Let me begin by asking how a scientific idea arises and what are its characteristics. In asking these questions I cannot attempt, of course, to analyze the delicate mental processes taking place in the investigator’s mind and, what is more, largely in his subconscious mind. These processes are mysteries which can be revealed only to a limited extent if at all, and it would be equally foolish and rash to attempt any study of their inmost nature. The most that we can do is to begin with the obvious facts, which means that we investigate those ideas which have actually proved their leavening force for any branch of science; and this in turn means that we ask in what form they first occurred and what was their content at that time.
The first result of such an investigation is the discovery of the following rule: any scientific idea arising in the mind of a scholar is based on a concrete experience, a discovery, an observation, or a fact of any kind, whether it is a physical or an astronomical measurement, a chemical or a biological observation, a discovery among the archives or the excavation of some valuable relic of an earlier civilization. The content of the idea consists in this experience being compared and being brought into contact with certain different experiences in the mind of the scholar, in other words, in the fact that it establishes a link between the old and the new, so that a number of facts which had hitherto co-existed loosely are now definitely inter-related. The idea becomes fruitful and hence attains value for science if the interconnection thus established can be applied more generally to a series of cognate facts: for the establishment of an interconnection creates order, and order simplifies and perfects the scientific view of the universe. What is most important, however, is that the task of applying the new idea in its entirety shall lead to new questions and hence to new studies and to new successes. And this is true of the physicist’s hypotheses no less than of the interpretations established by the philologist.
I propose now to exemplify the above in some detail, and in doing so I desire to confine myself to my own subject of physics. The angle of vision may appear somewhat restricted; on the other hand I shall be able to throw a clearer light upon the subject.
A classical example of the sudden emergence of a great scientific idea is found in the story of Sir Isaac Newton who, sitting under an apple tree, was reminded by a falling apple of the movement of the moon around the earth and thus connected the acceleration of the apple with that of the moon. The fact that these two accelerations are to each other as the square of the radius of the moon’s orbit is to the square of the earth’s radius, suggested to him the idea that the two accelerations might have a common cause and thus provided him with a foundation for his theory of gravitation.
We thus find that it is a characteristic of every new idea occurring in science that it combines in a certain original manner two distinct series of facts; and this can be traced in every instance, though certain differences occur with regard to content and formation. These differences in turn bring about differences in the effect and the fate of the different scientific ideas. Some of them eventually become the common property of science, are taken for granted and cease to be stressed. Such has been the fate of the two ideas just mentioned: of Newton’s idea about the similarity between the acceleration of the moon and the gravitational acceleration on earth; and of Maxwell’s idea about the electromagnetic nature of light. It is true that a good deal of time had to elapse before the latter idea won acceptance; at first, it tended to be disregarded, especially in Germany, where Wilhelm Weber’s theory, which was based on the assumption of immediate action at a distance, held the stage. It was not until Heinrich Hertz made his brilliant experiment with ultra-rapid electric oscillations that Maxwell’s theory obtained the recognition it deserved.
Other ideas which have become the lasting heritage of science are those which hold that sound waves are of a mechanical nature and that rays of light and heat are identical. Teachers of physics tend to deal all too briefly with these ideas, and they should be reminded that there was a time when these ideas were far from being commonplaces. The second of the two just mentioned was indeed for years the subject of fierce controversy. It may be mentioned as a curiosity that the scientist whose experiments contributed most to its success —the Italian physicist, Macedonio Melloni—began by being one of its opponents, an instructive example showing that scientific values are independent of their theoretical interpretation.
But most of the ideas which play a part in science are different from those enumerated. The latter were perfect when they first took shape and will always retain their validity unchanged; these others assume their final form gradually, retain their value for a time and eventually either die or are modified to a more or less considerable degree. Frequently enough they resist modification and this resistance tends to be obstinate in proportion to their past successes: there have been occasions when this resistance has sensibly hampered the progress of science. Physics offers some instructive examples which it may be worth while to discuss in detail.
I propose to begin with the idea of the nature of heat.
The first stage in the development of the theory of heat consisted in calorimetry. It was based on the assumption that heat behaves like a delicate substance which flows from the hotter to the colder body whenever there is contact between two bodies having different temperatures. No quantitative change is supposed to take place during this process. This hypothesis worked well so long as no mechanical effects entered into play. A difficulty consisted in the production of heat by friction or compression, and this it was sought to overcome by assuming that the capacity of bodies for heat was variable, so that heat could be pressed out of a body under compression, like water being pressed out of a wet sponge, during which process the quantity of water remains unchanged. Later, when the invention of heat-utilizing power systems made more urgent the question of the laws governing the production of mechanical work from heat, Sadi Carnot tried to formulate the production of work out of heat on the analogy of the production of work out of gravity. As the falling of a weight from a greater to a less height can produce work, so the transition from a higher to a lower temperature can be used for the same purpose; and as the work obtained from gravitation varies as the weight of the body and the difference in height, so the work produced by heat varies as the amount of heat transferred and the difference in temperature.
Carnot’s theory to the effect that the transition from a higher to a lower temperature was analogous to the falling of a weight from a higher to a lower level was not, however, to be so easily refuted. There were physicists who considered Clausius’ ideas unnecessarily complicated and vague and who objected particularly to the introduction of the idea of irreversibility, by which a unique position among the various kinds of energy was assigned to heat. Accordingly they formed the theory of energetics in opposition to Clausius’ thermo-dynamics. The first principle of this theory agrees with that of Clausius in enunciating the preservation of energy; the second principle, however—that which indicates the sense of events—postulated a thoroughgoing analogy between the transition from a higher to a lower temperature and the falling of a weight from a higher to a lower level, or again, the passing of electricity from a higher to a lower potential. Hence it came about that irreversibility was declared superfluous in order to prove the second principle, and that the existence of an absolute zero was denied, it being pointed out that temperature resembled levels of height and levels of potential in that only differences and nothing absolute could be measured. The fundamental distinction which consists in the fact that a pendulum swings past the position of equilibrium before coming to rest and that a spark passing between two conductors having opposite charges oscillates, whereas there is no such thing as an oscillation of heat between two bodies between which heat is passing, was considered irrelevant by the energetist school and was passed over in silence.
I myself experienced during the ’80’s and ’90’s of the last century what the feelings of a student are who is convinced that he is in possession of an idea which is in fact superior, and who discovers that all the excellent arguments advanced by him are disregarded simply because his voice is not powerful enough to draw the attention of the scientific world. Men having the authority of Wilhelm Ostwald, Georg Helm, and Ernst Mach were simply above argument.
The change originated from a different side altogether: atomism began to make itself felt. The atomic idea is extremely old; but its first adequate formulation took shape in the kinetic gas theory which originated more or less contemporaneously with the discovery of the mechanical heat equivalent. The energetists at first opposed it vigorously, and it led a modest existence; towards the end of last century, however, experimental investigation led to its rapid success. According to the atomist idea the transference of heat from the hotter to
the colder body does not resemble the falling of a weight; what it resembles is a mixing process, as when two different kinds of powder in a vessel, having first constituted different layers, eventually mingle with each other if the vessel is continually shaken. If this happens the powder does not oscillate between a state of complete mixture and complete isolation of the constituent powders; what happens is that the change takes place once in a certain sense, viz., in the direction towards complete mixture, and is then at an end: the process is an irreversible one. Seen in this light the second principle of thermo-dynamics is found to be of a statistical nature: it states a probability. The arguments supporting this view and indeed raising it beyond any doubt have been well stated by my colleague, Max von Laue.
What is learned at school is not as important as how it is learned. A single mathematical proposition which is really understood by a scholar is of greater value than ten formulae which he has learned by heart and even knows how to apply, without, however, having grasped their real meaning. The function of a school is not so much to teach a business-like routine as to inculcate logical and methodical thought. It may be objected that ultimately it is the ability to do things rather than knowledge that matters; and it is true that the latter is valueless without the former, just as any theory is ultimately important only by reason of its particular applications. Yet routine can never be a substitute for theory, for in any cases that fall outside the rule, routine breaks down. Hence the first requisite, if good work is to be done, is a thorough elementary training; and here it is not so much the quantity of facts learned as the manner of treatment that matters. Unless this preliminary training is acquired at school, it is hard to obtain it at a later stage: training colleges and universities have other tasks. For the rest, the last and highest aim of education is neither knowledge nor the ability to do things, but practical action. Now practical action must be preceded by the ability to act, and the latter in turn demands knowledge and understanding. The present age, which lives at such a rapid rate, and shows so much interest for every innovation having an immediate sensational effect, provides us with instances where scientific training tends to anticipate certain exciting results before they have properly ripened; for the public is favorably impressed if the curriculum of an intermediate school already contains modern problems of scientific investigation. Yet such a practice is exceedingly dangerous. The problems cannot possibly be dealt with thoroughly, and the consequence may easily be to induce a certain intellectual superficiality and empty pride in knowledge. I should consider it extremely dangerous if the intermediate schools were to deal with the theory of relativity or the quantum theory. Specially gifted scholars always require exceptional treatment; but the curriculum is not designed for such, and I would definitely condemn any attempt to take such a question as that of the universal validity of the principle of the preservation of energy—which, of course, to-day is seriously regarded as an open one in nuclear physics—and to treat it as debatable before pupils who cannot have properly grasped the meaning of the principle involved, much less its potential scope.
The results of such an up-to-the-minute method of teaching become all too plain when we consider the way in which the breakdown of the exact sciences is occasionally spoken of to-day. It is characteristic of the prevalent confusion that there are numbers of inventive minds busying themselves to-day upon devices which aim at the unlimited production of energy or the utilization of the fashionable mysterious earth rays. And it is even more surprising that credulous persons provide ample funds for such inventors, while really valuable and hopeful scientific investigations are hampered or actually stopped by lack of means. A thorough school training might here prove a useful remedy, and this would apply to the patrons no less than to the inventors.
Zdeněk Pešánek: Light-kinetic sculpture on the building of Edison transformer station in Prague, 1929–30. Iron, glass, electrical circuits, color electric bulbs, pneumatic piano. Height ca 4 m, length ca 4 m
After this educational digression I should like to deal briefly with another physical idea whose varying fate may prove even more instructive than the changes undergone by the theory of heat. What I have now in mind is the idea of the nature of light.
The study of the nature of light began with the measurements of the speed of light. The idea which led Newton to his emanation theory established a comparison between a ray of light and a jet of water; the velocity of light was compared with the velocity of particles of water flying in a straight line. This hypothesis, however, failed to give an account of ihe phenomenon of light interference, i.e., of the fact that two rays of light meeting at a point can in certain circumstances produce darkness at this point. Accordingly the emanation theory was given up and its place was taken by Huygens’ theory of undulations, where the underlying idea is that light is propagated like a wave of water which spreads concentrically in all directions from its point of origin at a velocity which, of course, is not connected in any way with the velocity of the particles of water. This theory succeeded completely in accounting for the phenomena of interference: two waves on impinging on each other can cancel each other whenever the crest of one wave impinges on the trough of another. However, this theory, too, did not last longer than a century. The undulation theory failed to explain the effect at a great distance of a ray of light having a short wave length. The intensity of light decreases as the square of the distance, so that if light is radiated equally in all directions it is impossible to understand how a ray is capable of producing, even at a very great distance, a quantity of energy which is entirely independent of its intensity, and which is relatively very considerable in the case of short waves like those of Röntgen rays or Gamma rays. Such powerful effects combined with extremely feeble intensity become intelligible only if we imagine the energy of light to be concentrated upon distinct, unchangeable particles or quanta. In a sense, this is a return to Newton’s hypothesis of light particles.
At present, then, the position is an exceedingly unsatisfactory one. We have two theories facing each other like two equally powerful rivals. Each possesses keen weapons, and each has a vulnerable spot. It is hard to foretell the ultimate issue, but it is probably correct to say that neither theory will prove completely victorious. It is more likely that in the end a higher standpoint will be reached, where we shall be able to survey clearly the claims and the deficiencies of each of the two hypotheses.
Such a standpoint can probably be found only if we intensify our search for the source of all experience, which would mean in the present case that we would turn our attention to the measurement of optical phenomena. This in turn would imply that we would turn our investigation upon the actual measuring instruments, a step which, in principle, is of enormous importance since it may be described as the introduction of totality into physics. According to this principle the laws of an optical phenomenon can be completely understood only if the peculiarities of the process of measurement are studied as well as the physical events at the points where the light originates and spreads. The measuring instruments are not merely passive recipients simply registering the rays impinging upon them: they play an active part in the event of measuring and exert a causal influence upon its result. The physical system under consideration forms a totality subject to law only if the process of measuring is treated as forming part of it.
How progress is to be made by this road is a difficult question and of much importance for the future. In order to appreciate its significance I propose to extend the scope of my survey, to go beyond the special conditions of optics and to approach the problem from a more general point of view.
Is it at all possible to predict with confidence the mutations of any scientific idea? Is it possible to claim that there is so much as an approximate law governing the development of scientific ideas ? Looking back on the historical development of events one is tempted to suspect such a law, on considering that many important ideas began by existing in the dark, uncomprehended by the many and at best dimly foreseen by a few students who were in advance of their age; but that once mankind had become ripe for them, they came to life suddenly and simultaneously in a number of different places. The principle of the preservation of energy can be traced back for centuries in a rudimentary form; but it was not until the middle of last century that the principle was given a scientifically practical foundation, more or less simultaneously, by four or six students between whom there was no connection whatever. We may probably assert that even if Julius Robert Mayer, James Prescott Joule, Ludwig August Colding, and Hermann von Helmholtz had not been living at that time, the principle of the preservation of energy would, nevertheless, have been discovered only a little later. I would even venture to assert much the same of the origin of the modern theory of relativity or the quantum theory, were I not reluctant to face the obvious rejoinder that such prophecies after the event are somewhat cheap. I consider the inevitable element of such a process to consist in the fact that with the spread of experimentation and the improvements in methods of measurement, theoretical investigation has been forced in a certain direction almost automatically.
Yet there could be no greater mistake than to assume that the laws governing the growth and effect of scientific ideas can ever be reduced to an exact formula valid for the future. Ultimately any new idea is the work of its author’s imagination, and to this extent progress is tied to the irrational element at some point even in mathematics, the most exact of the sciences; for irrationality is a necessary component in the make-up of every intellect.
If we bear in mind that any given idea is due to a given experience, we shall find it natural that the present time, so rich in numbers of new events, has proved a fruitful soil for the production and promulgation of new ideas. If, further, we consider that whenever an idea is formulated a relation is established between two different events, we shall find, even by the formal rules of combinations, that the number of possible ideas exceeds by an order of magnitude the number of available events.
Another circumstance explaining the vast output of scientific ideas at the present day possibly consists in the fact that owing to the spread of unemployment there are many lively intellects which experience a desire for productive work, and welcome a pre-occupation with general theoretical and philosophical problems as a cheap and satisfactory escape from the emptiness of their everyday existence. Valuable results, unfortunately, are rare exceptions. I do not exaggerate when I say that hardly a week passes in which I do not receive one or more papers of varying length from members of every profession—teachers, civil servants, writers, lawyers, doctors, engineers, architects—with a request for my opinion. A thorough examination of these would take up all and more than all of my spare time.
These communications can be divided into two classes. The first is entirely naive and their authors have never considered that a new scientific idea to be valuable must be based on certain facts, so that specialized knowledge is essential for their formulation. The authors of these contributions, on the other hand, imagine that they have a fine prophetic gift enabling them to guess the truth direct, never suspecting that every important discovery is preceded by a period of hard individual work. These people, on the other hand, imagine that a happy fate has allowed the desired fruit to drop into their lap in the way in which Newton, sitting under the apple tree, received the idea of universal gravitation. What is worse is that these visionaries float above the surface, never penetrating to the depths, and are too ignorant scientifically to be capable of seeing their error. The dangers which flow from them should not be underestimated. It is satisfactory to note that modern youth shows a growing interest in general questions and in the acquisition of a satisfactory view of life; but for this very reason it should never be forgotten that such a view is baseless and doomed to sudden destruction unless it has a firm foundation in reality. Anyone desirous of obtaining a scientific view of the world must first acquire a knowledge of the facts.
Today the individual student can no longer form a comprehensive view of every department of science and in most instances he must take his facts at second-hand. It is all the more important that he should be master of one trade and have an independent judgment on his own subject. Personally, as a member of the philosophical faculty, I have always asked that candidates for a philosophical doctorate should give evidence of special knowledge in one given special science. Whether this department belonged to the natural sciences or to the intellectual sciences is not important: what is important, is that the candidate should have acquired by actual study an idea of scientific method.
It is generally easy to demonstrate the worthlessness of the type of papers just mentioned; but there is another class which requires much more serious attention because the authors are careful students turning out excellent work in their special field. The scale of scientific work being such as it is to-day, specialization continually becomes more intense and consequently the more serious student experiences a desire to look beyond the limits of his own subject and to apply the knowledge acquired to other departments of science. There is thus a tendency to link two distinct departments by one idea which seems convincing to the student, who in this way transfers the laws and methods with which he has grown familiar within his own sphere to an alien one whose problems he thus tries to solve. There is especially among mathematicians, physicists, and chemists, a tendency to employ their own exact methods in order to throw light on biological, psychological, and sociological questions. Yet it must not be forgotten that such a new intellectual bridge to be sound requires both its pillars to be securely founded: it cannot fulfill its purpose unless the further pillar, too, has a proper foundation. In other words, it does not suffice for an ingenious student to be thoroughly acquainted with his original subject; if his more widely ranging ideas are to be fruitful, he must also have some knowledge of the facts and problems of the other sphere to which he is applying his idea. This deserves all the more emphasis because every expert tends to exaggerate the importance of his special field in proportion to the length of time spent on it and to the difficulties encountered. And once he has discovered the solution of a problem, he tends to exaggerate its scope and to apply the solution to cases of a totally different nature. Those who feel the desire to take up a higher standpoint than that which their own restricted field allows them, should never forget that there are students at work in other departments of science who are working with equal care and under equal difficulties although with different methods. The history of every science shows how frequently this rule is disregarded. In selecting my examples, however, I shall take care to confine myself to physics in order to avoid the mistake I have just been criticizing.
Among the more general ideas of physics there is practically none which has not been transferred with more or less skill to some other sphere by means of some association of ideas, an association depending frequently enough merely upon such contingent externals as terminology. Thus the term “energy” leads students to apply the physical concept of energy and with it the physical proposition enunciating the preservation of energy to psychology, and serious attempts have been made to subject the cause and degree of human happiness to certain mathematically formulated laws. The same must be said of attempts to apply the principle of relativity outside physics, e.g., in esthetics, or even in ethics. Yet there could be nothing more misleading than the meaningless statement that everything is relative. The proposition does not apply even in physics. All the so-called universal constants—the mass or the charge of an electron or a proton, or Planck’s quantum—are absolute magnitudes: they are the fixed and unchangeable components of which the structure of atomism is built up. Of course a magnitude which once was considered absolute has often been found to be relative later; but whenever this happened another and more fundamental absolute magnitude was substituted. Unless we assume the existence of absolute magnitudes no concept can be defined and no theory can be formed.
The second principle of thermo-dynamics, the principle of the increase of entropy, has frequently been applied outside physics. For example, attempts have been made to apply the principle that all physical events develop in one sense only to biological evolution, a singularly unhappy attempt so long as the term evolution is associated with the idea of progress, perfection, or improvement. The principle of entropy is such that it can only deal with probabilities and all that it really says is that a state, improbable in itself, is followed on an average by a more probable state. Biologically interpreted, this principle points towards degeneration rather than improvement: the chaotic, the ordinary, and the common is always more probable than the harmonious, the excellent, or the rare.
Besides the misleading ideas which we have been considering there is another class which consists of those ideas which, looked at carefully, are seen to have no meaning at all. These play a fairly important part in physics, too. A comparison between the movement of an electron around a proton and the movement of a planet around the sun has caused investigators to study the velocity of the electron, although later investigation showed that it is completely impossible to answer these two questions simultaneously. Once again we see the danger of applying ideas and propositions which have proved their value in one department of science to another, and we perceive how great is the need of care in testing and formulating a new idea.
Yet there is also a theoretical side to the matter, of which it is now high time to speak. If a new idea were to be admitted only when it had definitely proved its justification, or even if we merely demanded that it must have a clear and definite meaning at the outset, then such a demand might gravely hamper the progress of science. We must never forget that ideas devoid of a clear meaning frequently gave the strongest impulse to the further development of science. The idea of an elixir of life or of the transmutation of base metals gave rise to the science of chemistry; that of perpetual motion to an intelligent comprehension of energy; the idea of the absolute velocity of the earth gave rise to the theory of relativity, and the idea that the electronic movement resembled that of the planets was the origin of atomic physics. These are indisputable facts, and they give rise to thought, for they show clearly that in science as elsewhere fortune favors the brave. In order to meet with success it is well to aim beyond the goal which will eventually be reached.
Looked at in this light the ideas of science wear a new aspect. We find that the importance of a scientific idea depends, frequently enough, upon its value rather than on its truth. This applies, e.g., to the concept of the reality of an external world or to the idea of causality. With both the question is not whether they are true or false, but whether they are valuable or valueless. This fact will appear all the more striking if we consider that the values of an objective science like physics are, to start with, wholly independent of the objects to which they relate; and the question arises how it comes about that the importance of a physical idea can be fully exploited only if we take its value into consideration.
In my opinion the only possible method available here is that which we followed when dealing with optics, a method applicable not only to physics, but to every department of science. We must go back to the source of every science, and we do this when we remember that every science requires some person to build it up and to communicate it to others. And this means once again the introduction of the principle of totality.
In principle a physical event is inseparable from the measuring instrument or the organ of sense that perceives it; and similarly a science cannot be separated in principle from the investigators who pursue it. A physicist who studies experimentally some atomic process interferes with its course in proportion as he penetrates into its details, and the physiologist who subdivides a living organism into its smallest parts injures or actually kills it; by the same token the philosopher, who in examining a new idea confines himself to asking to what extent its meaning is evident a priori, hampers the further development of science. Hence a positivism which rejects every transcendental idea is as one-sided as a metaphysics which scorns individual experience. Each method has its justification, and each can be carried through consistently; but if carried to an extreme they paralyze the progress of science because they prohibit the asking of certain fundamental questions, although they do so for opposite reasons: positivism, because the questions are meaningless, and metaphysics, because the answer to them is already available. The rivalry between the two parties will never be decided in favor of either, and in the course of history success has always wavered between the two. A century ago metaphysics enjoyed a hegemony which was followed by a melancholy collapse. To-day positivism is striving after the leading position, which it will fail to obtain just as metaphysics failed.
Nobody had a deeper sense of this persistent antagonism than Goethe, who struggled with it all his life and has given it masterly expression in a number of different forms. He tried to overcome this antagonism by rising to the concept of totality, the introduction of which does justice to both views. Yet even Goethe’s all-embracing mind was subject to the limits of time; he declined to admit the distinction between the rays of light in external space and the sensation of light in consciousness, and hence was prevented from doing justice to the brilliant progress made by physical optics in his time. Nevertheless, on observing the modern introduction of the idea of totality in physics, he might see in this change a confirmation of his way of thought.
Thus we observe, what we have already observed on several occasions, that there is an irrational core at the center of science which no intelligence can solve, and which no modern attempt at limiting by definition the tasks of science can remove. At first such a state of affairs may appear strange and unsatisfactory; on reflection, however, it will be seen that it could not be otherwise. For a close examination will show that every science really tackles its task at the center and not at the beginning, and that it is compelled to grope its way more or less laboriously towards the beginning without any hope of ever quite reaching it. Science does not find ready-made the concepts with which it operates: it has to form them artificially and their perfecting is a gradual process. It draws its material from life and it reacts upon life; its impulse, its consistency, and its vitality came from the ideas at work in it. It is the ideas which place before the student the problems with which he deals, which impel him to work without cease, and which enable him correctly to interpret the results he obtains. Without ideas investigation becomes aimless and the energy expended upon it is wasted. Ideals alone make a physicist of an experimenter, an historian of a chronicler, and a philologist of a graphological expert. We have already seen that the truth or falsity of an idea and the question whether it has a definite meaning is relatively unimportant: what matters is that it shall give rise to useful work. In science, as in every other sphere of cultural development, it is the work done which is the sole certain criterion of the health and the success of the individual as well as of the community. Accordingly, I wish to conclude these observations on the growth and effect of scientific ideas by quoting words in praise of work as applied to science; words which the Association of German Engineers, justly appreciating its theoretical and practical value, has made into its motto: “What is needed is investigation.”
Light Sculpture by Diet Wiegman