.
In the case of the ray of light, which is sent backwards and forwards by
means of a contrivance of mirrors, this fact should be clearly
demonstrated by means of the interference-fringes, which are able to
show much smaller effects than the experiment demands. The experimental
oracle was to speak, but it remained silent. This portentous silence
signified: no interference-effect, no action of the ether-current, no
influence due to translation--nothing!
This "nothing" compelled a decision of a very startling kind, for the
result of this experiment was in direct contradiction to another famous
experiment. Fizeau had proved that the ether is practically rigid and
remains fixed in interstellar space. A decision had to be taken in
favour of Fizeau or Michelson and Morley. Yet this was impossible, for
both had operated with unsurpassable accuracy. It was impossible to
reconcile both views as they were diametrically opposed. This
contradiction remains, even if we assume a different hypothesis, not
involving the ether, for Fizeau's experiment. A solution was impossible
without undertaking revolutionary changes in the whole of physical
thought.
This radical change was effected by Einstein; and this mysterious
contradiction disappeared in the resulting revolution of thought.
Einstein supplanted the absolute time-conception by a new relative
conception, and thus the perplexing problem disappeared. Two great
principles arose as regulative factors in thought, and wherever these
were applied, they achieved wonders: one was the new conception of time
that deprived the earth of her unique position as the sovereign of time
by the introduction of the principle that the rate at which time elapses
is different in media moving at different speeds; the other is the
principle of the constancy of the velocity of light. One feels a
temptation to apply a mythical allegory: just as the world, according to
the Biblical story, originated from nothing, so there arose from the
"nothing" of the Michelson-Morley experiment a new world, a world of
knowledge, a cosmos of thought, in which perfect harmony reigns.
Its truth was contained in itself before the experimental proof was
furnished. And this realization of truth has become a fact in the
_experimentum crucis_ for which the sun and stars formed the material.
This will be discussed in another part of the book.
"The really important factor is ultimately intuition," Einstein had said
to me. It made me think of Huyghens' remark about the genius who would
have been able to create the telescope without the help of chance. Was
not this intellect, imagined by Huyghens, sitting opposite me at that
moment? An inner voice answered in the affirmative, for Einstein's
thought-complex seemed to me at that moment a kind of telescope for the
human mind, a telescope that had arisen out of pure intuition, and whose
range stretched to the limits of the universe.