[In the following excerpt, Reichenbach offers a brief overview of how the scientific treatment of the problems of space and time developed from Copernicus to Newton.]

… Men have been forming ideas concerning space and time since times immemorial, and curiously enough, have been writing and fighting about these things with the greatest interest, even fanaticism. This has been a strange strife, indeed, having little to do with economic necessities; it has always dealt with abstract things, far removed from our daily life and with no direct influence upon our daily activities. Why do we need to know whether the sun revolves around the earth or vice versa? What business of ours is it, anyway? Can this knowledge be of any use to us?

No sooner have we uttered these questions than we become aware of their foolishness. It may not be of any use to us, but we want to know something about these problems. We do not want to go blindly through the world. We desire more than a mere existence. We need these cosmic perspectives in order to be able to experience a feeling for our place in the world. The ultimate questions as to the meaning of our actions and as to the meaning of life in general always tend to involve astronomical problems. Here lies the mystery surrounding astronomy, here lies the wonder we experience at the sight of the starry sky, the wonder growing in proportion to our understanding of immense distances of space and of the stars' inner nature. Here is the source of scientific as well as popular astronomy.

These two branches have diverged in the course of their development. Astronomy, as a science, has come to forget its primitive wonder: instead, it approaches the realm of stars with sober research and calculation. This disenchantment with its subject-matter, which scientific study invariably entails, has permeated astronomy to a greater degree than the layman realizes. In observing the astronomers of today, how they measure, take notes, calculate, how little attention they pay to mysterious speculations, one may be surprised to find the wonderful structure of learning so cut and dry at a close range. Yet nothing is more wrong and more objectionable than the feeling of a heartbreaking loss, with which some people regard the vanishing mysticism of the skies. Although science may have destroyed a few naive fantasies, what she has put in their place is so immensely greater that we can well bear the loss.

It takes perseverance and energy, of course, to comprehend the discoveries of science; but whoever undertakes the study is bound to learn many more surprising things from it than a naive study of nature can disclose. Scientific astronomy has always exercised, in fact, a great influence upon everyday thinking and upon the popular conception of the universe. If it is difficult today to pronounce the name of Copernicus without thinking of a turning point of history, it is not only because the name is connected with a profound transformation in the science, but also because all our knowledge and thinking have been deeply affected by his discovery. The statement that the earth does not occupy the center of the world means more than an astronomical fact; we interpret it as asserting that man is not the center of the world, that everything which appears large and mighty to us is in reality of the smallest significance, when measured by cosmic standards. The statement has been made possible as a result of scientific development in the course of thousands of years, yet it definitely contradicts our immediate experience. It takes a great deal of training in thinking to believe in it at all. Nowadays we are no longer conscious of these things, because we have been brought up since childhood in the Copernican view of the world. However, it cannot be denied that the view belies the testimony of our senses, that every immediate evidence shows the earth as standing still while the heavens are moving. And who among us can declare in all seriousness that he is able to imagine the tremendous size of the sun or to comprehend the cosmic distances defying all earthly ways of measurement? The significance of Copernicus lies precisely in the fact that he broke with an old belief apparently supported by all immediate sensory experiences. He could do it only because he had at his disposal a considerable amount of accumulated scientific thought and scientific data, only because he himself had followed the road of disillusionment in knowledge before he glimpsed new and broader perspectives.

If we endeavor to trace … the development of the problems of space and time, beginning with the discovery of Copernicus and closing with the still less accessible theory of the Copernicus of our day, we have no other alternative than to apply hard scientific thought to every step of the way. We must add that the discoveries of modern science have been made possible only by the abundance of new scientific materials. Einstein's doctrines are by no means an outgrowth of astronomical reflections alone; they are grounded in the facts of the theory of electricity and light as well. We are able to comprehend them only insofar as we get acquainted with all of their sources. This derivation from several sources is characteristic of the theory of relativity. While the modern source gave rise to the special theory of relativity, the older sources provided the material for the construction of the general theory of relativity, in which the old and new knowledge became blended in a magnificent unity.…

The world-picture found by Copernicus goes back to the ancient Greeks. It was systematized about 140 A.D. by Ptolemy Claudius of Alexandria and outlined in his famous work Almagest. The most important feature of the Ptolemaic scheme of the universe is the principle that the earth is the center of the world. The heavenly globe revolves around it; and Ptolemy knew full well that it has the same spherical shape below the horizon, which it assumes above the horizon. In fact, Ptolemy knew even that the earth is a sphere. His proofs to this effect reveal a great knowledge of astronomy. He shows, first of all, the existence of curvature from north to south. As the Polar Star stands higher in the north and lower in the south, the surface of the earth must be correspondingly curved. The proof of the existence of curvature from west to east reveals even better observation. When the clocks are set by the sun in two places located west and east, and when an eclipse of the moon is thus observed, it will be seen at different times. However, the eclipse is a single objective event and should be seen everywhere at the same time. Hence we conclude that the clocks at the two places are not in accord. This can be accounted for by the curvature of the earth in the west-east direction: the sun passes the line of the meridian at different moments in different places.

In spite of the recognition of the spherical shape of the earth, Ptolemy was far from admitting its movement. He contended, on the contrary, that it was impossible for the earth to be moving at all, either in a rotating or in a progressive manner. As far as the former is concerned, he admitted the possibility of such an opinion, as long as the movement of the stars was considered. However, when we take into consideration everything that happens around us and in the air, this view—so he argues—becomes obviously absurd. For the earth, during its rotation, would have to leave the air behind. Objects in the atmosphere, such as flying birds, not being able to follow the rotation, would have to be also left behind. A progressive motion of the earth is equally impossible for, in that case, the earth would leave the center of the heavenly sphere, and we would see by night a smaller part of the sphere and by day a larger one.

One can see from these arguments that the great astronomer has devoted much serious thought to the problem. In the light of his rather limited knowledge of mechanics and of the heavenly spaces, his reasoning must have seemed quite conclusive. As far as his last objection was concerned, he could not have suspected that the interstellar distances were so great as to make the lateral shift of the earth completely unnoticeable.

The planets are characterized, according to Ptolemy, by common movements. Their path, as observed in the sky, is determined by superimposed circular orbits. As a result, there arise the so-called "epicycles." One must admit that Ptolemy has deeply understood the nature of planetary movements. When one gets acquainted with the Copernican conception, one discovers the facts revealed behind Ptolemy's epicycles: the loop of the planets' course mirrors their double motion as regards the earth. In the first place, they move in a circle around the sun, and in the second place, this movement is observed from the earth which, in its turn, revolves around the sun.

The Ptolemaic conception of the universe dominated the learned people's minds for more than one thousand years. The man who undermined this firm tradition—Nicholas Copernicus—required great independence of thought as well as great scientific knowledge, for only an insight into the ultimate relations of nature could give him the ability to discern new approaches to truth.

The canon of Frauenburg was long known as a learned astronomer before his new ideas were presented; he had studied in Italy all branches of science, he had acted as doctor and church administrator in his home town, and his astronomic knowledge was so well recognized that in 1514 he was asked by the Lateran Council for his opinion on questions of calendar reform. His new ideas concerning the system of the universe were formed, in their essence, at the age of 33. However, he did not promulgate them at that time, but devoted the following years to a thorough elaboration and demonstration of his theories. Only excerpts of his doctrine were published during his lifetime. His main work entitled Of the Rotation of Celestial Bodies appeared only after his death in 1546. He read the proofs only on his death-bed and thus failed to notice that his friend Osiander supplied the work with a foreword which contained a cautious compromise with the opinions of the Church.

If we examine the proofs given by Copernicus of his new theory, we find them quite insufficient from the point of view of present-day knowledge. He was able, in fact, to cite as a distinct advantage only the greater simplicity of his system. He regards it as improbable that the stars move with great speed in their large orbits and finds it more likely that the earth rotates on its axis, so that the speed of motion in each particular point is considerably smaller. Against Ptolemy's objection to this he urges that Ptolemy considered the rotating movement of the earth as implying force, whereas it is simply natural; its laws differ completely from those of a sudden jerky movement. All of this is certainly inconclusive. We know today that Newton's theory contains the first real proof of the Copernican conception of the universe. But it seems that new ideas are able to gain foothold by the sheer power of their inherent truth long before their objective verification has been obtained.

On the other hand, it is very important to acknowledge that the Copernican theory offers a very exact calculation of the apparent movements of the planets and that the tabulations (the so-called "Ephemerides") accompanying it are far superior to the older ones. Here lies one of the reasons which led the scientists to accept the Copernican system, even though it must be conceded that, from the modern standpoint, practically identical results could be obtained by means of a somewhat revised Ptolemaic system. Furthermore, Copernicus calculated quite accurately the radii of the planetary orbits (within less than 1%). In fact, he knew already that the sun must be slightly off the center of the solar system, for an assumption to the contrary led to estimable discrepancies.

Yet there was still a long way from this discovery to the recognition of the elliptic shape of the orbits; any conclusive evidence to this effect required above all better astronomic instruments. In this important connection, we must consider Tycho Brahe who is less prominent as a theoretician than as a builder of outstanding instruments. Brahe was able to work for many decades under the protection of the Danish king. He built the castle Uranienburg on an island, to which was attached a large settlement where precise instruments were prepared for him in special plants. It is amazing how the precision of instruments was increased in this manner. For instance, Copernicus had to be satisfied with measurements within 10' of the arc. This corresponds approximately to an angle covered by a five-pence piece at a distance of six meters. Tycho increased the precision to within half a minute of the arc. This angle would be enclosed by the same coin at a distance of 120 meters. With the instruments of today, of course, angles can be measured within one hundredth of a second of the arc. The coin would have to be placed at a distance of 360 kilometers to enclose such a small angle.

This precision we owe mainly to the use of the telescope. Tycho had to work without a telescope. One of his sextants with which he conducted his observations of Mars still stands in the Prague observatory, where Tycho, exiled from Denmark, spent the last years of his life (c. 1600).…

… By means of such a crude-looking apparatus, Tycho found the data on which modern astronomy is historically resting.

The man who continued Tycho Brahe's work was his assistant Johann Kepler whose name surpasses by far that of his master. Kepler carried on his observations with the sextants of Tycho. He determined the course of the motion of Mars by means of so many individual observations that he was able to pronounce it with certainty as elliptical in shape. He discovered through mere measurement also other laws of planetary motion, called after him "the Kepler's laws." One must admire the strength of character of this man, which manifests itself in his zeal for factual accuracy. Kepler was at first a mystic and speculative dreamer, disinclined to sober observations. He concentrated in his early works on searching for strange mathematical 'harmonies' of nature, and such a goal inclines one to distort facts rather than to establish them. It remains true, however, that Kepler has accomplished much more for his own aim by his zeal for factual accuracy than by his speculations. He himself expresses this thought. In his work entitled Harmony of the World, which appeared in 1619, he writes concerning the discovery of his laws: "At last I have found it, and my hopes and expectations are proven to be true that natural harmonies are present in the heavenly movements, both in their totality and in detail—though not in a manner which I previously imagined, but in another, more perfect, manner … If you forgive me, I shall be glad; if you are angry, I shall endure it. Here I cast my dice and write a book to be read by my contemporaries or by the future generations. It may wait long centuries for its reader. But even God himself had to wait for six thousand years for those who contemplate his work."

We must not forget, however, that, though the astronomic picture of the universe was considerably advanced, in regard to precision, by Kepler's discoveries, nevertheless, that world-view, though basically Copernican, differed very considerably from our Copernican idea of the world. Copernicus as well as Kepler was of the opinion that the solar system virtually exhausted the space of the universe. The stars, according to them, were tiny dots in the sphere of heavenly matter, which circumscribed the whole of space. When Giordano Bruno expressed his thoughts on the infinity of the firmament and maintained that fixed stars were independent solar systems, Kepler proceeded immediately to combat the idea. How difficult it must have been to climb the stairs leading to our present-day knowledge!

Astronomy made its decisive advance over Kepler's knowledge again through an improvement in the means of observation—through the invention of the telescope. The great merit of having made the first serviceable telescope and of having used it for the observation of the sky belongs to Galileo; though not the original inventor of the telescope, he constructed it after hearing of such instruments. He directed his telescope toward the moon and recognized the spots on the moon, on account of their jagged outline and shifting illumination, as tremendous mountains (1610). He pointed it towards Venus and saw its sickle-like shape, similar to that of the moon, which it periodically assumes as a result of receiving light from the sun. He directed the telescope towards Saturn and saw its 'triple' figure the details of which he could not yet discern. He directed it towards Jupiter and saw its satellites (the four brighter ones) designated by him as "medizeic planets."

All these facts, with their enlargement and enrichment of the Copernican world, must have greatly astonished his contemporaries. It also provoked, to be sure, the opposition of the old school of scientists who saw their tenets grounded in Aristotle seriously endangered. Galileo's most precarious position can be best envisaged from a letter written by him to Kepler: "I am very grateful that you have taken interest in my investigations from the very first glance at them and thus have become the first and almost the only person who gives full credence to my contentions; nothing else could be really expected from a man with your keenness and frankness. But what will you say to the noted philosophers of our University who, despite repeated invitations, still refuse to take a look either at the moon or the telescope and so close their eyes to the light of truth? This type of people regard philosophy as a book like Aeneid or Odyssey and believe that truth will be discovered, as they themselves assert, through the comparison of texts rather than through the study of the world or nature. You would laugh if you could hear some of our most respectable university philosophers trying to argue the new planets out of existence by mere logical arguments as if these were magical charms." Galileo relates how another scientist refused to take a look through the telescope "because it would only confuse him." The tragic fate of Galileo, caused by such antagonism, is well known. He had to pay with many years of incarceration and imprisonment for his sponsorship of the Copernican theory.

Another achievement of Galileo had apparently no direct connection with astronomy; but this connection was discerned soon enough. Galileo was the first man to investigate the laws of falling bodies. He has thereby established the basic laws on which the science of mechanics was destined to grow. The apparatus he built was quite primitive. For instance, he had no watch in the modern sense of the word, but had to measure time by means of water running out of a vessel. In spite of everything, he was able to determine the relationship between the distance and the time of the fall, and also the law of acceleration. He also discovered the fact—a most surprising fact for his day—that all bodies fall equally fast. Finally, he formulated the basic law of motion, named after him: that every body unaffected by external forces moves in a straight line at a uniform speed, and that this motion can never stop by itself. Although these laws seem to be merely bits of factual information, nevertheless they signify an extraordinary progress as compared to the preceding era. There was no inclination at that time to collect data. It was believed that all one wanted to learn could be disclosed by speculative thinking. Galileo's great achievement was that he resorted to direct investigation of nature. Moreover, the facts he discovered were destined to attain a significance far beyond their own realm, namely, when Newton constructed the mechanics of heavens on them.

Fate allotted to the English physicist Isaac Newton (1643-1727) an outstanding role in the history of the natural sciences of the described period. He was the great unifier who combined the individual discoveries of Copernicus, Kepler and Galileo into one magnificent system. His intellectual achievement cannot be estimated too highly. With the vision of a genius he realized that the power of gravitation perceived by Galileo in his doctrines concerning falling bodies had a significance far transcending the region of the earth, that this power of attraction constituted a property of all mass, and that it determined the planets' behavior across cosmic distances. This far-reaching insight into the nature of things was accompanied by Newton's great caution in scientific investigation. He started with the correct premise that the power of attraction must diminish with distance. He then calculated what the magnitude of this power, already estimated by Galileo on the surface of the earth, could be at the distance of the moon. Next he computed the length of time required for the revolution of the moon around the earth, if this gravitational power was indeed responsible for the motion of the moon. All this was a magnificent elaboration of the original idea. Unfortunately, luck was against Newton, and his investigations resulted in anything but agreement with facts. Yet nothing shows better the greatness of the scholar's character than his conduct in the face of failure: he put his calculations away in a closet without publishing a single word concerning his profound meditations (1666). Only twenty years later could the mistake be explained. The length of the earth's radius, taken by Newton as the basis of his calculations, had been inexact; new estimates on the astronomers' part gave a new measurement with which Newton's reflections about the moon proved to be in full accord.

The mechanics of Newton has thus received confirmation, and it must have seemed like a magic key to his contemporaries. His theory transformed the fundamental facts of the preceding centuries into a uniform system, including the Copernican theory of the heliocentric motion of the planets, Kepler's laws concerning their orbits, and Galileo's laws of falling bodies in a gravitational field. Kepler did not live to greet this triumph of thought; no doubt, he would have rejoiced over this proof of the harmony of cosmic motions. The Copernican conception of the universe was at last scientifically established, insofar as the laws underlying it stood revealed. Up to that time the Copernican conception of the universe, as compared to the Ptolemaic conception, could justify itself only by its claim of representing the world-picture in simpler terms. But now, with the addition of Newtonian mechanics, it became the only acceptable one. Its real merit was made explicit: the Copernican conception of the world provided an explanation of natural phenomena, a cosmic order governed by laws. It was the destiny of the Western mind to absorb this worldview which so much corresponded to its innate tendencies of thought.

Thus ends the first period of new physics; and with it has come a new method of inquiry to dominate the natural sciences ever since. The collection of facts is the starting point of investigation; but it does not mark its end. Only when an explanation comes like a bolt of lightning and melts separate ideas together in the fire of thoughtful synthesis, is that stage reached which we call understanding and which satisfies the seeking spirit.…