"My own associations with the world of practice are not, indeed, of recent date. My own parents originally wanted me to become a technical scientist, and I was expected to choose this profession to earn my livelihood. I was not, however, sympathetically inclined to it, for even at an early age these practical aims were to me, on the whole, indifferent and depressing. My idea of human culture did not coincide with the current view, that cultural development is to be measured in terms of technical progress. Doubts, indeed, arose in me as to whether technical improvements and advances would actually contribute to the well-being of mankind. I must add that, later, when I came into actual touch with technical science, my opinion became somewhat modified, for the reason that, here too, pleasures of theory often visited me."
The true position is probably that the technical worker who does not merely think out improvements for machines, but occupies himself with inventions on a higher plane, never ceases to feel himself a theorist, since his achievements are dependent for their inspiration on the fruits of theory. The practical results of to-day are rooted in the theoretical results of decades ago, and what is nowadays regarded as an idea of pure research may in later decades acquire practical value. Whether it actually becomes of value, or not, is of little account in judging the idea. At any rate experience has shown that the beginning of theoretical investigations hardly ever gives us the chance of making prognostications. We spoke of the discoveries of Volta, Ampère, and Faraday. When these were first known, the world might have asked: Why have they been disclosed? To what can they be applied? Of what use are they? Nowadays we know the answers that still lay hidden at that time, and we proudly point to modern dynamos. But does a dynamo really represent the significance of these discoveries? Would the importance and rank of Volta, Ampère, and Faraday be less if the dynamo had not come into existence? Only an out-and-out materialist would affirm this, and, strictly speaking, the question should not even be raised. For it is in a sense equivalent to wishing to judge of the importance and significance of the Polar Star from its usefulness to the navigator on the earth's surface in finding his bearings. We may put the question (although only in the spirit of psychological curiosity, and without expecting much elucidation): Would these discoverers have been particularly happy if they had divined the far-reaching consequences of their work? Did they, indeed, in the course of their abstract researches, have a pre-vision of the future dominated by the dynamo? Einstein refused to answer this in the decisive negative. He left room, if ever so little, for doubts—that is, he considered that, in all probability, these three discoverers had no presentiment of these consequences, and even if they had in a dream caught a glimpse of our present electrical age, their zest for discovery, their "pleasure in theory," could scarcely have been increased; for they were discoverers by nature, who, swept along by their own spirits, did not need to wait to satisfy the desires of practical application.
In Einstein's opinion, the presentiment that a discovery may have practical applications in the future may react on pure research. He quoted bacteriology as a proof of this. In the series of eminent bacteriologists, ranging from Spallanzani to Schwann and Pasteur, there were certainly some whose desire for knowledge was directed primarily towards discovering purely scientific relationships. Pasteur himself started from the theoretical question of the creation of life, that is, from the problem of the origin of organic creatures from inorganic matter without the medium of parent organisms. As a pan-spermist he took up a negative attitude, that is, he tried to prove that it is impossible to discover a bridge between organic and inorganic matter. Yet he doubtless knew that his theoretical efforts stretched out into practical regions, and he may easily have foreseen that they would exert a very important influence on Medicine and Hygiene, although he could not measure its full extent. In this case, then, we cannot fail to recognize that a certain connexion between the desire for pure knowledge and the impulse to apply it practically is possible, serviceable, and justified in itself.
An influence in the opposite direction is also possible, and when, during the course of our conversation, we went in search of examples, we came across one of great interest. It shows us that a question may arise out of ordinary practice that may open up an immense field of pure knowledge, nay, it may lead to a science of very wide scope. As this example is not well known, I shall mention it here; I do so with additional pleasure as the scientist involved is one of those whom Einstein quotes most frequently and for whom he has the greatest admiration, namely, Johannes Kepler. First we have the surprising fact that Kepler, who, even when at the height of his fame, was not free from care, was once the possessor of some money. In the year 1615, his blessed year of fortune, the great astronomer owned a comfortable home in Linz, and even dared to conceive the idea of placing some well-filled casks in his cellar; nay, more, he was in a position to publish a new scientific work at his own expense, and thus appear as his own publisher.
This production of Kepler and his casks of wine are directly connected, as we see clearly from the title: Doliometrie, literally, "The Measurement of Casks." But the title of the work gives not the slightest hint of its importance. For these investigations relating to wine-casks actually became the foundation of a science of sovereign power, the Infinitesimal Calculus.
What was Kepler's aim? It was something entirely practical, and directed to a definite purpose, quite independent of "pleasures of theory," to repeat Einstein's expression. His problem was a question of economy, of using material sparingly and appropriately, in accordance with the requirements of the careful head of a house. How must such a cask be constructed from a minimum of wood to give the greatest cubical content?
His deliberations began by regarding wine as the precious content enclosed by a figure in space, and then conceiving the cask as representing a particular class of "bodies of revolution," that is, of figures in space that may be regarded as produced by the revolution of a curved line about an axis. At this point he at first endeavoured to gain a complete survey of the question. He varied the boards along the sides, the staves, and formed successively ninety-two such bodies of revolution, some of which he named after the fruits which they resembled in shape, as, for example, apple-shaped, lemon-shaped, olive-shaped bodies. He started out by measuring casks, and the final result was that his work, Doliometrie, became the source of all future cubatures or measurements of volume.
Now we come to the deciding point. What conditions has the limiting surface of such a cask-like body of revolution to fulfil, if the body is to have a maximum volume? An epochal discovery here came to light. The practical head of the house soars up into the sublime realms of the theory of magnitudes. Kepler discovered the conception of changes in functions, and their peculiarities at the maximum point. (He did not, of course, use these modern terms.) By this means, long before Newton and Leibniz, he laid the foundations of Infinitesimal Calculus, which later became the heart and soul of mathematics, of astronomy, of theoretical physics, and of technical science, in so far as it is founded in mechanical relations.
On the other hand, Einstein who now, three hundred years later, has set up his differential equations, and, with them, a new world-system, stands before us as a pure discoverer, devoid of practical aims. But in these equations there are elements of analysis that once came to light in a happy idyll. This event did not come out of the grey obscurity of abstraction, but out of a region of earthly happiness, when a ray of light found its way into Kepler's gloomy existence. No poet has yet expressed this curious complex of events in a ballad, telling how Truth, the only object of Science, was pressed out of the grape, and how Practice, inspired by the inquiry of a cooper, found its way to a Theory that stretches to the confines of the Universe.
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