18 January 1921, Stuttgart
If we recall what I said yesterday about the opposite character of Earth and Sun, we shall perceive that in answering such questions it is all-important to follow up the empirical facts in the right way. We cannot form true ideas of what we see if we do not recognize from the outset that radical differences may be called for in the whole way we interpret what is seen in one case and in another. The phenomena that present themselves to us when looking at the so-called body of the Sun will only find their true interpretation if we start from such premises as we were indicating, for example, when we put this question: —
On Earth there are many phenomena the characteristic of which is that they work outward from the given center to the wide circumference, — out into cosmic space We interpret them accordingly. How must we then interpret similar phenomena — or rather, phenomena that seem superficially similar — when we are looking, with or with-out the help of optical instruments, towards the Sun? Truth is, the empirically observed phenomena will only reveal themselves in their true light if we then take our start from some such idea as this: whilst on the surface of the Earth an eruption or the like will naturally be interpreted as tending up and outward (Fig. 1a), a process on the Sun — a Sun-spot for example — must be interpreted rather as tending from without inward (Fig. 1b). Continuing this line of thought: Just as we have to imagine that if we went through and beneath the surface of the Earth we should get into dense matter, so shall we have to imagine that if we moved from outside the Sun towards the Sun's interior we should come into an ever more attenuated state of matter. And we may truly say: Look at the Earth and the whole way it is placed into the Universe. It manifests as so much ponderable matter in the Universe. Not so the Sun. Here we shall only come near the truth if we imagine that as we go from the circumference towards the interior we get ever mere remote from ponderable matter and ever more and more into the imponderable. We have precisely the opposite behavior as we draw near the middle point. The Sun must be conceived as a hollowing-out, shall we say, of cosmic matter, a hollow space, a hollow sphere, — a sphere enveloped by matter, — in contrast to the Earth where we have denser matter enveloped by more attenuated. As to the Earth, we think of air around it. Air is outside and denser matter inside. For the Sun it is the opposite; as we go inward we go from relatively denser matter into more attenuated and at long last into the very negation of matter whoever takes the phenomena with open mind and puts them all together will be obliged to recognize that this is so. The Sun is not only a more attenuated heavenly body, of a materiality less dense than earthly matter, but if we call the Earth's materiality positive, then in the Sun — in the Sun's interior — we shall have negative matter in a certain sense. We only do justice to the phenomena if we conceive that there is negative matter in the inner space of the Sun.
Now, my dear friends, as compared with positive matter negative matter is suctional. Positive matter exerts pressure, negative suction. And if you now conceive the Sun as a collection of suctional force, you need no further explanation of Gravitation. This is the explanation, Now think of it as I explained it yesterday. The movement of Earth and Sun is such that the Earth follows the Sun in the same path, in the same direction. Here then you have the cosmic relation between Sun and Earth. The Sun as a gathering of suctional forces goes on in front, and by this suctional force the Earth is drawn on after, moving through cosmic space in the same course and in the same direction in which the Sun thrusts forward.
You thus perceive and understand what you would otherwise fall short of in your thinking. In no other way will you reach an adequate idea, to comprise all the phenomena. You have to start from such ideas as these. You must imagine that in the realm of matter there is a positive and a negative intensity. Matter itself, — that is, earthly matter — is positive; it is of positive intensity. Solar matter on the other hand is negative — of negative intensity — and is therefore not only empty in relation to matter-filled space, but even “less than empty”. It is a hollowing-out of space itself.
This may be difficult to conceive. Yet if you are accustomed to having mathematical ideas, why should you not think of a certain degree of the fullness of space as a corresponding magnitude, say +a? Empty space would then be Zero, and a space less than empty would be conceivable as -a. This granted, you will be able to conceive a truly mathematical relation — or at least, a relation analogous to mathematical — between the different intensities of matter, as in this instance between terrestrial and solar matter.
As it were in parenthesis I may add the following: No matter how you think of the relation of positive and negative real numbers to imaginary numbers (I will not go into this question now), some interpretation of the so-called imaginary numbers must be discoverable, and since they too emerge in the solution of equations and the like. If in the way we have been saying you recognize a positive and a negative of intensity, you may well conceive that there is also an imaginary [intensity]. You must then have which would enable you to add to positive matter and negative the kind of matter for example (or if you will, the kind of spirituality) which Anthroposophy describes as the Astral. Thus you would find a mathematical way of approach to the Astral too. However, as I said before, this only in parenthesis.
Once again take the connection of what I have been saying with man himself. You will admit: without any doubt the human physical body is related to ponderable earthly matter, and since it is as waking man — upright in his physical body — that man is related to earthly matter, we may compare man's relation to earthly matter with the upright direction of the plant, following what was said in preceding lectures. However, yesterday we saw that the plant must be imagined with the very opposite direction in the human being, while the outer plant must naturally be conceived as growing upwards from below, the plant we have to think of in the human being moves in a manner speaking, from above downward (Fig. 2). What is it then that grows from above downwards? Certainly nothing visible; it must be something invisible. Now we related this to the Sun. It there fore in relating the forces of plant-growth to the path of the Sun and Earth we think of them as tending from the Earth towards the Sun, we must needs think of what grows in the reverse direction in the human being as growing, in effect, in his etheric body. This force of suction therefore, proceeding from the Sun, works also in the human being. permeating his etheric body from above downward. Upon the human being — the human body in this instance — two opposite entities are at work; Sun-entity, Earth-entity.
We should be able to prove in detail that these things are there, and we can indeed, once we perceive the true interpretation. This that is working in the human being from above downward may resolve itself in very many ways. For if we have a force, say, in the direction a - b, we can trace it not only in this direction but also in an imaginary sense. Namely if this (Fig. 3) is its intensity, we need only imagine it resolved into two components. Thus we can every where form components of forces in the direction of the path of Earth and Sun. If I press here with my finger, there will arise over this surface the force or pressure whereby the ponderable matter presses against me. The counter-pressure will then correspond to the force of the Sun that is working through me — through my etheric body, that is to say. Imagine a surface here pressing against the human being, — or against which he is pressing. Here you already have the opposition — the working of the ponderable and of the imponderable able force. It is the interplay of the ponderable pressure from without inward and of the imponderable from within outward (Fig. 4) which gives you the conscious sensation of pressure. If in our mind we see all these things clearly and comprehensively, we may truly say that the polarity of Sun end Earth into the midst of which the human being is placed, is felt by us in every sense-perception. In like manner, everything about the human being can be traced in such a way as to perceive the cosmic realities that are involved. Cosmic forces work into the human being upon every hand.
It is of untold importance for us to overcome the method that excludes the human being and that is always haloing fast to isolated things, see it without any connection with their surroundings. You will remember, I used the same comparison before. If we place man into the world in such a way as to study head, limbs, etc., one by one and in a merely outward sense, it is as though we were to study a magnet-needle, tending as it does ever in the same direction, and seek the cause of this behaviour not in the magnetic pole of the Earth but inside the needle. To understand any fact or object, we must go to the totality from which alone it can be understood. What matters is in every case to look for the totality in question. Precisely this, alas, is foreign to the habitual ways or thought in our time. Before attempting to decide a problem, look first for the totality on which it all depends. You take a crystal of salt into your hand. You may regard it as a totality, just as it is. Even this is only relatively true, but at least relatively you can so regard it. It is, in a sense, a self-contained entity. Not so if you have picked and place a rose before you. Placed there before you in this way, the rose is not a self-contained entity at all. It could not be there in the same way as salt-crystal can. The crystal, it is true, must also have been formed in a surrounding medium; nevertheless it is a totality, the rose can only be looked upon as a totality when seen in connection with the shrub on which it grew. Only there has it the kind or totality which the crystal-cube of salt has on its own. Likewise if we look at man with respect to his full being, we cannot stop short at the limits of his skin, we must regard him in connection with the great universe that is visible to us; only in this connection is he to be understood. Such then must be our method, and as we persevere in it we become able to see a deeper meaning in the phenomenon that present themselves to us, — that can indeed be mastered by our cognition.
During these lectures we haves recalled the fact that in comparing the periods of revolution of the planets incommensurable magnitudes emerge. For if they were commensurable, the planetary paths would presently come into such relation to one another that the whole system would rigidify. Our planetary system does indeed also contain this tendency to become rigid and dead.
We can express what confronts us in the planetary system by means of certain curves — and arithmetical formulae. Yet as we saw, these curves and formulae are never in full agreement with reality. We must therefore admit that if we try to contain the phenomena of the Heavens in succinct formulae or geometrical figures the phenomena elude us. Time and again they elude us. This then is true: — look outward on the one hand and behold the given picture of the celestial phenomena. Look on the other hand at what we are able to make of it by dint of calculation. We never do contrive a formula that coincides entirely with the phenomena. We may devise such a drawing as I was sketching yesterday — the system of lemniscates. We can do so indeed. Even this system however, — we only understand it rightly if we admit the following. Suppose I managed to draw this lemniscatory system in a precise and finished form; it would at most be true of present time. Even a time comparatively near our own — the time I indicated when speaking of the coming ice-age — would require me to modify the system not a little. The constants of the curves must themselves be taken as variable. The very constants would therefore be curves of some complexity by virtue of their variations. Thus I can never draw staple straightforward curves, but only complicated ones. Even when drawing these lemniscate-curves (Fig. 5) I should have to say: Good and well, — I draw a path for some heavenly body. (As we saw yesterday, it will always be a lemniscatory path.) I draw the path. Yet when a certain time has elapsed I must disqualify it; it is no longer valid. I must make the Lemniscate a little broader. And then again after a time I must draw such a Lemniscate (Fig. 5 once more), and so on.
In effect, my dear friends, if I were to trace the paths of the heavenly bodies, I should really have to go out into the Universe and trace them ever anew, varying them all the time. There is no constant path which I may draw. Whatever path I may work out, I must remember in so doing that I ought really to be changing it all the time, since every lapse of time involves a change of path, however slight. To apprehend the heavenly bodies and their paths of movement in any adequate way, I cannot draw ready-made lines at all. Ready-made lines, if I do draw them, will only be lines of approximation, and I shall have to bring in corrections. Whatever finished lines I may devise, the phenomena in the Heavens will presently elude them, No matter what mathematical curve I may devise, once it is fixed and finished the reality will certainly escape me; my finished curve will not contain it, yet in the very act of saying this, I am giving voice to an important reality. Namely, a planetary system has this essential feature: It tends in both directions, — on one hand towards rigidity and on the other hand to the forming of ever-mobile Lemniscates. In the solar Saturn or planetary system there is this contrast between the tendency to become rigid and the tendency to be ever variable, ever escaping from its established form.
If we now follow up this very contrast, not in the way of speculation but in the actual seeing and contemplating of the phenomena, we shall be led to recognize that what we call a comet, a cometary body, is not a body at all in the same sense that a planet is. (What I am giving her, I give once more as guiding lines which you can verify for yourselves. You need only observe the empirical data. Observe them with the greatest possible precision, but do not cling to the theories with which so many scientists would fetter them — theories that lie like shackles upon the facts, You will convince yourselves: what I am about to say is verifiable. It will be verified increasingly, the more the given facts are put together.)
Truth is that in studying the cometary phenomena we get into difficulties if we conceive the cometary body too in the same way as we are wont to think of a planetary body. The planetary body (I refer again to the same question of principle and method as in an earlier lecture), — the planetary body you may represent as though it were a self-contained body moving on in space. You will not go much against the facts in so conceiving it. Not so a cometary body. Again and again you will find yourself in contradiction to the phenomena if you conceive it after the same pattern as the planetary body. You will never understand the cometary body, in the way it moves — or seems to move — through cosmic space, if you regard it as you are accustomed to regard the planetary body.
See what becomes of it on the other hand it you regard it as I shall now describe. Take all the empirical facts that are available and try to thread them on this line of thought. Imagine that in this direction (Fig. 6) — towards the Sun, as we may say — the comet comes into being at every moment. It is for ever coming into existence in this direction. It pushes towards its cometary nucleus, or what appears as such. Behind, it melts away again. In this way it thrusts forward — for ever coming into being on the one hand, passing away again upon the other. It is not a body in the same sense as a planet is, — not at all. It is perpetually coming into being and passing away again — renewed in front, accruing all the time in this direction; losing the old at its tail. It pushes forward like a mere effulgence, a mere phenomenon of light; but please, I do not say that that is all it is.
And now remember what we were saying a few days ago. There is not merely the Moon up there and the Earth here (Fig. 7), but every planet has a certain sphere, and what we see is only a point at the periphery of the said sphere. The true Moon is the sphere, bounded by the lunar orbit. We, with the Earth, are in the Lunar Sphere. So also, in a certain sense, are we in the Solar Sphere and in the spheres of all the planets. The planets are not merely what is out there, moving in lemniscates, — what is at yonder point or yonder at any given moment. The visible point is only a specialized part of the whole; it is, as I was saying, like the ares of germination in the germinal vesicle of the human embryo.
If you remember this, then you will say to yourselves: Here now I have the Earth and the Sun. In fact, two spheres are interpenetrating, thrusting into each other, — spheres which are really due to materialities of opposite tendency and kind. The one comes from the centre of the Sun, towards which negative matter is tending; the other from the centre of the Earth, from which positive matter is raying out. Positive and negative materialities are interpenetrating here. Naturally, the interpenetration will not everywhere be homogeneous. Not even clouds that move through one another would interpenetrate homogeneously. It is essentially inhomogeneous. Imagine how, in this mutual penetration, the different densities will impinge on one another. Then, in the penetration of the one substantiality by the other you have the requisite conditions for such phenomena as comets to arise. Comets are ever-nascent phenomena, perpetually coming into being, passing away again; and if we draw our ideal picture of a planetary system, say the Copernican picture, with the Sun here and Uranus and Saturn here (Fig. 8), we have not to imagine that the comet is arriving there from some great distance and then making its departure. Out there — outside the system — we need not imagine it to exist at all, It is not there to begin with, but becomes; then, at the perihelion, changes the gesture of its form, which is in fact ever-becoming, ever-nascent. Out there at last it melts away again and is no more, The comet comes into being and passes away; that is its very nature. Hence it can sometimes have apparent paths that are not closed at all — parabolic paths or hyperbolic, — for there is nothing moving round such as would have to move in a closed path. All that there is comes into being, and may well do so in a parabolic direction and then vanish and be no more.
Altogether, we must look upon the comet as a fleeting thing. In relation to Sun and Earth, it is a phenomenon of compensation between ponderable and imponderable matter, — a meeting of the two kinds of matter, which do not immediately balance-out as when light extends in air. For in the latter instance too, there is a meeting of the ponderable and the imponderable; here however they spread continuously, homogeneously as it were, — do not impinge on one another. Take for example air, with light of a certain intensity passing through it. The light spreads homogeneously; but if so be the light does not adapt itself to the air quickly enough, a kind of inner friction will ensue between the ponderable and imponderable matter; only I beg you not to understand this in a mechanical sense but as an inward process (Fig. 9). Follow the comet in its movement. It is a mutual friction of ponderable and imponderable matter that moves on through space. It comes into being at every moment and passes away again.
What I have tried to give you in these studies, my dear friends, was meant to bear on scientific method above all. Although the shortness of time has obliged me to deal with some of these things in bare outline, scarcely more than hinting at them, yet if you follow up the thoughts and indications of these lectures you will see that this is what I have been pointing to: It is a transmutation of method, in the whole way of scientific thinking and research. It would be most important for such lectures to become a starting-point for real work. I can only give general directions, as it were; and yet again and again, where we may only seem to have been working with mathematical curves and the like, you will find inspiration for empirical research and experiment. On every hand, both in the coarser and in the finer aspects, you may attempt to verify what has here been presented in seemingly mathematical and geometrical guise. You may take one of those blue or red toy balloons and examine the effect when you forcibly indent it from without inward, where the indentation will of course follow certain laws. See then what form is taken by the same type or phenomenon when in another experiment you make the forces work from within outward radially. Whether, I say, you are examining only this crude phenomenon of stress and deformation or whether you follow the lines along which the heating effect will spread when you heat certain substances — from within outward in one case, from the periphery inward in another, — or again whether you try your hand it optical, magnetic or other phenomena, in every instance you will find that what has here been said about the contrast of Sun and Earth (to mention only this example) can be detected experimentally.
Above all, if such experiments are carried out, you will begin to penetrate the realities quite differently than has been done before. For you will meet with conditions, factual distributions, which have not hitherto been met with, or have been overlooked. From the realms of light and heat and so on, quite other effects will be derivable than hitherto, for the simple reason that the phenomena have not yet been approached in such a way as to become fully manifest.
Such, my dear Friends, are the developments which I would like to have suggested to you. May-be in future lectures, before very long, we can continue and make actual experiments. It will depend on how our physical and other laboratories prosper, — whether you will have reached experimental methods or real value for the future. Let us not pursue the ideal of equipping our new laboratories with the most costly and perfect apparatus from the scientific instrument makers and then experimenting in the same way as other people do. For on these lines they have done splendid work on every hand. What we must do, as I said before, is to devise new kinds of experiment. We should begin therefore, not with a fully equipped Physics Laboratory, but as far as may be with an empty room, which we go into with the thoughts of a new Physics growing in our minds and souls, not with the usual instruments all ready-made. The emptier our laboratories and the fuller our own heads, the better experimenters we shall grow to be in course of time, my dear Friends.
This is what matters most in the present connection, and in this sense we must do justice to the tasks of our time. Think only of the fetters that are cast around you in the different experimental sciences in the normal course of study nowadays; you had no opportunity to see or to set out the phenomena in any other form than was provided for by the accustomed apparatus. With these instruments, how can you expect to study the spectrum in Goethe's sense? You can not possibly. Given these instruments, nothing else can emerge than what you read of in your text books. You cannot even see why we reject the artificial insertion of “light-rays” in the interpretation of the phenomena of light, where in fact, there are no rays at all. We say to ourselves: There is a vessel filled with water (Fig. 10); on the bottom of it lies a coin. The coin seems to be at a different place. We hardly begin to think of this phenomenon, and we have already drawn our diagram with the normal and sundry other lines and rays (Fig. 10). We follow the whole process with such lines, where from the very outset we ought not to be pursuing such an isolated thing at all. Nowhere in reality are we confronted with such isolated things. If this (Fig. 11) is the bottom of the vessel and a coin is lying here, we only begin to see how the coin is to be treated when we think as follows. Imagine on the bottom of the vessel, not an isolated coin, but a circle, for example, made of paper (as in Fig. 12). The phenomenon is, that when seen through a surface of water the paper circle appears lifted and enlargerd. That is the pure phenomenon, — that you can draw. If then at the bottom of the vessel you have not the whole circle but only a little bit of it, you have no right to treat it differently. The coin in effect is like a little fragment of the paper circle. You have not to draw all manner of lines into the picture but to treat it as a portion of the circle, nay of the bottom of the vessel as a whole, — of what is there all the time even if not made visible by differentiation. The mere fact that I have made one point visible at the bottom of the vessel does not justify me theoretically, in treating this visible point as a point by itself. It has not the significance of a point, but only of a part of the larger circle (Fig. 13).
Likewise a magnet-needle: In its reality I may not treat it as though there were a centre here, and here a north pole and a south pole; but I must realize that purely and simply by virtue of this arrangement the whole of it is one unlimited line, with forces working peripherally on the one hand and centrically on the other (Fig. 14). In the electrical phenomena this finds expression in that we set the cathode on the one hand, the anode on the other. On the one hand we can only explain the luminous phenomenon by regarding it at a portion of a sphere, the radius of which is given by the direction in which the electricity is working; whereas the other pole is given as a tiny portion of the radius itself. It Is not justifiable to speak of a simple polarity of poles. We should speak in quite another way. Namely, wherever anode and cathode make their appearance, this will belong to an entire system; purely and simply by virtue of the simple arrangement it belongs to an entire system. Only by speaking in this way shall we attain true understanding of the phenomena.
Now, my dear Friends, I have been reading through the written questions; but I believe, if those concerned will reflect a little, they will find the necessary elements of an answer to their questions in what I have set forth. They should but try, in every case, to find the way from what I have been saying to their several questions. We shall advance in this bit by bit. Only one question I should like to deal with briefly. It is as follows: —
“In representing a Science of this kind to the outer world the question may easily arise, to what extent the higher powers of cognition — Imagination, Inspiration and Intuition — are needed for the discovery of these relations between phenomenon. What will be the answer to this question?”
Well, my dear Friends, and if it were the fact that Imagination, Inspiration and Intuition are needed for the discovery of certain things? How then are we to do without Imagination,Inspiration and Intuition, if the fact is that ordinary, “objective”, intellectual cognition will not reveal the truth and the reality? What else are you to do than to proceed to higher 'modes of knowledge — Imagination, Inspiration and Intuition? That there is still this possibility — If it is really so that one is quite reluctant to advance to higher modes of knowledge — there is the possibility of simply taking the results of such research and testing them by what is found in the field of external empirical fact. One will always find them verified, of that you may be sure.
Yet in our time these things are not so remote as is commonly supposed. If only the path were really taken, from the ordinary analytical treatment of mathematics to the projective treatment — to a projective form of mathematics and beyond it — if one would cultivate and pay more heed to the idea from which I took my start some days ago, speaking or curves for which one has to go right out of space, one would not find it so very difficult to press forward to Imagination. It is indeed simply a question of inner courage — courage of soul. Today you need this inner courage of the soul for scientific work. Hence it is needful to maintain, for it is true: to the ordinary forms of observation and reflection the full reality will not reveal itself. But if one does not shrink from developing the latent forces of the human soul, depths of reality which would otherwise remain concealed will become ever more unveiled.
This I would like to have said to you in conclusion. For the rest, I would express the wish that all these things, which I can only claim to have imparted by way of stimulus and suggestion and in the barest outline, may stimulate you to research, experimental above all. For this is what we need. We need empirical verification of these truths, which must be taken hold of to begin with in the way we have been doing here. Sooner or later we must get beyond the old foundations of judgment, which have so long been responsible for such conditions as in the instance I shall now relate. I say again, we must get beyond them.
I was speaking to a Professor of Physics about Goethe's Theory of Color. The man has even published an edition of it, with his own commentary. When we had been discussing Goethe's Theory of Color for some time the man declared himself a strict Newtonian. He said, it is in fact impossible for any man to get a clear conception or Goethe's Theory of Color; no physicist can set a clear idea of what it means. You see, his education as a physicist had brought him to this point; he could get no real notion of Goethe's Theory of Color. I for my part could understand it. The modern physicist if he is candid, will have to admit that he cannot. He must first transcend the accepted foundations of present-day physical thinking; he must somehow be able to get away from these old foundations. If he succeeds in this, then he will find the way — for it can be found — from the actual phenomena to that interpretation which is contained in Goethe's Theory of Color and which can also provide an important starting-point for other physical researches, extending even to Astronomy.
Consider without bias the warmth-region of the spectrum and the chemical region of the spectrum, their quite different behavior towards a number of reagents. Even in the spectrum you will detect the contrast I have been describing — the contrast of terrestrial effects and solar. In the spectrum itself we have a picture of the contrast of Earth end Sun, — the same contrast which finds expression in the whole bodily organization of man. Every time you touch another body, perceiving it with your sensation of touch, Sun and Earth are at work. So too, in the spectrum, Sun and Earth are at work. Taking it as the solar spectrum you cannot truly think of it as being put into space just arbitrarily here or there. You must be clear that it is always in the real space — the space that is between Sun and Earth.
Indeed you never have to do with space in the abstract where real phenomena are concerned, for the real things are always there and have to be included. If you do not bear this in mind, you will at last be explaining the origin of the celestial system on the good old pattern — a little drop of oil floating in water, bearing a disk of paper with a pin stuck through it as a pivot, which you begin to turn. The drop of oil gets flattened and little drops detach themselves. A planetary system has arisen: You explain it to your audience: “You see, it is a planetary system”. You compare it with the solar system in the Universe outside — the Copernican conception, — it is the very same! Well and good. Yet you must not forget: There were you the teacher, turning the pin, and therefore — not to be untrue — you should also add the demon giant in the universe outside, turning the cosmic axis, for only so can there arise what you have been alleging. You have no right to use this illustration if you do not include the giant demon. In scientific explanation too, we need to be more scrupulous and careful.
Upon these inner and methodical conditions above all, I have been wanting to lay stress in the present lectures. Next time then we will speak again from other points of view, of certain realms of Science.