Lecture III Stuttgart January 3, 1921 I have brought to your notice on the one hand how problematical it is to conceive the celestial phenomena in their mathematical and geometrical aspect alone. This is now being recognized by many people and from diverse angles. Only quite unadvanced thinkers still maintain that the world-picture of Copernicus and Galileo represents downright reality. Increasingly, we hear the voice of those who find this way of thinking of the celestial phenomena useful and practical, no doubt, for purposes of calculation, yet emphasize that it represents only a certain mode of understanding, and that quite other syntheses might be conceived. There are even those who say, somewhat as Ernst Mach used to say: In the last resort, one can uphold the Ptolemaic just as well as the Copernican world-system, and a third system might equally well be devised. These are but practical ways of correlating the observed facts. The entire realm should now be confronted with a far freer kind of outlook. You see from this that the problematical nature of the celestial charts, described but a short time ago as replicas of the real facts, is now conceded by the widest circles. On the other hand an escape from the manifest problems and uncertainties of this realm can only be found through such views as were brought forward in outline yesterday, -- views which no longer remove Man from the whole cosmic background, but on the contrary, put him into it from the outset. We have to recognize the processes within Man himself in their connection with solar phenomena, lunar phenomena and terrestrial phenomena, thus taking as a starting-point all that goes on in Man, in order to find the way to what is going on out there in the Cosmos, the latter being in some sense the cause of the processes in Man. A path like this can of course only be trodden from the standpoint of Spiritual Science. Precisely when we try to bring Astronomy into connection with the most varied spheres of life, we shall find that we are being led through Astronomy itself into the views of Spiritual Science. Bear in mind that the visible celestial phenomena, perceptible to our senses and also to our reinforced senses, appear at first a manifestation of something outside of man. Man confronts and, as it were, arrests with his senses whatever approaches him, introducing it into his conscious world-picture. But the impulses streaming towards us from all sides, certainly do not come to a standstill before our senses. All that goes on without being held up by man's senses and brought into consciousness, all that lives in the celestial influences that stream towards us from all sides, must be sought for within our bodily organism. The organism must in a certain way reflect it all, and it does this in the unconscious and subconscious processes which can only be raised into consciousness in more complicated ways. We will now continue in a certain direction what we began yesterday. Only an abstraction of our earthly world is dealt with in Geology or Mineralogy; the Earth as described by Geology consists of minerals has evolved in the mineral sphere; true as it is that forces are there in the Earth by virtue of which it brings forth the minerals; yet is is equally true that all that is living in plants, animals and physical human beings also belongs to the Earth. We only see the Earth in its totality when we do not simply cast aside what lives in plant, animal and man and have in mind the mere abstraction "mineral earth ", but bring it all into our consciousness. The living beings and entities that grow up out of the Earth are also part and parcel of the whole. Of all that belongs in this way to the Earth, let us first take the plant kingdom. We will approach it in order then to find the transition to what meets us in man. Whereas the mineral kingdom to a certain extent carries on an independent Earth-existence and is only related to the Cosmos outside the Earth in such a way as is shown, for example, in the changing of water into ice in winter, the plant kingdom retains a much greater inner connection with the cosmic surroundings of the Earth -- with all that enters the Earth from the Cosmos. Through the plant-world the life of the Earth as it were opens itself to the Universe. In geographical regions where in a given season an intensive interaction is taking place between Earth and Cosmos. We must pay heed to a phenomenon like this, for it will lead us into the realm of Astronomy not only quantitatively, but qualitatively. We must be able to derive our ideas from such a thing as this, even as the astronomers of our time derive their ideas from angles, parallaxes and so on. Then we shall say to ourselves, for example: -- The plant-life, covering a given region of the Earth, is a kind of sense-organ, sensitive to all that is revealed towards the Earth out of the Cosmos. At seasons when the interplay is more intense between a portion of the Earth's surface and the Universe, it is as though a human being were opening his eyes to the outer world to receive sense-impressions. And when the interplay is less intense between the Earth and the Cosmos, the consequent decline and inward closure of the vegetative life is like a closing of the eyes to the Cosmos. It is more than a mere comparison to say that through its vegetation a given territory opens its eyes to the Universe in spring and summer and shuts its eyes in autumn and winter, and as by opening and closing of our eyes we do in a way converse with the outer world, so too it is a kind of information or revelation from the Universe which the Earth receives by the opening and closing of its eyes through the life of plants. And to describe it a little more precisely, we may consider the vegetation of a given region of the Earth when exposed, as it were, so to speak, to the most vivid interplay with the solar life, and we may then turn our attention to the state of vegetation in this region when it is not thus exposed. The winter, I need hardly say, does not interrupt the vegetative life of the Earth. It goes without saying that the vegetative life continues through the winter. But it expresses itself in quite another way than when exposed to the intensive working of the Sun's rays -- or, shall we say, of the Cosmos. Under the influence of the solar life, the vegetative life of the Earth shoots outward into form. The leaves unfold and grow more complex; flowers develop. But when this is followed by the closing of the eyes to the Universe, if we may call it so, the vegetative life goes back into itself -- into the seed. Withdrawing from the outer world, it no longer shoots into outward form; it concentrates, if I may put it so, into a point; it becomes centered in itself. We say describe this contrast truly as a law of Nature. The interplay between the earthly and the solar life reveals itself in the Earth's vegetation. Under the solar influence the vegetative life shoots outward into form; under the influence of the earthly life it closes up into a plant, -- it becomes seed or germ. In all this there is a quality of expansion and contraction or gathering into a center. Here we begin to apprehend the relationships of space itself in a directly qualitative aspect. This is the very thing which we must practice in the development of our ideas, if we would attain to really fruitful notions and perceptions in this sphere. And now we pass from plant-life to the life of man. Naturally, what comes to expression in the life of plants will find expression in man too. In what way will it do so? What we somehow perceive, my dear Friends, so outwardly and evidently in the life of plants - what we have visibly before our eyes if only we are attentive to the qualitative aspect - this we can recognize in man, properly speaking, only in the first years of childhood. Let us then trace the interaction of the solar and terrestrial life for man in the age of childhood, as we have just been doing for the plant kingdom. The little child opens through the senses to receive the impressions of the outer world. In doing so, the human being is really opening to receive the solar life. You only need see things in the proper light to recognize that what pours in upon our senses is inherently connected with what is brought about in the terrestrial sphere by the Cosmos. You can reflect upon the special case of light. When light and darkness succeed each other in the alternation of day and night, impressions are made upon our eyes by day, and no impressions are made by night. You can apply this also to other perceptions, though it is more difficult to make it clear. You will then say that a certain effect of the daily alternations, solar and earthly, expresses itself in man's soul-life. Man has an activity of soul through what arises in the rhythm of the day. What the Sun here brings to the Earth comes to expression in the soul-life of man. But if we follow the growth of the child, particularly until the 7th year - the change of teeth - and go into all the details, we find how, notably in the first years of the child's development (less and less, the older the child becomes), it is plainly perceptible that the changing seasons, year by year, have just as much significance for human growth as for the sprouting and dying-down of the vegetation. We will represent it diagrammatically. If, for example, we study carefully and intelligently the development of the human brain in the earliest stages from year to year, we shall find the following. We have the human skull with its brain-content. It remodels itself, and one can follow how it remodels itself through what in the course of the changing year. Something which works formatively and creatively upon the human head, molding it from outside in a corporeal, physical sense, - we find this intimately connected with the forces playing between Earth and Sun in the course of the year. In the daily rhythm we find what enters through the senses, independent of growth, to work on the soul and spirit of man. We see how what takes place in man by reason of the Sun's activity in the daily rhythm, has an inner effect which frees itself from the external world and becomes of a soul-and-spirit nature it is what the child learns, what it assimilates through observation, what takes place in effect, in soul and spirit. Then we see how in a totally different tempo -- from a different aspect -- the brain remodels itself, organizes itself, and grows. That is the other activity, the yearly activity of the solar forces. We will say nothing yet of the changes occurring in the Universe between Sun and Earth; we will consider manifestations in man himself which are united with certain changes in the solar and terrestrial life. We consider the day and find the soul- and spirit-life of man connected with the course of the Sun. We consider the change of seasons through the year and find man's life of growth, the physical, corporeal life, connected with the course of the Sun. We can say, The change taking place between Earth and Sun in 24 hours has certain effects on the spirit and soul of man. What happens between Earth and Sun in the course of the year has certain effects on the physical, corporeal part of man. We shall have to bring these effects into connection with others and thence arrive at a world-concept which can no longer be deceptive, for it speaks to us of real processes within ourselves, no longer dependent on illusory sense-impressions or the like. Thus we must gradually draw near to what can give us a sure basis for the astronomical world-conception. We can only take our start from what appears in man himself. So we can say: the day is something in man's connection with the Cosmos that expresses itself in soul and spirit; the year is something in man's connection with the Cosmos that expresses itself in the physical-corporeal life, as for example in growth, and so on. Now let us look at another complex of facts, referred to yesterday. With human reproduction we must relate certain ideas referring to the life of the Cosmos. We indicated yesterday that the female organism shows in a striking manner how the monthly functions connected with the sex-life -- though not, to be sure, coinciding with the Moon's phases -- are yet a reflection of them in their time rhythm. The process wrests itself free from the Cosmos, as it were, but still reflects the Cosmic Moon-process in its periodic course. We have here an indication, my dear friends, of inner processes in the human organism which we can study better if we turn our attention to more familiar phenomena, such as may make these more remote phenomena easier to understand. There is something in the soul-life which actually reproduces in miniature the organic processes to which we have just alluded. Let us say, we have an outer experience which affects us through the senses and the mind, -- perhaps also through our feelings. We retain a memory of the experience. The recollection -- the retention of the experience -- leads to the possibility of the picture of it emerging again at a later time. Anyone who considers these facts, not on the basis of fanciful theories, but with sound qualitative observation, will have to admit that in all that arises within us by way of memory, our physical bodily organization plays a part. The remembering itself is no doubt an event in the life of soul, but it needs the inner basis of the physical body in order to come into being. The activity of remembering is directly interrelated with bodily processes; though this has not yet been investigated sufficiently by external science. Comparing what occurs in the female organism in the monthly periods (it occurs in the male organism too, only it is less evident; it can be observed more in the etheric organism and this is not usually done) -- comparing this with what happens in ordinary experience when we remember something, one will certainly find a difference. Yet if with sound inner perception one recreates the process in one's consciousness, one cannot but say that the activity of remembering, this soul-occurrence arising out of the physical organism, is similar to what takes place in the monthly functions of the female organism, only is in miniature and is more drawn into the realm of soul, less impressed upon the body. From this point of view you will be able to say: Inasmuch as man individualizes himself from the Cosmos, he develops the faculty of memory; inasmuch as he still lives within the Cosmos, developing more his sub-conscious functions, something in the nature of a common experience with the Cosmos arises, connected with the Moon-processes in the Cosmos. This experience remains, just as a past experience remains in our memory, and later it emerges in an inner constitutional process, like a remembrance which has been drawn into the body and has become organic. There is no other way, my dear friends, of understanding these matters than by thus proceeding from the simpler to the more complex. Just as it is not necessary for a recollection to coincide with a fresh outer experience, so it is not necessary for what appears in the female organism, as a memory of an earlier cosmic connection of the human organism with the phases of the Moon, to coincide in time with these phases. Nevertheless, it is connected with the Moon's phases no less essentially than is the recollection of an earlier experience with the experience itself. Here then we have an activity in the human organism, more on the psychological side and yet not unlike the effects -- precipitated, as it were, into the life of time -- of influences due originally to the Moon. For the organic periodicity of which we have been speaking embraces about 28 days, as you know. Now take the following. If we consider the daily influence of the Sun, we find an inner activity of soul and spirit; if we consider the yearly influence of the Sun, then we find laws of growth belonging to the outer physical body. Thus we can say, for the Sun life: Soul and Spirit: Day Physical bodily nature: Year And now we come to the Lunar activity. We pass on to consider the lunar life, the life of the Moon. What I have just described as taking place in rhythm of 28 days belongs indeed to the soul and spirit; it has only impressed itself deeply into the body. Physiologically, there is really no difference, in a finer sense, between what takes place in the body on the arising of a memory with respect tot the event to which the memory refers, and what takes place in the monthly periods of the female body with respect to what the female organism experienced long ago in conjunction with the phases of the Moon. Only the latter is a stronger, a more intensive experience, -- a soul spiritual experience pressed more intensively into the body. Thus, for the Lunar life: 1. Soul and Spirit: 28 day's activity Let us now seek the corresponding phenomena for the physical body. What will they be? You can find it for yourselves by deduction. We will have bodily, physical effects with a 28-year period. As a day here corresponds to a year, we shall have 28 years. 2. Physical bodily nature: 28 year's activity You need only remember that 28 years is the period bringing us to our full inner maturity of growth. It is then that we first cease to be in the ascending scale of growth. Just as the Sun works upon us from outside in its yearly activity, in order to complete in us an outward process corresponding to the daily process in the inner life o soul and spirit, so something works in the Cosmos in a 28-year period, organizing us from outside even as the female human being is organized inwardly. (In her it is more obvious than in the male, for in the man the corresponding daily rhythm is more withdrawn into the etheric.) Here then a 28-day period impresses itself inwardly in the realm of the soul and spirit, and we can say: As the daily Sun-life is related to the yearly Sun-life in regard to man, so the 28-day Moon-life related to the 28-year Moon-life with respect to the whole man (the former belonging, in effect, more to the human head). You see how we place man, and rightly place him, into the whole Cosmos. We leave off speaking of Sun and Moon merely as if we stood isolated here on Earth, and only looked out with our eyes or with our telescopes to Sun and Moon. We speak of Sun and Moon as of something inwardly united with our very life, and we perceive the connection in the special configurations of our life in time. Until we place man again, my dear friends, into the picture of the doings of Sun and Moon, we shall not have evolved a firm foundation for true Astronomy. Thus a new science of Astronomy must be built upon a spiritual-scientific basis. It must be evolved out of a more intimate knowledge of man himself. We shall only be able to find a meaning in what is taught by the external Astronomy of today, when we are in a position to base our hypotheses on man himself. We shall then be able profitably to study the rather schematic statements made in Astronomy today and we shall also be able to make essential corrections in this external Astronomy. What follows from all this? It follows that in these processes -- no matter, for the moment, what the underlying basis of them is -- a universal life reveals itself. Whether it by (and we will speak of this later) that the daily and yearly rotations of the Earth underlie what I have here described as solar life with respect to the soul and spirit for the day, and to the physical bodily nature for the year; whether it be the movements of the Moon described by modern Astronomy or something very different; -- we shall never reach an understanding of it merely by setting up the well-known picture taught in the Schools. But we must understand all that is expressed in this picture as being in reality a continuing, enduring universal life -- a life which cannot be approached in its fullness by a mere series of diagrammatic pictures. We will now set to work in another way. We will Bet to work from the standpoint offered us in the Astronomical ideas of a man who still had very much from the past. We do not want to return to the older ideas; we must work out of new ideas This man, however, still had much of the old qualitative virtues in his ideas. I refer to Kepler. Astronomy has become more and more quantitative in modern time, and it would be a delusion to look on Astrophysics as the entry of a qualitative element into Astronomy; of an universal life that lay behind the work of Kepler. In him a feeling still persisted that behind all that is manifest to ordinary astronomical observation there lies hidden something like the gesture of a vast cosmic life - a cosmic life that here reveals its presence. If we have a man before us and see him move a hand or an arm, we do not merely calculate the mechanics of the movement; we recognize it as the outer revelation of an inner life of soul and spirit. We understand as an expressive gesture something that can, after all, also be looked on from a purely spatial, mathematical point of view. The further back one goes in the history of man' e approach to Astronomy, the more one find men conscious that the pictures they conceived of the path of the Sun or of the stars were no mere passive pictures of indifferent events but that these pictures were gestures of life and being. It is quite easy to discern in olden times this feeling of the gesture-like nature of the movements of the heavenly bodies. When my hand moves through the air I shall not merely calculate its path, but in this path I see an expression of the soul . So did the earlier observer see in the path of the Moon an expression. of a life of soul. In all the movements of the heavenly bodies he saw expressions of a soul-nature lie pictures it somewhat in this s way -If I could held an umbrella here so that only my hand were seen, my hand would make an inexplicable movement, for I am there behind the umbrella; only the hand is to be seen. Somewhat in this way the men of ancient times pictured that the movement of the Moon up in the sky was but the outer expression - a sort of terminal 'limb' - end that the really active being stood behind it. So too in earlier times men did not speak of isolated heavenly bodies of the planets; they spoke of planetary spheres. They spoke of the several spheres, belonging to the heavenly bodies. Thus they distinguished the Moon-sphere, the Mercury-sphere, the Venus-sphere, the Sun-sphere, the Mars-sphere, the Jupiter-sphere, the Saturn-sphere, and then the eighth sphere - the Heaven of Fixed Stars They distinguished these eight spheres and saw in them something which expressed itself in outer gestures, so that a certain sphere expressed itself by lighting up now here, now there, and so on. The reality, for instance, was the sphere of the Moon. The Moon itself was not a separate entity, - only the gesture. Where the Moon appeared, the Moon-sphere was making a definite gesture I am relating this to show you the living nature of the old conceptions. Kepler still retained in his whole consciousness a feeling for this universal life in space Only on this account was he able to draw up his three famous Laws For modern Astronomy the three famous Laws of Kepler are purely of a quantitative nature, to be regarded simply from the aspect of spatial and temporal concepts. For a man who still worked out of such a life of ideas as Kepler did, this was not the case. Let us now call to mind these Laws of Kepler. They are: The First Law: The Planets move in ellipses round the central body, which is situated in one of the foci of the ellipse. The Second Law: The Radius-vector of a Planet describes equal sectors, equal areas, in equal periods of time. The Third Law: The squares of the periods of revolution of the different Planets are proportional to the cubes of the major semi-axes Now as we said, to the modern, purely quantitative view these laws too are purely quantitative To anyone like Kepler, the very (:expression 'elliptical' and the corresponding curve signified a greater livingness when it only moves in a circle, for it must use an inner impulse in order continually to alter the radius. When something simply moves in a circle it need do nothing to alter the radius. A more intense inner life must be employed in the radius-vector is continually altered. The simple. statement: "The Planets move in ellipses round the central body and the central body is not in the mid-point but in one of the foci of the ellipse", implied an element of greater livingness than when something moves in a perfect circle. Further: "The radius-vector describes equal sectors in equal periods of time". We have here the transition from the line to the surface, to the plane. Please notice this.' Inasmuch as at first only the ellipse is described, we remain in the line - the curve- When we are directed to the path that the radius-vector describes, we are led to the surface - the area. A more intensive condition in the planetary movement is disclosed, When the planet 'rolls along' - if I may express so myself - it is not only expressing something within itself, but draws its tail after it, as it were. The whole area which the radius-vector describes belongs to it spiritually. Moreover, in equal periods of time equal areas are described, Special attention is thus drawn to the quality, the inherent character of the movement of the planets. The third Law above all relates to the life that plays its part between the various planets. This Law assumes a more complicated form. "The squares of the periods of revolution of the Planets are in proportion to the cubes of the semi-major axes" (or of the mean distance from the central body). This Law, you see, contains a great deal if one still understands it in Kepler's living way. Newton then killed the law. He did this in a very simple fashion. Take Kepler's Third Law. You can write it thus: or, written differently: Now write it in a somewhat different form. Write it thus: I might of course also have written it in the reverse order.) What have we on the left-hand side of the equation, here in the left-hand ratio? No less than what is expressed by one half of Newton's Law. and oil the other side the other hail', the forces of Newton's Law-. You need only write Kepler's Law thus differently and you can say: ' The forces or attraction are inversely proportional to the squares of the distances." Here then you have the Newtonian Law of Gravity deduced from the Law of Kepler. The force of gravity between the planets, the celestial bodies, is in inverse proportion to the squares of their distances apart. It is nothing else than the killing of Kepler's Third Law. In principle that is what it is. But now take the matter actively and livingly. Do not set before yourself the dead product " force of gravity" - "the forces of attraction decrease with the squares of the distances", - but take what is living still in Kepler's form, the squares of the periods of time. Fill out the caput mortum of the Newtonian force of attraction, which is a mere external concept, with what is implied in the square of the period of time, and you will fill with inner life of the Newtonian concept, which is really the corpse of an idea.' For inner life has to do with time. And here you have before you not only time in its simple course, you have time squared -time to the second power! We shall yet have to come back to what it means to speak of 'time squared' But you can realize that to speak of time to the second power is to speak or something of an inward nature. It is, indeed, time which in the life of man actually represents the course of his inner soul-life. The point is that we should look right through it dead concept of the Newtonian force of attraction to that which suddenly darts into the center, bringing time into it and therewith bringing in an element of inner life. Now look at the matter from another point of view. Notice that Kepler's first Law also has reference to the Earth. Not only does the Earth describe an ellipse, but you, since you are on the Earth, describe an ellipse together with it. What takes place outwardly is in you an inner process. Thus the arising of the ellipse from the circle, in the living way in which Kepler still conceived it, corresponds to a process in your own inner being. And inasmuch as you move in the line which is formed by the radius-vector describing equal sectors in equal times, it is you who continually relate yourself to the central body, placing yourself in relation to your own Sun. You, together with the curve, are describing a path in time, along which you are in continual relation to the Sun. If I may put it a little quaintly You must take care all the time that you do not 'skid' or side-slip, that you do not go too fast, - that your radius-vector does not describe too great an area. This outer point which moves in the ellipse must be continuously in the right relation to the Sun. There you have the movement you yourselves make, characterized as a pure line in space. The relation to the Sun is characterized in the Second Law. And if we pass on to the Third Law, you have an inner experience of the relation to the other planets - your own living connection with the other planets. Thus we not only have to find, in man himself, processes that lead us out again into the Cosmos. If we interpret rightly the mathematical pictures presented to us by the cosmic process, we also turn into an inner experience what is apparently external and quantitative. For the cosmic Mathematics indwells man. Man is himself in the midst of the living Mathematics. Of this we shall speak more tomorrow.