In 1543 Nicolaus Copernicus published his book De revolutionibus orbium coelestium in which he announced what is now known as the Copernican system. The sun, according to this system, is at rest near the centre of the universe. The earth, on the other hand, has a double motion: it is rotating around its own axis in 24 hours and revolving around a point near the sun in one year.

This system had been known to Greek astronomy. It had been known and rejected. Aristarchus of Samos in the 3rd century BC seems to have put it in a shape most similar to that it received by Copernicus. Hipparchus, who lived about a hundred years later, and who is regarded as the greatest observer in ancient astronomy, rejected it. He offered another interpretation of planetary motion which was later known as the Ptolemaic system, getting its name from Ptolemy of Alexandria who about AD 150 wrote the classical textbook on ancient astronomy. If we want to understand modern astronomy it will be useful first to learn why, probably, the Greeks rejected what we think to be the correct system although they knew it and understood it very well.

That the earth is at rest is certainly the most natural view, if we start from everyday experience. But then the sky seems to be at rest too, and the earth seems to be a flat disk. As I said when speaking of the atomists, Greek science had abandoned these naive and natural views at an early time. The earth was recognized to be a sphere, surrounded by the sky as a sphere concentric with that of the earth. Since the stars including the sun, and less accurately, also the moon, complete their diurnal motions without an appreciable change of their relative positions it is a good starting point to think of them as fixed to the sphere of the sky. If we accept that, one thing is certain: there is a motion of the sky relative to the earth; one rotation is completed within 24 hours. But then the question may be asked: Is the earth at rest and the sky moving around it, or is the sky at rest and the earth turning within it? Or are both moving, perhaps? Their relative motion is the only thing we can see; what is the absolute motion?

Greek astronomers and philosophers were quite aware of this question. Several views were held; the final decision in which Aristotle and Ptolemy agree is that the earth is at rest. The main reason for this decision came from physics. The Greeks knew the size of the earth quite well. Hence they knew that the required motion of the earth—if we make the assumption that the sky is at rest—would have been more than 300 yards per second in the geographic latitude of Greece. Bodies which move far slower than that begin to tumble and you feel the oncoming air like a strong wind. In fact, the earth, moving with the speed mentioned, would go along under the air as under a terrible storm. Even more refined questions can be asked, e.g.: If you drop a stone from a high tower would it not fall down westward from the point vertically below the point where you dropped it; since while the stone is falling the earth has been moving on to the east? It is easy from a modern point of view to answer that the earth carries air, falling stones and everything with it. This idea had of course occurred to Greek thinkers as well. But they did not yet know the law of inertia, they did not even have an abstract concept of laws of nature. To them a body on which no force acts stays at rest. Hence they would have had to find out forces which can move thin air and freely falling stones with the earth. A force always meant a moving thing that exerted the force, if possible a moving thing contiguous with the moved one (just like the physicists of the 17th and 20th centuries AD the Greeks did not believe in action at a distance). You see easily that the famous principle, mostly quoted as “Occam’s razor” by modern English-speaking empiricists, the principle of not introducing more entities than necessary, was applied most sensibly by those Greeks who rejected the diurnal motion of the earth. Then, of course, they faced the question how the sky stands the stress of its far faster motion. But after all, the sky certainly consists of a material very different from all materials we know; its fast motion is only an additional wonderful quality added to the luminosity of its stars, to its evident lightness, and to its perfect circular shape.

But the real astronomical problem arose with the annual motion. To say that the sky moves as a whole is only a first approximation. Most stars, it is true, are fixed to it and are called fixed stars for that reason. But there are seven stars which wander their own paths between the others; these paths are not easily predicted and the seven stars are therefore rightly called planets, that is erratic stars. Five of them look like ordinary stars, though uncommonly bright and with a steady, untwinkling light: Mercury, Venus, Mars, Jupiter, Saturn. You see they bear the names of gods. The moon is to be added to them, wandering around the heavenly sphere within one month. The sun, too, is a planet. You cannot see the stars in its neighbourhood because of its own light, but at night you see what stars stand on the side of the sky opposite to the sun, and they change with the seasons. Hence it is easily seen that the year is just the period of one revolution of the sun.

As I said, the motions of the planets are somewhat erratic. They keep fairly well to one great circle on the sphere of heaven which is called the zodiac or the ecliptic. There again they wander on the average in the same direction but with different speeds, the moon revolving around the sky once in a month, Saturn once in 29 years. But besides that the five star-like planets act at certain times like dancers. They stop, turn backwards, complete a loop and go forward again. Thus Mercury and Venus dance around the sun; therefore Venus appears at times as morning star and at times as evening star, but never at midnight. Mars, Jupiter and Saturn move independently. But they make their loop once every year, precisely when their position in the sky is opposite the sun. Thus, in a way, the sun seems to be governing all the planetary motions.

How are we to explain that? Greek astronomers tried to give a rigorous mathematical theory which would explain or, as they used to say, save the phenomena. I omit the very ingenious earlier systems like that of 27 spheres rolling within each other, invented by Eudoxus. Aristarchus offered the Copernican solution. The sun is at rest in the centre of the system. In that sense it is not a planet but the governing body of the world. Its apparent annual motion is really a motion of the earth which revolves around the sun in one year. The earth is a planet like the other planets. The moon is a satellite of the earth, just moving around it without further complications. The five remaining star-like planets move around the sun. Mercury and Venus are closer to the sun than the earth. Hence they will never be seen at a great distance from the sun if they are observed from the earth. The three other planets are farther away from the sun than the earth. Hence there are times, roughly once a year, when the earth is situated between them and the sun. Seen from the earth they will then be located opposite to the sun. The earth is moving faster than the outer planets. Hence during these times when they are opposite the sun they must seem to move backwards to an observer who lives on the earth. I remember how, when I was a little child, I sat for the first time in a motor car and how surprised I was to see the trees of the roadside moving away from us with great speed. In fact, the loops in the apparent motions of the outer planets are inverted images of the annual motion of the earth around the sun. A slow advancement, superimposed on recurring loops, is precisely the relative motion between two bodies circling around the same centre at different speeds. Thus the explanation of the observed facts by this theory is excellent; more than that, we are accustomed to say in modern times that it is true.

But the Ptolemaic system is by no means inferior to the Copernican in explaining the apparent motions as far as I have described them. To the modern mind this can be made clear most easily by using the concept of relative motion. First consider the relative motion of the sun and the earth only. Aristarchus and Copernicus say that the sun is at rest and the earth revolves around it in a well-defined circle. There is no difficulty in assuming it to be the other way round, the earth being at rest and the sun being carried around in an exactly corresponding circle. Then imagine that the relative motions of the other five planets with respect to the sun are the same as in the Copernican system. But since now the sun is considered as moving, all the other planets will be carried around with the sun in addition to their own motion around the sun. Thus the five planets now have a double motion: around the sun and with the sun. The aspects of their orbits as seen from the earth will not be changed thereby; for the motion of the outer planets, i.e. with the sun, is seen from the earth as their annual loop, while their motion around the sun is interpreted in the Ptolemaic system as being the progression of the point around which they perform the loop. What we can observe, as long as we lack an absolute frame of reference, are only relative motions, and they are identical in the two systems.

Now this is a very modern way of describing the question (the specialists would say that I interpreted Tycho’s system in a relativistic manner, thus proving that a geocentric system, if adequately formulated, cannot be refuted by purely kinematic considerations at all). Greek and early modern astronomers used rather different terms, and hence they could think that there were real differences between the two systems. For instance, Ptolemy would of course not have taken the Copernican system as a starting-point, transforming it into his own by a change of the frame of reference. He started out assuming the earth at rest. The double motion of an outer planet then was described by saying that there is a circle around the earth on which an ideal point moves; and this ideal point is the centre of another circle, the so-called epicycle, on which the planet itself revolves. Thus the motion of the planet is like the motion of a point on the circumference of a little wheel.

I have so far always spoken of circles. In the modern view this is only approximately true; a better approximation is to speak of ellipses which are not very eccentric. But to ancient astronomy as well as to Copernicus it was a sacred truth that heavenly bodies had to move in exact circles. The circle was the most perfect line, and heavenly bodies were the most perfect bodies; in some views they were in fact held to be divine or angelic entities. Nobody in our time can imagine what a sacrilegious impossibility it would have been to assume these perfect bodies to move in an imperfect way. This forced restrictions upon those astronomers that made their systems less flexible than they might have been. Ptolemy had to compromise a great deal. In fact he composed his orbits from two superimposed circular motions. Further, he admitted that the centres of the circles of the planets were not in the sun, but in different places not far from the sun. Finally he had even to give up the idea of a constant angular velocity of the planet in its circle. All this was done in order to save the phenomena. It was the complication so well known to every scientist which arises when you try to adapt a theory, in which something is basically wrong, to carefully observed facts. But what was wrong was equally wrong in Copernicus and in Ptolemy; it was the veneration of the circle.

This, then, leads us back to the question: Why did the Greeks finally prefer Ptolemy, and why did the Moderns prefer Copernicus?

There are two arguments in favour of Ptolemy. The one is that the motion of the earth around the sun would have seemed quite as difficult to reconcile with physics as its motion around its own axis. The second is that if the earth moves, its true motion should be reflected not only in the apparent motions of the planets—the “loops”—but also in an apparent motion of the fixed stars. Nothing of the kind was observed. It is true, if you move on a road with high speed, neighbouring trees seem to move in the opposite direction very fast, but a distant mountain range will not change its apparent position for a long time. Thus, if the fixed stars do not reflect the motion of the earth they must be very far away. Today we know that the nearest fixed star is at a distance from the sun nearly 300,000 times the distance of the earth from the sun which, in its turn, is about 100 million miles. Again Occam’s razor can be invoked: Why introduce enormous distances if it is not necessary? And in Ptolemy’s system where the earth is at rest no reflection of a motion in the fixed stars is expected. The empirical proof of the existence of this reflected motion in the fixed stars was not produced before the middle of the 19th century.

Having understood these good scientific reasons which favour Ptolemy we will no longer wonder why the Copernican system was but slowly accepted in modern times. We may rather wonder why it was accepted at all. There were good astronomical reasons arising from more exact observations and from new theories on physics; I shall come to them immediately. But they were discovered by men who believed in Copernicus even before they had discovered them. I think what made Copernicus so attractive to people like, say, Kepler, Galileo, and Descartes, was in the beginning a psychological fact. The discussions that may have taken place among Greek astronomers were forgotten; Ptolemy was nearly all that was known. Ptolemaic astronomy and Aristotelian philosophy had become an entrenched, dogmatic system of thought, very different from the mood in which Aristotle or Hipparchus themselves had done their exciting researches. The Copernican system came as a completely new, original idea, daring to do away with the humbug of traditions; to accept it meant that men were then free to think about nature by themselves. New observations were made. They fitted in with the Copernican system very well. It was not always attempted to fit them into the Ptolemaic system equally well. (Tycho, it is true, tried precisely that.) Ptolemy’s system had become rather rigid, not so much owing to its essential structure as to its having been considered as true for so many centuries. Even a truth can be distorted by being publicly recognized for centuries; how much more so a still doubtful hypothesis. Thus the quiet revolutions of the planets around the sun offered the key-word of modern times, though in a very different sense: the word revolution.

It may be argued that the truly revolutionary discovery in modern theoretical astronomy was not the Copernican system but Kepler’s first law (1604). Kepler states that planets move in ellipses, the sun being situated in one focus of the ellipse. This discovery was made possible by the restless observations of Tycho Brahe. It was one of the lucky accidents in the history of science that the treasure of these long lists of numbers assembled during twenty years of unceasing work by the great Danish observer was entrusted to the hands of a scientific genius full of imagination, and at the same time scrupulous in the slightest detail, and of unswerving industry, like Johannes Kepler. Kepler believed in the mathematical perfection of the celestial spheres perhaps more intensely than any man before or after him has done. For that very reason he was not prepared to leave unexplained a difference less than eight minutes of arc between the theoretical and the observed motions of the planet Mars. Eight minutes of arc is the fourth part of the apparent diameter of the moon; this small distance between the predicted and the observed position of a planet had to be accounted for. Kepler sacrificed the idea of the circles after more than forty assumed theoretical orbits of Mars had failed to agree sufficiently well with the observations. He tried the ellipse as a working hypothesis, and he was struck by the discovery that it fitted the observations precisely. He then had enough mathematical imagination to think that an ellipse might be an element of a perfect system of celestial motions as well as a circle.

I am not going to describe here Kepler’s elaborate ideas about the harmony of the spheres. They are a work of mathematical art, perhaps somehow resembling Bach’s Kunst der Fuge; but they are not science in the modern sense and thus, in spite of their beauty, they are well and perhaps rightly forgotten. I want to ask another question: What has all that to do with cosmogony?

Since astronomy tries to describe the all-embracing structure of our world it seems natural that it should be the science predestined to produce cosmogonical theories. In fact, however, neither ancient nor early modern astronomy is in any known way connected with cosmogony. In antiquity I had to speak of philosophy when introducing cosmogonical theories, and even in modern times we will encounter cosmogony first in the ideas proposed by two philosophers: Descartes and Kant. Yet this is understandable. A precise observation of the motion of planets revealed only periodic movements without the slightest hint of an evolution, a growth or a decay, or any irreversible change. Mechanical causality seemed as remote from the celestial bodies as biological growth; heaven looked like a great finished work of art. The possibility of describing it in terms of invariable mathematical rules rendered its difference from all we know on earth even more striking, since everything under the moon is changing fast and in different ways from day to day. To Kepler astronomy was an adoration of the Creator by the medium of mathematics. In mathematical laws man, made in God’s image, rethinks God’s creative thought. This is the world of Timaeus and not of Democritus.

The necessary step before a scientific cosmogony could be tried was to bring heaven and earth together under the domination of common laws of physics. Mathematics had to be brought down to earth, mechanics up to heaven. This was done by the establishment of the science called celestial mechanics. This in its turn was achieved in three phases. Celestial motions had to be described exactly in mathematical terms: this was achieved by Kepler. Mechanics had to be established as a mathematical science; this was mainly done by Galileo. Mechanics had to be applied to celestial motions; this was Newton’s crowning work.

Speaking of Galileo Galilei I want to discuss two topics: his achievements in mechanics, and his fight for the Copernican system. In both fields I am more interested now in the questions of principle than in the details, which the interested reader can find in any sufficiently modern history of science.

By establishing the science of mechanics, Galileo brought mathematics down to the earth. In this he followed another great Greek thinker, Archimedes, whom he greatly admired. What Archimedes had done for statics he wanted to do for dynamics, for the theory of motion. This theory he did not leave to posterity in perfected form; later physicists, mainly Huygens and Newton, and even the great mathematicians of the 18th century, had still to add a great deal. Still, the decisive mental effort may be said to have been Galileo’s. Let us try to understand this mental effort.

Modern science has an historical myth of its own. It is the myth of Galileo. This myth asserts that in the dark ages the speculations of Aristotle, unfounded on observation, were held in high esteem, but that Galileo broke the path for science by describing the world as we really experience it. Like every myth, this myth expresses some truth; certainly it is right in its very high valuation of Galileo. But I think that it completely distorts the nature of Galileo’s real achievement. I should try to describe his achievement by saying exactly the opposite of the myth. Hence I say: The late middle ages are in no way dark ages, they are a time of high culture, bristling with intellectual energy. They adopted Aristotle because of his concern about reality. But the main weakness of Aristotle was that he was too empirical. Therefore he could not achieve a mathematical theory of nature. Galileo took his great step in daring to describe the world as we do not experience it. He stated laws which in the form in which he stated them never hold in actual experience and which therefore cannot be verified by any single observation but which are mathematically simple. Thus he opened the road to a mathematical analysis which decomposes the complexity of actual phenomena into single elements. The scientific experiment is different from everyday experience in being guided by a mathematical theory which poses a question and is able to interpret the answer. It thereby transforms the given “nature” into a manageable “reality”. Aristotle wanted to preserve nature, to save the phenomena; his fault was that he made too much use of common sense. Galileo dissects nature, teaches us to produce new phenomena; and to strike against common sense with the help of mathematics.

Take any simple example. Aristotle says that heavy bodies fall fast, light bodies fall slowly, very light bodies will even rise. This is exactly what everyday experience teaches us; a stone will fall fast, a sheet of paper more slowly, a flame will even rise. Galileo says that all bodies fall with equal acceleration and will therefore after equal time have acquired equal velocity. In everyday experience this is just wrong. Galileo goes on to tell us that in a vacuum bodies would really behave like that. Here he states the hypothesis that there is a vacuum, an empty space, again contradicting not only Aristotle’s philosophy but everyday experience. He was not able to produce a vacuum himself. But he greatly encouraged later 17th century physicists, like his pupil Torricelli, to make a vacuum; and in fact, when a sufficiently empty space was there, Galileo’s prediction proved true. Further, his assertion opened the way for a mathematical analysis of buoyancy and friction, the two forces responsible for the different behaviour of falling bodies of different specific weights, sizes, and shapes. Only if you know how a body would fall without these forces will you be able to measure them by their impeding effect.

The same considerations hold for the law of inertia. It says that a body on which no forces are acting will keep its state of rest or of moving on in a straight line with unchanging speed. (I shall not consider here the complication that Galileo himself never stated the law clearly in this form, but still considered the apparently straight lines in true fact to be segments of large circles; very soon after him this complication was eliminated by his own pupils.) Nobody has ever seen a body moving on in a straight line with unchanging speed. Of course this is due to the fact that always some forces act on a body. Then the law of inertia gives us a chance to define clearly what we mean by a force; according to Newton the force is proportional to the acceleration of the body on which it acts. The acceleration is the change of the velocity vector per unit time. Hence the force is defined as proportional to the deviation of the body from its inertial path. But what a scrutinizing analysis and what an intellectual daring was needed before Galileo could express such a law which at the same time was not clearly visible in any phenomenon and was contrary to all traditional views of causality! It was an axiom that no change would happen without a cause producing and maintaining it. Motion is a change of position. Hence there will be no motion without a cause, that is a force producing it. Now it is proposed that there is motion going on, though in the absence of any cause. Later thinkers like Descartes acquiesced in assigning a cause only to a change of state and defining the state of a body by its velocity. This is a clever trick; why did they not define the state by the position or the acceleration, or by the velocity of a constant circular motion? The law of inertia has its only justification in experience. Yet this experience is not present in any single case and certainly not in everyday experience. The empirical proof of the law is only in the comparison of the theory of mechanics as a whole with the realm of mechanical experiments as a whole.

I shall return to this epistemological problem in the second series of lectures. Now I want to point out only how this is connected with Platonism. Scientists of those times liked to invoke Plato against Aristotle in defence of their belief in mathematical laws. I think they were partly right in doing so. Compare the analysis of mathematics in Platonic terms which I tried to give in the fourth lecture. There we said: the true circle is not to be found in this world of the senses. Equally we can now say: the true inertial motion is not to be found in this world of the senses. True science must needs transcend what the senses tell us. But there the strict analogy comes to an end. To Plato only pure mathematics has any claim to be called true cognition, the real claim being reserved for the philosophical theory of the forms; of the sense world nothing more than a likely story can be told. To Galileo mathematical law holds strictly in nature and it can be discovered by an effort of the human mind which includes the performing of experiments. Nature, being complicated, does not always offer us the simple cases in which the one law we want to study is free from disturbances. But these disturbances, being caused by forces that obey their own laws, are equally open to mathematical study. Go on dissecting nature and you will be its master. The realism of modern science is neither a naive belief in the senses nor is it an aloof spiritual disdain of them.

There is a theological background to this attitude. The world of the senses is the world of nature in the Christian sense of the word. Platonism and Christianity both rely on what is beyond nature. But there is the difference that Plato’s God has not made matter; only the spiritual element in the world is divine; hence science, being a divine gift, does not apply to the material world in a strict sense. To Christians God has made everything. Hence man, made in his image, can understand all created things, that is, certainly the whole material world. The very idea that the Word has been made flesh, the dogma of Incarnation, shows that the material world is not too low to be accepted by God and hence to be understood by the light of reason given us by God. In his fight against the Inquisition for the Copernican system Galileo said clearly that we should read not only in the Book of Words given us by God for salvation but also in the Book of Nature given us by God in his creation.

But I want to speak about this famous fight in more detail. It has become another part of the Galilean myth. The myth says: “Galileo Galilei was a martyr for scientific truth versus medieval superstition.” Again, this myth expresses some aspect of truth. Again it rightly emphasizes the key rôle played by Galileo. Again it distorts the historical facts to such a degree that one is tempted to express them by contradicting nearly every single word of the sentence in which I expressed the myth. But here the situation is even more involved. We shall see reasons for turning the tables more than once.

Was Galileo a martyr? Martyr means witness. So far we can agree. He was a public witness. He spoke publicly for science with great fervour and great literary skill, and he spoke for a theory which we believe to be true. If science and the Church are considered to be opponents, then it might be added that he was a witness in the sense that perhaps no single act has in the end done more harm to the Church—not only to the Roman Church—than Galileo’s trial; it is even now one of the main arguments of anti-Christian propaganda.

But the word martyr has come to mean a witness who openly professes his faith even when threatened with death and whose decisive testimony is in his death for his faith. Galileo was threatened with less than death—it is true, he was once probably threatened with torture and he was then seventy years old—and he abjured the Copernican theory under this pressure. If we use the word in the full sense, Galileo was not a martyr.

The historical fact is that Galileo did not become a martyr because he never wanted to be a martyr. He was a man of the late renaissance who enjoyed life and wanted to enjoy life, who enjoyed science and scientific fame and wanted to do so, and who was a good and faithful Catholic who never thought of conflict with his Church. Probably he was a good enough Catholic and a good enough scientist to understand clearly that martyrdom is testimony for religious and ethical beliefs and not for scientific truth. For religious and ethical beliefs refer to human actions and can only be testified by human actions; scientific beliefs refer to facts and can only be proved by looking into the facts. What he wanted to do was to convince his Church of a fact. He wanted to convince them that the Copernican view was true, was relevant, and was in no way contrary to the Catholic faith. He tried to achieve that by writing books, by making people look through telescopes, by talking privately to cardinals and to the pope. When his book was condemned he was prepared to amend it, and when he was forced to abjure he hated the people who had brought him into this situation and never spoke of them later otherwise than with cold contempt; but we have no indication that he doubted at any moment that, if diplomatic means could not save him, he would have to submit to the inevitable and to pronounce his abjuration. It is certain that he thought at that moment: eppur si muove—“and still the earth moves”; it is equally certain that he did not say it aloud, for he was no fool.

But why, then, did he not convince his Church? I am afraid I must say: because he was not, after all, defending clear scientific truth against medieval backwardness. The situation was rather the opposite: he could not prove what he asserted, and the Church of his time was no longer medieval. To take the second point first: I think a modern biographer, G. de Santillana, is quite right in saying that the Roman Church of the early 17th century had gone so far on the way towards the modern totalitarian state that it could no longer admit of a latitude of thought which would have been possible in many medieval centuries and certainly in the renaissance. Galileo defended the then old-fashioned view that the dogmatic authority of the Church referred to those points which were relevant for salvation but not to conflicting views on nature. On the other hand, reading the documents of his trial I have had the impression that very few people in the Church were at all concerned whether he was really right or not. The Church was then rising from the blow of the Reformation; many doubtful questions of doctrine had been settled in the Council of Trent; the Jesuits had brought into the Church a far stricter idea of obedience; it was realized what strength the Church could gain from a monolithic adherence to dogma. The Thirty Years’ War in Germany was going on. The Bible was God’s word and it could not be easily reconciled with Copernicus—so why weaken the position of the Church in its fearful and perhaps final fight against the heretics by new internal quarrels on the motion of the earth? If we interpret it like that, the struggle between Galileo and the Inquisition was a struggle between two very modern powers: science and totalitarianism. Both sides believed in Christ, and probably each considered its side to represent the wheat, and the other side to represent the tares. Such is the ambivalence of history.

Each of the two sides was rather ambiguous in itself, and the opponent, with the keen eye of a clever adversary, saw its weakness, at least to some extent. Galileo’s weakness in representing science was, as I said, that he could not prove his case scientifically. I have just to remind you of what I said about the Copernican system in the earlier parts of this lecture in order to show that this was so. It is true, in Galileo’s hands the telescope had shown sunspots, mountains on the moon and a satellite system around Jupiter that looked like a minor model of Copernicus’ idea of the planetary system around the sun. Thus some ancient beliefs about the celestial bodies had been shattered, mainly the idea that they were very different from the earth, consisting of a stainless heavenly material, but no conclusive scientific proof for or against Copernicus could be deduced from those matters. The strongest argument then existing might have been that Kepler’s laws made sense in the Copernican system while their transformation into the language of Ptolemy would have been very awkward. But Galileo never used this argument; he does not seem even to have read Kepler’s rather ill-written book on this subject although Kepler had sent it to him. The good theologians of the Church like Cardinal Bellarmine and the Jesuit astronomers (some of whom may have been Copernicans at heart) were of course aware of this situation. In the first so-called trial of 1615 in which Galileo was treated with great courtesy the official position of Bellarmine was that the Copernican system might well be used as a mathematical hypothesis for an easier description of the motions of the planets; only it could not be asserted as true, because there was no proof for it and because Scripture taught us that it was wrong. Hypothesis here evidently means an assumption in which we do not believe but which is useful for the simplification of calculations. Galileo submitted to this formula, but only as a façon de parler. He brought upon himself the final blow of the second real trial of 1633 by writing a book, his famous Dialogues on the two principal world-systems, in which he shielded his true opinion in too transparent a manner behind the language of this formula.

Thus we may even say that the Inquisition did not demand more from Galileo than that he should not say more than he could prove. He was the fanatic in this case. But we have now to turn the tables once more: he was right in being the fanatic. Science is not advanced by meticulously sticking to what we can prove. Science is advanced by daring assertions which open the ways of their own proof or disproof. All I said about falling bodies and the law of inertia exemplifies this statement, and we cannot doubt that Galileo was aware of this methodological situation. Science needs faith as well as religion, both faiths, if they understand their own position, submitting to their relative ways of testing: religious faith in human life, scientific faith in further investigations.

But if Galileo understood the nature of science better than the Inquisition, did he understand the rôle of science in history? He stood for what I have called the historical position of reality in the last lecture. Man is free to investigate the truth about nature. This freedom should not be impeded. But what about the consequences of the scientific findings? We must try to do justice to the motivations of the Church. If Galileo undermined the authority of the Bible and of 1500 years of Church tradition, where would this undermining stop? This authority may have been a cover for many bad things; but after all it had made Europe. If I attribute a bit more of clairvoyance to Cardinal Bellarmine than he probably had—must he not have shuddered, thinking of the consequences of the oncoming age of unbridled research? A straight way of three hundred years leads from classical mechanics to the mechanics of the atom. A straight way of twenty years leads from the mechanics of the atom to the atom bomb. Whether this bomb will destroy the western civilization by which it has been made is not yet clear. If you had been a Cardinal in 1615, and if you had seen the future till 1964, and not further, would you have dared to take the risk of this development if there was a hope of stopping it?

What the Church did not know was that there was no hope of stopping it. Here, I think, is the ambiguity in the position of the Church. I think it would be absolutely unjust to deny that its attempt to establish a system of authority that would prevent dangerous developments was prompted by a true sense of responsibility for mankind. Can those who know the dangers best do better for their brethren in this time in which we wait for the last judgment than by protecting them from evil by every means open to prudence? Has God willed that we should pry into the mysteries of his creation before he wants to open them to us in a new world?

This is precisely what I have called conservative Christianity in the last lecture. Stoic Roman Emperors, when they accepted the offerings brought to their person and meant by their contemporaries to acknowledge their beneficial rule as the least of evils, may have thought similarly. The political rule of the Church transferred the Roman Empire to the spiritual scene. But Christian radicalism had refused to submit to the Divine Emperor in the first centuries; by its apparently foolish insistence on adoring only the true God it had drawn upon itself persecutions and conquered the world. The radicalism of modern science now refused to submit to those men who had taken a divine responsibility into their human hands; even when scientists still were Christians they could not believe that it was a Christian attitude to submit to prudential considerations rather than to truth. Let the consequences of our search for truth rest in the hands of God. I think that in their insistence on truth early Christians and modern scientists have something in common, differently though they interpret the meaning of truth.

However this may be, the Church had to learn that even if the world of science contained the tares, it was not possible to gather up the tares before the harvest.