Astronomy in Relation to the Other Scientific Disciplines. Lecture 13.
Thursday, February 5, 2015
The Ptolemaic Astronomical System and the Copernican System
Astronomy in Relation to the Other Scientific Disciplines. Lecture 13.
Rudolf Steiner, Stuttgart, January 13, 1921:
My Dear Friends,
In popular works, as you are well aware, the evolution of astronomical ideas is thus presented: Until Copernicus, they say the Ptolemaic system was prevailing. Then through the work of Copernicus the system we accept to this day — though with modifications — became the intellectual property of the civilised world. Now for the thoughts we shall pursue in the next few days it will be most important for us to be aware of a certain fact in this connection. I will present it simply by reading, to begin with, a passage from Archimedes. Archimedes describes the cosmic system or starry system as conceived by Aristarchus of Samos, in these words: “In Aristarchus' opinion the Universe is far, far greater. He takes the stars and the Sun to be immobile, with the Earth moving around the Sun as centre. He then assumes that the sphere of the fixed stars, — its centre likewise in the Sun, — is so immense that the circumference of the circle, described by the Earth in her movement, is to the distance of the fixed stars as is the centre of a sphere to the surface thereof.”
Taking these words to be a true description of the spatial World-conception of Aristarchus of Samos, you will admit: Between his spatial picture of the Universe and ours, developed since the time of Copernicus, there is no difference at all. Aristarchus lived in the third century before the Christian era. We must therefore assume that among those who like Aristarchus himself were leaders of cultural and spiritual life in a certain region at that time, fundamentally the same spatial conception of the world held good as in the Astronomy of today. Is it not all the more remarkable that in the prevailing consciousness of men who pondered on such things at all, this world-conception — heliocentric, as we may call it, — thereafter vanished and was supplanted by that of Ptolemy? Till, with the rise of the new epoch in civilisation, known to us as the Fifth post-Atlantean, the heliocentric idea comes forth again, which we have found prevailing among such men as Aristarchus in the 3rd Century B.C.! (For you will readily believe that what held good for Aristarchus held good for many people of this time.) Moreover if you are able to study the evolution of mankind's spiritual outlook — though it is difficult to prove by outer documents — you will find this heliocentric conception of the World the more widely recognised by those who counted in such matters, the farther you go back from Aristarchus into more distant times. Go back into the Epoch we are wont to call the Third post-Atlantean, and it is true to say that among those who were the recognised authorities the heliocentric conception prevailed during the Epoch. The same conception prevailed which Plutarch says was held by Aristarchus of Samos. Plutarch moreover described it in such terms that we can scarcely distinguish it from that of our own time.
This is the noteworthy fact. The heliocentric conception of the world is there in human thought, the Ptolemaic system supplants it, and in the Fifth post-Atlantean Epoch it is re-conquered. In all essentials we may aver that the Ptolemaic system held good for the Fourth post-Atlantean Epoch and for that alone. Not without reason do I bring this in today, after speaking yesterday of an ‘ideal point’ in the evolution of the Kingdoms of Nature. As we shall see in due course, there is an organic relationship between these diverse facts. But we must first enter more fully into the one adduced today.
What is the essence of the Ptolemaic cosmic system? The essence of it is that Ptolemy and his followers go back again to the idea of an Earth at rest, with the fixed-star Heavens moving around the Earth; likewise the Sun moving around the Earth. For the movement of the planets, the apparent forms of which we have been studying, he propounds peculiar mathematical formulae. In the main, he thinks in this way: Let this be the Earth (Fig. 1). Around it he conceives the Heaven of fixed stars. Then he imagines the Sun to be moving in an eccentric circle round the Earth. The planets also move in circles. But he does not imagine them to move like the Sun in one circle only. No; he assumes a point (Fig. 1) moving in this eccentric circle which he calls the ‘Deferent’, and he makes this point in its turn the centre of another circle. Upon this other circle he lets the planet move, so that the true path of the planet's movement arises from the interplay of movements along the one circle and the other. Take Venus, for example. Says Ptolemy: around this circle another circle is rotating; the centre of the latter circle moves along the former. The actual path of Venus would then be, as we should say, a resultant of the two movements. Such is the planet's movement around the Earth; to comprehend it we must assume the two circles, the large one, called the “deferent”, and the small one, know as the ‘epicyclic’ circle. Movements of this kind he attributes to Saturn, Jupiter, Mars, Venus and Mercury, only not to the Sun. The Moon he conceives to move in yet another small circle, — an epicyclic circle of its own.
These assumptions were due to the Ptolemaic astronomers having calculated with great care the positions on the Heavens at which the planets were at given times. They computed these circling movements so as to understand the fact that the planets were at given places at given times. It is astonishing how accurate were the calculations of Ptolemy and his followers, — relatively speaking at least. Draw the path of any planet — Mars, for instance — from modern astronomical data. Compare this 'apparent path', so-called, of Mars, drawn as observed today, with the path derived from Ptolemy's theory of deferent and epicyclic circles. The two curves hardly differ. The difference, relatively trifling, is only due to the still more accurate results of modern observation. In point of accuracy these ancients were not far behind us. That they assumed this queer system of planetary movements, which seems to us so complicated, was not due therefore to any faulty observation. Of course the Copernican system is simpler, — that will occur to everyone. There is the Sun in the midst, with the planets moving in circles or ellipses round it. Simple, is it not? Whereas the other is very complicated: a circular path superimposed upon another circle, and an eccentric one to boot.
The Ptolemaic system was adhered to with a certain tenacity throughout the Fourth post-Atlantean epoch, and we should ask ourselves this question: Wherein lies the essential difference in the way of thinking about cosmic space and the contents of cosmic space, such as we find it in the Ptolemaic school on the one hand and in Aristarchus and those who thought like him in the other? What is the real difference between these ways of thinking about the cosmic system? It is difficult to describe popularly, for many things seem outwardly alike, whilst inwardly they can be very different. Reading Plutarch's description of Aristarchus' system, we shall say: This heliocentric system is fundamentally no different from the Copernican. Yet if we enter more deeply into the spirit of the Aristarchian world-picture, we find it different. Aristarchus too, no doubt, follows the outer phenomena with mathematical lines. In mathematical lines he represents to himself the movements of the heavenly bodies.
The Copernicans do likewise. Between the two there intervenes this other system — the strange one of the Ptolemaic school. Here it cannot be said that the forming of mathematical pictures coincides in the same way with what is observed. The difference in this respect is all-important. In the Ptolemaic school, the mathematical imagination does not directly rest upon the sequence of observed points in space. It is rather like this: In order ultimately to do justice to them it goes right away from the observed phenomena and works quite differently, not merely putting the observed results together. Yet in the end it is found that if one does admit the mathematical thought-pictures of the Ptolemaic school, one thereby comprehends what is observed.
Suppose a man of today were to make a model of the planetary system. Somewhere he would attach the Sun, then he would draw wires to represent the orbits of the planets; he would really think of them as representing the true orbits. In purely mathematical lines he would comprise the logic of the planets' paths. Ptolemy would not have done so. He would have had to construct his model somewhat in this fashion (Fig. 2). Here would have been a pivot, fixed to it a rod, leading to the rim of a rotating wheel, upon this again another wheel rotating. Such would be Ptolemy's model. The model he makes, the mathematical picture living in his thought, is not in the least like what is outwardly seen. For Ptolemy the mathematical picture is quite detached from what is seen externally. And now, in the Copernican system we return to the former method, simply uniting by mathematical lines the several places, empirically observed, of the planet. These mathematical lines correspond to what was there in Aristarchus' system. Yet is it really the same? This is the question we must now be asking: Is it the same?
Bearing in mind the original premises of the Copernican system and the kind of reasoning by which it is maintained, I think you will admit: It is just like the way we relate ourselves, mathematically, to empirical reality in general. You may confirm it from his works. Copernicus began by constructing his planetary system ideally, much in the same way as we construct a triangle ideally and then find it realised in empirical reality outside us. He took his start from a kind of a priori mathematical reasoning and then applied it to the empirically given facts.
What then is at the bottom of this complicated Ptolemaic system, to make it so complicated? You remember the well-known anecdote. When it was shown to Alphonso of Spain, he from his consciousness of royalty declared: Had God asked his advice at the Creation of the World, he would have made it more simply than to require so many cycles and epicycles.
Or is there something in it after all — in this construction of cycles and epicycles — related to a real content of some kind? I put the question to you: Is it only fantasy, only a thing thought-out, or does this thought out system after all contain some indication that it relates to a reality? We can only decide the question by entering into it in greater detail.
It is like this: Suppose that taking your start from Ptolemaic theories, you follow the movements, or, as we should say, the apparent movements of the Sun, and of Mercury, Venus, Mars, Jupiter, and Saturn: to begin with you will have angular movements of a certain magnitude each time. You can therefore compare the movements indicated by the successive positions of these heavenly bodies in the sky. The Sun has no epicyclic movement. The epicyclic daily movement of the Sun is therefore zero. For Mercury on the other hand we must put down a number, representing his daily movement along his epicyclic circle, which we shall them compare with that of other planets. Let us call the epicyclic daily movements —
x3 + x’ = y
x4 + x ’ ’ = y
x5 + x’ ’ ’ = y.
Now take the movements Ptolemy attributes to the centres of the epicycles along their different circles. Let the daily movement be y for the Sun. It is then remarkable that if we seek the corresponding value for Mercury we get precisely the same figure. The movement of the centre of Mercury's epicycle equals the movement of the Sun. We must write y again, and so for Venus. This then holds good of Mercury and Venus. The centres of their epicycles move along paths which correspond exactly to the Sun's path, — run parallell to it. For Mars, Jupiter, and Saturn, on the other hand, the movements of the centres of the epicycles are diverse, — shall we say
x for Mars,
x for Jupiter,
x for Saturn.
Yet the remarkable fact is that by taking the corresponding sums, namely x3 + x + x4 + x , x5 _ x, adding the movements along the several epicycles to the movements of the centres of these epicycles, — I get the same magnitude for all three planets. Nay more, it is the identical which we obtained just now for the movement of the Sun and of the centres of the epicycles of Mercury and Venus —
x3 + x = y,
x4 + x = y,
x5 + x = y.
A noteworthy regularity, you see. This regularity will lead us to attribute a different cosmic significance to the centres at the epicycles of Venus and Mercury, the planets near the Sun as they are called, and of Jupiter, Mars, Saturn, etc., called distant from the Sun. For the distant planets, the centre of the epicycle has not the same cosmic meaning. Something is there by virtue of which the whole meaning of the planet's course is different than for the planets near the Sun.
The fact was well-known in the Ptolemaic school and helped determine the whole idea — the peculiar construction of cycles and epicycles in the mind, detached from the empirically given facts. This very fact obliged them, as they saw it, to propound their system, and is implicit in it. The human being of today would scarcely recognise it there; he listens more or less obtusely when told how they set up their cycles and epicycles. To their way of thinking, on the other hand, the thought was palpable and eloquent: If Mercury and Venus have the same values as Jupiter, Saturn and Mars, yet in another realm, we cannot treat the matter so simply, with an indifferent circling motion or the like. A planet, in effect, is of significance not only within the space it occupies but outside it. We have not merely to stare at it, fixing its place in the Heavens and in relation to other celestial bodies; we must go out of it to the centre of the epicycle. The centre of its epicycle behaves in space even as the Sun does. Once more, translated into modern forms of speech, the Ptolemaists said: For Mercury and Venus the centres of the epicycles so far as movement is concerned behave in cosmic space as the Sun itself behaves. Not so the other planets — Mars, Jupiter and Saturn. They claim another right. In effect, only when we add their epicyclic movements to their movements along the deferent, only then do they grow like the Sun in movement. They therefore are differently related to the Sun.
This difference of behaviour in relation to the Sun was what they really built on in the Ptolemaic system. This among others was an essential reason for its development. Their aim was not merely to join the empirically given places in the Heavens by mathematical lines, building it all into a system of thought in this way. They were at pains to build a thought-system on another basis — and what is more, a piece of true knowledge underlay their efforts; it is undeniable if we go into it historically. Modern man naturally says: We have advanced to the Copernican system, why bother about these ancient thinkers? He bothers not, but if he did, he would perceive that this was what the Ptolemaists meant: 'Truth is', they said to themselves, 'Mars, Jupiter and Saturn have quite another relation to Man than Mercury and Venus. What corresponds to them in Man is different.' Moreover they connected Jupiter, Saturn and Mars with the forming of the human head, Venus and Mercury with the forming of what is beneath the heart in man. Rather than speak of the head, perhaps I should put it in these words: they related Jupiter, Saturn and Mars with the forming of all that is above the heart; Venus and Mercury with what is situated below the heart in man. The Ptolemaists did indeed relate to man what they were trying to express in their cosmic system.
What underlay it really? To gain true judgement on this question, my dear friends, I think you should read and mark the inmost tone and essence of my Riddles of Philosophy, in writing which I tried to show how very different was the way man met the world in his life or knowledge before the 15th century and after. Since then, if I may use this image, we unpeel ourselves from the world, — we detach ourselves completely. Before the 15th century we did not do so. I must admit, at this point it is difficult to make oneself understood in the modern world. Man of today says to himself: “I think thus and thus about the world. I have my sense perceptions, thus or thus. In modern times we have become enlightened; the men of former times were simple, with many childish theories.” And as to our enlightenment and their simplicity, the modern man's idea of it amounts to this, or something very like it: "If only they had tried hard enough, they might have grown just as clever as we are. But it took time, this eduction of mankind; it evidently had to take some time for men to get as enlightened as they afterwards became.”
What is today left unconsidered is that man's very seeing of the world, his seeing and his contemplating, his whole relation to the world was different. Compare the different stages of it, described in my Riddles of Philosophy. Then you will say: Through the whole time from the beginning of the Fourth Epoch until the end, the sharp distinction we now have, of concept and idea on the one hand and sense-perceived data on the other, did not exist. They coincided, rather. In and with the sensory quality, men saw the quality of thought, the idea. And it was ever more so the farther we go back in them. In this respect we need more real notions as to the evolution of mankind. What Dr. Stein has written for example in his book, upon the essence of sense-perception, is true of our time and excellently stated. If he had had to write a dissertation on this subject in the School of Alexandria in olden time, he would have had to write very differently of sense-perception. This is what people of today persist in disregarding; they will have everything made absolute.
And if we go still farther back, for example into the time when the Egypto-Chaldean Epoch was at its height, we find an even more intensive union of concept and idea with sense-perceptible, outward and physical reality. It was from this moreover — from this more intensive union — that the conceptions arose which we still find in Aristarchus of Samos. They were already decadent in his time; they had been entertained even more vividly by his predecessors. The heliocentric system was simply felt, when with their thoughts and mental pictures men lived in and with the outer sense-perceptible reality. Then, in the Fourth post-Atlantean Epoch, man had to get outside the sense-world; he had to wean himself of this union of his inner life with the sense-world. In what field was it easiest to do so? Obviously, in the field where it would seem most difficult to bring the outer reality and the idea in the mind together. Here was man's opportunity to wrest himself away — in his life of ideas — from sense-impressions.
Look at the Ptolemaic system from this angle; see in it an important means toward the education of mankind; then only do we recognise the essence of it. The Ptolemaic system is the great school of emancipation of human thoughts from sense-perception. When this emancipation had gone far enough — when a certain degree of the purely inner capacity of thought had been attained — then came Copernicus. A little later, I may add, this attainment became even more evident, namely in Galileo and others, whose mathematical thinking is in the highest degree abstracted and complicated. Copernicus presented to himself the facts of which we have been speaking — the observation of the equality of y at diverse points in the equation — and, working backward from these mathematical results, was able to construct his cosmic system. For the Copernican system is based on these results. It represents a return, from the ideas now abstractly conceived, to the external, physically sense-perceptible reality.
It is most interesting to witness how, in the astronomical world-picture above all, mankind gets free of the outer reality. And in perceiving this, my dear friends, we also gain a truer estimate of the returning pathway, — for in a wider sense we must return. Yet how? Kepler still had a feeling of it. I have often quoted his rather melodramatic saying, to the effect: I have stolen the sacred vessels of the Egyptian Temples to bring them back again to modern man. Kepler's planetary system, as you know, grew from a highly romantic conception of how the Universe is built. Indeed he feels it like a renewal of the ancient heliocentric system. Yet the truth is, the ancient heliocentric system was derived not from a mere looking outward with the eyes, but from an inner awareness, an inner feeling of what was living in the stars.
The human being who originally set up the cosmic system, making the Sun the centre with the Earth circling round it after the manner of Aristarchus of Samos, felt in his heart the influences of the Sun, felt in his head the influences of Venus and Mercury. This was experience, direct experience throughout the human being, and out of this the system grew. In later time this all-embracing experience was lost. Perceiving still with eyes and ears and nose, man could no longer perceive with heart or liver. To have perception from the Sun with one's heart, or from Jupiter with one's nose, seems like sheer madness to the people of today. Yet it is possible, and it is exact and true. Moreover one is well aware why they think it madness.
This living with the Universe, intensively and all-awarely, was lost in course of time. Then Ptolemy conceived a mathematical world-picture still with a little of the old feeling to begin with, yet in its essence already detached from the world. The earlier disciples of the Ptolemaic school still felt, though very slightly, that it is somehow different with the Sun than with Jupiter, for instance. Later they felt it no more. In effect the Sun reveals his influence comparatively simply through the heart. Jupiter, we must admit, spins like a wheel in our head — it is the whirling epicycle — while in a different sense, here indicated (Fig. 1), Venus goes through beneath our heart. In later Ptolemaic times, all they retained of this was the mathematical aspect, the figure of the circle: the simple circle for the Sun's path, and the more complicated for the planets. Yet in this mathematical configuration there was at least some remnant of relation to the human being.
Then even this was lost and the high tide of abstraction came. Today we must look for the way back, — to re-establish once again from the entire Man an inner relation to the Cosmos. We have not to go on from Kepler, as Newton did, into still further abstractions. For Newton put abstractions in the place of things more real; he introduced mass etc. into the equations — a mere transformation, in effect, yet there is no empirical fact to vouch for it. We need to take the other road, whereby we enter reality even more deeply then Kepler did. And to this end we must include in our ambit what after all is in its life connected with the rising of the stars across the Heavens, namely the Kingdoms of external Nature in all their variedness of form and kind.
Is it not worthy of note that we find a contrast between the superior planets so-called and the inferior, with the Earth-entity between the mineral and plant kingdoms along the one branch, the animal and man along the other? And, that in drawing the two branches of the forked line, we must put plant and mineral in simple prolongation, while animal and man must be so drawn as to show the formative process returning upon itself? (Fig. 3)
We have put two different kinds of things before us: on the one hand the paths of the epicycle-centres and of the points on the epicyclic circumference, revealing a quite different relation to the Sun for the superior and inferior planets respectively; on the other hand the prolongation of the plant-forming process speeding on into the mineral, while the animal-forming process turns back upon itself to become man. (The symbolism of our diagram is justified; as I said yesterday, to recognise it you need only make a study of Selenka's work.)
These two things side by side we put as problems, and we will try from thence to reach a cosmic system true to reality.