Essays in Humanism (12 page)

All the foregoing might be described—though in the extremely modest manner of speaking—as an exact formulation of something the essence of which had already been recognized by Galileo. But it by no means succeeded in solving the main problem. In other words, the law of motion yields the movement of a body, only when the direction and magnitude of the force exerted upon it are known for all times. Thus the problem reduced itself to another problem: how to find out the operative forces. To a mind any less bold than Newton’s it must have seemed hopeless, considering the immeasurable multifarity of the effects which the bodies of a universe seem to produce upon each other. Moreover, the bodies whose motions we perceive are by no means dimensionless points—that is to say, perceptible as material points. How was Newton to deal with such chaos?

If we push a cart moving without friction on a horizontal plane it follows that the force we exert upon it is given directly. That is the ideal case from which the law of motion is derived. That we are not here dealing with a dimensionless point appears unessential.

How does it stand then with a falling body in space? A freely falling body behaves almost as simply as the dimensionless point, if one regards its movement as a whole. It is accelerated downwards. The acceleration, according to Galileo, is independent of its nature and its velocity. The earth, of course, must be decisive for the existence of this acceleration. It seemed, then, that the earth by its mere presence exerted a force upon the body. The earth consists of many parts. The idea seemed inevitable that each of these parts affects the falling body and that all these effects are combined. There seems then to be a force which bodies by their very presence exert upon each other through space. These forces seem to be independent of velocities, dependent only upon the relative position and quantitative property of the various bodies exerting them. This quantitative property might be conditioned by its mass, for the mass seems to characterize the body from the mechanical point of view. This strange effect of things at a distance may be called gravitation.

Now to gain precise knowledge of this effect, one has only to find out how strong is the force exerted upon each other by two bodies of given mass from a given distance. As for their direction, it would probably be no other than the line connecting them. Finally then, what remains unknown is only the dependence of this force upon the distance between the two bodies. But this one cannot know
a priori.
Here, only experience could be of use.

Such experience, however, was available to Newton.

The acceleration of the moon was known from its orbit and could be compared with the acceleration of the freely falling body on the surface of the earth. Furthermore, the movements of the planets about the sun had been determined by Kepler with great exactness and comprehended in simple empirical laws. So it was possible to ascertain how the effects of gravitation coming from the earth and those coming from the sun depended on the factor of distance. Newton found that everything was explainable by a force which was inversely proportional to the square of the distance. And with that the goal was reached, the science of celestial mechanics was born, confirmed a thousand times over by Newton himself and those who came after him. But how about the rest of physics? Gravitation and the law of motion could not explain everything. What determined the equilibrium of the parts of a solid body? How was light to be explained, how electrical phenomena? By introducing material points and forces of various kinds acting at a distance, everything seemed in a fair way to be derivable from the law of motion.

That hope has not been fulfilled, and no one any longer believes in the solution of all our problems on this basis. Nevertheless, the thinking of physicists today is conditioned to a high degree by Newton’s fundamental conceptions. It has so far not been possible to substitute for the Newtonian unified conception of the universe a similarly unified comprehensive conception. But what we have gained up till now would have been impossible without Newton’s clear system.

From observation of the stars have chiefly come the intellectual tools indispensable to the development of modern technique. For the abuse of the latter in our time creative intellects like Newton’s are as little responsible as the stars themselves, contemplating which their thoughts took wing. It is necessary to say this, because in our time esteem for intellectual values for their own sake is no longer so lively as it was in the centuries of the intellectual renascence.

22. Johannes Kepler

IN KEPLER’S LETTERS
we find ourselves confronted with a sensitive personality, passionately devoted to the quest for deeper insight into the character of natural processes—a man who reached the exalted goal he set himself in spite of all internal and external difficulties. Kepler’s life was devoted to the solution of a dual problem. The sun and the planets change their apparent position with reference to their background of fixed stars in a complex manner open to immediate observation. In other words, all the observations and records compiled with such care dealt not actually with the movements of the planets in space but with temporal shifts undergone by the direction earth-planet in the course of time.

Once Copernicus had convinced the small group capable of grasping it that in this process the sun must be regarded as being at rest, with the planets, including the earth, revolving about the sun, the first great problem proved to be this: to determine the true motions of the planets, including the earth, as they might be visible to an observer on the nearest fixed star who was equipped with a perfect stereoscopic double-telescope. This was Kepler’s first great problem. The second problem was embodied in this question: What are the mathematical laws under which these motions proceed? It is plain that the solution of the second problem, if at all within reach of the human mind, was predicated on the solution of the first. Before a theory explaining a certain process can be tested, that process must first be known.

Kepler’s solution of the first problem is based on a truly inspired notion that made possible the determination of the true orbit of the earth. To construct that orbit, a second fixed point in planetary space, in addition to the sun, is required. When such a second point is available, it and the sun may both be used as points of reference for angular measurements, and the earth’s true orbit can be determined by the same methods of triangulation that customarily serve in surveying and cartography.

But where was such a second fixed point to be found, since all visible objects, except the sun, themselves execute motions that are not known in detail? This was Kepler’s answer: The apparent motions of the planet Mars are known with great accuracy, including the time of its revolution about the sun (the “Martian year”). It is probable that at the end of each Martian year Mars is at the same spot in (planetary) space. If we limit ourselves for the time being to these points in time, then the planet Mars represents for them a fixed point in planetary space, a point that may be used in triangulation.

Employing this principle, Kepler first of all determined the true motion of the earth in planetary space. Since the earth itself may be used as a point for triangulation at any time, he was also able to determine the true motions of the other planets from his observations.

This is how Kepler gained the basis for formulating the three fundamental laws with which his name will remain associated for all time to come. Today, after the fact, no one can fully appreciate how much ingenuity, how much hard and tireless work was required to discover these laws and ascertain them with such precision.

The reader ought to know this as he learns from the letters under what hardships Kepler accomplished this gigantic work. He refused to be paralyzed or discouraged either by poverty or by the lack of comprehension among those of his contemporaries who had the power to shape his life and work. Yet he was dealing with a subject that offered immediate danger to him who professed the truth. But Kepler was one of the few who are simply incapable of doing anything but stand up openly for their convictions in every field. At the same time he was not one who took undiluted pleasure in personal controversy, as was plainly the case with Galileo, whose inspired barbs delight the informed reader even today. Kepler was a devout Protestant, but he made no secret of the fact that he did not approve of all decisions by the Church. He was, accordingly, regarded as a kind of moderate heretic and treated as such.

This brings me to the inner difficulties Kepler had to overcome—difficulties at which I have already hinted. They are not as readily perceived as the outward difficulties. Kepler’s lifework was possible only once he succeeded in freeing himself to a great extent of the intellectual traditions into which he was born. This meant not merely the religious tradition, based on the authority of the Church, but general concepts on the nature and limitations of action within the universe and the human sphere, as well as notions of the relative importance of thought and experience in science.

He had to rid himself of the animist approach in research, a mode of thought oriented toward ulterior ends. He first had to recognize that even the most lucidly logical mathematical theory was of itself no guarantee of truth, becoming meaningless unless it was checked against the most exacting observations in natural science. But for this philosophical orientation Kepler’s work would not have been possible. He does not speak of it, but the inner struggle is reflected in his letters. Let the reader watch out for remarks concerning astrology. They show that the vanquished inner foe had been rendered harmless, even though he was not yet altogether dead.

23. Marie Curie in Memoriam

AT A TIME WHEN
a towering personality like Mme. Curie has come to the end of her life, let us not merely rest content with recalling what she has given to mankind in the fruits of her work. It is the moral qualities of its leading personalities that are perhaps of even greater significance for a generation and for the course of history than purely intellectual accomplishments. Even these latter are, to a far greater degree than is commonly credited, dependent on the stature of character.

It was my good fortune to be linked with Mme. Curie through twenty years of sublime and unclouded friendship. I came to admire her human grandeur to an ever growing degree. Her strength, her purity of will, her austerity toward herself, her objectivity, her incorruptible judgment—all these were of a kind seldom found joined in a single individual. She felt herself at every moment to be a servant of society and her profound modesty never left any room for complacency. She was oppressed by an abiding sense for the asperities and inequities of society. This is what gave her that severe outward aspect, so easily misinterpreted by those who were not close to her—a curious severity unrelieved by any artistic strain. Once she had recognized a certain way as the right one, she pursued it without compromise and with extreme tenacity.

The greatest scientific deed of her life—proving the existence of radioactive elements and isolating them—owes its accomplishment not merely to bold intuition but to a devotion and tenacity in execution under the most extreme hardships imaginable, such as the history of experimental science has not often witnessed.

If but a small part of Mme. Curie’s strength of character and devotion were alive in Europe’s intellectuals, Europe would face a brighter future.

24. Max Planck in Memoriam

A MAN TO
whom it has been given to bless the world with a great creative idea has no need for the praise of posterity. His very achievement has already conferred a higher boon upon him.

Yet it is good—indeed, it is indispensable—that representatives of all who strive for truth and knowledge should be gathered here today from the four corners of the globe. They are here to bear witness that even in these times of ours, when political passion and brute force hang like swords over the anguished and fearful heads of men, the standard of our ideal search for truth is being held aloft undimmed. This ideal, a bond forever uniting scientists of all times and in all places, was embodied with rare completeness in Max Planck.

Even the Greeks had already conceived the atomistic nature of matter and the concept was raised to a high degree of probability by the scientists of the nineteenth century. But it was Planck’s law of radiation that yielded the first exact determination—independent of other assumptions—of the absolute magnitudes of atoms. More than that, he showed convincingly that in addition to the atomistic structure of matter there is a kind of atomistic structure to energy, governed by the universal constant h, which was introduced by Planck.

This discovery became the basis of all twentieth-century research in physics and has almost entirely conditioned its development ever since. Without this discovery it would not have been possible to establish a workable theory of molecules and atoms and the energy processes that govern their transformations. Moreover, it has shattered the whole framework of classical mechanics and electrodynamics and set science a fresh task: that of finding a new conceptual basis for all physics. Despite remarkable partial gains, the problem is still far from a satisfactory solution.

In paying homage to this man the American National Academy of Sciences expresses its hope that free research, for the sake of pure knowledge, may remain unhampered and unimpaired.

25. Paul Langevin in Memoriam

THE NEWS OF
Paul Langevin’s death dealt me a greater blow than most of the events of these fateful years, so fraught with disappointment. Why should this have been the case? Was his not a long life, crowded with fruitful creative work—the life of a man in harmony with himself? Was he not widely revered for his keen insight into intellectual problems, universally beloved for his devotion to every good cause, for his understanding kindness toward all creatures? Is there not a certain satisfaction in the fact that natural limits are set to the life of the individual, so that at its conclusion it may appear as a work of art?