The Rudolf Steiner Archive

Yesterday I tried to show the methods used by Eastern spirituality for approaching the super-sensible world. I pointed out how anybody who wished to follow this path into the super-sensible more or less dispensed with the bridge linking him with his fellows. He preferred to avoid the communication with other human beings that is established by speaking, thinking and ego-perception. I showed how the attempt was first of all made not to hear and understand through the word what another person wished to say, but actually to live in the words themselves. This process of living-in-the-word was enhanced by forming the words into certain aphorisms. One lived in these and repeated them, so that the soul forces acquired by thus living in the words were further strengthened by repetition.

I showed how in this way a soul-condition was attained that we might call a state of Inspiration, in the sense in which I have used the word. What distinguished the sages of the ancient Eastern world was that they were true to their race; conscious individuality was far less developed with them than it came to be in later stages of human evolution. This meant that their penetration of the spiritual world was a more or less instinctive process. Because the whole thing was instinctive and to some extent the product of a healthy human impulse, it could not in ancient times lead to the pathological disturbances of which we have also spoken. In later times steps were taken by the so-called Mystery centres to guard against such disturbances as I have tried to describe to you. What I said was that those in the West, who wish to come to grips with the spiritual world, must attempt things in a different way.

Mankind has progressed since the days of which I was speaking. Other soul forces have emerged, so that it is not simply a matter of breathing new life into the ancient Eastern way of spiritual development. A reactionary harking back to the spiritual life of prehistoric times or of man's early historical development is impossible. For the Western world, the way of initiation into the super-sensible world is through Imagination. But Imagination must be integrated organically with our spiritual life as a whole. This can come about in the most varied ways: as it did, after all, in the East. There, too, the way was not determined unequivocally in advance. To-day I should like to describe a way of initiation that conforms to the needs of Western civilisation and is particularly well suited to anyone who is immersed in the scientific life of the West.

In my book, Knowledge of the Higher Worlds, I have described a sure path to the super-sensible. But this book has a fairly general appeal and is not specially suited to the requirements of someone with a definite scientific training. The path of initiation which I wish to describe to-day is specifically designed for the scientist. All my experience tells me that for such a man the way of knowledge must be based on what I have set out in The Philosophy of Spiritual Activity. I will explain what I mean by this.

This book, The Philosophy of Spiritual Activity, was not written with the objects in mind that are customary when writing books to-day. Nowadays people write simply in order to inform the reader of the subject-matter of the book, so that he learns what the book contains in accordance with his education, his scientific training or the special knowledge he already possesses. This was not basically my intention in writing The Philosophy of Spiritual Activity. For this reason it will not be popular with those who read books only to acquire information. The purpose of the book is to make the reader use his own processes of thought on every page, In a sense the book is only a kind of musical score, to be read with inward thought-activity in order to be able of oneself to advance from one thought to the next. This book constantly expects the reader to co-operate by thinking for himself.

Moreover, what happens to the soul of the reader, when he makes this effort of co-operation in thought, is also to be considered. Anybody who works through this book and brings his thought-activity to bear on it will admit to gaining a measure of self-comprehension in an element of his soul-life where this had been lacking. If he cannot do this, he is not reading The Philosophy of Spiritual Activity in the right way. He should feel how he is being lifted out of his usual concepts into thoughts which are independent of his sense-life and in which his whole existence is merged. He should be able to feel how this kind of thinking has freed him from dependence on the bodily state. Anyone who denies experiencing this has fundamentally misunderstood the book. It should be more or less possible to say: “Now I know through what I have achieved in the thought-activity of my soul what true thinking really is.”

The strange thing is that most Western philosophers utterly deny the reality of the very thing that my Philosophy of Spiritual Activity seeks to awaken in the soul of the reader. Countless philosophers have expounded the view that pure thinking does not exist, but is bound to contain traces, however diluted, of sense-perception. A strong impression is left that philosophers who maintain this have never really studied mathematics, or gone into the difference between analytical and empirical mechanics. The degree of specialisation required to-day will alone account for the fact that a great deal of philosophising goes on nowadays without the remotest understanding of mathematical thinking. Philosophy is fundamentally impossible without a grasp of at least the spirit of mathematical thinking. Goethe's attitude to this has been noticed, even though he made no claim himself to any special training in mathematics. Many would deny the existence of the very faculty which I should like readers of The Philosophy of Spiritual Activity to acquire.

Let us imagine a reader who simply sets about working through The Philosophy of Spiritual Activity within the framework of his ordinary consciousness in the way I have just described. He will not of course be able to claim that he has been transported into a super-sensible world; for I intentionally wrote this book in the way I did so as to present people with a work of pure philosophy. Just consider what advantage it would have been to anthroposophically orientated science if I had written works of spiritual science from the start. They would of course have been disregarded by all trained philosophers as the amateurish efforts of a dilettante. To begin with I had to concentrate on pure philosophy: I had to present the world with something thought out in pure philosophical terms, even though it transcended the normal bounds of philosophy.

However, at some point the transition had to be made from pure philosophy and science to writing about spiritual science. This occurred at a time when I had been asked to write about Goethe's scientific works, and this was followed by an invitation to write one particular chapter in a German biography of Goethe that was about to appear. It was in the late 1890's and the chapter was to be concerned with Goethe's scientific works. I had actually written it and sent it to the publisher when another work of mine came out, called Mysticism at the Dawn of the Modern Age. This book was a link between pure philosophy and philosophy based on Anthroposophy. When this came out, my other manuscript was returned to me. Nothing was enclosed apart from my fee, the idea being that any claim I might make had thus been met. Among the learned pedants there obviously was no interest in anything written—not even a single chapter devoted to the development of Goethe's attitude to natural science—by one who had indulged in such mysticism.

I will now assume that The Philosophy of Spiritual Activity has already been studied with one's ordinary consciousness in the way I have suggested. We are now in the right frame of mind to guide our souls in the direction briefly indicated yesterday—along the first steps of the way leading to Imagination. It is possible to pursue this path in a form consonant with Western life if we simply try to surrender ourselves completely to the world of outer phenomena, so that we absorb them without thinking about them. In ordinary waking life, you will agree, we are constantly perceiving, but in the very act of doing so we are always permeating out perceptions with concepts. Scientific thinking involves a systematic interweaving of perceptions with concepts, building up systems of concepts and so on. In acquiring a capacity for the kind of thinking that gradually results from reading The Philosophy of Spiritual Activity, we become capable of such strong inner activity that we are able to perceive without conceptualising.

There is something further we can do to strengthen our soul-forces so that we are enabled to absorb perceptions in the way I have just described: that is, by refraining from elaborating them with concepts in the very act of absorbing them. We can call up symbolic or other kinds of images—visual images, sound images, images of warmth, taste, and so on. If we thus bring our activity of perception into a state of flux, as it were, and infuse it with life and movement, not in the way we follow when forming concepts, but by working on our perceptions in an artistic or symbolising manner, we shall develop much sooner the power of allowing the percepts to permeate us in their pure essence. Simply to train ourselves rigorously in what I have called phenomenalism—that is, in elaborating the phenomena—is an excellent preparation for this kind of cognition. If we have really striven to reach the material boundaries of cognition—if we have not lazily looked beyond the veil of sense for metaphysical explanations in terms of atoms and molecules, but have used concepts to set in order the phenomena and to follow them through to their archetypes—then we have already undergone a training which can enable us to keep all conceptional activity away from the phenomena. And if at the same time we turn the phenomena into symbols and images, we shall acquire such strength of soul as to be able, one might say, to absorb the outer world free from concepts.

Obviously we cannot expect to achieve this all at once. Spiritual research demands far more of us than research in a laboratory or observatory. Above all an intense effort of will is required. For a time we should strive to concentrate on a symbolic picture, and occupy ourselves with the images that arise, leaving them undisturbed by phenomena present in the soul. Otherwise they will disappear as we hurry through life from sensation to sensation and from experience to experience. We should accustom ourselves to contemplating at least one such image—whether of our own creation or suggested by somebody else—for longer and longer periods. We should penetrate to its very core, concentrating on it beyond the possibility of being influenced by mere memory. If we do all this, and keep repeating the process, we can strengthen our soul forces and finally become aware of an inner experience, of which formerly we had not the remotest inkling.

Finally—it is important not to misunderstand what I am going to say—it is possible to form a picture of something experienced only in our inner being, if we recall especially lively dream-pictures, so long as they derive from memories and do not relate directly to anything external, and are thus a sort of reaction stemming from within ourselves. If we experience these images in their fullest depth, we have a very real experience; and the point is reached when we meet within ourselves the spiritual element which actuates the processes of growth. We meet the power of growth itself. Contact is established with a part of our human make-up which we formerly experienced only unconsciously, but which is nevertheless active within us. What do I mean by “experienced unconsciously?”

Now I have told you how from birth until the change of teeth a spiritual soul force works on and through the human being; and after this it more or less detaches itself. Later, between the change of teeth and maturity, it immerses itself, so to speak, in the physical body, awakening the erotic impulse—and much else besides. All this happens unconsciously. But if we consciously use such soul-activities as I have described in order to observe how the qualities of soul and spirit can penetrate our physical make-up, we begin to see how these processes work in a human being, and how from the time of his birth he is given over to the external world. Nowadays this relation to the outer world is regarded as amounting to nothing more than abstract perception or abstract knowledge. This is not so. We are surrounded by a world of colour, sound and warmth and by all kinds of sensory impressions. As our thinking gets to work on them, our whole being receives yet further impressions. When unconscious experiences of childhood come to be experienced consciously, we even find that, while we were absorbing colour and sound impressions unconsciously, they were working spiritually upon us. When, between the change of teeth and maturity, erotic feelings make their first impact, they do not simply grow out of our constitution but come to meet us from the cosmos in rays of colour, sound and warmth.

But warmth, light and sound are not to be understood in a merely physical sense. Through our sensory impressions we are conscious only of what I might call outer sound and outer colour. And when we thus surrender ourselves to nature, we do not encounter the ether-waves, atoms and so on which are imagined by modern physics and physiology. Spiritual forces are at work in the physical world; forces which between birth and death fashion us into the human beings we are.

When once we tread the paths of knowledge which I have described, we become aware of the fact that it is the outer world which forms us. As we become clearly conscious of spirit in the outer world, we are able to experience consciously the living forces at work in our bodies. It is phenomenology itself that reveals to us so clearly the existence of spirit in the outer world. It is the observation of phenomena, and not abstract metaphysics, that brings the spiritual to our notice, if we make a point of observing consciously what we would otherwise tend to do unconsciously; if we notice how through the sense-world spiritual powers enter into our being and work formatively upon it.

Yesterday I pointed out to you that the Eastern sage virtually ignores the significance of speech, thought and ego-perception. His attitude towards these activities is different, for speech, perception of thoughts and ego-perception tend at first to lead us away from the spiritual world into social contact with other human beings. We buy our way into social life, as it were, by exposing our thoughts, our speech and our ego-perception and making them communicable. The Eastern sage lived in the word and resigned himself to the fact that it could not be communicated. He felt the same about his thoughts; he lived in his thinking, and so on. In the West we are more inclined to cast a backward glance at humanity as we follow the path into the super-sensible world.

At this point it is well to remember that man has a certain kind of sensory organisation within him. I have already described the three inner senses through which he becomes aware of his inner being, just as he perceives what goes on around him. We have a sense of balance, which tells us of the space we occupy as human beings and within whose limits our wills can function. We have a sense of movement, which tells us, even in the dark, that we are moving. This knowledge comes from within and is not derived from contact with outside objects that we may touch in passing. We have a “sense of life,” through which we are aware of our general state of health, or, one might say, of our constantly changing inward condition.

It is just in the first seven years of our life that these three inner senses work in conjunction with the will. We are guided by our sense of balance: and a being that, to begin with, cannot move about and later on can only crawl, is transformed into one that can stand upright and walk. When we learn to walk upright, we are coming to grips with the world. This is possible only because of our sense of balance. Similarly, our sense of movement and our sense of life contribute to our development as integrated human beings.

Anybody able to apply laboratory standards of objective observation to the study of man's development—spirit-soul as well as physical—will soon discover how those forces that form the human being and are especially active in the first seven years free themselves and begin to assume a different aspect from the time of the change of teeth. By this time a person is less intimately connected with his inner life than he was as a child. A child is closely bound up inwardly with human equilibrium, movement and processes of life. As emancipation from them gradually occurs, something else is developing. A certain adjustment is taking place to the three senses of smell, taste and touch.

A detailed observation of the way a child comes to grips with life is extraordinarily interesting. This can be seen most obviously, of course, in early life, but anybody trained to do so can see it clearly enough later on as well. I refer to the process of orientation made possible by the senses of smell, of taste and of touch. The child in a manner expels from himself the forces of equilibrium, movement and life and, while he is so doing, draws into him the qualitative senses of smell, taste and touch. Over a fairly long period the former are, so to speak, being breathed out and the latter breathed in; so that the two trinities encounter each other within our organism—the forces of equilibrium, movement and life pushing their way outward from within, while smell, taste and touch, which point us to qualities, are pressing inwards from without. These two trinities of sense interpenetrate each other; and it is through this interpenetration that the human being first comes to realise himself as a true self.

Now we are cut off from outer spirituality by speech and by our faculties of perceiving the thoughts and perceiving the egos of others—and rightly so, for if it were otherwise we could never in this physical life grow into social beings. [See previous lecture.] In precisely the same way, inasmuch as the qualities of smell, taste and touch wax counter to equilibrium, movement and life, we are inwardly cut off from the last three—which would otherwise disclose themselves to us directly. One could say that the sensations of smell, taste and touch form a barricade in front of the sensations of balance, movement and life and prevent our experiencing them.

What is the result of that development towards Imagination of which I spoke? It is this. The oriental stops short at speech in order to live in it; stops at thought in order to live in it; stops at ego-perception in order to live in it; and by these means makes his way outward into the spiritual world. We, as the result of developing Imagination, do something similar when we absorb the external percept without conceptualising it. But the direction we take in doing this is the opposite to the direction taken by an oriental who practises restraint in the matter of speech, thought-perception and ego-perception. He stays still in these. He lives his way into them. The aspirant to Imagination, on the other hand, worms his way inward through smell, taste and perception; he penetrates inward and, ignoring the importunities of his sensations of smell, taste and touch, makes contact with the experiences of equilibrium, movement and life.

It is a great moment when we have penetrated the sensory trinity, as I have called it, of taste, smell and touch, and we stand naked, as it were, before essential movement, equilibrium and life.

Having thus prepared the ground, it is interesting to study what it is that Western mysticism so often has to offer. Most certainly, I am very far from decrying the elements of poetry, beauty and imaginative expression in many mystical writings. Most certainly I admire what, for instance, St. Theresa, Mechthild of Magdeburg and others have to tell us, and indeed Meister Eckhardt and Johannes Tauler; but all this reveals itself also to the true spiritual scientist. It is what arises if one follows an inward path without penetrating through the domain of smell, taste and touch. Read what has been written by individuals who have described with particular clarity what they have experienced in this way. They speak of an inner sense of taste, experienced in connection with the soul-spiritual element in man's inner being. They refer also to smell and touch in a special way. Anybody, for instance, who reads Mechthild of Magdeburg or St. Theresa rightly will see that they follow this inward path, but never penetrate right through smell, taste and touch. They use beautiful poetic imagery for their descriptions, but they are speaking only of how one can smell, taste and touch oneself inwardly.

It is indeed less agreeable to see the true nature of reality with spiritually developed senses than to read the accounts given by a sensual mysticism—the only term for it—which fundamentally gratifies only a refined inward-looking egotism of soul. As I say, much as this mysticism is to be admired—and I do admire it—the true spiritual scientist has to realise that it stops half-way. What is manifest in the splendid poetic imagery of Mechthild of Magdeburg, St. Theresa and others is really only what is smelt, tasted and touched before attaining to true inwardness.

Truth can be unpleasant, perhaps even cruel, at times. But modern man has no business to become rickety in soul through following a vague incomplete mysticism. What is required to-day is to penetrate the true mysteries of man's inner nature with all our intellectual powers—with the same powers that we have disciplined in the cause of science and used to effect in the outer world. There is no mistaking what science is. It is respected for the very method and discipline it demands. It is when we have learnt to be scientific that we appreciate the achievements of a vague mysticism at their true worth but we also discover that they are not what spiritual science has to foster. On the contrary, the task of spiritual science is to reveal clearly the true nature of man's being. This in turn makes possible a sound understanding of the outer world.

Instead of speaking in this way, as the truth demands of me, I could be claiming the support of every vague, woolly mystic, who goes in for mysticism to satisfy the inward appetite of his soul. That is not our concern here, but rather the discovery of powers that can be used for living; spiritual powers that are capable of informing our scientific and social life.

When we have come to grips with the forces that dwell in our senses of balance, life and movement, then we have reached something that is first of all experienced through its transparency as man's essential inward being. The very nature of the thing shows us clearly that we cannot penetrate any deeper. What we do find is quite enough to be going on with, for what we discover is not the stuff of vague mystical dreams but a genuine organology. Above all, we find within ourselves the true nature of balance and movement, and of the stream of life. We find this within ourselves.

When this experience is complete, something unique has taken place. In due course we discover something. An essential prerequisite is, as I have said, to have worked carefully through The Philosophy of Spiritual Activity. The Philosophy is then left, so to speak, on one side, while we pursue the inward path of contemplation and meditation. We have advanced as far as balance, movement and life. We live in this life, balance and movement. Parallel with our pursuit of the way of contemplation and meditation, but without any other activity on our part, our thinking in connection with The Philosophy of Spiritual Activity has undergone a transformation. We have been able to experience as pure thought what a philosophy such as this has to offer; but now that we have worked upon ourselves in another sphere, our inner soul life; this has turned into something quite different. It has taken on new dimensions and is now much more full of meaning. While on the one hand we have been penetrating our inward being and have deepened our power of Imagination, we have also lifted out of the ordinary level of consciousness the fruits of our thinking on The Philosophy of Spiritual Activity. Thoughts which formerly had a more or less abstract existence in the realm of pure cerebration have now become significant forces. They are now alive in our consciousness, and what was once pure thinking has become Inspiration. We have developed Imagination; and thinking has been transformed into Inspiration.

What we have attained by these two methods in our progress along this road has to be clearly differentiated. On the one hand we have gained Inspiration from what was, to begin with, pure thought. On the other hand, there is the experience that comes to us through our senses of balance, movement and life. We are now in a position to unite the two forms of experience, the outer and the inner. The fusion of Inspiration and Imagination brings us to Intuition.

What have we accomplished now? I can answer this question by approaching it from the other side. First of all I must draw attention to the steps taken by the Oriental seer, who wishes to advance further after being trained in the mantras and experiencing the living word and language. He now learns to experience not only the rhythms of language but also, and in a sense consciously, the process of breathing. He has, as it were, to undergo an artificial kind of breathing by varying it in all kinds of ways. For him this is one step up; but this is not something to be taken over in its entirety by the West.

What does the Eastern student of yoga attain by consciously regulating his breathing in a variety of ways? He experiences something very remarkable when he breathes in. As he does so, he is brought into contact with a quality of air that is not to be found when we experience air as a purely physical substance, but only when we unite ourselves with the air and so experience it spiritually. A genuine student of yoga, as he breathes in, experiences something that works upon his whole being, an activity that is not completed in this life and does not end with death. The spiritual quality of the outer air enters our being and engenders in us something that goes with us through the gate of death. To experience the breathing process consciously means taking part in something that continues when we have laid aside our bodies. To experience consciously the process of breathing is to experience both the reaction of our inner being to the drawing in of breath and the activities of our soul-spiritual being before birth: or let us say rather that we experience our conception and the factors that contribute to our embryonic development and work on us further within our organism as children. Breathing consciously means realising our own identity on the far side of birth and death. Advancing from the experience of the word and of language to that of breathing means penetrating further into an inspired realisation of the eternal in man. We Westerners have to experience much the same—but in a different sphere.

What in fact is the process of perception? It is only a modification of the breathing process. As we breathe in, the air presses on our diaphragm and on our whole being. Brain fluid is driven up through our spinal column into our brain. This establishes a connection between breathing and cerebral activity. Breathing, in so far as it influences the brain, works upon our sense-activity in the form of perception. Drawing in breath has various sides to it, and one of these is perception.

How is it when we breathe out? Brain fluid descends and exerts pressure on the circulation of the blood. The descent of brain fluid is bound up with the activity of will and also with breathing out. Anybody who really makes a study of The Philosophy of Spiritual Activity will discover that when we attain to pure thinking, a fusion of thinking and willing takes place. Pure thinking is fundamentally an expression of will. So it comes about that what we have characterised as pure thinking is related to what the Easterner experiences in the process of breathing out.

Pure thinking is related to breathing out, just as perception is related to breathing in. We have to go through the same process as the yogi, but in a more inward form. Yoga depends on the regulation of breathing, both in and out, and in this way comes into contact with the eternal in man. What should Western man do? He can transform into soul-experience both perception on the one hand and thinking on the other. He can unite in his inner experience perception and thinking, which would otherwise only come quietly together in a formal abstract way, so that he has the same experience inwardly in his soul and spirit as he has physically in breathing in and out. Breathing in and out are physical experiences. When they are harmonised, we experience the eternal.

We experience thought-perception in our everyday lives. As we bring movement into our soul life, we become aware of rhythm, of the swing of the pendulum, of the constant movement to and fro of perception and thinking. Higher realities are experienced in the East by breathing in and out. The Westerner develops a kind of breathing process in his soul and spirit, in place of the physical breathing of yoga, when he develops within himself, through perception, the vital process of transformed in-breathing and, through thinking, that of out-breathing; and fuses concept, thought and perception into a harmonious whole. Gradually, with the beat of this rhythmical breathing process in perception and thinking, his development advances to true spiritual reality in the form of Imagination, Inspiration and Intuition.

In my Philosophy of Spiritual Activity I indicated as a philosophical fact that reality is the product of the interpenetration of perception and thinking. Since this book was designed to deal with man's soul activity, some indication should also be given of the training that Western man needs if he is to penetrate the spiritual world. The Easterner speaks of the systole and diastole, breathing in and out. In place of these terms Western man should put perception and thinking. Where the Oriental speaks of the development of physical breathing, we in the West say: development of soul-spiritual breathing in the course of cognition through perception and thinking.

All this should perhaps be contrasted with the kind of blind alley reached by Western spiritual development. Let me explain what I mean. In 1841 Michelet, the Berlin philosopher, published Hegel's posthumous works of natural philosophy. Hegel had worked at the end of the eighteenth century, together with Schelling, at laying the foundations of a system of natural philosophy. Schelling, with the enthusiasm of youth, had built his natural philosophy in a remarkable way on what he called intellectual contemplation. But he reached a point where he could make no further progress. His immersion in mysticism produced splendid results in his work, Bruno, or concerning the Divine and Natural Principle in Things, and that fine piece of writing, Human Freedom, or the Origin of Evil. But for all this he could make no progress and began to hold back from expressing himself at all. He kept promising to follow things up with a philosophy that would reveal the true nature of those hidden forces at which his earlier natural philosophy had only hinted.

When Hegel's natural philosophy appeared in 1841, through Michelet, the position was that Schelling's expected and oft-promised philosophical revelations had still not been vouchsafed to the public. He was summoned to Berlin. But what he had to offer contained no spiritual qualities to permeate the natural philosophy he had founded. He had struggled to create an intellectual picture of the world. He stood still at this point, because he was unable to use Imagination to enter the sphere of which I have been speaking to you to-day. So there he was at a dead end.

Hegel, who had a more rational intellect, had taken over Schelling's thoughts and carried them further by applying pure thinking to the observation of nature. That was the origin of Hegel's natural philosophy. So Schelling's promise to explain nature in spiritual terms was never fulfilled, and we got Hegel's natural philosophy which was to be discarded by science in the second half of the nineteenth century. It was not understood and was bound to remain so, for there was no connection between phenomenology, or the true observation of nature, and the ideas contained in Hegel's natural philosophy. It was a strange confrontation: Schelling travelling from Munich to Berlin, where something great was expected of him, and it turned out that he had nothing to say. This was a disappointment for all those who believed that through Hegel's natural philosophy revelations about nature would emerge from pure thinking. The historical fact is that Schelling reached the stage of intellectual contemplation but not that of genuine Imagination; while Hegel showed that if pure thinking does not lead on to Imagination, it cannot lead to Inspiration and to an understanding of nature's secrets. This line of Western development had terminated in a blind alley.

There was nothing—nothing permeated with the spirit—to set against Eastern teaching, which only engendered scepticism in the West. Anyone who has lovingly immersed himself in the true Schelling and Hegel, and has thus been able to see, with love in his heart, the limitations of Western philosophy, should turn his attention to Anthroposophy. He should work to bring about an anthroposophically orientated Spiritual Science for the West, so that we come to possess something of spiritual origin to compare with what the East has created through the interaction of systole and diastole.

For us in the West, there is the spiritual-soul rhythm of perception and thinking, through which we can rise to something more than a merely abstract science. It opens the way to a living science, which on that account enables us to live in harmony with truth. After all the misfires of the Kantian, Schellingian and Hegelian philosophies, we have come to the point where we need something that can show, by revealing the way of the spirit, how truth and science are related. The truth that dwells in a spiritualised science would be a healing power in the future development of mankind.

To-day I should like to make some introductory remarks to what I am going to lay before you in the coming days. My reason for doing this is that you may know the purpose of these talks from the outset.

It will not be my task during the following days to deal with any narrowly defined, special branch of science, but to give various wider viewpoints, having in mind a quite definite goal in relation to science. I should therefore like to warn people not to describe this as an ‘Astronomical Course’. It is not meant to be that. But it will deal with something that I feel is especially important for us to consider at this time. I have therefore given it the title “The relation of the diverse branches of Natural Science to Astronomy,” and today in particular I shall explain what I actually intend with the giving of this title.

The fact is that in a comparatively short time much will have to be changed within what we call the sphere of science, if it is not to enter upon a complete decline. Certain groups of sciences which are now comprised under various headings and are permitted to be represented under these headings, in our ordinary schools, will have to be taken out their grooves and be classified from quite other aspects. This will necessitate a far reaching regrouping of our sciences. The grouping at present employed is entirely inadequate for a world-conception based upon reality, and yet our modern world holds so firmly to such traditional classification that it is on this basis that candidates are chosen to occupy the professorial chairs in our Universities. People confine themselves for the most part to dividing the existing, circumscribed fields of Natural Science into yet further special branches, and they then look to the specialists or experts as they are called. But a change must come into the whole scientific life by the advent of quite different categories, within which will be united, as in a whole new field of science, things that today are dealt with in Zoology or Physiology, or again, let us say, in the Theory of Knowledge. The older forms of scientific classification, often extremely abstract, must die out, and quite new scientific combinations must arise. This will meet with great obstacles at first, because people today are trained in the specialized branches of science and it will be difficult for them to find an approach to what they will urgently need in order to bring about a combination of scientific material in accordance with reality.

To put in concisely, I might say: We have today a science of astronomy, of Physics, of Chemistry, of Philosophy, we have a science of Biology, of Mathematics, and so on. Special branches have been formed, almost, I might say, so that the various specialists will not have such hard work in order to become well grounded in their subject. They do not have too much to do in mastering all the literature concerned, which, as we know, exists in immense quantities. But it will be a matter of creating new branches which will comprise quite different things, including perhaps at the same time something from Astronomy, something from Biology, and so on. For this, a reshaping of our whole life of science will of course be essential. Therefore, what we term Spiritual Science, which does indeed aim to be of a universal nature, must work precisely in this direction. It must make it its special mission to work in this direction. For we simply cannot get any further with the old grouping. Our Universities confront the world today, my dear friends, in a way that is really quite estranged from life. They turn out mathematicians, physiologists, philosophers, but none of them have any real relation to the world. They can do nothing but work in their narrowly confined spheres, putting before us a picture of the world that becomes more and more abstract, less and less realistic.

It is the change here indicated—a deep necessity for our time—to which I want to do justice in these lectures. I should like you to see how impossible it will be to continue the older classifications indefinitely, and I therefore want to show how other branches of science of the most varied kinds, which, in their present way of treatment, take no account of Astronomy, have indeed definite connections with Astronomy, that is, with a true knowledge of universal space. Certain astronomical facts must perforce be taken into account in other branches of science too, so that we may learn to master these other fields in a way conformable to reality.

The task of these lectures is therefore to build a bridge from the different fields of scientific thought to the field of Astronomy, that astronomical understanding may appear in the right way in the various fields of science.

In order not to be misunderstood, I should like to make one more remark about method. You see, the manner of presenting scientific facts which is customary nowadays must undergo considerable change, because it actually arises out of the scientific structure which has to be overcome. When today facts are referred to, which lie somewhat remote from man's understanding,—remote, just because he does not meet with them at all in his scientific knowledge,—it is usual to say: “That is stated, but no proved.” Yet in scientific work is often quite inevitable that statements must be made at first purely as results of observation, which only afterwards can be verified as more and more facts are brought to support them. So it would be wrong to assume, for instance, that right at the beginning of a discourse someone could break in and say, “That is not proved.” It will be proved in the course of time, but much will first have to be presented simply from observation, so that the right concept, the right idea, may be created.

And so I beg of you to take these lectures as a whole, and to look in the last lectures for the plain proof of many things which seem in the first lectures to be mere statements. Many things will then be verified which I shall have to handle at first in such a way as to evoke the necessary concepts and ideas.

Astronomy as we know it today, even including the domain of Astrophysics, is fundamentally a modern creation. Before the time of Copernicus or Galileo men thought about astronomical phenomena in a way which differed essentially from the way we think today. It is even extraordinarily difficult to indicate the way in which man still thought of Astronomy in, say, the 13th and 14th centuries, because this way of thinking has become completely foreign to modern man. We only live in the ideas which have been formed since the time of Galileo, Kepler, Copernicus; and from a certain point of view that is perfectly right. They are ideas which treat of the distant phenomena of universal space, in so far as they are concerned with Astronomy, in a mathematical and mechanical way. Men think of these phenomena in terms of mathematics and mechanics. In observing the phenomena, men base their ideas upon what they have acquired from an abstract mathematical science, or an abstract science of mechanics. They calculate distances, movements and forces. But the qualitative outlook still in existence in the 13th and 14th centuries, which distinguished Individualities in the stars, an Individuality of Jupiter, of Saturn ... this has become completely lost to modern man. I will make no criticism of the things at the moment, but will only point out that the mechanical and mathematical way of treating what we call the domain of Astronomy has become the exclusive one. Even if we acquaint ourselves with the stars in a popular fashion without understanding mathematics or mechanics, we still find it presented, even if in a manner suitable for the lay-mind, entirely in ideas of space and time, of a mathematical and mechanical kind. No doubts of any kind exist in the minds of our contemporaries—who believe that their judgment is authoritative—that this is the only way in which to regard the starry heavens. Anything else, they are convinced, would be merely amateurish.

Now, if the question arises as to how it has actually come about that this view of the starry heavens has emerged in the evolution of civilization, the answer of those who regard the modern scientific mode of thought as absolute, will be different from the reply which we are able to give. Those who regard the scientific thought of today as something absolute and true, will say: Well, you know, among earlier humanity there were not yet any strictly scientifically formed ideas; man had first to struggle through to such ideas, i. e., to the mathematical, mechanical mode of regarding celestial phenomena of the Universe, a later humanity has worked through to a strictly scientific comprehension of what does actually correspond to reality.

This is an answer that we cannot give, my dear friends. We must take up our position from the standpoint of the evolution of humanity, which in the course of its existence, has introduced various inner forces into its consciousness. We must say to ourselves: The manner of observing the celestial phenomena which existed among the ancient Babylonians, the Egyptians, perhaps even the Indian people, was due to the particular form which the development of the human soul-forces was taking in those times. Those human soul-forces had to be developed with the same inner necessity with which a child between the 10th and 15th year must develop certain soul-forces, while in another period it will developing other faculties, which lead it to different conclusions about the world. Then came the Ptolemaic system. That arose out of different soul-forces. Then our Copernican system. That arose from yet other soul-forces. The Copernican system did not develop because humanity had happily struggled through to objectivity, whereas before they had all been as children, but because humanity since the middle of the 15th century needed precisely the mathematical, mechanical faculties for its development. That is why modern man sees the celestial phenomena in the picture formed by the mathematical, mechanical faculties. And he will some day see them again in a different way, when in his development he has drawn up out of the depths of the soul other forces,—to his own healing and benefit. Thus it depends upon humanity what form the world-concept takes. But it is not a question of looking back in pride to earlier times when men were “more childlike,” and then thinking that in modern times we have at last struggled through to an objective understanding which can now endure for all future ages.

There is something which has become a real necessity to later humanity and has given color to the requirements of the scientific mind. It is this: Men strive on the one hand for ideas that are clear and easy to control—namely, mathematical ideas—, and on the other hand they strive for ideas through which they can surrender most strongly to an inner compulsion. The modern man at once becomes uncertain and nervous when he does not feel the strong inner compulsion presented, for instance, by the argument of the Pythagorean theorem, but realizes, let us say, that the figure which is drawn does not decide for him, but that he must develop an activity of soul and decide for himself. Then he at once becomes uncertain and nervous and is no longer willing to continue the line of thought. So he says: That is not exact science; subjectivity comes into it. Modern man is really dreadfully passive; he would like to be led everywhere by a chain of infallible arguments and conclusions. Mathematics satisfies this requirement, at least in most cases; and where it does not, where man have interposed their own opinion in recent times,—well, my dear friends, the results are according! Men still believe that they are being exact, while they hit upon the most incredible ideas.

Thus in mathematics and mechanics men think they are being led forward by leading-strings of concepts which are linked together through their own inherent logic. They feel then as if they had ground under their feet, but the moment they step off it they do not want to go on any further. Concepts which are easy to grasp on the one hand, and the element of inner compulsion on the other: this is what modern man needs for his “safety.” Fundamentally, it is on this basis that the particular form of world-conception, supplied by the modern science of Astronomy, has been built up. I am not at the moment speaking of the single facts, but merely of the world-conception as a whole.

This attitude towards a mathematical, mechanical conception of the world has so penetrated the consciousness of humanity, my dear friends, that people have come to regard everything that cannot be treated in this way as more or less unscientific. From this feeling proceeded such a phrase as that of Kant, who said: In every domain of science there is only so much real science as there is mathematics in it; one ought really to bring Arithmetic or Geometry into all the sciences. But this idea, as we know, breaks down when we think how remote the simplest mathematical ideas are to those, for instance, who study Medicine. Our present division of the sciences gives to a medical student practically nothing in the way of mathematical ideas.

And so it comes about that on the one hand what is called astronomical knowledge has been set up as an ideal. DuBois-Raymond has defined this in his address on the limits of the knowledge of Nature by saying: We only grasp truths in Nature and satisfy our need of causality inasmuch as we can apply the astronomical type of knowledge. That is to say, we regard the celestial phenomena in such a way that we draw the stars upon the chart of the sky and calculate with the material which is there given us. We can state exactly: There is a star, it exercises a force of attraction upon other stars. We begin to calculate, having the different things, to which our calculations apply, visibly before us. This is what we have brought into Astronomy in the first place. Now we observe, let us say, the molecule. Within the complex molecule we have the atoms, exercising a force of attraction on one another, moving around each other,—forming, as it were, a little universe. We observe this molecule as a small cosmic system and are satisfied if it all seems to fit. But then there is the great difference that when we look out into the starry sky all the details are given to us. We can at most ask whether we understand them rightly, whether after all, there might not be some other explanation than the one given by Newton. We have the given details and then we spin a mathematical, mechanical web over them. This web of thought is actually added to the given facts, but from a scientific point of view it satisfies the modern need of man. And now we carry the system, which we have first thought out and devised, into the world of the molecule and atom. Here we add in thought what in the other case was given to us. But we satisfy our so-called need of causality by saying: What we think of as the smallest particle, moves in such and such a way, and it is the objective counterpart of what we experience subjectively as light, sound, warmth etc. We carry the astronomic form of knowledge into every phenomenon of the world and thus satisfy our demand for causality. Du-Bois Raymond has expressed it quite bluntly: “When one cannot do that, there is no scientific explanation at all.”

Yes, my dear friends, what is here claimed should actually imply that if, for example, we wished to come to a rational form of therapy, that is to say, to understand the activity of a remedy, we should have to be able to follow the atoms in the substance of the remedy as we follow the movements of the Moon, the Sun, the planets and the fixed stars. They would all have to become little cosmic systems. We should have to be able to calculate how this or that remedy would work. This was actually an ideal for some people not so very long ago. Now they have given up such ideals. Such an idea collapses not only in reference to such a far off sphere as a rational therapy, but in those lying more within reach, simply because our sciences are divided as they are today. You see, the modern doctor is educated in such a way that he masters extraordinarily little of pure mathematics. We may talk to him perhaps of the need for a knowledge of astronomy but it would be of no use to speak of introducing mathematical ideas into his field of work. But as we have seen, everything outside mathematics, mechanics and astronomy should be described, according to the modern notion, as being unscientific in the strict sense of the word. Naturally that is not done. People regard these other sciences too as exact, but this is most inconsistent. It is, however, characteristic of the present time that the demand should have been made at all for everything to be understood on the model of mathematical Astronomy.

It is hard today to talk to people in a serious way about such thing; how hard this is I should like to make clear to you by an example.

You know of course that the question of the form of the human skull has played a great role in modern biology. I have also spoken of this matter may times in the course of our anthroposophical lectures. Goethe and Oken put forward magnificent thoughts on this question of the human skull-bones. The school of Gegenbauer also carried out classical researches upon it. But something that could satisfy the urge for a deeper knowledge in this direction does not in fact exist today.

People discuss, to what extent Goethe was right in saying that the skull-bones are metamorphosed vertebrae, bones of the spine. But it is impossible to arrive at any really penetrating view of this matter today, because in the circles where these things are discussed one would scarcely be understood, and where an understanding might be forthcoming these things are not talked of because they are not of interest. You see, it is practically impossible today to bring together in close working association a thoroughly modern doctor, a thoroughly modern mathematician,—i.e., one who is master of higher mathematics—, and a man who could understand both of them passably well. These three men could scarcely understand one another. The one who would sit in the middle, understanding both of them slightly, would be able at a pinch to talk a little with the mathematician and also with the doctor. But the mathematician and the doctor would not be able to understand each other upon important questions, because what the doctor would have to say about them would not interest the mathematician, and what the mathematician would have to say—or would say, if he found words at all,—would not be understood by the doctor, who would be lacking the necessary mathematical background. This is what would happen in an attempt to solve the problem I have just put before you. People imagine: If the skull-bones are metamorphosed vertebra, then we ought to be able to proceed directly, through a transformation which it is possible to picture spatially, from the vertebra to the skull. To extend the idea still further to the limb-bones would, on the basis of the accepted premises, be quite out of the question. The modern mathematician will be able, from his mathematical studies, to form an idea of what it really means when I turn a glove inside out, when I turn the inside to the outside. One must have in mind a certain mathematical handling of the process by which what was formerly outside is turned inward, and what was inside is turned to the outside. I will make a sketch of it (Fig. 1)—a structure of some sort that is first white on the outside and red inside. We will treat this structure as we did the glove, so that it is now red outside and white inside (Fig. 2).

But let us go further, my dear friends, and picture to ourselves that we have something endowed with a force of its own that does not admit of being turned inside out in such a simple way as a glove which still looks like a glove after being inverted. Suppose that we invert something which has different stresses of force on the outer surface from those on the inner. We shall then find that simply through the inversion quite a new form arises. The form may appear thus before we have reversed it (Fig. 1): we turn it inside out and now different forces come into consideration on the red surface and on the white, so that perhaps, purely through the inversion, this form arises (Fig. 3). Such a form might arise merely in the process of inversion. When the red side faced inward, forces remained dominant which are developed differently when it is turned outward. And so with the white side; only when turned towards the inside can it develop its inherent forces.

It is of course quite conceivable to give a mathematical presentation of such a subject, but people are thoroughly disinclined nowadays to apply to reality what is arrived at conceptually in such a way. The moment, however, we learn to apply this to reality, we become able to see in our long bones or tubular bones (that is, in the limb bones), a form which, when inverted, becomes our skull bones! In the drawing, let the inside of the bone, as far as the marrow, be depicted by the red, the outside by the white (Fig. 4). Certain forms and forces, which can of course be investigated, are turned inward, and what we see when we draw away the muscle from the long bone is turned outward. But now imagine these hollow bones turned inside out by the same principle as I have just given you, in which other conditions of stress and strain are brought into play;

then you may easily obtain this form (Fig. 5). Now it has the white within, and what I depicted by the red comes to the outside. This is in fact the relationship of a skull-bone to a limb-bone, and in between lies the typical bone of the back—the vertebra of the spinal column. You must turn the tubular bone inside out like a glove according to its indwelling forces; then you obtain the skull-bone. The metamorphosis of the bones of the limbs into the skull-bones is only to be understood when keeping in mind the process of inversion, or ‘turning inside-out’. The important thing to realizes is that what is turned outward in the limb-bones is turned inward in the skull. The skull-bones turn towards a world of their own in the interior of the skull. That is one world. The skull-bone is orientated to the world, just as the limb-bone is orientated outward, towards the external world. This can be clearly seen in the case of the bones. Moreover, the human organism as a whole is so organized that it has on the one hand a skull organization, and on the other a limb-organization, the skull-organization being oriented inward, the limb-organization outward. The skull contains an inner world, the limb-man an outer world, and between the two is a kind of balancing system which preserves the rhythm.

My dear friends, take any literature dealing with the theory of functions, or, say, with non-Euclidean geometry, and see what countless ideas of every kind are brought forward in order to get beyond the ordinary geometrical conception of three-dimensional space;—to extend the domain—widen out the concept of geometry. You will see what industry and ingenuity are employed. But now suppose that you have become an expert at mathematics, who knows the theory of functions well and understands all that can be understood today of non-Euclidean geometry. I should like now to put a question concerning much that tends in this direction (Forgive me if it seems as if one did not value them highly, speaking of these things in such trivial terms. And yet I must do so, and I beg the audience, especially trained mathematicians, to turn it over in their minds and see if there is not truth in what I say.) The question could be put as follows: What is the use of all this spinning of purely mathematical thoughts? What is it worth to me, so to speak, in pounds, shillings and pence? No one is interested in the spheres in which it might perhaps find concrete application. Yet if we were to apply to the structure of the human organism all that has been thought out in non-Euclidean geometry, then we should be in the realm of reality, and applying immeasurably important ideas to reality, not wandering about in mere speculations. If the mathematician were so trained as to be interested also in what is real,—in the appearance of the heart, for example, so that he could form an idea of how through a mathematical process he could turn the heart inside out, and how thereby the whole human form would arise,—if he were taught to use his mathematics in actual life, then he could be working in the realm of the real. It would then be impossible to have the trained mathematician on the one hand, not interested in what the doctor learns, and on the other, the physician, understanding nothing of of how the mathematician—though in a purely abstract element—is able to change and metamorphose forms. This is the situation we must alter. If not, our sciences will fall into decay. They grow estranged from one another; people no longer understand each other's language.

How then is science to be transformed into a social science, as is implied in all that I shall be telling you in these lectures? A science which leads over into social science is not yet in existence.

On the one hand we have Astronomy, tending more and more to be clothed in mathematical forms of thought. It has become so great in its present form just because it is a purely mathematical and mechanical science. But there is another branch of science which stands, as it were, at the opposite pole to Astronomy, and which cannot be studied in its real nature without Astronomy. It is however, impossible, as science is today, to build a bridge between Astronomy and this other pole of science, namely, Embryology. He alone is studying reality, who on the one hand studies the starry skies and on the other hand the development of the human embryo. How is the human embryo generally studied today? Well, it is stated: The human embryo arises from the interaction of two cells, the sex-cells or gametes, male and female. These cells develop in the parent organism in such a way as to attain a certain state of independence before they are able to interact. They then present a certain contract, the one cell, the male, calling forth new and different possibilities of development in the other, the female. The question is put: What is a cell? As you know, since about the middle of the 19th century, Biology has largely been built upon the cell theory. The cell is described as a larger or smaller, spherule, consisting of albuminous or protein-like substances. It has a nucleus within it of a somewhat different structure and around the whole is an enclosing membrane. As such, it is the building-stone for all that arising by way of living organisms. The sex-cells are of a similar nature but are formed differently according to whether they are male or female, and from such cells every more complicated organism is built up.

But now, what is actually meant when it is said that an organism builds itself up from these cells? The idea is that substances which are otherwise in Nature are taken up into these cells and then no longer work in quite the same way as before. If oxygen, nitrogen or carbon are contained in the cells, the carbon, for instance, does not have the effect upon some other substance outside, that it would have had before; such power of direct influence is lost to it. It is taken up into the organism of the cell and can only work there as conditions in the cell allow. That is to say, the influence is exerted not so much by the carbon, but by the cell, which makes use of the particular characteristics of carbon, having incorporated a certain amount of it into itself. For example, what man has within him in the form of metal—iron for instance—only works in a circuitous way, via the cell. The cell is the building-stone. So in studying the organism, everything is traced to the cell. Considering at first only the main bulk of the cell, without the nucleus and membrane, we distinguish two parts: a transparent part composed of this fluid, and another part forming sort of framework. Describing it schematically, we may say that there is the framework of the cell, and this is embedded, as it were, in the other substance which, unlike the framework, is quite unformed. (Fig. 6) Thus we must think of the cell

as consisting of a mass which remains fluid and unformed and a skeleton or framework which takes on a great variety of forms. This then is studied. The method of studying cells in this way has been pretty well perfected; certain parts in the cell can be stained with color, others do not take the stain. Thus with carmine or saffron, or whatever coloring matter is used, we are able to distinguish the form of the cell and can thus acquire certain ideas about its inner structure. We note, for instance, how the inner structure changes when the female germ-cell is fructified. We follow the different stages in which the cell's inner structure alters; how it divides; and how the parts become attached to one another, cell upon cell, so that the whole becomes a complicated structure. All this is studied. But it occurs to no-one to ask: With what is this whole life in the cell connected? What is really happening? It does not occur to anyone to ask this.

What happens in the cell is to be conceived, my dear friends, in the following way,—though to be sure, it is still a rather abstract way. There is the cell. For the moment let us consider it in its most usual form, namely the spherical form. This spherical form is partially determined by the thin fluid substance, and enclosed within it is the delicate framework. But what is the spherical form? The thin fluid mass is as yet left entirely to itself and therefore behaves according to the impulses it receives from its surroundings. What does it do? Well, my dear friends, it mirrors the universe around it! It takes on the form of the sphere because it mirrors in miniature the whole cosmos, which we indeed also picture to ourselves ideally as a sphere. Every cell in its spherical form is no less than an image of the form of the whole universe. And the framework inside, every line of the form, is conditioned by its relationship to the structure of the whole cosmos. To express myself abstractly to begin with, think of the sphere of the universe with its imaginary boundary (Fig. 7). In it, you have here a planet, and there a planet (a,a₁). They work in such a way as to exert an influence upon one another in the direction of the line which joins them. Here (m) let us say—diagrammatically, of course,—a cell is formed; its outline mirrors the sphere. Here, within the framework it has a solid part which is due to the working of the one planet on the other. And suppose that here there were another constellation of planets, working upon each other along the line joining them (b,b₁).

And here again there might be yet another planet (c), this one having no counterpart;—it throws the whole construction, which might otherwise have been rectangular, out of shape, and the structure takes on a somewhat different form. And so you have in the whole formation of the framework of the cell a reflection of the relationships existing in the planetary system,—altogether in the whole starry system. You can enter quite concretely into the formation of the cell and you will reach an understanding of this concrete form only if you see in the cell an image of the entire cosmos.

And now take the female ovum, and picture to yourselves that this ovum has brought the cosmic forces to a certain inner balance. They have taken on form in the framework of the cell, and are in a certain way at rest within it, supported by the female organism as a whole. Then comes the influence of the male sex-cell. This has not brought the macrocosmic forces to rest, but works in the sense of a very specialized force. It is as though the male sex-cell works precisely along this line of force (indicated by Dr. Steiner on the blackboard) upon the female ovum which has come to a condition of rest. The cell, which is an image of the whole cosmos, is thereby caused to relinquish its microcosmic form once more to a changing play of forces. At first, in the female ovum, the macrocosm comes to rest in a peaceful image. Then through the male sex-cell the female is torn out of this state of rest, and is drawn again into a region of specialized activity and brought into movement. Previously it had drawn itself together in the resting form of the image of the cosmos, but the form is drawn into movement again by the male forces which are, so to speak, images of movement. Through them the female forces, which are images of the form of the cosmos and have come to rest, are brought out of this state of rest and balance.

Here we may have some idea, from the aspect of Astronomy, of the forming and shaping of something which is minute and cellular. Embryology cannot be studied at all without Astronomy, for what Embryology has to show is only the other pole of what is seen in Astronomy. We must, in a way, follow the starry heavens on the one hand, seeing how they reveal successive stages, and we must then follow the process of development of a fructified cell. The two belong together, for the one is only the image of the other. if you understand nothing of Astronomy, you will never understand the forces which are at work in Embryology, and if you understand nothing of Embryology, you will never understand the meaning of the activities with which Astronomy has to deal. For these activities appear in miniature in the processes of Embryology.

It is conceivable that a science should be formed, in which, on the one hand, astronomical events are calculated and described, and on the other hand all that belongs to them in Embryology, which is only the other aspect of the same thing.

Now look at the position as it is today: you find that Embryology is studied on its own. It would be regarded as madness if you were to demand of a modern embryologist that he should study Astronomy in order to understand the phenomena in his own sphere of work. And yet it should be so. This is why a complete regrouping of the sciences is necessary. It will be impossible to become a real embryologist without studying Astronomy. It will no longer be possible to educate specialists who merely turn their eyes and their telescopes to the stars, for to study the stars in that way has no further meaning unless one knows that it is out of the great universe that the minute and microscopical is fashioned.

All this,—which is quite real and concrete,—has in scientific circles been changed into the utmost abstraction. It is reality to say: We must strive for astronomical knowledge in cellular theory, especially in Embryology. If DuBois-Raymond had said that the detailed astronomical facts should be applied to the cell-theory, he would have spoken out of the sphere of reality. But what he wanted corresponds to no reality, namely that something thought-out and devised—the atoms and molecules—should be examined with astronomical precision. He wanted the astronomical type of mathematical thoughts, which have been added to the world of the stars, to be sought for again in the molecule.

Thus you see, upon the one hand lies reality: movement, the active forces of the stars and the embryonic development in which there lives, in all reality, what lives in the starry heavens. That is where the reality lies and that is where we must look for it. On the other hand lies abstraction. The mathematician, the mechanist, calculates the movements and forces of the heavenly bodies and then invents the molecular structure to which to apply this kind of astronomical knowledge. Here he is withdrawn from life, living in pure abstractions.

These are the things about which we must think, remembering that now we must renew, in full consciousness, something which was in a certain sense present in earlier times. Looking back to the Egyptian Mysteries, we find astronomical observations such as were made at that time. These observations, my dear friends, were not used merely to calculate when an eclipse of the Sun or Moon would take place, but rather to arrive at what should come about in social evolution. Men were guided by what they saw in the heavens, as to what must be said to the people, what instructions should be given, so that the development of the whole social life should take its right course. Astronomy and Sociology were dealt with as one. We too, though in a different way from the Egyptians, must again learn how to connect what happens in social life with the phenomena of the great universe. We do not understand what came about in the middle of the 15th century, if we cannot relate the events of that time to the phenomena which then prevailed in the universe. It is like a blind man talking about color to speak of the changes in the civilized world in the middle of the 15th century without taking all this into account.

Spiritual Science is already a starting point. But we shall not succeed in bring together the complicated domain of Sociology—social science—with the observations of natural phenomena, unless we first begin by connecting Astronomy with Embryology, linking the embryonic facts with astronomical phenomena.

Yesterday I showed a connection between two branches of science which according to our modern ideas are widely separated. I sought to show that the science of Astronomy should provide certain items of knowledge which must then be turned to account in quite a different branch of science, from which the study and method of Astronomy is completely excluded nowadays. In effect, I sought to show that Astronomy must be linked with Embryology. It is impossible to understand the phenomena of cell-development, especially of the sex-cells, without calling to our aid the realities of Astronomy, which lie apparently so far removed from Embryology.

I pointed out that there must come about a regrouping of the sciences, for a man specializing nowadays along certain lines finds himself hemmed in by the circumscribed divisions of science. He has no possibility of applying his specialized knowledge and experience to spheres which may lie near to hand but which will only have been presented to him from certain aspects, insufficient to give him a deeper understanding of their full significance. If it is true, as will emerge in these lectures, that we can only understand the successive stages in human embryonic development when we understand their counterpart, the phenomena of the Heavens; if this is a fact—and it will turn out to be so—then we cannot work at Embryology without working at Astronomy. Nor can we occupy ourselves with Astronomy without bringing new light to the facts of Embryology. In Astronomy we are studying something which reveals its most important activity in the development of the human embryo. How, then, shall we explain the meaning and reason of astronomical facts, if we bring into the kind of connection with these facts the very realm in which this meaning and reason are revealed?

You see how necessary it is to come to a reasonable world-conception, out of the chaos in which we are today in the sphere of science. If, however, one only accepts what is fashionable nowadays, it will be very difficult to grasp, even as a general idea, anything like what I said yesterday. For the evolution of our time has brought it about that astronomical facts are only grasped through mathematics and mechanics, while embryological facts are recorded in such a way that in dealing with them anything of the nature of mathematics or mechanics is discarded. At most, even if the mathematical-mechanical is brought into some kind of relation to Embryology, it is done in a quite an external way, without considering where lies the origin of what, in embryonic development, might truly be expressed in mathematical and mechanical terms.

Now I need only point to a saying of Goethe's, uttered out of a certain feeling—a ‘feeling knowledge’ I might call it—but indicating something of extraordinary significance. (You can read of it in Goethe's “Spruche in Prosa”, and in the Commentary which I added to the publication in the Kurschner edition of the Deutsche National-Literatur, where I spoke in detail about this passage.) Goethe says there: People think of natural phenomena so entirely apart from man that they are tending ever more and more to disregard the human being in their study of the phenomena of Nature. He, on the contrary, believed that natural phenomena only reveal their true meaning if they are regarded in full connection with man—with the whole organization of man. In saying this, Goethe pointed to a method of research which is well-nigh anathematized nowadays. People today seek an 'objective' understanding of Nature through research that is completely separated from the human being. This is particularly noticeable in such a science as Astronomy, where no account at all is taken of the human being. On the contrary, people are proud that the apparently ‘objective’ facts have shown that man is only a grain of dust upon an Earth which has somehow been fused into a planet, moving first round the Sun and then, in some way or other, moving with the Sun in space. They are proud that one need pay no attention to this ‘grain of dust’ which wanders about on Earth,—that one need only pay attention to what is external to the human being in considering the great celestial phenomena.

Now the question is, whether any real results are to be obtained by such a method.

I should like once more to call attention, my dear friends, to the path we must pursue in these lectures. What you will find as proof will only emerge in the further course of the lectures. Today we must take a good deal simply from observation in order to form certain preliminary ideas. We must first build up certain necessary concepts; only then shall we be able to pass on to the verification of these concepts.

From what source, then, can we gain a real perception of the celestial phenomena merely through the mathematics which we apply to them? The course of development of human knowledge can disclose—if one does not take up the proud position of thinking how ‘wonderfully advanced’ we are today and how all that went before was childish—the course of human development can teach us how the prevailing points of view can change.

From certain aspects one can have great reverence for the celestial observations carried out, for instance, by the ancient Chaldeans. The ancient Chaldeans made very exact observations concerning the connection of human time-reckoning with the heavenly phenomena. They had a highly develop ‘Calendar-Science’. Much that appears to us today as self-evident really dates back to the Chaldeans. Yet the Chaldeans were satisfied with a mathematical picture of the Heavens which portrayed the Earth more or less as a flat disc, with the hollow hemisphere of the heavenly vault arched above, the fixed stars fastened to it, and the planets moving over it. (Among the planets they also included the Sun.) They made their calculations with this picture in the background. Their calculations for the most part were correct, in spite of being based upon a picture which the science of today can only describe as a fundamental error, as something ‘childish’.

Science, or more correctly, the scientific tendency and direction, then went on evolving. There was a stage when men pictured that the Earth stood still, but that Venus and Mercury moved round the Sun. The Sun formed the central point, as it were, for the motions of Venus and Mercury, while the other planets—Mars, Jupiter and Saturn—moved round the Earth. Thereafter, men progressed to making Mars, Jupiter and Saturn also revolved around the Sun, but the Earth was still supposed to stand still, while the Sun with its encircling planets as well as the starry Heavens revolved round the Earth. This was still the fundamental view of Tycho Brahe, whereas his contemporary Copernicus established the other concept, namely, that the Sun was to be regarded as standing still and that the Earth was to be reckoned among the planets revolving round the Sun. Following hard one upon the other in the time of Copernicus were the two points of view, one which existed in ancient Egypt, of the stationary Earth with the other planets encircling the Sun, still represented by Tycho Brahe; the other, the Copernican concept, which broke radically with the idea of the center of coordinates being in the center of the Earth, and transferred it to the center of the Sun. For in reality the whole alteration made by Copernicus was nothing else than this,—the origin of coordinates was removed from the center of the Earth to the center of the Sun.

What was actually the problem of Copernicus? His problem was, how to reduce to simple lines and curves these complicated apparent motions of the planets,—; for so they appear as observed from the Earth. When the planets are observed from the Earth, their movements can only be described as a variety of looped lines, such as these (Fig. 1). So, when taking the center of the Earth as the center of coordinates it is necessary to base the planetary movements on all sorts of complicated curves. Copernicus said, in effect: ‘as an experiment, I will place the center of the whole coordinate system in the center of the Sun.’ Then the complicated planetary curves are reduced to simple circular movements, or as was stated later, to ellipses. The whole thing was purely the construction of a world-system which aimed at being able to represent the paths of the planets in the simplest possible curves.

Now today we have a very remarkable fact, my dear friends. This Copernican system, when employed purely mathematically, supplies the necessary calculations concerning the observed phenomena as well as and no better than any of the earlier ones. The eclipses of the Sun and Moon can be calculated with the ancient Chaldean system, with the Egyptian, with the Tychonian and with the Copernican. The outer occurrences in the Heavens, in so far as they relate to mechanics or mathematics, can thus be foretold. One system is as well suited as another. It is only that the simplest thought-pictures arise with the Copernican system. But the strange thing is that in practical Astronomy, calculations are not made with the Copernican system. Curiously enough, in practical Astronomy,—to obtain what is needed for the calendar,—the system of Tycho Brahe is used! This shows how little that is really fundamental, how little of the essential nature of things, comes into question when the Universe is thus pictured in purely mathematical curves or in terms of mechanical forces.

Now there is another very remarkable fact which I will only indicate today, so that we shall understand each other about the aim of these lectures. I shall speak further about it in succeeding lectures. Copernicus in his deliberations bases his cosmic system upon three axioms. The first is that the Earth rotates on its own North-South axis in 24 hours. The second principle on which Copernicus bases his picture of the Heavens is that the Earth moves round the Sun. In its revolution round the Sun the Earth itself, of course, also revolves in a certain way. This rotation, however, does not occur round the North-South axis of the Earth, which always points to the North Pole, but round the axis of the Ecliptic, which, as we know, is at an angle with the Earth's own axis. Therefore the Earth goes through a rotation during a 24-hour day round its own N. S. Axis, and then, inasmuch as it performs approximately 365 such rotations in the year, there is added another rotation, an annual rotation, if we disregard the revolution round the Sun. The Earth, then, if it always rotates thus, and then again revolves round the Sun, behaves like the Moon as it rotates round the Earth, always turning the same side towards us. The Earth does this too, inasmuch as it revolves round the Sun, but not on the same axis as the one on which it rotates for the daily revolution. It revolves through this 'yearly day' on another axis; this is an added movement, besides the one taking place in the 24-hour day.

Copernicus' third principle is that not only does such a revolution of the Earth take place round the North-South axis, but that there is yet a third revolution which appears as a retrograde movement of the North-South axis round the axis of the Ecliptic. Thereby, in a certain sense, the revolution round the axis of the Ecliptic is canceled out. By reason of this third revolution the Earth's axis continuously points to the North celestial Pole (the Pole-Star). Whereas, by virtue of revolving round the Sun, the Earth's axis would have to describe a circle, or an ellipse, round the pole of the Ecliptic, its own revolution, which takes the opposite direction (every time the Earth proceeds a little further its axis rotates backwards), causes it to point continually to the North Pole. Copernicus adopted this third principle, namely: The continued pointing of the Earth's axis to the Pole comes about because, by a rotation of its own—a kind of ‘inclination’ (?)—it cancels out the other revolution. This latter therefore has no effect in the course of the year, for it is constantly being annulled.

In modern Astronomy, founded as it is on the Copernican system, it has come about that the first two axioms are accepted and the third is ignored. This third axiom is lightly brushed aside by saying that the stars are so far away that the Earth-axis, remaining parallel to itself, always points practically to the same spot. Thus it is assumed that the North-South axis of the Earth, in its revolution, remains always parallel to itself. This was not assumed by Copernicus; on the contrary, he assumed a perpetual revolving of the Earth's axis. Modern Astronomy is therefore not really based on the Copernican system, but accepts the first two axioms because they are convenient and discards the third, thus becoming lost in the prevarication that it is not necessary to suppose that the Earth's axis itself must move in order to keep pointing to the same spot in the Heavens, but that the place itself is so far away that even if the axis does move parallel to itself it will still point to the same spot. Anyone can see that this is a prevarication. To-day therefore we have a ‘Copernican system’ from which a most important element has actually been discarded.

The development of modern Astronomy is presented in such a way that no one notices that an important element is missing. Yet only in this way is it possible to describe it all so neatly: “Here is the Sun the Earth goes round in an ellipse with the Sun in one of the foci.” (Fig. 2)

As time went on it became no longer possible to hold to the starting-point of the Copernican theory, namely that the Sun stands still. A movement is now attributed to the Sun, which is said to move forward with the whole ellipse, perpetually creating new ellipses, so to speak (Fig. 3). It became necessary to introduce the Sun's own movement, and this was done simply by adding something new to the picture they had before. A mathematical description is thus obtained which is admittedly convenient, but few questions are asked as to its possibility or its reality. It is only from the apparent movement of the stars that the Earth's movement is deduced by this method. As we shall presently see, it is of great significance whether or no one assumes a movement—which indeed must be assumed—namely the aforesaid ‘inclination’ (?) of the Earth's axis, perpetually annulling the annual rotation. Resultant movements, after all, are obtained by adding up the several movements. If one is left out, the whole is no longer true. Thus the whole theory that the Earth moves round the Sun in an ellipse comes into question.

You see, purely from these historical facts, that burning questions exist in Astronomy today, though it is seemingly a most exact science because it is mathematical. The question arises: Why do we live in such uncertainty with regard to a real astronomical science? We must then ask further, turning the question in another direction: Can we reach any real certainty through a purely mathematical approach? Only think that in considering a thing mathematically we lift the observation out of the sphere of external reality. Mathematics is something that ascends from our inner being; in mathematics we lift ourselves out of external reality. It must therefore be understood from the outset that if we approach an external reality with a method of investigation that lifts itself out of reality, we can, in all probability, only arrive at something relative.

To begin with, I am merely putting forward certain general considerations. We shall soon come to the realities. The point is that in regarding things purely from the mathematical standpoint, man does not put reality into his thought with sufficient energy, in order to approach the phenomena of the outer world rightly. This, indeed, demands that the celestial phenomena be brought nearer to man; they must not be regarded as quite apart from man, but must be brought into relationship with man. It was only one particular instance of this associating of the heavenly phenomena with the human being, when I said that we must see what takes place out there in the starry world in its reflection in the embryonic process. But let us look at the matter at first somewhat more generally. Let us ask whether we cannot perhaps find another approach to the celestial phenomena than the purely mathematical one.

We can indeed bring the celestial phenomena, in their connection with earthly life, somewhat nearer to man in a purely qualitative way. We will not disdain to form a basis today with seemingly elementary ideas, these ideas being just the ones that are excluded from the foundations of modern Astronomy. We will ask the following question: How does man's life on Earth appear, in relation to Astronomy? We can regard the external phenomena surrounding man from three different points of view. We can regard them from the standpoint of what I will call the solar life, the life of the Sun; the lunar life; and the terrestrial, the tellurian life.

Let us think first in quite a popular, even elementary way how these three domains play around man and upon him. Clearly there is something on the Earth which is in complete dependence upon the Sun-life, including also that aspect of the Sun's life which we shall have to look for in the Sun's movement or state of rest, and so on. We will leave aside the quantitative aspect and today merely consider the qualitative. Let us try to be clear as to how, for instance, the vegetation of any given region depends upon the solar life. Here we need only call to mind what is very well known with regard to vegetation, namely, the difference in the vegetation of spring, summer, autumn and winter; we shall be able to say that we see in the vegetation itself an imprint of the solar life. The Earth opens herself in a given region to what is outside her in heavenly space, and this reveals itself in the unfolding of vegetative life. If the Earth closes herself again to the solar life, the vegetation recedes.

There is, however, an interplay of activity between the terrestrial or tellurian and the solar life. There is a difference in the solar life according to the variation of tellurian conditions. We must here bring together quite elementary facts and you will see how they lead us further. Take, for example, Egypt and Peru, two regions in the tropical zone.—Egypt, a low-lying plain, Peru a table land, and compare the vegetation. You will see how the tellurian element, simply the distance from the center of the Earth in this instance, plays its part in conjunction with the solar life. You only need study the vegetation over the earth, regarding the Earth, not as mere mineral but as incorporating plant-nature as well, and in the picture of vegetation you have a starting-point for an understanding of the connection of the earthly with the celestial. But we perceive the connection most particularly when we turn our attention to mankind.

We have, in the first place, two opposites on the Earth: the Polar and the Tropical. The Polar and the tropical form a polarity, and the result of this polarity shows itself very clearly in human life.

Is it not so that life in the polar regions brings forth in man a condition of mind and spirit which is more or less a state of apathy: The sharp contrast of a long winter and a long summer which are almost like one long day and one long night, produces a certain apathy in man; it is as though the setting in which man lives makes him apathetic. In the Tropics, man also lives in a region which makes him apathetic. But the apathy of the polar region is based upon a sparse external vegetation—sparse and meager in a peculiar way even where it develops to some extent. The tropical apathy of man is caused by a rich, luxuriant vegetation. Putting together these two pictures of environment one can say that the apathy which affects man in polar regions is different from that affecting him in tropical regions. He is apathetic in both regions, but the apathy results from different causes. In the Temperate Zone lies the balance. Here the human capacities are developed in a certain equilibrium.

No-one will doubt that this has something to do with the solar life. But what is the connection: (I will, as I said, first make a few remarks based on observation and in this way arrive at essential concepts.) Going to the root of things, we find that in the life around the Poles there is a very strong working-in of the Sun-forces upon man. In those regions the Earth tends to withdraw from the life of the Sun; she does not let her activity shoot upward from below into the vegetation. But the human being is exposed in these parts to the true Sun-life (you must not only look for the Sun-life in mere warmth). That this is so, the vegetation itself bears witness.

We have, then, a preponderance of solar influence in the Polar zones. What kind of life predominates in the Tropical? There it is the tellurian, the Earth-life. This shoots up into the vegetation, making it rich and luxuriant. This also robs man of a balanced development of his capacities, but the causes in the North and in the Tropics come from different directions. In Polar regions the sunlight represses man's inner development. In the Tropics, what shoots up from the Earth represses his inner powers. We thus see a certain polarity, the polarity shown in the preponderance of the Sun-life around the Poles, and of the tellurian life in tropical regions—; in the neighborhood of the Equator.

If we then observe man and have in mind the human form, we can say the following. (Please do not object at once if it seems paradoxical, but wait a little. We shall be taking the human form seriously.) The head, the part of the human form which in its outer configuration copies universal space,—namely the sphere, the spherical shape of the Universe as a whole—the head is exposed by life in polar regions to what comes from the Cosmos outside the Earth. In the Tropics, the metabolic system in its connection with the limbs is exposed to the Earth-life as such.

We come to a special relationship, you see, of the human head to the cosmic life outside the Earth and of the human metabolic and limb-system to the Earth-life. Man is so placed in the Universe as to be more co-ordinated with the cosmic surroundings of the Earth in his head, his nerve-senses system, and with the Earth-life in his metabolic system. And in the temperate zones we shall have to look for a kind of perpetual harmonizing between the head-system and the metabolic system. In the temperate zones there is a primary development of the rhythmic system in man.

You see then that there exists a certain connection between this threefold membering of man—nerves-and-senses system, rhythmic system, metabolic system—and the outer world. The head-system is more related to the whole Cosmos, the rhythmic system is the balance between the Cosmos and the earthly world, and the metabolic system is related to the earth itself. Then we must take up another indication, which points to a working of the solar life upon mankind in a different direction.

The connection of the solar life with the life of man which we have just been considering can only be related to the interplay of the earthly and extra-earthly life in the course of the year. But as a matter of fact, in the course of the day we are also concerned with a kind of repetition, even as in the yearly course. The yearly course is determined by the relation of the Sun to the Earth, and so is the daily course. In the language of purely mathematical astronomy we speak of the daily rotation of the Earth on its axis, and of the revolution of the Earth round the Sun in the course of the year. But we are then confining ourselves to very simple aspects. We have then no justification for assuming that we are really starting from adequate premisses, giving an adequate basis for our investigations. Let us call to mind all that we have considered with regard to the yearly course. I will not say ‘the revolution of the Earth round the Sun’, but the course of the year with its alternating conditions. This must have a connection with the three-fold being of man. Since through the earthly conditions it finds different expression in the Tropics, in the Temperate Zones and at the Poles, this yearly course must be connected in some way with the whole formation of man—with the relations of the three members of the threefold man. When we bring this into consideration, we acquire a wider basis from which to proceed and can perhaps arrive at something quite different from what we reach when we merely measure the angles which one telescopic direction makes with another. It is a matter of finding broader foundations in order to be able to judge the facts.

Speaking of the daily course, we speak in the astronomical sense of the rotation of the Earth on its axis. But something rather different is here revealed. There is revealed a far-reaching independence of man upon this daily course. The dependence of man on the yearly rhythm, namely on what is connected with the yearly course, the shaping of the human form in the various regions of the Earth, shows us a very great dependence of man on the solar life,—on the changes that appear on Earth in consequence of the solar life. The daily course shows it far less. True, very much of interest will also be revealed in connection with the daily course, but as regards the life of mankind as a whole it is relatively insignificant. The differences appear in individual human beings. Goethe, who can be regarded in a certain respect as a normal type of man, felt himself best attuned to production in the morning; Schiller at night. This points to the fact that the daily rhythm has a definite influence upon certain subtler parts of human nature. A man who has a feeling for such things, will tell us that he has met many persons in his life who have confided to him that their really important thoughts were worked out in the dusk, that is, in the temperate period of the day-to-day rhythm, not at midday nor at midnight, but in the temperate time of the day. It is however, a fact that man is in a way independent of the daily course of the Sun. We have still to go into the significance of this independence and to show in what way a certain dependence does nevertheless exist.

A second element is the lunar life, the life that is connected with the Moon. It may be that a great deal of what has been said on this subject in the course of human evolution appears today as mere fantastic nonsense. But in one way or another we see that the Earth-life as such, for example in the phenomena of tidal ebb and flow, is connected quite evidently with the movement of the Moon. Nor must it be overlooked that the female functions, although they do not coincide in time with the Moon's phases, coincide with them in their periodicity, and that therefore something essentially concerned with human evolution is shown to be dependent in time and duration upon the phases of the Moon. It is as though this process of the female function were lifted out of the general course of Nature, but has remained a true image of Nature's process; it is accomplished in the same period of time as the corresponding natural phenomenon.

Just as little must it be overlooked—only people do not make rational, exact observations of these things if they turn aside from them at the very outset—just as little must it be overlooked that as a matter of fact, man's life of fancy and imagination is extraordinarily bound up with the phases of the Moon. If anyone were to keep a calendar-record of the upward and downward flow of his life of imagination, he would notice how much it had to do with the Moon's phases. The fact that the Moon-life, the lunar life, has an influence upon certain lower organs should he studied in the phenomenon of the sleep-walker. In the sleep-walker, interesting phenomena can be studied; phenomena which are overlaid by normal human life, but are present in the depths of human nature and point in their totality to the fact that the lunar life is just as much connected with the rhythmic system of man as is the solar life with his nerves-and-senses system.

This gives a sort of crossing of influences. We have seen how the solar life, in its interplay with the forces of the Earth, works on the rhythmic system in the temperate zones. Crossing this influence, we now have the direct influence of the lunar life upon the rhythmic system.

When we now look at the tellurian, the Earth-life as such, we must not disregard a domain in which the earthly influence makes itself felt; though, to be sure, this is not ordinarily taken into account. I ask you to turn your attention to such as phenomenon as home-sickness. It is difficult to from any clear ideas about home-sickness. It can no doubt be explained from the point of view of habit, custom, and so on. But I ask you to note that real physiological effects can be produced entirely as a result of this so-called home-sickness. Home-sickness can go so far as to make a man ill. It can express itself in such phenomena as asthma. Study the complex of the phenomena of home-sickness with its consequences, asthmatic conditions and general ill-health, a kind of emaciation, and it is possible to come to the following conclusion. One comes to see that ultimately the feeling of home-sickness results from an alteration of the metabolism—the whole metabolic system. Home-sickness is the reflection in consciousness of changes in the metabolism—changes entirely due to the man's removal from one place, with its tellurian influences from below, to another place, with different influences coming from below. Please take this in connection with other things which, unfortunately, Science as a rule leaves unconsidered.

Goethe, I said, felt most inspired to poetry, to the writing of his works in the morning. If he needed a stimulant however, he took that stimulant which in its nature takes least hold of the metabolic system, but only stirs it up via the rhythmic system, namely wine. Goethe took wine as a stimulant. In this respect he was, indeed, altogether a Sun-man; he let the influence of the solar life work upon him. With Schiller or Byron this was reversed. Schiller preferred to write his poetry when the Sun has set, that is to say when the solar life was hardly active any more. And he stimulated himself with something which takes thorough hold of the metabolic system—with hot punch. The effect was quite different from that obtained by Goethe from wine. It worked into the whole metabolism. Through the metabolism the Earth works upon man; so we can say that Schiller was essentially tellurian—an Earth-man. Earth-men work more through the emotions and what belongs to the will; the Sun-man works rather through calm and contemplation. For those persons, therefore, who could not endure the solar element, but only liked the tellurian, only what is of the Earth Goethe increasingly became “the cold literary Greybeard” as they called him in Weimar—“the cold, literary greybeard with the double chin.” That was the name which was so often given to Goethe in Weimar in the 19th century.

Now I should like to bring something rather different to your notice. We have observed how man is set into the universal connections of Earth, Sun, Moon: the Sun working more on the nerves-and-senses system; the Moon working more on the rhythmic system; the Earth, inasmuch as she gives man of her substance as nourishment and makes substance directly active in him, working upon the metabolic system, working tellurically. We see something in man through which we can perhaps find starting-point for an explanation of the Heavens as they exist outside man, upon broader foundations than merely through the measurement of angles by the telescope and so on.

This is especially so if we go yet further, if we now consider Nature outside of man,—but consider it so as to see more in it than a mere register of external data. Look at the metamorphosis of insects. In the course of the year it is a complete reflection of the external solar life. I would say that with man we must make our researches more in the inner being in order to follow what is solar, lunar and tellurain in him, whereas in the insect-life with its metamorphoses, we see the direct course of the year expressed in the successive forms the insect assumes. We can now say to ourselves: Maybe we have not to only proceed quantitatively, but should also take into account the qualitative impression which such phenomena make upon us Why always merely ask what a phenomenon of the outer Universe looks like in the objective of the telescope? Why not ask what relation is given, not merely by the objective of the telescope, but by the insect? How does human nature react? Is anything revealed to us through human nature regarding the celestial phenomena? Are we not led in this way to broader foundations, making it impossible that on the one hand, theoretically, we should be Copernicans when desiring to explain the world philosophically, while on the other we use Tychonic System as our basis for calculating the calendar etc., as practical Astronomy still does to this day. Or that we are Copernicans, but set aside the most important part of his theory, namely his third axiom Can we not overcome the uncertainties which create burning problems even in the most fundamental realms of Astronomy today, by working on a broader basis—working in this sphere too from the quantitative to the qualitative?

Yesterday I sought to point out the connection of the celestial with the embryonic phenomena; today, the connection with fully developed man. Here you have an indication towards a necessary regrouping of the sciences. Now take another thing to which I have also referred to in the course of today's remarks. I indicated the connection of human metabolism with the Earth-life. In man we have the faculties of sense-perception mediated through the nerves-and-senses system, connected as a whole with the solar and cosmic life. We have the rhythmic system connected with what lies between Heaven and Earth. We have the metabolism related especially to the Earth, so that in contemplating metabolic man we should be able to get nearer to the real essence of the tellurian. But what do we do today if we want to approach the tellurian realm? We behave as we habitually do, and investigate things from the outside. But things have an inner side also! Will they perhaps only show it in its true form when they pass through the human being?

It has become an ideal nowadays to regard the relationship of substances quite apart from man and to rest there; to observe by experimentation in chemical laboratories the reciprocal actions of substances in order to arrive at their nature. But if the substances only disclosed their nature within the human being, then we should have to practice Chemistry in such a way as to reach man. Then we should have to form a connection between true Chemistry and the processes undergone by matter within man, just as we see a connection between Astronomy and Embryology, or between Astronomy and the whole human form—the threefold being of man. Thus do the things work into one another. We only come to real life when we perceive them in their interpenetration.

On the other hand, inasmuch as the Earth is poised in cosmic space, we shall have to see the connection between the tellurian and the starry realm.

Now we have seen a connection between Astronomy and the substances of Earth; also between the Earth and human metabolism; and again a direct influence of the solar and celestial events upon man himself. In man we have a kind of meeting of what comes directly from the Heavens and what comes via earthly substance. Earthly substances work on the human metabolism, while the celestial influences work directly upon man as a whole. In man there meet the direct influences for which we are indebted to the solar life, and those influences which, passing indirectly through the Earth, have undergone a change by reason of the Earth. Thus we can say: The interior of the human being will become explicable even in a physical, anatomical sense as a resultant of cosmic influences coming directly from the Universe outside the Earth, and cosmic influences which have first passed through the earthly process. These flow together in man (Fig. 4).

You see how, contemplating man in his totality, the whole Universe comes together. For a true knowledge of man, it is essential to perceive this.

What then has come about by scientific specialization? It has led us away from reality into a purely abstract sphere. In spite of its 'exactness', Astronomy—to calculate the calendar—cannot help using in practice something other than it stands for in theory. And then again, Copernican though it is in theory, it discards what was of great importance to Copernicus, namely the third axiom. Uncertainty creeps in at every point. These modern lines of research do not lead to what matters most of all,—to perceive how Man is formed from the entire Universe.

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 re-inforced 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 may 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. (Fig. 1)

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:

1. Soul and Spirit: Day

2. 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 to 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:

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.

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 be (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 begin 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's 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 on the other side the other half, 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.

If I had the task of presenting my subject purely according to the methods of Spiritual Science, I should naturally have to start from different premises and we should be able to reach our goal more quickly. Such a presentation, however, would not fulfill the special purpose of these lectures. For the whole point of these lectures is to throw a bridge across to the customary methods of scientific thought. Admittedly, I have chosen just the material which makes the bridge most difficult to construct, because the customary mode of thought in this realm is very far from realistic. But in contending against an unreal point of view, it will become apparent how we can emerge from the unsatisfying nature of modern theories and came to a true grasp of the facts in question. Today, then, I should like to consider the whole way in which ideas have been formed in modern times about the celestial phenomena.

We must, however, distinguish two things in the formation of these ideas. First, the ideas¹ are derived from observation of the celestial phenomena, and theoretical explanations are then linked on to the observations. Sometimes very far-reaching, spun-out theories have been linked on to relatively few observations. That is the one thing, namely, that a start is made from observations out of which certain ideas have been developed. The other is that, the ideas having been reached, they are further elaborated into hypotheses. In this creating of hypotheses,—a process which ends in the setting up of some definite cosmology,—much arbitrariness prevails, since in the setting-up of theories, any preconceived ideas existing in the minds of those who put forward the theory, make themselves strongly felt.

I will therefore first call your attention to something which will perhaps strike you as paradoxical, but which, when carefully examined, will none the less prove fruitful in the further course of our studies.

In the whole mode of thought of modern Science there prevails what might be called, and indeed has been called, the ‘Regula philosophandi’. It consists in saying: What has been traced to definite causes in one realm of reality, is to be traced to the same causes in other realms. In setting up such a ‘regula philosophandi’ the starting-point is as a rule apparently self-evident. It will be said—scientists of the Newtonian school will certainly say—that breathing must have the same causes in man as in the animal, or again, that the ignition of a piece of wood must have the same cause whether in Europe or in America. Up to this point the thing is obvious enough. But then a jump is made which passes unnoticed,—is taken tacitly for granted. Those who are wont to think in this way will say, for example, that if a candle and the Sun are both of them shedding light the same causes must surely underlie the light of the candle and the light of the Sun. Or again, if a stone falls to Earth and the Moon circles round the Earth, the same causes must underlie the movement of the stone and the movement of the Moon. to such an explanation they attach the further thought that if this were not so, we should have no explanations at all in Astronomy. The explanations are based on earthly things. If the same causality did not obtain in the Heavens as on Earth, we should not be able to arrive at any theory at all.

Yet when you come to think of it, this regula philosophandi is none other than a preconceived idea. Who in the world will guarantee that the causes of the shining of a candle and of the shining of the Sun are one and the same? Or that in the falling of a stone, or the falling of the famous apple from the tree by which Newton arrived at his theory, there is the same underlying cause as in the movements of the heavenly bodies? This would first have to be established. As it is, it is a mere preconceived idea. Prejudices of this kind enter in, when, having first derived theoretical explanations and thought—pictures inductively from the observed phenomena, people rush headlong into deductive reasoning and construct world-systems by deductive methods.

What I am now describing thus abstractly has, however, become a historical fact. There is a continuous line of development from what the great thinkers at the opening of the modern age—Copernicus, Kepler, Galileo—concluded from comparatively few observations. Of Kepler—notably of his third Law, quoted yesterday—it must be said that his analysis of the facts which were available to him is a work of genius.

It was a very great intensity of spiritual force which Kepler brought to bear when, from the little that lay before him, he discovered this ‘law’ as we call it, or better, this ‘conceptual synthesis’ of the phenomena of the universe. Then however, by way of Newton a development set in which was not derived from observation but from theoretical constructions, including concepts of force and mass and the like, which we must simply omit if we only want to hold to what is given. The development in this direction reaches a culminating point—conceived, admittedly, with genius and originality—in Laplace, where it leads to a genetic explanation of the entire cosmic system (as you will convince yourselves if you read his famous book Exposition du Systeme du Monde ), or again in Kant, in his Natural History and Theory of the Heavens. In all that has followed in this trend we see the effort constantly made to come to conclusions based on the thought pictures that have thus been conceived of the connections of the celestial movements, and resulting in such explanations of the origin of the universe as the nebular theory and so on.

It must be noted that in the historical development of these theories we have something which is put together from inductions made, once again, with no little genius in this domain—and from subsequent deductions in which the special predilections of their authors were included. Inasmuch as a thinker was imbued with materialism it was quite natural for him to mingle materialistic ideas with his deductive concepts. Then it was no longer the facts which spoke, for one proceeded on the basis of the theories which had emerged from the deductions. Thus, for example, inductively men first arrived at the mental pictures which they summed up in the notion of a central body, the Sun, with the planets revolving around it in ellipses according to a certain law, namely: the radius-vectors describe equal areas in equal periods of time. By observing the different planets of a solar system, it was moreover possible to summarize their mutual relations in Kepler's third law: ‘For different planets the squares of the periods of revolution are proportional to the cubes of the radius-vectors’. Here was a certain picture. The question, however, was not decided, whether this picture completely fitted the reality. It was in truth an abstraction from reality; to what extent it related to the full reality, was not established. From this picture—not from reality, but from this picture—people deduced what then became a whole genetic system of Astronomy. All this must be borne in mind. Modern man is taught from childhood as if the theories which have been reached in the past few centuries by deductive reasoning were the real facts. We will therefore, while taking our start from what is truly scientific, disregard as far as is possible all that is merely theoretical and link on to those ideas which only depart from reality to the extent that we shall still be able to discover in them a connection with what is real. It will be my task, in all that I give to-day, to follow the direction of modern scientific thought only up to those ideas and concepts which still permit one to find the way back again into reality. I shall not depart so far from reality that the concepts become crude enough to allow of the deduction of nebular hypotheses.

Proceeding in this way,—pursuing the modern method of forming concepts in this particular field,—we must first form a concept which presented itself inductively to Kepler and was then developed further I repeat expressly, I will only go so far in these concepts that even if the picture in the form in which it was conceived should be mistaken, it has departed only so far from reality that it will be possible to eliminate the mistake and return to what is true. We need to develop a certain flair for reality in the concepts we entertain. We cannot proceed in any other way if we wish to throw a bridge across from the reality to the spun-out theories of modern scholarship and science.

Here then, to begin with, is a concept which we must examine. The planets have eccentric orbits,—they describe ellipses. This is something with which we can begin. The planets have eccentric orbits and describe ellipses, in one focus of which is the Sun. They describe the ellipses in accordance with the law that the radius—vectors describe equal areas in equal periods of time.

A second essential for us to hold to is the idea that each planet has its own orbital plane. Although the planets carry out their evolutions in the neighborhood of each other, so to speak, yet for each planet there is the distinct plane of its orbit, more or less inclined to the plane of the Sun's equator: If this depicts the plane of the Sun's equator (Fig.1), an orbital plane of a planet would be thus; it would not coincide at all with the plane of the Sun's equator.²

These are two very significant mental pictures, to be formed from the facts of observation. And yet, in the very forming of them we must take note of something in the real world-picture, which as it were, rebels against them. For instance, if we are trying to understand our solar system in its totality, and only base it upon the picture of the planets moving in eccentric orbits, the orbital planes being inclined at varying degrees to the plane of the solar equator, we shall be in difficulties if we also take into account the movements of the comets. The moment we turn our attention to the cometary movements, the picture no longer suffices. The outcome will be better understood from the historical facts than from any theoretical explanations.

Upon these two thought-pictures,—that the orbital planes of the planets lie in the proximity of the plane of the Sun's equator, and that the orbits are eccentric ellipses,—Kant, Laplace and their successors built up the nebular hypothesis. Follow what emerges from this. At a pinch, and indeed only at a pinch, it is a way of imagining the origin of the solar system. But the astronomical system thus constructed contains no satisfactory explanation of the part played by the cometary bodies. They always fall out of the theory. This discordance of the comets with the theories which were formed, as described, in the course of scientific history, proves that the cometary life somehow rebels against a concept formed, not from the whole but only from a part of the whole. We must be clear, too, that the paths of the comets frequently coincide with those of other bodies which also play into our system and present a riddle precisely through their association with the comets. These are the meteoric swarms, whose paths very frequently—perhaps even always—coincide with the cometary paths. Here, my dear friends, taking into account the totality of our system, we are led to say: A sea of ideas has gradually been formed from the study of our planetary system as a whole,—ideas with which we cannot do justice to the seemingly irregular and almost arbitrary paths of the comets and meteoric swarms. They simply refuse to be included in the more abstract pictures that have been reached. I should have to give you long historical descriptions to show in detail how many difficulties have arisen in connection with the concrete facts, when the investigators—or rather, thinkers—approached the comets and meteoric swarms with their astronomical theories.

I wish only to point out the directions in which a sound understanding can be sought. We shall come to such an understanding if we pay attention to yet another aspect.

Starting in this way from concepts which still have a remnant of reality in them, we will now try to go back a little towards what is real. It is indeed always necessary to do this in relation to the outer world, in order that our concepts may not stray too far from reality,—for this is a strong propensity of man. We must go back again and again to the reality.

There is already no little danger in forming such a concept as that the planets move in ellipses, and then beginning at once to build a theory upon this concept. It is far better, after forming such a concept, to turn back to reality in order to see if the concept does not need correcting, or at least modifying. This is important. It is very clearly seen in astronomical thinking. Also in biological and especially in medical thought, the same failing has led people very far astray. They do not take into account, how necessary it is directly they have formed a concept, to go back to reality in order to make sure that there is no reason to modify it.

The planets, then, move in ellipses. But these ellipses vary; they are sometimes more circular, sometimes more elliptical. We find this if we return to reality with the ellipse idea. In the course of time the ellipse becomes more bulging, more like a circle, and then again more like an ellipse. So I by no means include the whole reality if I merely say, ‘the planets move in ellipses’. I must modify the concept and say: The planets move in paths which continually struggle against becoming a circle or remaining one and the same ellipse. If I were now to draw the elliptic line, to be true to the reality I should have to make it of india-rubber, or form it flexibly in some way, continually altering it within itself. For if I had formed the ellipse which is there in one revolution of the planet, it would not do for the next revolution, and still less for the following one. It is not true that when I pass from reality to the rigid concept I still remain within the real. That is the one thing.

The other is: We have said that the planes of the planetary orbits are inclined to the plane of the Sun's equator. Where the planets cross the point of intersection of their orbits (with the Ecliptic) in an upward or downward direction, they are said to form Nodes. The lines, joining the two Nodes (K-K 1 in Fig. 1), are variable. So too are the inclinations of the planes to one-another, so that even these inclinations, if we try to express them in a single concept, bring us to a rigid concept which we must immediately modify in face of the reality. For if an orbit is inclined at one time in one way, and at another time in another way, the concept we deduce in the first instance must afterwards be modified. To be sure, once such a point has been reached, we can take an easy line and say that there are ‘disturbances’ and that the reality is only grasped ‘approximately’ with our concepts. We then go on swimming comfortably in further theories. But in the end we swim so far that the fanciful and theoretic pictures we are constructing no longer correspond to the reality, though they are meant to do so.

It is easy to agree that this mutability of the eccentric orbits, and of the mutual inclination of the planes of the orbits, must somehow or other be connected with the life of the whole planetary system, or shall we say, with its continuing activity. It must be connected in some way with the living activity of the whole planetary system. That is quite evident. Starting from this, one might again try to form the concept, saying: Well now, I will bring such mobility into my thoughts that I picture the ellipses continually bulging out and contracting, the planes of the orbits ascending, descending and rotating, and then from this starting-point I will build up a world-system according to reality. Good. But if you think the idea through to the end, then precisely as the outcome of such logical thought, the result is a planetary system which cannot possibly go on existing. Through the summation of the disturbances which arise especially through the variability of the Nodes, the planetary system would move towards its own ultimate death and rigidity. Here there comes in what philosophers have pointed out again and again. While such a system can be thought out, in reality it would have had ample time to reach the ultimate finale. There is no reason why it should not. The infinite possibility would have been fulfilled; rigidity would long ago have set in.

We enter here into a realm where thought apparently comes to a standstill. Precisely by following my thinking through to the very last, I arrive at a world-system which is still and rigid. But that is not reality.

Now, however, we come to something else, to which we must pay special attention. In pursuing these things further—you can find the theory of it in the work of Laplace; I will only relate the phenomena—one finds that the reason why the system has not actually reached rigidity under the influence of the disturbances—the variability of the Nodes, etc.,—is that the ratios of the periods of revolution of the planets are not commensurable. They are incommensurable quantities, numbers with decimals to an infinite number of places. Thus we must say: If we compare the periods of revolution of the planets in the sense of Kepler's Third Law, the ratios of these periods cannot be given in integers, nor in finite fractions, but only in incommensurable numbers. Modern Astronomy is clear on this. It is to the incommensurability of the ratios between the periods of revolution of the several planets (in Kepler's third Law) that the planetary system owes its continued mobility. Otherwise, it must long ago have come to a standstill.

Observe now, what has happened. In the last resort, we are obliged to base our thoughts about the planetary system upon numbers which in the end elude our grasp. This is of no little importance.

We are therefore led, by the very requirements of scientific development, to think of the planetary system mathematically in such a way that the mathematical results are no longer commensurable. We are at the place, where in the mathematical process itself we arrive at incommensurable numbers. We have to let the number stand,—we come to a stop. We can write it in decimals no doubt, but only up to a certain place. Somewhere or other we must leave off when we come to the incommensurable. The mathematicians among you will be clear about this. You will see that in dealing with incommensurable number I reach the point where I must say: I calculate up to here and then I can go no further. I can only say (forgive my using a somewhat amusing comparison for a serious subject) that this coming to an inevitable halt in mathematics reminds me of a scene in which I was once a participator in Berlin. A fashion in Variety-entertainment came about through certain persons, one of whom was Peter Hill. He had founded a kind of Cabaret and wanted to read his own poems there. He was a very lovable person, in heart and soul a Theosophist, he had rather gone to seed in Bohemian circles. I went to a performance in which he read his own poems. The poem had got so far that single lines were finished, and so he read it aloud:

The Sun came up. ... etc. (The first line.)
The Moon rose. ... etc. (That was the second line.)

At each line he said ‘etc.’ That was a reading I once attended. As a matter of fact it was most stimulating. Everyone could finish the line as he chose! Admittedly with incommensurable numbers [you] cannot do this, yet here too you can only indicate the further process. You can say that the process continues in a certain direction, but nothing is given by which you might form an idea as to what numbers may yet be coming. It is important that precisely in the astronomical field we are led into incommensurabilities. We are forced by Astronomy to the very limits of mathematising; here the reality escapes us. Reality escapes us, we can say nothing else; reality eludes our grasp.

What does this mean? It means that we apply the most secure of our sciences, Mathematics, to the celestial phenomena, and in the last resort the celestial phenomena do not submit; the moment comes where they elude us. Precisely where we are about to reach their very life, they slip away into the incommensurable realm. Here then, our grasp of reality comes to an end at a certain point and passes over into chaos.

We cannot say without more ado, what this reality, which we are trying to follow mathematically, actually does when it slides away into the incommensurable. Undoubtedly this is related to its power of continued life. To enter the full astronomical reality we must take leave of what we are able to master mathematically. The calculation plainly shows this; the very history of science shows it.

Such are the points which we must work towards, if we would proceed in a realistic spirit. Now I would like to set before you the other pole of the matter. If you follow it physiologically you can begin from any point you like in embryonic development, whether it be from the development of the human embryo in the third or second month,—or the embryo of some other creature. You can follow the development back as far as ever you can with the means of modern science. (it is in fact only possible to a limited extent, as those of you who have studied it will know.) You can trace it back to a certain point, from which you cannot get much further, namely to the detachment of the ovum—the fertilized ovum. Picture to yourselves how far you can go back. If you wished to go still further back you would be entering the indeterminate realm of the whole maternal organism. This means that in going back you come into a kind of chaos. You cannot avoid this, and the fact that it cannot be avoided is shown by the course of scientific development. Think of such scientific hypotheses as the theory of “Panspermia” for instance, where they speculated as to whether the single germ-cell was prepared out of the forces of the whole organism, which was more the point of view of Darwin, or whether it developed in a more segregated way in the purely sexual organs. You will see when you study the course of scientific development in this field that no little fantasy was brought to bear on the attempt to explain the underlying genesis, when tracing backward the arising of the germ cell from the maternal organism. You come into a completely indeterminate realm. There is little but speculation in the external science of today as to the connection between the germ-cell and the maternal organism.

Then at a certain point in its development this germ appears in a very definite way, in a form which can be grasped at least approximately by mathematical or at any rate geometrical means. Diagrams can be made from a certain point onward. Many such diagrams exist in Embryology. The development of the germ-cell and other cells can be delineated more or less exactly. So one begins to picture the development in a geometrical way, representing it in forms similar to purely geometrical figures. Here we are following up a reality which in a way is the reverse of what we had in Astronomy. There we pursued a reality with our cognitional process and came to incommensurable numbers; the whole thing slips into chaos through the process of knowledge itself. In Embryology we slip out of chaos. From a certain moment onward we can grasp what emerges from chaos through forms that are like purely geometrical forms. Thus in effect, in employing Mathematics in Astronomy we come at one point into chaos. And by pure observation in Embryology we have at a certain point nothing before us but chaos; it all seems chaotic at first, observation is impossible. Then we come out of chaos into the realm of Geometry. It is therefore an ideal of certain biologists—a very justifiable ideal—to grasp in a geometrical form what presents itself in Embryology; not merely to make illustrations of the growing embryo naturalistically, but to construct the forms according to some inherent law, similar to the laws underlying geometrical figures. It is a justifiable ideal.

Now therefore we can say: When in Embryology we try to follow up the real process by observation, we emerge out of a sphere which lies about as near to our understanding as that which is beyond the incommensurable numbers. In Astronomy on the one hand, we proceed with our understanding up to the point where we can no longer follow mathematically. In Embryology on the other hand our understanding begins at a certain point, where we are first able to set to work with something resembling Geometry.

Think the thought through to its conclusion. You can do so, since it is a purely ‘methodological’ thought, that is to say the reality of it is in our own inner life.

If in arithmetic we reach the incommensurable numbers,—that is, we reach a point where the reality is no longer represented by a number that can be shown in its complete form—then we should also begin to ask whether the same thing may not happen with geometrical form as with arithmetical analysis. (We shall speak more of this in the next lecture.) The analytical process leads to incommensurable number. Now let us ask: How do geometrical forms image the celestial movements? Do not these images perhaps lead us to a certain point. Similar to that to which arithmetical analysis is leading when we reach incommensurable number? Do we not in our study of the heavenly bodies—namely the planets—come to a boundary, at which we must admit we can no longer use geometrical forms as a means of illustration; the facts can no longer be grasped with geometrical forms? Just as we must leave the region of commensurable numbers, it may well be that we must leave the region where reality can still be clothed in geometrical (or again arithmetical, algebraic, analytical) forms, such as in drawings of spirals and other figures derived from Geometry. So, in Geometry too, we should be coming into the incommensurable realm. In this sense it is indeed remarkable that in Embryology, though arithmetical analysis is not yet of much use, Geometry makes its presence felt pretty strongly the moment we begin to take hold of the embryological phenomena as they emerge from chaos. Here we are dealing, not indeed with incommensurable number but with something that tends to pass from incommensurable into commensurable form.

We have thus sought to grasp reality at two poles: On the one hand where the process of cognition leads through analysis into the incommensurable, and on the other where observation leads out of chaos to a grasping of reality in ever more commensurable forms. It is essential that we bring these things before our minds with full clarity, if we would add reality to what is presented by the external science of today. In no other way can we reach this end.

I should now like to add a methodical reflection, from which we can tomorrow make our way into more realistic problems.

In all that we have spoken of hitherto, we have been taking it for granted that the cosmic phenomena have been approached from the standpoint of Mathematics. It appeared that at one point the mathematician comes up to a limit—a limit he encounters too in purely formal Mathematics. Now there is something underlying our whole way of thinking in this realm, which perhaps passes unnoticed because it always wears the mask of the ‘obvious’ and we therefore never really face the problem. I mean the whole question of the application of mathematics to reality. How do we proceed? We develop Mathematics as a formal science and it appears to us absolutely cogent in its conclusions; then we apply it to reality, without giving a thought to the fact that we are really doing so on the basis of certain hypotheses. Today however, sufficient ground has already been created for us to see that Mathematics is only applicable to outer reality on the basis of certain premises. This becomes clear when we try to continue Mathematics beyond certain limits. First, certain laws are developed,—laws which are not obtained from external facts, as for example are Kepler's Laws, but from the mathematical process itself. They are in fact inductive laws, developed within Mathematics. They are then employed deductively; highly elaborate mathematical theories are built upon them.

Such laws are those encountered by anyone who studies Mathematics. In lectures given recently in Dornach by our friend Dr. Blumel, significant indications were given of this line of mathematical research. One of the laws in question is termed the Commutative Law. It can be expressed in saying: It is obvious that \(a+b\) equals \(b+a\), or \(a•b\) equals \(b•a\). This is a self-evident fact so long as one remains within the realm of real numbers: But it is merely an inductive law derived from the use of the implicit postulates in the arithmetic of real numbers.

The second law is the Associative Law. It is expressed as \((a + b) + c = a + (b + c)\). Again this is a law, simply derived by working with the implicit postulates in the arithmetic of real numbers.

The third is the so-called Distributive Law, expressible in the form: \(a (b + c) = ab + ac\). Once more, it is a law obtained inductively by working with the implicit postulates in the arithmetic of real numbers.

The fourth law may be expressed as follows: ‘A product can only equal zero if at least one of the factors equals zero.’ This law again is only an inductive one, derived by working with the implicit postulates in the arithmetic of real numbers.

We have, then, these four laws; the commutative law, the associative law, the distributive law, and this law about the product being equal to zero. These laws underlie the formal Mathematics of today, and are used as a basis for further work. The results are most interesting, there is no question of that. But the point is this: These laws hold good so long as we remain in the sphere of real numbers and their postulates. But no thought is ever given to the question, to what extent the real facts are in accord with them. Within our ordinary formal modes of experience it is true, no doubt that \(a + b = b + a\), but does it also hold good in outer reality? There is no ascertainable reason why it should. We might be very astonished one day to find that it did not work if we applied to some real process the idea that \(a + b\) equals \(b + a\). But there is another side to it. We have within us a very strong inclination to cling to these laws; with them therefore. We approach reality and everything that does not fit in escapes our observation. That is the other side.

In other words: We first set up postulates which we then apply to reality and take them as axioms of the reality itself. We ought only to say: I will consider a certain sphere of reality and see how far I get with the statement \(a + b = b + a\). More than that, I have no right to say. For by approaching reality with this statement we meet what answers to it, and elbow aside anything that does not. We have this habit too in other fields. We say for example, in elementary physics: Bodies are subject to the law of inertia. We define ‘inertia’ as consisting in the fact that bodies do not leave their position or alter their state of motion without a definite impelling force. But that is not an axiom; it is a postulate. I ought only so say: I will call a body which does not alter its own state of motion ‘inert’, and now I will seek in the real world for whatever answers to this postulate.

In that I form certain concepts, I am therefore only forming guiding lines with which to penetrate reality, and I must keep the way open in my mind for penetrating other facts with other concepts. Therefore I only regard the four basic laws of number in the right way if I see them as something which gives me a certain direction, something which helps me regulate my approach to reality. I shall [be] wrong if I take Mathematics as constituting reality, for then in certain fields, reality will simply contradict me. Such a contradiction is the one I spoke of, where incommensurability enters in, in the study of celestial phenomena.

• 1. Note by translators: In the first few pages of this lecture, the word Vorstellungen has been translated, either as “mental pictures” or “thought-pictures”, or by the word “ideas” as in Prof. Hoernle's original English edition of Dr. Steiner's Philosophie der Freiheit. In other translations, including the later editions of this book, the word is rendered “representations”, or again, “Mental presentations”. Dr. Steiner's use of Vorstellung corresponds, we believe, to the colloquial, work-a-day meaning of the word “idea” in current English. (Where Idea is meant in its deeper, more spiritual meaning—German Idee—it can be distinguished by the use of a capital.)
• 2. Note by Editor: This plane is inclined at an angle of about seven degrees to the plane of the ecliptic.

For the further progress of our studies I must today insert a kind of interlude, for we shall then understand more easily the real nature of our task. From a particular point of view we will reflect on the cognitional theory of Natural Science altogether. Let us link on to yesterday's lecture by calling to mind once more the provisional conclusions to which we came. The verification of them will emerge in the further course.

We have seen that in the study of celestial phenomena, in so far as these are expressed by our Astronomy in geometrical forms and arithmetical figures, we are led to incommensurable qualities. There is a moment in our process of cognition—in the attempt to understand the celestial phenomena—when we must come to a standstill, as it were, and can no longer declare the mathematical method to be competent. From a certain point onward, we simply cannot continue merely to draw geometrical lines, tracing the movements of the heavenly bodies. We can no longer employ mathematical analysis; we can only admit that analysis and geometry take us up to a certain point, whence we can go no further. At least provisionally, we come to the very significant conclusion that in reflecting on what we see, whether with the naked eye or with the aid of instruments, we can never fully compass it was geometrical figures or mathematical formulae. We do not contain the whole of the phenomena in algebra, analysis and geometry.

Think of the significance of this. If we are claiming to include the totality of the celestial phenomena, we must no longer imagine that we can do so by thinking of the Sun as moving in such a way that its movement can be represented by a definite geometry line, or that the Moon's movement can be so represented. Precise our most ardent wish must be renounced when we confront the phenomena in their totality. This is the more significant, since nowadays, the moment someone says ‘The Copernican System works no more satisfactorily than the Ptolemaic’, someone else will answer, ‘Let us then design another system’. We shall see the in the further course of these lectures, what must be put in the place of mere geometrical designs in order to comprehend the phenomena in their totality.

I must put this negative aspect before you first, before we can enter into the positive, for it is most important that we clear our thought in this respect.

On the other hand, we saw yesterday that what confronts us in Embryology emerges as if from indefinite, chaotic regions, and from a certain point onward can be grasped in picture-form, or even geometrically. As I said yesterday, in studying the celestial phenomena, through the very process of cognition we come to a point where we must recognize that the world is different from what this process of cognition might at first have led us to believe. And in the embryonic phenomena we are led to see that there must be something which preceeds the facts to which we still have access.

Now among other things there recently appeared a certain divergence of outlook among embryologists. (I will only give a rough description.) On the one hand there were the strict followers of biogenetic law, which states, as you know, that the development of the individual embryo is a kind of shortened recapitulation of the development of the race. These people wished to trace the cause of the development of the embryo to the development of the race. On the other hand, others came forward who would not hear of the derivation of the individual from the racial development, but held to a more or less mechanical conception of embryonic development saying that it was only necessary to take into account the forces directly present in what takes place in the embryo itself. For example, Oscar Hertwig left the strict biogenetic school of Haeckel and changed over to the more mechanical school. Now the mechanical needs to be grasped in a way that is at least similar to mathematics even though it be not pure mathematics. We therefore see, from the very history of Science, how front a certain stage onward (something as I said, must be presumed to have gone before this stage) embryological development is taken hold of by a mechanical, mathematical method of research. It is the history of these things to which I now wish to point.

All this appears in the field which one might call the theory of knowledge. On the one hand we are driven to a boundary in the cognitional process, where we can get no further with our favorite modern method of approach. On the other hand, in studying the embryonic life our only possibility of grasping it with ordinary methods is to start from a certain point: what goes before this has to be taken fro granted. We must admit that we find something in the realm of reality, the beginnings of which we must leave vague and unexplored; then from a certain point onward we can set to work, describing what we observe in terms of diagrams, formulas and relationships which are at least similar to those of mathematics and mechanics.

Bearing these things in mind, I deem it necessary in today's lecture to insert a kind of general reflection. As I have often pointed out, it is the ideal of modern scientific research to observe outer Nature as independently of man as possible,—to establish the phenomena in pure objectivity, as it were, excluding man altogether from the picture. We shall see that precisely through this method of excluding, it is impossible to transcend such barriers as we have now observed from two distinct sides.

This is connected with the fact that the principle of metamorphosis, which, as you know,was first conceived and presented in an elementary way by Goethe, ha so far hardly been followed up at all. It has no doubt been used to some extent in morphology, yet even here, as we saw yesterday, one essential principle is lacking. Morphology today cannot yet recognize the form and construction of a tubular or long bone, for example, in its relation to that of a skull-bone. To do this, we should have to reach a way of thinking whereby we should first study what is within, say, the inner surface of a tubular bone and then relate this to the outer surface of a skull-bone. This means a kind of inversion, as when a glove is turned inside-out; but at the same time there is an alteration of the form, an alteration of the surface-tensions through the reversing or turning of inside outward. Only if we follow the metamorphosis of forms in this way, though it may seem complicated, shall we reach true conclusions.

But when we leave the morphological and enter more into the functional domain, there are but the barest indications, in the existing ways of thought, towards a true pursuit of the idea of metamorphosis in this domain. Yet this is what is needed. A beginning was made in my book, “Riddles of the Soul”, wherein I indicated at least sketchily—the three-foldness of the being of man, recognized as a sum-total of interrelated functions. At least in outline, I explained how we must first distinguish those functions and processes in man which may be regarded as belonging to the nerves and senses; how we then have to recognize, as relatively independent processes, all that is rhythmical in the human organism; and how again we must recognize the metabolic processes as distinct. I pointed out that in these three forms of processes all that is functional in man is included. Anything else which appears functional in the human organism is derivable from these three.

It is essential to see that all phenomena in the organic realm although appearing outwardly side by side, are related to one-another through the principle of metamorphosis. People today are disinclined to look at things macroscopically. We must find our way back to the macroscopic aspect. Otherwise, through the very lack of synthetic understanding of what is living, problems will arise which are not inherently insoluble, but are made so by our methodical prejudices and limitations.

You see, in learning to understand man in this threefold aspect we must observe that he is connected with the outer world in a three fold way His life of nerves and senses is one way in which man is related to the outer world; through all rhythmic processes he is related to it in another way. It lies in the very nature of the rhythmical processes that they cannot be considered as isolated within man, apart from the rest of the world, for they depend upon the breathing,—a process of perpetual interchange between the human body and the outer world. Again, in the metabolism there is a very obvious process of interchange between man and the outer world. Also the nerves-and-senses process may be regarded as a continuation of the outer world into the inner man. This becomes easier to understand if the distinction is made between the actual perceptions, given to us through the senses, and the accompanying process of cognition—the forming of ideas and mental pictures. It is unnecessary here now to go into these things more deeply, for it is evident enough. In relation between man and the outer world during sense-perception the emphasis is more on the outer world, while the forming of ideas and mental pictures takes us more into the inner man. (I am referring to the bodily processes, not to the life of soul.)

Again, leaving aside for the moment the rhythmic system—breathing and blood-circulation—the metabolic system brings us to something else, which is in definite contrast to this inward-leading process from sense perception to ideation. A thorough study of the metabolic system establishes a connection between the inner metabolic processes and the functions of the human limbs. The limb-functions are connected with the metabolism.

If people would proceed more rationally than they are wont to be they would discover the essential connection between the metabolism, situated as it is more deeply within the body, and the processes by means of which we move our limbs. These too are metabolic. The actual organic functions which underlie the movements of the limbs are processes of metabolic. Consumption of material substances is what we find if we examine the organic functions here.

But we must not stop short at the metabolic process as such. There is a way in which this process leads as much from man towards the outer world, as sense-perception leads from the outer world towards the interior of the human body. (Such methods of research, which are really fundamental, need to be undertaken, otherwise no progress will be made in certain essential directions.)

What is it that is directed outward from the metabolism even as something is directed inward from sense-perception to the creating ideas and mental pictures? It is the process of fertilization. Fertilization points in the opposite direction,—from the bodily organism outward. Representing it diagrammatically (Fig.1): In sense-perception the direction is from without inward; this in—coming process of sense-perception is then ‘fertilized’ by the organism and we get the forming of ideas. (Please do not take offense at the expression ‘fertilized’; we shall soon replace, what may look like a symbolical way of speaking, by the reality it indicates.) In the metabolic process the direction is from within outward, and we get actual fertilization. In what is manifested therefore at the two poles of threefold human nature, we are led in two opposite directions.

In the middle is all that belongs to the rhythmic system. Now we may ask, what in the rhythmic system is directed outward and what inward? Here it is not possible to find such precise distinctions as between the inner metabolism and fertilization, or between perception and ideation. The processes in the rhythmic system rather merge into one-another. In the in-breathing and out breathing the process is more of a unity. It cannot be distinguished quite so sharply, yet it is still possible to say (Fig.1): As sense perception comes from outside and fertilization goes outward, so too in inspiration and expiration there is a going inward and outward. Breathing is intermediate.

Here is a true example of metamorphosis: a single entity, underlying threefold human nature, organized now in one way, now in another.

In the upward direction this can be followed to some extent physiologically. (Some of you already know what I Shall now refer to.) Observe the breathing process. The intake of air influences the organism in a certain way; namely, in in-breathing, the cerebro—spinal fluid, in which the spinal cord and brain are stepped, is pressed upward. You must remember that the brain is in fact floating in cerebral fluid, and is thus buoyed up. We should not be able to live at all without this element of buoyancy. We will not go into that now, however, but only draw attention to the fact that here is an upward movement of the cerebral fluid in in-breathing and a downward movement in out-breathing. So that the breathing process actually plays into the skull, into the head. In this process we have a real interplay and co-operation of the nerves-and-senses system with the rhythmic system.

You see how the organs work, to bring about what we may call metamorphosis of functions. Then we can say, however hypothetical or only as a postulate: perhaps something similar will be found as regards metabolism and fertilization. But in this realm of the body we shall less easily reach a conclusion. This is indeed characteristic of the human organism; it is comparatively easy to understand the interpenetrating relation between the rhythmic system and the nerves-and-senses system in process accessible to thought, but we cannot so easily find an evident relation between the rhythmic system and the processes of metabolism and fertilization.

Call to your aid the physiological knowledge at your disposal, and the more exactly you go into the matter the better you will perceive this. Moreover it is quite obvious why it is so. Consider the regular alternation of sleeping and waking. Through sense-perception you are open to the outer world, continuously exposed to the outer world. Then you set to work with your thinking and ideation and bring a certain order and orientation into what you see around you in your waking life. It becomes ordered through an activity which works from within outward; the orientation comes from within. Actually we can say: We confront an external world which is already ordered according to its own laws, and we ourselves bring another order into it out of our own inner being. We think about the outer world, we put together the facts and phenomena according to our own liking—unhappily, often a very bad liking! From our inner being, something is introduced into the outer world which by no means necessarily corresponds to this outer world. If this were not so, we should never fall a victim to error. Out of our own inner being comes an arbitrary remolding of the world around us.

But now, looking at the other pole of human nature, you will agree that the disordering comes from without, both in metabolism and fertilization. For it is left very largely to our own arbitrary choice and free will, how we sustain our metabolism by taking food, and even more so, how we behave as regards fertilization. But here the arbitrary element has much to do with the outer world, which in the first place is foreign to us. We do at least feel at home in the arbitrary element we introduce, out of our own inner being, into the process of perception. But we do not feel familiar with all that we bring into ourselves from the outer world. We have, for instance but a very slight idea—at least, most people have very little idea of what actually happens in our relationship with the world when we eat or drink. And as to what happens in the intervals of time between our meals,—to this we pay very little attention, and even if we did it would not help as much. Here we come into an indefinite, impalpable region, I would say. Thus at the one place of man's being we have the ordered Cosmos which extends its gulfs, as it were, in our sense organs (Fig.2). (The world ‘ordered’ must not be misunderstood, it is only used to characterize the facts; we will not lose ourselves in philosophical arguments as to whether the Cosmos is really ordered or not, we want only o characterize the given facts.) The pole is in contrast to the other, which, we are bound to admit, is an un-ordered Cosmos, considering all that comes into us from without all that we stuff into ourselves, or again, how the process of fertilization is entered into in quite irregular intervals of time and so on. Contemplating this invasion of the metabolism by the outer world, we must admit that we are here confronted by an unordered Cosmos—un-ordered at least to begin with, so far as we are concerned.

And now we may put the question—from the more general aspects of the theory of human knowledge: How and to what extent are we really connected with the starry Heavens? In the first place, we see them. But you will have a vivid feeling by this time of the uncertainties which assail us when we being to think about the starry Heavens. Not only have the men of different ages felt convinced of the truth of the most diverse astronomical world—systems. As we saw yesterday, we have to face the fact that we cannot contain the totality of the starry Heavens in the mathematical and mechanical forms of thought in which we feel most secure.

Not only must we admit that we cannot trust to mere sensory appearances as regards the Heavens, but we must recognize that when we take our start from what we see and then work upon it with the life of thought, which, as we saw, belongs more to the inner man,we cannot ever really get at this world of stars. It is the truth, it is no mere comparison to say: The starry Heavens only present themselves to us in their totality—a relative totality, of course—through sense perception. Taking our start from sense-perception, when we as man try to go farther inward, to understand the starry Heavens, we feel somewhat foreign to them. We get a strong feeling of our inadequacy. And yet we feel that something intelligible must be there in the phenomenon which we behold.

Outside us, then , is the ordered Cosmos; it only presents itself to our senses. It most certainly does not at once reveal itself to our intellectual understanding. We have this ordered Cosmos on the one hand; with it, we cannot enter into man. We try to lead on from outer sense-perception of the Cosmos towards the inner man—the life of thought and ideation—and find we cannot enter. We must admit: Astronomy will not quite go into our head. This is not said in the least metaphorically. It is a demonstrable fact in the theory of knowledge. Astronomy will not go into the human head; it simply will not fit there.

What do we see now at the other pole—that of the unordered Cosmos? Let us but look at the facts; we do not want to set up theories or hypotheses, but only to see the facts clearly.

Look for what is in contrast, in the outer Universe to the astronomical domain, and in man to the processes of perception and ideation (the continuation of the ‘ordered Cosmos’ into man). In man you come into the realm of metabolism and fertilization—and Astronomy (Fig.2) and look downward in an analogous way, into what realm are you led? You are led into Meteorology—all the phenomena of the outer world once more, relating to Meteorology. For if you try to understand meteorological phenomena in terms of ‘natural law’, the amount of law you can bring in is to the ordered Cosmos of Astronomy in just the same proportion as is the temperamental region of metabolism and fertilization in man to the realm of sense perception, into which the whole starry Heaven sheds its light,—which only begins to get into disorder in our own inner life, namely in our forming of ideas.

If therefore we regard man not as an isolated being, but in connection with the whole of Nature, then we can place him into the picture in the following way. Through his head, he takes part in the astronomical, through his metabolism in the meteorological domain. Man is thus interwoven with the Cosmos on either hand.

Let us here add another thought. Yesterday we spoke of those processes which may be looked upon as an inner organic imagining of Moon-events, namely the processes in the female organism. In the female organism there is something like an alternation of phases, a succession of events, taking their course in 28 days. Although, as things are now, these events are not at all dependent on any actual Moon-events, yet they are somehow an inner reflection of the moon. I also drew your attention to the following psycho-physiological fact. If we really analyze human memory and take into account the underlying inner organic process, we cannot but compare it with this functioning of the female body. Only that in the latter the bodily nature is taken hold of more intensely than it is when holding fast in memory some outer experience which it has undergone. What comes to expression in these 28 days as a result of erstwhile our impressions is no longer contained within the individual life between birth and death, whereas the experiencing of outer events and the memory of them comes into a shorter period and takes its course between birth and death, within the single life of the individual. Considered in their psychological-physiological aspect, the two processes are however essentially the same—a functional reexperiencing of an external process or event. (In my ‘Occult Science’ I clearly hinted at this kind of experience in relation to the outer world.)

Now, study the functions of the ovum before fertilization and you will find that they are entirely involved in this 28-day inner rhythm; they belong to this process. But as soon as fertilization takes place, the processes in the ovum immediately fall out of this inner rhythmic life of the human being. A mutual relation with the outer world is at once established. Observing the process of fertilization, we are led to see that what is happening in the ovum from then onward no longer has to do with mere inner processes in the human body. Fertilization tears the ovum out of the purely inner organic process and leads it over into the realm of those processes which belong in common to the inner being of man and to the Cosmos,—a realm in which there are no barriers between what takes place within man and in the Cosmos. Therefore, what occurs after fertilization,—all that happens in the forming of the embryo,—must be studied in connection with external cosmic events, and not merely in terms of developmental mechanisms within the ovum itself in its successive stages.

Think what this means. All that goes on in the ovum before fertilization is, so to speak, within the domain of the human being's own inner organic process. But in what happens after fertilization and is brought about thereby—the human being opens himself to the Cosmos. Cosmic influences here prevail.

Thus on the one hand we have the Cosmos working in upon us up to the point where the life of ideas begins. We have, in sense—perception, a mutual relation, between man and the Cosmos. We investigate this relation, for example, by means of the laws of perception. The physiology of the senses and so on. The way in which we see an object must be investigated through such laws. Suppose we watch a railway-train traveling past us. We see the whole movement lengthwise. If, however, we are at a point directly in front of the train far enough away—however fast the train is going, we see it as if it were stationary. Pictorially, therefore, what takes place in us depends on the relation of the cosmos to us. We are in the midst of pictures and we ourselves belong to the picture. However, we become entangled in something chaotic,—for ultimately, our world systems are chaotic,—if we try to draw conclusions as to the real events from what we see externally.

On the other hand, in regard to fertilization, man is involved not in pictorial but in real cosmic processes.

Thus at the one role man is immersed in the Cosmos in a pictorial, and at the other in a real way. The very thing that eludes him when he looks out into the Cosmos, works in upon him when he undergoes the process of fertilization. Here therefore something, in itself a whole, is drawn apart into two members. In the one case a mere picture is before us and we cannot strike through to the reality. In the other the reality confronts us; through it a new man comes into being. But it does not become clear picture; it remains for us as devoid of law as do the manifestations of the weather, or meteorological conditions generally. Here we are face to face with a duality—here are two poles. From either side we receive half thrilled. It is as though we received the picture from the one side and the reality which underlies it from the other.

You see, the way man confronts the world is not as simple as one might assume in saying: The sensory picture of the world is given; now let us devise the reality by philosophical methods. This problem of finding the underlying reality in sense-perception is, of course, fundamental in the philosophic theory of cognition. But man is curiously balanced between the picture and reality in quite other ways than by mere philosophic speculation.

Now in the course of world-evolution, men have already tried to approach this secret through an experience of the intermediary realm: in-breathing and out-breathing. The ancient Indian wisdom which, as I often say, it would be wrong for us to imitate today—proceeded more or less instinctively from the following hypotheses. Sense-perceptions are of no use in the striving for reality; nor are the sexual processes or those of fertilization, for they give no clear picture. Therefore, let us keep to the middle region, which is metamorphosed at one time towards picture-forming and at another time towards reality. We must keep to the middle region, for through it the approach to reality and yet at one and the same time to the picture must in some way be possible. This is why the special breathing exercises of the Yoga system were perfected by the wisdom of Ancient India. Men sought to reach reality by experiencing the breathing process consciously, thus grasping at the same time both picture and reality. And if one asks why this should be, the answer is given: Breathing unites picture and reality. (The answer may be more or less instinctive, though not entirely so, as you can see if you will study, in the Indian philosophy itself, how this strange system of breathing-exercises arose.) Breathing unites picture and reality. The picture is experienced in its relation to the reality, if once the breathing process is lifted out of the unconscious into consciousness. We shall never understand what thus appeared in the historic evolution of mankind, unless we regard it from the point of view of the inner physiology of man. Looking at it in this light, you can say: There was a time when men sought to comprehend reality by turning to man himself. For pictures of the world, we have the senses; for the reality, something quite different. Therefore men turned to that part of the world human being which is neither shutoff in finished pictures, nor on the other hand in the mere experiencing of reality; they turned to what is not yet differentiated or divided—to the breathing process. And in so doing, they brought man into the Cosmos. They did not contemplate a world separate from man like the world of our Natural Science; they beheld a world for which man, as rhythmic man, became a real organ of perception. This world, they said, can be grasped neither by the nerves-and-senses man, nor by the metabolic man. In his life of nerves and senses, man becomes conscious in such a way that what presented itself to nerves and senses is thinned out to a mere picture; in the metabolism, reality meets him in such a way as not to be raised into consciousness at all. The interweaving of the real but unconscious experience with what is thinned out to a picture was sought by the wise men of ancient India in the regulated breathing process. Nor shall we ever understand the ancient cosmic systems, previous to the Ptolemaic, till we are able to divine how the Universe appears to man when in this was a synthesis, however undifferentiated, is achieved between the process of cognition on the one hand, and on the other the intense realty of the reproduction-process.

Consider now from this point of view the teachings about the creation of the world which are to be met with particularly in the Bible: teachings which, as things are today, are not so easy to see through. Consider the Bible story of the Creation, particularly as interpreted by those who still had the old traditions. Fundamentally, the Biblical story of Creation can only be understood if we are able to combine the genesis of the world which we derive by looking at the outer Universe, with that which we derive by Embryology. What is set forth in the Book of Genesis is in fact compounded of Embryology and of what is seen in the outward glory of the sense world. Hence the repeated attempts to interpret the Biblical story of Creation, even word for word, by embryological facts. Truly, it calls for such interpretation.

I introduced this today, my dear friends, for quite a definite reason.

You see, if our present studies—intended, as they are, to form a bridge between the external Science of today and Spiritual Science—are to have any meaning at all, we must first acquire a quite definite feeling and must permeate ourselves with this feeling otherwise we can get no further. We must become able to feel that certain modern ways of thought are superficial and external,—to feel this in a thoroughly deep way. We must learn to see the superficiality, on the one hand, of setting up pictures of the Universe which only try to make some slight corrections in the Copernican System, and on the other hand, of researching into the embryonic life in the ways which are customary today. One might say that Nietzsche's dictum: “The world is deeply thought and wrought; more deeply than the passing day”, proceeded from such a feeling. The impulses must be acquired not to seek explanations in the mere superficial acceptance of what presents itself directly, even if it be to the enhanced sight of telescope or microscope or X-ray apparatus. We must learn to have respect for explanations of another nature, aspiring to other faculties of knowledge, such as were sought by the old Indian sages in the Yoga System, so as to penetrate into reality and find the means of forming an adequate picture of reality.

Since we have now outgrown the Yoga system, we must feel impelled towards a new way of penetrating into the Universe by processes which still remain to be developed—which are not to be derived so simply from the habitual methods of today. For man is placed in the midst between the picture of the world,—a picture which presents itself to him in an overwhelmingly forceful way in the starry Heavens, the secrets of which will never be disclosed through the mere intellectual faculties,—and what meets him with ever—changing mood and temperament in the processes of reproduction, by virtue of which the human race exists. Into the midst of this great whole which is thus separated for him into two halves, man is placed. to find a connection between the two, he must look for a way of spiritual development, even as he did in an older form in the Yoga system,—a form no longer possible today.

Astronomy, practiced as hitherto, will never lead to a grasp of reality; it will only give us pictures. And Embryology, though in this realm we seize reality, will no enable us to penetrate the reality with ideas and mental pictures. Astronomical pictures of the world are poor in reality; embryological pictures are poor in idea—we fail to penetrate the facts with clear ideas. Thus in the theory of knowledge too we must approach the human being as a whole, instead of merely indulging in philosophical and psychological speculations about sense-perception. We must take our start from the whole of man. We must learn how to place man as a whole into the Universe. That is our task today.

It is very evident today, how on the one hand in Astronomy the ground of knowledge is being lost. And it is evident how on the other hand in Embryology, where knowledge fails to reach the well-springs of reality, all that results is a mere talking round and round the given facts, whether in terms of the biogenetic law or of developmental mechanisms. Amplification of our fundamental methods is quite evidently needed in both of these directions.

I had to put all this before you, so that we might understand each other better in what follows. For it will help you see that it would be no use if I were simply to add another formal picture of the Universe to the existing ones, although admittedly that is the kind of thing which people nowadays desire.

You will have seen, from what has been said so far, that in the explanation of natural phenomena we need to find a path leading beyond the intellectually mathematical domain. That we do not dispute the justification of a mathematical approach is implicit in the whole spirit of these lectures. But we were able sharply to define the point beyond which it is impossible to go with mathematical thought-forms, in the celestial spaces on the one hand, and in the realm of embryology on the other. We must hew out a path to other methods of cognition. It is the purpose of these lectures to show the scientific need of other methods.

I shall try to show that what is looked for nowadays merely by gazing outward into celestial space—whether with the unaided eye or with the help of optical instruments—needs to be put on a far wider basis, so that not only a part but the whole of man becomes the ‘reagent’ for a deeper penetration of the Heavens. Today I shall try, if not to prove, at least to indicate the validity of such a widening of method, by approaching the problem from quite another side. It may seem paradoxical in relation to our present theme, but the reason will soon become plain.

In studying the evolution of mankind on Earth we must surely find something within human evolution itself to guide us to the essential source of the celestial phenomena. For otherwise we should be assuming that what goes on in the Universe beyond the Earth is without influence on man,—on human evolution. No-one will make such an assumption, although admittedly the influences may be over-estimated by some and under-estimated by others. It will therefore be plausible—at least from a methodic point of view—to put the question: ‘Can we find anything in the evolution of mankind itself to indicate ways of access to the secrets of celestial space?’ Asking this question, we will take our start, not from Spiritual Science, but from the facts which anyone can gather for himself by empirical, historical research.

Looking back in the evolution of mankind in the realm where human thoughts, the human faculties of knowledge find expression, where, so to speak, the relation of man to the world takes on the most highly sublimated forms—we are led back, to begin with (as you may gather from my ‘Riddles of Philosophy’), only a few centuries into the past. Indeed I have often pointed to a certain moment during the 15th century, one of the most essential in the more recent phase of human evolution. The indication is of course approximate. We have to think of the period about the middle of the Middle Ages. Needless to say, we are referring only to what was going on within civilized mankind.

It is not generally seen clearly or sharply enough, how deep and incisive a change was then taking place in human thought and cognition. There has unfortunately for some time been a downright aversion—among philosophers especially—to a real study and appreciation of the epoch in European civilization which may be called the Age of Scholasticism. During that age, deeply significant questions came to the surface of man's life of knowledge. It one goes into them deeply enough, one feels that these questions did not merely spring from the realm of logical deduction—the form in which the Middle Ages used to clothe them—but from the very depths of man's being.

One need only recall what then became a fundamental question in human knowledge—the question of Nominalism and Realism. Or again, what it betokened in the spiritual development of Europe that attempts were made to prove the existence of God. There was for instance the so-called ontological proof of the existence of God. From thought itself—from the pure concept—men wanted confirmation of God's existence. Think what it means in the whole evolution of human knowledge. Something was stirring in the inmost depths of human being; in the philosophical deductions of the time it only found fully conscious expression. Men were perplexed as to whether the concepts and ideas, which man forms and puts into words, in some way stand for a reality, or whether they are merely formal summarizations of the external sensory data. The Nominalists regarded the general concepts which man creates for himself as a mere formal summary, having no significance for the external reality but only helping man to find his way about—to orientate himself in an otherwise confusing outer world. The Realists (an expression used in a rather different sense than today) declared that something real is to be found in general or universal concepts,—that in these concepts man in his inner life takes hold of something real,—that they are no mere convenient generalizations or abstractions from the world.

Often in more public lectures I have related how my old friend Vinsenz Knauer—a latter-day scholastic, though he would not have claimed to be one—showed himself very clearly, in his interesting work “The Central Problems of Philosophy, from Thales to Robert Hamerling”, to be thoroughgoing Realist. The Nominalists, he said, assert that the concept ‘lamb’ is nothing but a convenient generalization arising in the human mind; so too the concept ‘wolf’. Matter is only put together in a different way in the lamb and in the world. We only summarize it in the convenient abstraction, ‘lamb’ or ‘wolf’ as the case may be. Well, he suggested, try for some time to keep a wolf away from all other food and give it only lambs to eat, after the necessary lapse of time the matter in the wolf will be nothing but lamb, and yet it will not have lost its wolfishness. Therefore the wolf-nature, expressed in the general concept ‘wolf’ must be something real.

Now the fact that the so-called ‘ontological’ proof of God's existence could arise at all, bears witness to a deep and thorough going change then taking place in human nature. Quite a short time before, it simply would not have occurred to anyone within European culture to want to prove God's existence, for this was felt to be self-evident. Only when this feeling was no longer alive in men, did they begin to crave for proof. If you have living inner certainty about a thing, you do not want to prove it. But at that time something was slipping away from man, which until then had been alive in him quite as a matter of course, and the human spirit was thus led into quite other channels—quite other needs. I could adduce many another example, showing precisely at the highest levels of thought and knowledge (though you may take the word 'highest' with a grain of salt) what a deep stirring and rumbling was going on in human nature during that period of the Middle Ages.

Now we can surely not deny that there must be some connection between what is going on in the life of mankind and the phenomena in the Heavens beyond the Earth. In the most general sense, we must assume that there is some connection; what it is in detail, we shall discover in due course. Hence we may ask—we want to proceed very carefully, so we need only ask—‘How were these inner experiences which man on Earth was undergoing at that time, connected with the evolution of the Earth-plant altogether?’,—a question which may obviously lead us into realms beyond the earth. Was it perhaps a special moment in the evolution of the Earth a such? Is there anything that we can point to as a more definite criterion of what this moment was in human evolution?

We can indeed point to something of significance in this connection. There was another time which made a deep incision in the name regions of the Earth where in the Middle Ages these events were taking place in the most highly sublimated realm of human life the spiritual life of thought. The medieval time, when this deep moving and stirring of humanity took place, lies in the very midst between two end-points, as it were, in the scale of time. For European regions these ‘end-points’ do not represent the kind of times in which intense activity of human life and culture would be possible at all. In effect, if from this medieval moment, which I will call A (Fig. 1), we go backward and forward an equal length of time into a fairly distant past and future, we come to points of time representing a certain barrenness and death of civilization in the very regions where this deep stirring of human life was going on in the 13th, 14th, and 15th centuries. About 10,000 years forward and 10,000 years back from this moment (A in Figure 1) we reach the maximum development of the Ice Ages in these very regions Ice Ages certainly would not allow of any outstanding development in human life and culture.

Surveying therefore the evolution of these European regions we find an Ice Age—a laying-waste of civilization—10,000 years before the Christian era, and we should find the same again 10,000 years after this time. The deep stirring of human life, of which we have been speaking, happened midway between two such barren epochs.

As I said just now, there is a certain reluctance to pay attention to this period in the development of philosophy—the 13th and 14th centuries;—it is not seen clearly and accurately for what it is. Yet if one has a feeling for the evolution of the life of knowledge in mankind, one is aware that to this day our philosophic history is influenced by the after-effects of what was stirring and rumbling in the life of mankind at that time. It showed itself in other domains of civilization too; it only came to expression most clearly and symptomatically in this phase of development of the life of thought and knowledge.

Now as you know, this phase of development—appearing about the middle of the Middle Ages—was an incisive one in European civilization. I have often spoken of it in anthroposophical lectures. It was an incision. Something was changed in the whole trend of human evolution. It had been beginning long before—in the 8th century B.C. We may describe it as a most intense development of human intellectuality.

Since then, in the life and civilization of mankind, we have been looking especially at the development of Ego-consciousness. All aberrations and all wisdom gained in the general life of humanity since that medieval time are really due to this Ego-development to the ever-growing elaboration of the consciousness of “I” in man. The consciousness of the ancient Greeks and even of the Latins (both the ancient Latins and their descendants, the Latin peoples of today) did not lay so much stress on the Ego. Even in language for the most part, in grammar and syntax, they do not pronounce the “I” so outspokenly, but still include it in the verb. The “I” is not yet so blatantly set forth. Take Aristotle and Plato, and above all the greatest philosopher of antiquity, Heraclitus. Throughout their work the Ego is not yet so prominent. The way in which they take hold of the world-phenomena with the intellectual reasoning principle is as yet rather more selfless. (Please do not over stress this, but in a relative sense the word ‘selfless’ may be used.) There is not yet so sharp a dissociation of the self from the world-phenomena as there tends to be in the new age—the Age of Consciousness in which we are now living.

Going still farther back—beyond the 8th century B.C.—we come into the Egyptian and Chaldean Age as I have called it (you will find the details in my “Occult Science”). Once again, the condition of the human soul was different. During this age—which like the others, lasted for over 2,000 years—man was not yet relating external phenomena to one-another by intellectual reasoning at all. He apprehended the world—the Heavens too—rather in feeling and direct sensation. It is mistaken and fruitless to approach what is still extent of the Astronomy of Egypt and Chalden with present-day intellectual judgments—the kind of judgment which we ourselves have inherited from the Graeco-Latin Age. We must achieve a certain metamorphoses or soul so as to enter into the quite different soul-condition then prevailing, where man took hold of the world in simple feeling and sensation (where the concept was not yet separated from the sensation).

Even in the realm of actual sensations or sense-impressions—as can be shown historically and philologically—they attached no great importance to the precise description of the blue and violet shades of color, whereas (they had a very keen sensation of the red and yellow regions of the spectrum. Indeed the sensation of the dark colors can be seen to have arisen simultaneously with the capacity for intellectual concepts.

The Egypto-Chaldean Age—from 747 B.C. about 2160 years into the past,—takes us to the beginning of the third millennium BC. Still earlier, say in the fourth or fifth millennium BC, we come into an age when man's whole outlook and mode of perception were so different from ours today that it is hard for us, without recourse to spiritual-scientific methods, to transplant ourselves at all into the way in which the man of that time was the world around him. It was not only a feeling and sensing,—it was a living with the outer happenings, being right in them. Man felt himself a part and member of all Nature around him, much as my arm, if it were conscious, would feel itself a member of my body.

Here therefore was an altogether different trend and quality in man's relation to the world. And if we go still farther back, we find this union of man with the surround world even more enhanced. In those very early times, civilizations were only able to develop where special geographical conditions made it possible. I mean the time described in my Occult Science as the Ancient Indian civilization—much earlier than the culture of the Vedas, which was but a later echo of it. The Ancient Indian epoch comes very near to the time when glacial conditions prevailed in our regions of the Earth. A culture like the Ancient Indian could only develop when such climatic conditions, more or less, as we enjoy in the Temperate zone today, extended to what is now the Equator. You can deduce it simply from the relative advance or retreat of the ice; tropical conditions did not come about in India until a must later time, when in more northerly regions the ice had receded.

We see therefore how the inner evolution of mankind undergoes modifications hand in hand with changing terrestrial conditions—changing conditions, that is to say, on the Earth's surface. Only those who take a very short-term view of mankind's evolution upon Earth will imagine that the scientific ideas we entertain today have any absolute validity—that we have now at last got through to the scientific truth, so to speak. To anyone who looks more deeply into these regions of the Earth which are today enjoying certain forms of cultural and spiritual life will at some future time inevitably be laid waste again; they will be desolate once more. From the past length of time you may reckon out how long ahead it will be till a new glacial age overtakes our present civilization. Moreover assuming that we can find some connection between the celestial phenomena and these facts of earthly evolution—the successive Ice-ages and the mid-point between them—this will lead on to a further insight. That which take place on Earth in the most highly sublimated realms of cultural life—in the life of thought and knowledge—will be related now not only to these changing conditions on the Earth itself, but to conditions in the outer Cosmos. Purely empirical reflection shows that man is what he is by virtue of conditions on the planet Earth and in the Universe beyond.

Once more then taking the facts empirically as is usual in Science, only with a somewhat wider range, our vision is extended until we recognize such a relationship as we have just been describing. Now in a sense, even in present time we can perceive how the quality and trend of human spiritual life is brought about by the relation between the Earth and the celestial bodies. In an earlier lecture it was pointed out how different the spiritual configuration of mankind tends to be in Equatorial and in Polar regions. Investigating this more closely, the different relation of the Earth to the Sun proves to be the determining factor. It makes man in the Polar regions less free of his bodily nature. Man in the Polar regions is less able to lift himself out of the bodily organism,—to pain free use and manipulation of his life of soul (As to the different mutual relations of Earth and Sun, there will be more in it than that, as we shall find in due course; but to begin with we can take our start from the conventional notions.)

We need only picture to ourselves how differently the men of Polar regions are taken hold of by something which in ourselves keeps more in the background. We of the Temperate zone have the quick alternation of day and night. Think how long this alternation becomes as you approach the Polar zone. It is as though the day were to lengthen out into a year. I told you of what works in the little child, deep in the bodily nature from year to year, from birth to the change of teeth, and of how the independent working of the life of soul, given up as it is to the quicker rhythm of the day, gradually frees and detaches itself from this more bodily working. This is not possible to the same extent in Polar regions. It is the yearly rhythm which will there tend to make itself felt. The emphasis is more on the bodily side. The human being will not wrest himself free to the same extent from what works within the body.

Think now of the scanty relics that have been preserved from the civilization of very early times,—that have survived the Ice Age. Then you will see that there were times in which a kind of ‘Polarization’ (giving the word its proper meaning in this context) extended right across the present Temperate zone, so that conditions were prevailing here not unlike those in the present Polar regions. You can use this comparison for what was working in the Ice Age; you can truly say: What is now pressed back towards the North Pole, extended then over a considerable part of the Earth. (Please keep this free of present-day explanations and ideas, for otherwise the pure phenomenon will be obscured. Take only the pure phenomenon as such.)

Conditions on the Earth today are such that we have the three types; the human beings of the Tropical, the Temperate and the Polar zones respectively. Of course they influence each other, so that in outer reality the phenomenon does not appear quite so purely. Nevertheless, what you here have in a spatial form—you find it again in time as you go backward. Going back in time, we come to a ‘North Pole’, as it were, in time—in the history of civilization. Going forward, we come to a Pole again. Remembering that the Polar influence on man is connected with the mutual relations between Earth and Sun. We must conceive that the change which has taken place since the Ice Age—the de-polarization, so to speak—is connected with a changed relation between Earth and Sun. Something must have happened as regards the mutual relation between Earth and Sun. What was it then? The facts themselves suggest the question. What is the source of this in the celestial spaces?

Consider it more nearly. Of course these things will be different in the Northern and Southern hemispheres, but the facts remain. We shall at most have to extend our picture, adapting it to the real facts. We can only take our start from the empirically given data. What is revealed then, if we approach the phenomena without preconceived ideas? The Earth and the events on Earth appear as an expression of cosmic happenings—cosmic happenings which manifest themselves in certain rhythms. Something that showed itself about the tenth millennium before the origin of Christianity, will show itself again about the eleventh millennium after. What is in between, will also in a sense be repeated. What we here have between the two Ice Ages, will undoubtedly have been there before—in former cycles. It is a rhythm; our attention is drawn to a rhythmic process.

And now look out into the celestial phenomena. To emphasize one fact especially, which I have often pointed to in my lectures, you have the following. (I will only characterize it roughly.) You know that the vernal point—where the Sun rises in spring-time gradually moves through the Ecliptic. Today the vernal point is in the constellation of Pisces; before, it was in Aries; still earlier in Tauraus,—that was the time of the cult of the Bull among the Egyptians and Chaldeans. Still earlier, it was in the constellation of Gemini, and then in Cancer; in Leo. This already brings us very nearly to the last Ice Age. Thinking it through to a conclusion, we know that the vernal point goes all the way round the Ecliptic, and that the time it takes is called the Platonic Year—the great Cosmic Year, lasting approximately 25,920 years.

A whole number of processes are comprised in these 25,920 years, involving among other things this rhythmic alternation on the Earth; Ice Age., intermediate period, Ice Age, intermediate period, and so on. At the time we spoke of, when there was that deep stirring of the spiritual life in mankind, the vernal point was entering the sign of Pisces. In the Graeco-Latin Age it had been in the sign of Aries, previous to that in Taurus, and so on. We get back to Leo or Virgo, more or less, during the time when glacial conditions prevailed over the greater part of Europe and in America too. Looking into the future, there will be another Ice Age in these regions when the vernal point reaches the sign of Scorpio. This rhythm is contained within what takes its course in 25,920 years. Although admittedly of vast extent, it is a true rhythm none the less.

Now as I have often mentioned, this rhythm is reminiscent—purely numerically—of another rhythm. If it is simply a question of rhythms and the rhythms are expressible in numbers, if the numbers are the same the rhythms too are the same. You know that the number of breaths man takes—in breathing and out breathing—is approximately 18 to the minute. Reckon out the number of breaths in a 24-hour day and you get the same number as before—25,920. Man therefore shows in his daily life the same periodicity, the same rhythm, as is revealed by the movement of the vernal point in the great Cosmic Year. Now it is in the day that man shows this rhythm. A day therefore, with respect to breathing, corresponds to the Platonic Year. The vernal point—connected as it is with the Sun—goes round apparently in 25,920 years. But there is also the apparent movement of the Sun through the 24 hour day, while man is taking 25,920 breaths. It is the same picture here as in the great Universe. If then there were a Being who breathed in and out once a year (a simple-minded hypothesis no doubt, but we will use it for comparison),—such a Being, if living long enough, would undergo in 25,920 years the same process as man does in a day. Man reproduces, as it were in miniature, what is manifested in the great cosmic process.

These things make little impression on the people of today, for they are not accustomed to look at the qualitative aspect of the world. Quantitatively, the mere rhythm appears less important. Therefore the scientists are out to find other relations between numbers than these that find expression in pure rhythms. They pay less heed to the latter: But in the epochs when man experienced more nearly the relation between himself and the Universe—when he felt himself more immersed in the phenomena of the Cosmos—these things made a deep impression on him. As we go back in the history of mankind—beyond the second or third millennium B.C.—we find great attention paid to the Platonic Year. I mentioned yesterday not to explain it, but by way of illustration—the ancient Indian Yoga system. Man entered deeply into a living inner experience of the breathing process, trying to make it conscious. In doing so there dawned upon him this relation between the rhythm that goes on in man—breathed, as it were, into man in a concentrated and contracted form—and the phenomena of the great Universe. Therefore he spoke of his own in- and out-breathing and of the mighty in- and out-breathing of Brahma, a single breath spanning an entire year, for which 25, 920 years are a day—a day of the Great Spirit.

I do not wish to make an unkind remark, my dear friends, but we do here begin to get some notion of the great distance which men at one time felt between themselves and the Spirit of the Macrocosm whom they revered. Man felt himself about as far beneath the Spirit of the Macrocosm as a day is beneath 25,920 years. It was indeed a great Spirit—a very great Spirit—whom man conceived in this way and whose relation to himself he experienced with due modesty. It would not be uninteresting to compare how great is the distance often felt by modern man between himself and his God. Does he not often conceive the Deity as little more than a slightly idealized human being?

This may not seem very relevant to our subject, but in fact it is. If we want to develop real means of knowledge in this sphere, we must find our way from what is merely calculable into quite other realms. Indeed our study of Kepler's Laws and all that followed from them showed how our very calculations, leading as they do to incommensurable numbers, impel us of their own accord into a realm beyond mere calculation.

You will have seen how we are trying in these lectures to prepare the ground for an adequate World-picture. As I have pointed out again and again, the astronomical phenomena themselves impel us to advance from the merely quantitative to the qualitative aspect. Under the influence of Natural Science there is a tendency, in modern scholarship altogether, to neglect the qualitative side and to translate what is really qualitative into quantitative terms, or at least into rigid forms. For when we study things from a formal aspect we tend to pass quite involuntarily into rigid forms, even if we went to keep them mobile. But the question is, whether an adequate understanding of the phenomena of the Universe is possible at all in terms of rigid, formal concepts. We cannot build an astronomical World-picture until this question has been answered.

This proneness to the quantitative, abstracting from the qualitative aspect, has led to a downright mania for abstraction which is doing no little harm in scientific life, for it leads right away from reality. People will calculate for instance under what conditions, if two sound-waves are emitted one after the other, the sound omitted later will be heard before the other. All that is necessary is the trifling detail that we ourselves should be moving with a velocity greater than that of sound. But anyone who thinks in keeping with real life instead of letting his thoughts and concepts run away from the reality, will, when he finds them incompatible with the conditions of man's co-existence with his environment, stop forming concepts in this direction. He cannot but do so. There is no sense whatever in formulating concepts for situations in which one can never be.

To be a spiritual scientist one must educate oneself to look at things in this way. The spiritual scientist will always want his concepts to be united with reality. He does not want to form concepts remote from reality, going off at a tangent,—or at least not for long. He brings them back to reality again and again. The harm that is done by the wrong kinds of hypothesis in modern time is due above all to the deficient feeling for the reality in which one lives. A conception of the world free of hypotheses, for which we strive and ought to strive, would be achieved far more quickly if we could only permeate ourselves with this sense of reality. And we should then be prepared, really to see what the phenomenal world presents. In point of fact this is not done today. If the phenomena were looked at without prejudice, quite another world-picture would arise than the world-pictures of contemporary science, from which far-fetched conclusions are deduced to no real purpose, piling one unreality upon another in merely hypothetical thought-structures.

Starting from this and from what was given yesterday, I must again introduce certain concepts which may not seem at first to be connected with our subject, though in the further course you will see that they too are necessary for the building of a true World-picture. I shall again refer to what was said yesterday in connection with the Ice-ages and with the evolution of the Earth altogether. To begin with however, we will take our start from another direction.

Our life of knowledge is made up of the sense-impressions we receive and of what comes into being when we assimilate the sense-impressions in our inner mental life. Rightly and naturally, we distinguish in our cognitional life the sense-perceptions as such and the inner life of ‘ideas’—mental pictures. To approach the reality of this domain we must being by forming these two concepts: That of the sense-perception pure and simple, and of the sense-perception transformed and assimilated into a mental picture.

It is important to see without prejudice, what is the real difference between our cognitional life insofar as this is permeated with actual sense-perceptions and insofar as it consists of mere mental picture. We need to see these things not merely side by side in an indifferent way; we need to recognize the subtle differences of quality and intensity with which they come into our inner life.

If we compare the realm of our sense-perceptions—the way in which we experience them—with our dream-life, we shall of course observe an essential qualitative difference between the two. But it is not the same as regards our inner life of ideas and mental pictures. I am referring now, not to their content but to their inner quality. Concerning this, the content—permeated as it is with reminiscences of sense-perceptions—easily deludes us. Leaving aside the actual content and looking only at its inner quality and character—the whole way we experience it,—there is no qualitative difference between our inner life in ideas and mental pictures and our life of dreams. Think of our waking life by day, or all that is present in the field of our consciousness in that we open our senses to the outer world and are thereby active in our inner life, forming mental pictures and ideas. In all this forming of mental pictures we have precisely the same kind of inner activity as in our dream-life; the only thing that is added to it is the content determined by sense-perception.

This also helps us realize that man's life of ideation—his forming of mental pictures—is a more inward process than sense-perception. Even the structure of our sense-organs—the way they are built into the body—shows it. The processes in which we live by virtue of these organs are not a little detached from the rest of the bodily organic life. As a pure matter of fact, it is far truer to describe the life of our senses as a gulf-like penetration of the outer world into our body (Fig. 1) than as something primarily contained within the latter. Once more, it is truer to the facts to say that through the eye, for instance, we experience a gulf-like entry of the outer world. The relative detachment of the sense-organs enables us consciously to share in the domain of the outer world. Our most characteristic organs of sense are precisely the part of us which is least closely bound to the inner life and organization of the body. Our inner life of ideation on the other hand—our forming of mental pictures—is very closely bound to it. Ideation therefore is quite another element in our cognitional life than sense-perception as such. (Remember always that I am thinking of these processes such as they are at the present stage in human evolution.)

Now think again of what I spoke of yesterday—the evolution of the life of knowledge from one Ice-Age to another. Looking back in time, you will observe that the whole interplay of sense-perceptions with the inner life of ideation—the forming of mental pictures—has undergone a change since the last Ice-Age. If you perceive the very essence of that metamorphosis in the life of knowledge which I was describing yesterday, then you will realize that in the times immediately after the decline of the Ice-Age the human life of cognition took its start from quite another quality of experience than we have today. To describe it more definitely; whilst our cognitional life has become more permeated and determined by the senses and all that we receive from them, what we do not receive from the senses—what we received long, long ago through quite another way of living with the outer world—has faded out and vanished, ever more as time went on. This other quality—this other way of living with the world—belongs however to this day to our ideas and mental pictures. In quality they are like dreams. Fro in our dreams we have a feeling of being given up to, surrendered to the world around us. We have the same kind of experience in our mental pictures. While forming mental pictures we do not really differentiate between ourselves and the world that then surrounds us; we are quite given up to the latter. Only in the act of sense-perception do we separate ourselves from the surrounding world. Now this is just what happened to the whole character of man's cognitional life since the last Ice-Age. Self-consciousness was kindled. Again and again the feeling of the “I” lit up, and this became ever more so.

What do we come to therefore, as we go back in evolution beyond the last Ice-Age? (We are not making hypotheses; we are observing what really happened.) We come to a human life of soul, not only more dream-like than that of today, but akin to our present life of ideation rather than to our life in actual sense-perception. Now ideation—once again, the forming of mental pictures—is more closely bound to the bodily nature than is the life of the senses. Therefore what lives and works in this realm will find expression rather within the bodily nature than independently of the latter. Remembering what was said in the last few lectures, this will then lead you from the daily to the yearly influences of the surrounding world. The daily influences, as I showed, are those which tend to form our conscious picture of the world, whereas the yearly influences affect our bodily nature as such. Hence if we trace what has been going on in man's inner life, as we go back in time we are led from the conscious life of soul deeper and deeper into the bodily organic life.

In other works; before the last Ice-Age the course of the year and the seasons had a far greater influence on man than after. Man, once again, is the reagent whereby we can discern the cosmic influences which surround the Earth. Only when this is seen can we form true ideas of the relations—including even those of movement—between the Earth and the surrounding heavenly bodies. To penetrate the phenomena of movement in the Heavens, we have to take our start from man—man, the most sensitive of instruments, if I may call him so. And to this end we need to know man; we must be able to discern what belongs to the one realm, namely the influences of the day, and to the other, the influences of the year.

Those who have made a more intensive study of Anthroposophical Science may be reminded here of what I have often described from spiritual perception; the conditions of life in old Atlantis, that is before the last Ice-Age. For I was there describing from another aspect—namely from direct spiritual sight—the very same things which we are here approaching more by the light of reason, taking our start from the facts of the external world.

We are led back then to a kind of interplay between the Earth and its celestial environment which gave men an inner life of ideation—mental pictures—and which was afterwards transmuted in such a way as to give rise to the life of sense-perception in its present form. (The life of the senses as such is of course a much wider concept; we are here referring to the form it takes in present time.)

But we must make a yet more subtle distinction. It is true that self-consciousness or Ego-consciousness, such as we have it in our ordinary life today, is only kindled in us in the moment of awakening. Self-consciousness trikes in upon us the moment we awaken. It is our relation to the outer world—that relation to it, into which we enter by the use of our senses—to which we owe our self-consciousness. But if we really analyze what it is that thus strikes in upon us, we shall perceive the following. If our inner life in mental pictures retained its dream-like quality and only the life of the senses were added to it, something would still be lacking. Our concepts would remain like the concepts of fantasy or fancy (I do not say identical with these, but like them). We should not get the sharply outlined concepts which we need for outer life. Simultaneously therefore with the life of the senses, something flows into us from the outer world which gives sharp outlines and contours to the mental pictures of our every-day cognitional life. This too is given to us by the outer world. Were it not for this, the mere interplay of sensory effects with the forming of ideas and mental pictures would bring about in us a life of fantasy or fancy and nothing more; we should never achieve the sharp precision of every-day waking life.

Now let us look at the different phenomena quite simply in Goethe's way, or—as has since been said, rather more abstractly—in Kizchhoff's way. Before doing so I must however make another incidental remark, Scientists nowadays speak of a “physiology of the senses”, and even try to build on this foundation a “psychology of the senses”, of which there are different schools. But if you see things as they are, you will find little reality under these headings. In effect, our senses are so radically different from one-another that a “Physiology of the senses”, claiming to treat them all together, can at more be highly abstract. All that emerges, in the last resort, is a rather scanty and even then very questionable physiology and psychology of the sense of touch, which is transferred by analogy to the other senses. If you look for what is real, you will require a distinct physiology and a distinct psychology for every one of the senses.

Provided we remember this, we may proceed. With all the necessary qualifications, we can then say the following. Look at the human eye. (I cannot now repeat the elementary details which you can find in any scientific text-book.) Look at the human eye, one of the organs giving us impressions of the outer world,—sense-impressions and also what gives them form and contour. These impressions, received through the eye, are—once again—connected with all the mental pictures which we then make of them in our inner life.

Let us now make the clear distinction, so as to perceive what underlies the sharp outline and configuration which makes our mental images more than mere pictures of fancy, giving them clear and precise outline. We will distinguish this from the whole realm of imagery where this clarity and sharpness is not to be found,—where in effect we should be living in fantasies. Even through what we experience with the help of our sense-organs—and what our inner faculty of ideation makes of it—we should still be floating in a realm of fancies. It is through the outer world that all this imagery receives clear outline, finished contours. It is through something from the outer world, which in a certain way comes into a definite relation to our eye.

And now look around. Transfer, what we have thus recognized as regards the human eye, to the human being as a whole. Look for it, simply and empirically, in the human being as a whole. Where do we find—though in a metamorphosed form—what makes a similar impression? We find it in the process of fertilization. The relation of the human being as a whole—the female human body—to the environment is, in a metamorphosed form, the same as the relation of the eye to the environment. To one who is ready to enter into these things it will be fully clear. Only translated, one might say, into the material domain, the female life is the life of fantasy or fancy of the Universe, whereas the male is that which forms the contours and sharp outlines. It is the male which transforms the undetermined life of fancy into a life of determined form and outline. Seen in the way we have described in today's lecture, the process of sight is none other than a direct metamorphosis of that of fertilization; and vice-versa.

We cannot reach workable ideas about the Universe without entering into such things as these. I am only sorry that I can do no more than indicate them, but after all, these lectures are meant as a stimulus to further work. This I conceive to be the purpose of such lectures; as an outcome, every one of you should be able to go on working in one or other of the directions indicated. I only want to show the directions; they can be followed up in diverse ways. There are indeed countless possibilities in our time, to carry scientific methods of research into new directions. Only we need to lay more stress on the qualitative aspects, even in those domains where one has grown accustomed to a mere quantitative treatment.

What do we do, in quantitative treatment? Mathematics is the obvious example; ‘Phoronomy’ (Kinematics) is another. We ourselves first develop such a science, and we then look to find its truths in the external, empirical reality. But in approaching the empirical reality in its completeness we need more than this. We need a richer content to approach it with, than merely mathematical and phoronomical ideas. Approach the world with the premises of Phoronomy and Mathematics, and we shall naturally find starry worlds, or developmental mechanisms as the case may be, phoronomically and mathematically ordered. We shall find other contents in the world if once we take our start from other realms than the mathematical and phoronomical. Even in experimental research we shall do so.

The clear differentiation between the life of the senses and the organic life of the human being as a whole had not yet taken place in the time preceding the last Ice-Age. The human being still enjoyed a more synthetic, more ‘single’ organic life. Since the last Ice-Age man's organic life has undergone, as one might say, a very real ‘analysis’. This too is an indication that the relation of the Earth to the Sun was different before the last Ice-Age from what it afterwards became. This is the kind of premise from which we have to take our start, so as to reach genuine pictures and ideas about the Universe in its relation to the Earth and man.

Moreover our attention is here drawn to another question, my dear Friends. To what extent is ‘Euclidean space’—the name, of course, does not matter—I mean the space which is characterized by three rigid directions at right angles to each other. This, surely, is a rough and ready definition of Euclidean space. I might also call it ‘Kantian space’, for Kant's arguments are based on this assumption. Now as regards this Euclidean—or, if you will, Kantian—space we have to put the question: Does it correspond to a reality, or is it only a thought-picture, an abstraction? After all, it might well be that there is really no such thing as this rigid space. Now you will have to admit; when we do analytical geometry we start with the assumption that the X-, Y- and Z-axes may be taken in this immobile way. We assume that this inner rigidity of the X, Y and Z has something to do with the real world. What if there were nothing after all, in the realms of reality, to justify our setting up the three coordinate axes of analytical geometry in this rigid way? Then too the whole of our Euclidean Mathematics would be at most a kind of approximation to the reality—an approximation which we ourselves develop in our inner life,—convenient framework with which to approach it in the first place. It would not hold out any promise, when applied to the real world, to give us real information.

The question now is, are there any indications pointing in this direction,—suggesting, in effect, that this rigidity of space can not, after all, be maintained? I know, what I am here approaching will cause great difficulty to many people of today, for the simple reason that they do not keep step with reality in their thinking. They think you can rely upon an endless chain of concepts, deducing one thing logically from another, drawing logical and mathematical conclusions without limit. In contrast to this tendency in science nowadays, we have to learn to think with the reality,—not to permit ourselves merely to entertain a thought-picture without at least looking to see whether or not it is in accord with reality. So in this instance, we should investigate. Perhaps after all, by looking into the world of concrete things, there is some way of reaching a more qualitative determination of space.

I am aware, my dear Friends, that the ideas I shall now set forth will meet with great resistance. Yet it is necessary to draw attention to such things. The theory of evolution has entered ever more into the different fields of science. They even began applying it to Astronomy. (This phase, perhaps, is over now, but it was so a little while ago.) They began to speak of a kind of natural selection. Then as the radical Darwinians would do for living organisms, so they began to attribute the genesis of heavenly bodies to a kind of natural selection, as though the eventual form of our solar system had arisen by selection from among all the bodies that had first been ejected. Even this theory was once put forward. There is this p to the whole Universe the leading ideas that have once been gaining some particular domain of science.

So too it came about that man was simply placed at the latter end of the evolutionary series of the animal kingdom. Human morphology, physiology etc. were thus interpreted. But the question is whether this kind of investigation can do justice to man's organization in its totality. For, to begin with, it omits what is most striking and essential even from a purely empirical point of view. One saw the evolutionists of Haechel's school simply counting how many bones, muscles and so on man and the higher animals respectively possess. Counting in that way, one can hardly do otherwise than put man at the end of the animal kingdom. Yet it is quite another matter when you envisage what is evident for all eyes to see, namely that the spine of man is vertical while that of the animal is mainly horizontal. Approximate though this may be, it is definite and evident. The deviations in certain animals—looked into empirically—will prove to be of definite significance in each single case. Where the direction of the spine is turned towards the vertical, corresponding changes are called forth in the animal as a whole. But the essential thing is to observe this very characteristic difference between man and animal. The human spine follows the vertical direction of the radius of the Earth, whereas the animal spine is parallel to the Earth's surface. Here you have purely spatial phenomena with a quite evident inner differentiation, inasmuch as they apply to the whole figure and formation of the animal and man. Taking our start from the realities of the world, we cannot treat the horizontal in the same way as the vertical. Enter into the reality of space—see what is happening in space, such as it really is,—you cannot possibly regard the horizontal as though it were equivalent or interchangeable with the vertical dimension.

Now there is a further consequence of this. Look at the animal form and at the form of man. We will take our start from the animal, and please fill in for yourselves on some convenient occasion what I shall now be indicating. I mean, observe and contemplate for yourselves the skeleton of an mammal. The usual reflections in this realm are not nearly concrete enough; they do not enter thoroughly enough into the details.

Consider then the skeleton of an animal. I will go no farther than the skeleton, but what I say of this is true in an even higher degree of the other parts and systems in the human and animal body. Look at the obvious differentiation, comparing the skull with the opposite end of the animal. If you do this with morphological insight, you will perceive characteristic harmonies or agreements, and also characteristic diversities. Here is a line of research which should be followed in far greater detail. Here is something to be seen and recognized, which will lead far more deeply into realty than scientists today are wont to go.

It lies in the very nature of these lectures that I can only hint at such things, leaving out many an intervening link. I must appeal to your own intuition, trusting you to think it out and fill in what is missing between one lecture and the next. You will then see how all these things are connected. If I did otherwise in these few lectures, we should not reach the desired end.

Diagrammatically now (Fig. 2), let this be the animal form. If after going into an untold number of intervening links in the investigation, you put the question: ‘What is the characteristic difference of the front and the back, the head and the tail end due to?’, you will reach a very interesting conclusion. Namely you will connect the differentiation of the front end with the influences of the Sun. Here is the Earth (Fig. 3). You have an animal on the side of the Earth exposed to the Sun. Now take the side of the Earth that is turned away from the Sun. In one way or another it will come about that the animal is on this other side. Here too the Sun's rays will be influencing the animal, but the earth is now between. In the one case the rays of the Sun are working on the animal directly; in the other case indirectly, inasmuch as the Earth is between and the Sun's rays first have to pass through the Earth (Fig. 3).

Expose the animal form to the direct influence of the Sun and you get the head. Expose the animal to those rays of the Sun which have first gone through the Earth and you get the opposite pole to the head. Study the skull, so as to recognize in it the direct outcome of the influences of the Sun. Study the forms, the whole morphology of the opposite pole, so as to recognize the working of the Sun's rays before which the Earth is interposed—the indirect rays of the Sun. Thus the morphology of the animal itself draws our attention to a certain interrelation between Earth and Sun. For a true knowledge of the mutual relations of Earth and Sun we must create the requisite conditions, not by the mere visual appearance (even though the eye be armed with telescopes), but by perceiving also how the animal is formed—how the whole animal form comes into being.

Now think again of how the human spine is displaced through right angle in relation to the animal. All the effects which we have been describing will undergo further modification where man is concerned. The influences of the Sun will therefore be different in man than in the animal. The way it works in man will be like a resultant (Fig. 4). That is to say, if we symbolize the horizontal line—whether it represent the direct or the indirect influence of the Sun—by this length, we shall have to say; here is a vertical line; this also will be acting. And we shall only get what really works in man by forming the resultant of the two.

Suppose in other words that we are led to relate animal formation quite fundamentally to some form of cosmic movement—say, a rotation of the Sun about the Earth, or a rotation of the Earth about its own axis. If then this movement underlies animal formation, we shall be led inevitably to attribute to the Earth or to the Sun yet another movement, related to the forming of man himself,—a movement which, for its ultimate effect, unites to a resultant with the first. From what emerges in man and in the animal we must derive the basis for a true recognition of the mutual movements among the heavenly bodies.

The study of Astronomy will thus be lifted right out of its present limited domain, where one merely takes the outward visual appearance, even if calling in the aid of telescopes, mathematical calculations and mechanics. It will be lifted into what finds expression in this most sensitive of instruments, the living body. The forming forces working in the animal, and then again in man, are a clear indication of the real movements in celestial space.

This is indeed a kind of qualitative Mathematics. How, then, shall we metamorphose the idea when we pass on from the animal to the plant? We can no longer make use of either of the two directions we have hitherto been using. Admittedly, it might appear as though the vertical direction of the plant coincided with that of the human spine. From the aspect of Euclidean space it does, no doubt (Euclidean space, that is to say, not with respect to detailed configuration but simply with respect to its rigidity.) But it will not be the same in an inherently mobile space. I mean a space, the dimensions of which are so inherently mobile that in the relevant equations, for example, we cannot merely equate the \(x\)- and the \(y\)-dimensions: \(y = ƒ(x)\). (The equation might be written very differently from this. You will see what I intend more from the words I use than from the symbols; it is by no means easy to express in mathematical form.) In a co-ordinate system answering to what I now intend, it would no longer be permissible to measure the ordinates with the same inherent measures as the abscissae. We could not keep the measures rigid when passing from the one to the other. We should be led in this way from the rigid co-ordinate system of Euclidean space to a co-ordinate system that is inherently mobile.

And if we now once more ask the question: How are the vertical directions of plant growth and of human growth respectively related?—we shall be led to differentiate one vertical from another. The question is, then, how to find the way to a different idea of space from the rigid one of Euclid. For it may well be that the celestial phenomena can only be understood in terms of quite another kind of space—neither Euclidean, nor any abstractly conceived space of modern Mathematics, but a form of space derived from the reality itself. if this is so, then there is no alternative; it is in such a space and not in the rigid space of Euclid that we shall have to understand them.

Thus we are led into quite other realms, namely to the Ice-Age on the one hand and on the other to a much needed reform of the Euclidean idea of space. But this reform will be in a different spirit than in the work of Minkowski and others. Simply in contemplating the given facts and trying to build up a science free of hypotheses, we are confronted with the need for a thoroughgoing revision of the concept of space itself. Of these things we shall speak again tomorrow.

To lead our present studies to a fruitful conclusion we must still pursue the rather subtle course I have been adopting, bringing together a great variety of ideas from different fields. For this reason we shall have to continue with this course also while the other course¹ is going on—between the 11th and 15th January. We must arrange the times by agreement with the Waldorf School. There is so much to bring in that we shall need these days too. Now I am also well aware how many queries, doubts and problems may be arising in connection with this subject. Please prepare whatever questions you would like to put, if you need further elucidation. I will then try to incorporate the answers in one of next week's lectures, so as to make the picture more complete. Working in this way we shall be able to continue as heretofore, bringing in what I would call the subtler aspects of our theme.

Let us envisage once again the course we have been pursuing. Our aim is to gain a deeper understanding of Astronomy—the science of the Heavens—in connection with phenomena on Earth. To begin with, we pointed out that as a rule the Astronomy of our time only takes into account what is observed directly with the outer senses aided, no doubt, by optical instruments and the like. Such, in the main, were all the data hitherto adduced when seeking to explain and understand the phenomena of the Heavens. They took their start from the ‘apparent movements’, as they would now be called, or the celestial bodies. First they considered the apparent movement of the starry Heavens as a whole around the Earth and the apparent movement of the Sun. Then they observed the very strange paths described by the Planets. Such, in effect, is the immediate visual appearance; portions of the planetary paths look like loops (Fig. 1) the planet moves along here, reverses and goes back, and then forward again, here ... And now they reasoned; if the Earth itself is moving and we have no direct perception of this movement, the real movements of the heavenly bodies cannot but be different from the visual appearance. Interpreting along these lines—applying mathematical and geometrical laws—they arrived at an idea of what the ‘real’ movements might be like. So they arrived at the Copernican system and at its subsequent modifications. Such, in the main, were the methods of cognition used; first, what our senses when looking out into the Heavens, and then the intellectual assimilation, the reasoned interpretation of these sense-impression.

We then pointed out that this procedure can never lead to the adequate penetration of the celestial phenomena, if only for the reason that the mathematical method itself is insufficient. We begin our calculations along certain lines and are then brought to a stop. For as I was reminding you, the ratios between the periods of revolution of the several planets are incommensurable numbers,—incommensurable magnitudes. By calculation therefore, we do not reach the innermost structure of the celestial phenomena. Sooner or later we have to leave off.

It follows that we must adopt a different method. We have to take our start not only from what man observes when he looks out into the Universe with his senses; we must take man as a whole in his connection with the Universe, and perhaps not only man, but other creatures too,—the kingdoms of Nature upon Earth. All these things we pointed out, and I then showed how the whole organization of man can be seen in relation to certain phenomena in the evolution of the Earth, namely the Ice-Ages in their rhythmical recurrence. They also have to do with the inner evolution of man and of mankind. This too, I said, will give us indications of what the real movements in celestial space may be. These are the kind of things we must pursue.

Before continuing the rather more formal lines of thought with which we ended yesterday's lecture, let us consider once again this connection of man's evolution with the evolution of the Earth through the Ice-Ages. We saw that the special kind of knowledge or of cognitional life which the man of present time calls his own has only come into being since the last Ice-Age. Moreover all the civilization-epochs, of which I have so often told, have taken place since then—namely the Ancient Indian, the Persian, the Egypto—Chaldean, the Graeco-Latin and then the epoch in which we are now living. Before the last Ice-Age, we said, there must have been developing in human nature what in the man of today is more withdrawn, less at the surface of his nature, namely his power of ideation—the forming of mental pictures. The inner quality, we said, of this part of our inner life is truly to be understood only if we compare it with our dream-life. It is through sense-perception that our mental pictures receive clear and firm configuration and, as it were, a fully saturated content. The mental pictures are being formed in a more inward region of our bodily organic life—farther back, as it were behind the sense-perceptions,—and this activity is dim and hazy like our dream-life. Our forming of mental pictures would be as dim as it is in dreams, if the experiences of the senses did not strike in upon us every time we awaken. (We may allow the supposition, to help explain what is meant.)

More dim and hazy than our life in sense-perception, this inner life of ideation, mental imagery, is related to those earlier phases in the evolution of man's nature which preceded the last glacial epoch, or which—to speak in anthroposophical terms—belonged to old Atlantis.

What must it then have been like for man? In the first place he must have had a far more intimate inner connection with the surrounding world than he has today through sense-perception. We can control our sense-perception with our will. It is with our will at any rate that we direct the vision of our eyes, and by deliberate attention we can go even farther in governing our sense-perception by our own will. At all events, our will is very much at work in our sense—perceptions, making us to a large extent independent of the outer world. We orientate ourselves by our own arbitrary choice. Now this in only possible because as human beings we have in a way emancipated ourselves from the Universe. Before the last Ice-Age we cannot have been thus emancipated. (I say ‘cannot have been’ since I am wanting now to speak from the empirical aspect of external Science.) During that time, as we have seen, the power of ideation—the forming of mental images—was especially developed, and in his inner conditions man must have been far more dependent on all that was going on around him. Today we see the world around us shining in the sunlight, but the way we see it is considerably subject to the inner culture and control of our own life of will. In Atlantean time the way man was given up to the outer world must have been somehow dependent on the illumined Earth and its illumined objects, and then again—at night-time when the Sun was not shining—on the darkness, the gloaming. He must in other words have experienced periodic alternations in this respect. His inner life of mental imagery, which as we saw was then in process of development must alternately have been lighting up and ebbing down again. This inner periodicity, brought about by man's relation to the surrounding Universe, was indeed not unlike the peculiar periodicity of woman's organic functions of which we spoke before, which is related to the Lunar phases though only as regards length of time. This inner functioning of the woman's nature (I said, you will remember, it is there in man too but in a more inward way and therefore less easily perceived) was at one time actually linked with the corresponding events in the outer Universe. It then became emancipated—a property of human nature on its own,—so that what now goes on in the human being in this respect need not coincide with the outer events. yet the periodicity—the sequence of phases—remains the same as it was when the one coincided with the other.

Something quite similar is true of the rhythmic alternation in our inner life—in our ideation, our forming of mental images. The whole way we are organized in this respect, implanted in us in a far distant past, is to this day more or less independent of the life of the outer senses. Day by day we undergo an inner rhythm, our powers of mental imagery alternately lighting up and growing more dim; it is a daily ebb and flow. We only fail to notice it, since it is far less intense than that other periodicity which runs parallel to the Lunar phases. Nevertheless, in our head-organization to this day we have an alternation between a brighter and a dimmer kind of life. We carry in our head a rhythmic life. We are at one time more and at another less inclined to meet our sense-perceptions actively from within. It is a 24-hour rhythmic alteration. It would be interesting to observe—it might even be recorded in graphically—how human being vary as regards this inner period of the head, the forces of ideation and mental imagery alternating between brighter and more lively and then again dimmer and more sleepy times. The dim and sleepy times represent, so to speak, the inner night of the head, the brighter ones the inner day, but it does not coincide with the external alternation of day and night. It is an inner alternation of light and darkness, or relatively bright and dim conditions. And people vary in this respect. One human being has this inner alternation of light and dark in such a way that he tends rather to connect the lighter period of his mental image-forming power with his sense-perceptions. Another tends to it with the darker. Individuals are organized in one way or the other, and differ accordingly as to their power of observing the outer world. One human being will be inclined sharply to focus the phenomena of the outer world; another tends to do so less,—is more inclined to an inner brooding. All this is due to the alternating conditions I have been describing. Notably as educators, my dear Friends, we should cultivate the habit of observing things like this. They will be valuable signposts, indicating how we should treat the individual children both in our teaching and in education generally.

What interests us however here and now is the fact that man thus makes inward, as it were, what he once underwent in direct mutual relation with the outer world; so that it now works in him as an inner rhythm, the phases no longer coinciding with the outer yet still retaining the periodicity Before the Ice-Age, man's periods of brighter and more intimate participation in the surrounding Universe,. and then of dim withdrawal into himself, will have coincided regularly with the processes of the outer world. He still retains an echo of this rhythm, which in those long-ago times proceed from his living-together with the Universe around him, where at one moment his consciousness was lightened and filled with pictures while at another he withdrew into himself, brooding over the pictures. It is an echo of this latter state whenever we today are inclined to brood more or less melancholically in our own inner life. Once again therefore, what man experienced in and with the world in those older times has been driven farther back into his inner bodily nature, while at the outer periphery a new development has taken place in his faculties of sense-perception. He had these faculties, of course in earlier epochs too, but not developed in the way they now are.

While looking thus at what has taken place in man through his connection with the phenomena of the world around him, we are in fact looking into the Universe itself. Man then becomes the reagent for a true judgment of the phenomena of the Universe. But to complete this we need the other kingdoms of Nature too. Here I should like to draw your attention to something well-known and evident to everyone, the essential significance of which, however, remains unrecognized.

Consider the annual plant,—the characteristic cycle of its development. We see in it quite evidently what I was mentioning yesterday—the direct and indirect influences of the Sun. Where the Sun works directly, the flower comes into being; where the Sun works in such a way that the Earth comes in between, we get the root. The plant too makes manifest what we were speaking of yesterday as regards the animal and then applied in another way to man.

Yet we shall only see the full significance of this if we relate it to another fact. There are perennial plants too. What is the relation of the perennial plant to the annual, as regards the way in which plant-growth belongs to the Earth as a whole? The perennial retains its stem or trunk, and the truth is: Year by year a new world of plants springs, so to speak, from the trunk itself. Of course it is modified and metamorphosed, yet it is a vegetation growing on the trunk, which in its turn grows out of the Earth (Fig. 2). If you have morphological perception you will see it as clearly as can be,—it almost goes without saying. Here on the left I have the surface of the Earth, and the annual plant springing from it. Here on the right is the stem or trunk of the perennial, from which new vegetation, new plant-growth springs in each succeeding year. I must image something or other (to leave it vague, for the moment) continued from the Earth into the trunk. I must say to myself—what this plant here (Fig. 2 on the left) is growing on, must somehow be there in the trunk too (on the right). In other words there must be some element of the Earth—whatever it may be—entering into the trunk. I have no right to regard the trunk of the perennial as a thing apart, not belonging to the Earth; rather must I regard it as a modified portion of the Earth itself. Only then shall I be seeing it rightly; only then shall I discern the inner relationships, such as they really are. Something is there in the perennial plant, which otherwise is only in the Earth. It is through this that the plant becomes perennial. In effect, precisely by taking something of the Earth into itself it frees itself from dependence on the yearly course of the Sun. For we may truly say: The perennial wrests itself away from its dependence on the Sun's yearly course. it emancipates itself from the yearly course of the Sun, in that it forms the trunk, receiving into its own Nature—becoming able, as it were, to do for itself what otherwise could only come about through the working of the whole cosmic environment.

Do we not here see prefigured in the plant world, what I was just describing with regard to man in preglacial times? For in those times, as I was showing, the inner rhythm of the man's ideation—his life in mental pictures—developed by relation to the surrounding world. What then lived in the mutual relation between man and the surrounding world has since become a feature of his own inner life. There is an indication of the same kind of change in the plant kingdom, in that the annual is changed to a perennial. This is indeed a universal tendency in evolution; the living entities are on the way to emancipation from their original connections with the surrounding world.

Seeing the perennials arising, we have to say: It is as though the plant, when it becomes perennial, had learned something it you will allow the expression—learned from the time when it depended on cosmic environment, something which it can now do for itself. Now it is able of itself to bring forth fresh plant-shoots year by year. We do not reach an understanding of the phenomena of the world by merely staring at the things that happen to be side by side, or that are crowded into the field of view under the microscope. We have to see the larger whole and recognize the single phenomena in their connection with it.

Look at it all once more. The annual plant is given up to the cycle of the year, with all the changing relations to the Cosmos which this involves. This influence of the Cosmos beings to fade away in the perennial. In the perennial, what would otherwise vanish in the further course of the year is, as it were, preserved. In the trunk we see springing from the ground the working of the year, made permanent and lasting. This transition of what was first connected with the outer Universe into a more inward way of working we see it throughout the whole range of Nature's phenomena, in so far as they are cosmic. Hence too there are phenomena in which we can more quickly find the living connections between our Earth and the wider Cosmos, whilst there are others in which the cosmic influences are more concealed. We need to find out which of them are sensitive reagents, telling of the cosmic influences. The annual plant will tell us of the Earth's connection with Cosmos, the perennial will not be able to tell us much.

Again, the relation of the animal to man can give us an important clue. Look at the animal's development. (Though we might also include it, we will for the moment disregard the embryonic life.) The animal is born and grows up to a certain limit. It reaches puberty. Look at the animal's whole life, until puberty and beyond. Without any added hypotheses—taking the simple facts—you must admit that it is strange, what happens to the animal once puberty has been attained. For in a way the animal is finished then, so far as the earthly world is concerned. Any such statement is of course an approximation to the truth, needless to say; yet in the main we must admit that in the animal no further progression is to be seen, not after puberty. Puberty is the important goal of animal development. The immediate consequence of puberty—all that happens as an outcome of it—is there of course, but we cannot allege that anything takes place thence forward, deserving to be called a true progression.

With man it is different. Man remains capable of development far beyond puberty; but the development becomes more inward. Indeed it would be very sad for man if in his human nature he were to end his development at puberty in the way animals do. Man goes beyond this. He holds something in reserve by means of which he can go farther,—can undertake quite other journeys, unconnected with sexual maturity or puberty. This again is not unlike the “inwarding” of the cycle of the year in the perennial as against the annual plant. What is in evidence in the animal when puberty is reached, we see it transmuted into a more inward process in man, from puberty onward. Something therefore is at work in man, that is related to a cosmic process in his development from birth until puberty, and that then gets emancipated from the Cosmos—just as it does in the perennial plant—when puberty has been outgrown.

Here then you have a subtler way of estimating the phenomena among the kingdoms of Nature; so will you presently find signposts, indicating the connections between the creatures upon Earth and the Cosmos. We see how, when the cosmic influences cease as such, they are transplanted into the inner nature of the several creatures. We will take note of this and set it on one side for the moment; later we shall find the synthesis between this and quite another aspect.

Let us now take up again what I have frequently mentioned: The incommensurable ratios between the periods of revolution of the planets of the solar system. We may ask, what would the outcome be if they were commensurable? Cumulative disturbances would arise, whereby the planetary system would be brought to a standstill. This can be proved by calculation, though it would lead too far afield to do it now. Only the incommensurability between the periods of revolution enables the planetary system, so to speak, to stay alive. In other words, the solar system contains among other things a condition even tending to a standstill. It is precisely this condition which we are calculating. When in our calculations we get to the end of our tether, there is the incommensurable—and there, withal, is the very life of the planetary system! We are in a strange predicament when calculating the planetary system. If it were such that we could fully calculate it, it would die,—nay, as I said before, would have died long ago. It lives by virtue of the face that we can not calculate it fully. What is alive in the planetary system is precisely what we cannot calculate.

Now upon what do we base these calculations, from which once more, if we could pursue them to the end, we must deduce the inevitable death of the whole system? We base them on the force of gravitation—universal gravitation. Suppose we take our start from gravitation and nothing more, and think it out consistently. We get the picture of a planetary system subject to the force of gravitation. Then indeed we do arrive at commensurable ratios. But the planetary system would inevitably die. We calculate, in other words, to the extent that death prevails in the planetary system, basing our calculations on the force of gravity. In other words there must be something in the planetary system—different from gravitation—to which the incommensurability is due.

The planetary orbits can be brought into accord with the force of gravity very nicely, even as to their genesis, but their periods of revolution would then have to be commensurable. Now there is something which cannot be brought into accord with the force of gravitation, and which moreover does not so tidily fit into our planetary system. I mean what reveals itself in the cometary bodies. The comets play a very strange part in the system, and they have recently been leading scientists to some unusual ideas.

I leave aside the kind of explanations which often tend to arise, where anything most recently discovered is seized on to explain phenomena in other fields. In physiology for instance there was a time when they were fond of comparing the so-called sensory nerves to telegraph-wires leading in from the periphery. Through some central switch or commutator the impulse was supposed to be transmitted, leading to impulses and acts of will. From the centripetal nerves it was supposed to be switched over to the centrifugal; they compared it all to a telegraphic system. Maybe one day something quite different from telegraph-wires will be invented and by this way of thinking quite another picture will be applied to the same thing. So do the scientific fashions change. Whatever happens to have been discovered is quickly seized on as a handy way of explaining the phenomena in other fields. Much as they do in medicine! Scarcely has any new thing been found,—it is “discovered” to be a valuable remedy, though little thought is given to the inner reasons. Now that we have X-rays, X-rays are the remedy to use; we only use them because we happen to have found them. It is as though men let themselves be swept along chaotically, willy-nilly by whatever happens to turn up from time to time.

So for the comets: By spectroscopic investigation and by comparison with the corresponding results for the planets, the idea arose that the phenomena might be explained electromagnetically. Such ideas will at most lead to analogies, which may no doubt have some connection with the reality, but which will certainly not satisfy us if we are looking into it more deeply.

Yet as I said, leaving this aside, there was one thing which emerged quite inevitably when the phenomena of comets were studied in more detail. While for the rest of the planetary system they always speak of gravitational forces, the peculiar position of the comet's tail in relation to the Sun inevitably drove the scientists to speak of forces of repulsion from the Sun—forces, as it were of recoil. The terminology is not the main point; it will of course vary with the prevailing fashion. The point is that science was here obliged to look for something in addition to—and indeed opposite to gravity.

In effect, with the comets something different enters our planetary system,—something which in its nature is in a way opposite to the inner structure of the planetary system as such. Hence it is understandable that for long ages the riddle of the comets gave rise to manifold superstitions. Men had a feeling that in the courses of the planets laws of Nature, inherently belonging to our planetary system, find expression, while with the comets something contrary comes in. Here something disparate and diverse makes its way into our planetary system. Thus they inclined to see the planetary phenomena as an embodiment of normal laws of Nature, and to regard the cometary apparitions as something contrary to these normal laws. There were times—though not the most ancient times—when comets were associated, as it were, with moral forces flying through the Universe, scourges for sinful man.

Today we rightly look on that as superstition. Yet even Hegel could not quite escape associating the comets with something not quite explicable or only half explicable by ordinary means. The 19th century, of course, no longer believed the comets to appear like judges to chastise mankind. Yet in the early 19th century they had statistics purporting to connect them with good and bad vintage years. These too occur somewhat irregularly; their sequence does not seem to follow regular laws of Nature. And even Hegel did not quite escape this conclusion. He though it plausible that the appearance or non-appearance of comets should have to do with the good and bad vintage years.

The standpoint of the people of today—at least, of those who share the normal scientific outlook—is that our planetary system has nothing to fear from the comets. Yet the phenomena which they evoke within this planetary system somehow have little inner connection with it. Like cosmic vagrants they seem to come from very distant regions into the near neighborhood of our Sun. Here they call forth certain phenomena, indicating forces of repulsion from the Sun. The phenomena appear, was and wane, and vanish.

There was a man who still had a certain fund of wisdom where by he contemplated the Universe not only with his intellect but with the whole human being. He still had some intuitive perception of the phenomena of the Heavens. I refer to Kepler. He was the author of a strange saying about the comets—a saying which gives food for thought to anyone who is at all sensitive to Kepler; way of though and mood of soul. We spoke of his three Laws—a work of genius, when one considers the ideas and the data which were accessible in his time. Kepler arrived at his Laws out of a feeling for the inner harmony of the planetary system. For him it was no mere dry calculation; it was a feeling of harmony. He felt has three planetary Laws as a last quantitative expression of something qualitative—the harmony pervading the whole planetary system. And out of this same feeling he made a statement about the comets, the deep significance of which one feels if one is able to enter into such things at all. Kepler said: In the great Universe—even the Universe into which we look by night—there are as many comets as there are fishes in the ocean. We only see very, very few among them, while all the rest remain invisible, either because they are too small or for some other reason. Even external research has tended to confirm Kepler's saying. The comets seen were recorded even in olden time and it is possible to compare the number. Since the invention of the telescope ever so many more have been seen than before. Also when looking out into the starry Heavens under different conditions of illumination—that is to say, making provision for extreme darkness—a larger number of comets are recorded than otherwise. Even empirical research therefore comes near to what Kepler exclaimed, inspired as he was by a deep feeling for Nature.

Now if one speaks at all of a connection between the Cosmos and what happens on the Earth, it surely is not right to dwell one-sidedly on the relation to our Earth of the other planets of our system and to omit the heavenly bodies which come and go as the comets do. It is especially one-sided since we must now admit that the comets give rise to phenomena indicating the presence of quite other forces—forces opposite in kind to those to which we usually attribute the coherence of our planetary system. The comets do in fact bring something opposite into our system, and if we follow it up we must admit that this too is of great significance. Something in some way opposite in nature to the force which holds it together, comes with the comets into our planetary system.

In an earlier lecture-course about natural phenomena I drew attention to something of which I must here remind you. Those who were present—the course was mainly about Heat or Warmth²—will no doubt recall it. I said that when we look at the phenomena of warmth in their relation to other phenomena of the Universe we are obliged to form a far more concrete idea of the Ether, of which the physicists generally speak in rather hypothetical terms. I said that in the formulae of Physics, wherever the force of pressure occurs as regards ponderable matter, we have to replace it by a force of suction as regards the ether. In other words, if we insert a plus sign for the intensity of a force in the realm of ponderable matter, we must give a minus sign to the corresponding intensity in the ether. I suggested that the well-known formulae should be looked through with this end in view; for one would see how remarkably, when this is done, they harmonize with the phenomena of Nature.

Take for example that whole game of thought, if I may call it so, the Kinetic Theory of Gases, of of Heat itself,—the molecules impinging on each other and on the walls of the containing vessel. Take all this brutal play of mutual impact and recoil which is supposed to represent the thermal condition of gas. Instead of this phenomena will become clear and penetrable the moment we perceive that within warmth itself there are two conditions. akin to the conditions that prevail in ponderable matter; the other must be thought of as akin to the ether. Warmth is in this respect different from Air or Light. For light, if we are calculating truly we must use the negative sign throughout. Whatever in our formulae is to represent the effects of light, must bear a negative sign. For air or gas the sign must be positive. For warmth on the other hand, the positive and negative will have to alternate. What we are wont to distinguish as conducted heat, radiant heat and so on will only then become clear and transparent.

Within the realm of matter itself, these things reveal the need for a qualitative transition from the positive to the negative in characterizing the different kinds of force. And we now see, very significantly, how for the planetary system we also have to pass from the positive—that is, gravitation—to the corresponding negative, the repelling force.

One more thing I will say today, if only to formulate the problem. For the moment I will carry it no further, but only put the problem; we shall have time to go into these things in later lectures. Now that we have ascertained all this about the cometary bodies, let me compare the relation between our planetary system and the comets to what is there in the ovum, the female germ-cell, in its relation to the male element, the fertilizing sperm. Try to imagine, try to visualize the two processes, as you might actually see them. There is the planetary system; it receives something new into itself, namely the effects of a comet. There is the ovum; it receives into itself the fertilizing effect of the male cell, the spermatozoid.

Look at the two phenomena side by side without prejudice, as you might do in ordinary life when you see two things obviously comparable, side by side. Do you not find plenty of comparable features when you contemplate these two? I do not mean to set up any theory or hypothesis, I only want to indicate what you will see for yourselves if you once look at these things in their true connection.

Taking our start from this, tomorrow we may hope to enter into more concrete and more detailed aspects.

• 1. Examples of the relation of Spiritual Science to the different branches of Science. Four lectures to students, Stuttgart, 11th to 15th January, 1921. Published (in the original German) in the Swiss periodical “Gegenwart”, Vol. 14, nos. 2 to 8, Berne, 1952.
• 2. Stuttgart, 1st to 14th March 1920, generally known as the “Second Scientific Lecture-Course”. Issued (in the original German) by the Science Section of the Goetheanum, Dornach, Switzerland, 1925.

We have now reached a point in our studies from which we must proceed with extreme caution, in order to see where there is a danger of allowing our thought to depart from reality and to see also when we are avoiding this danger, by keeping within the bounds of what is real.

Last time, we suggested the comparison of two facts: The appearance within the planetary system of the cometary phenomena, and, alas within the planetary system, though perhaps not bearing quite the same relationship to it, all that we observe in the phenomena of fertilization. In order, however, to come to ideas about this which are at all justified, we must first see whether it is indeed possible to find connections between two so widely separated things, with which we are confronted in the external world of facts. In scientific method, we shall not make real progress, unless we can refer from one realm of facts to another, manifesting something of a similar nature and thus leading us on.

We have seen how on the one hand we have to use the element of figure and form, the mathematical, and then how we are again and again impelled to come to terms in one way or another with the qualitative aspect, in some way to find a qualitative approach. And so today we will bring in something which arises in regard to man if one really studies this man, who is, after all, in some way an image of the heavenly phenomena,—as the many statements in these lectures may enable us to deduce. Yet we still have to establish in what way he is this image. If this is what he is, we must first of all gain a clear understanding of man himself. We must understand the picture from which we intend to take our start,—understand its inner perspective. Just as in looking at a painting one must know what a foreshortening means, and so on, in order to pass from the picture to the real spatial relationships and to relate the picture to what it represents in reality, so, if we would approach reality in the universe, interpreting it through man, we must first be clear about man. Now it is, extraordinarily difficult, as a human being, to come near to the human being with palpable ideas. Therefore, I should like today to bring before your souls what I might call “palpably impalpable” thought-pictures arising from quite simple foundations, ideas with which most of you are probably already well acquainted, but which we must nevertheless bring before our minds in a certain connection. These ideas, which seem in part to be quite easy to grasp and yet again, beyond certain limits, to elude our comprehension, will afford us a means of orientation in the striving to take hold of the outer world through ideas.

It may appear somewhat forced to keep emphasizing the necessity of referring back to man's life of pictorial imagination in order to understand the phenomena of the heavens. But after all it is obvious that however carefully we may describe the heavenly phenomena, we have, to begin with, nothing more than a form of optical picture, permeated with mathematical thoughts. What Astronomy gives us has fundamentally the character of a picture. To be on the right path, we must therefore concern ourselves with the arising of the picture in man, otherwise we shall gain no true relationship to what Astronomy can say to us. And so I should like today to proceed from some quite simple mathematics and to show you how, in a different domain from that to which we were led through the ratios of the periods of revolution of the planets, there appears within Mathematics itself this element of the incomprehensible, the impalpable. We meet with it when in a certain connection we study quite familiar curves. (As I said, many of you already know what I am about to describe, I only want to elucidate the subject today from a particular aspect.)

Consider the Ellipse, with its two foci \(A\) and \(B\), and you know that it is a definition of the ellipse that for any point \(M\) of the curve, the sum of its distances \((a + b)\) from the two foci remains constant. It is characteristic of the ellipse, that the sum of the distances of any one of its points from two fixed points, the two foci, remains constant (Fig. 1).

Then we have a second curve, the Hyperbola (Fig. 2). You know that it has two branches. It is defined in that the difference of the distances of any point of the curve from the two foci, \((b - a)\) is a constant magnitude. In the ellipse, then, we have the curve of the constant sum, in the hyperbola, the curve of constant difference, and we must now ask: What is the curve of constant product?

I have often drawn attention to this: The curve of constant product is the so-called Curve of Cassini (Fig. 3). We find it when, having two points, \(A\) and \(B\), we consider a point M in regard to its distances from \(A\) and \(B\), and establish the condition that the two distances \(AM\) and \(BM\) multiplied together should equal a constant magnitude. For the sake of simplicity in the calculation, I will call the constant magnitude \(b^2\) and the distance \(AB\), \(2a\). If we take the mid-point between \(a\) and \(b\) as the center of the axes of a co-ordinate system and calculate the ordinates for each point that fulfills these conditions,—take \(C\) as the center of the co-ordinate system and let the point whose ordinate we will call y move round so that for each point of the curve \(AM•BM = b^2\), we get the following equation. (I will only give you the result, for the simply reason that everyone can easily work out the calculation for himself; it is to be found in any mathematical text-book relating to the subject.) We find for \(y\) the value:

Taking here into account that we cannot use the negative sign because we should then have an imaginary y, and considering therefore taking only the positive sign, we have:

If we then draw the corresponding curve, we have a curve, rather like but not identical with an ellipse, called the curve of Cassini (Fig. 4). It is symmetrical to the left and right of the ordinate axis and about and below the abscissa axis.

But now, this curve has various forms, and for us at any rate this is the important thing about it. The curve has different forms, according to whether b, as I have taken it here, is greater than a, equal to a, or less than a. The curve I have just drawn arises when b ˃ a, and furthermore when another condition is fulfilled, namely, that b is also greater than or equal to a √2. Moreover, when b ˃ a√2, there is a distinct curvature above and below, If b = a√2, then at this point above and below, the line of the curve becomes straightened,m it flattens so much that it almost becomes a straight line (Fig. 4). If, however, b ˂ a√2, then the whole course of the curve is changed and it takes on this form (Fig. 5). And if b = a, the curve passes over into a quite special form, it changes into this form (Fig. 6). It runs back into itself, cuts through itself and comes out on the other side, and we obtain the special form of the Lemniscate. The lemniscate, then, is a special form of Curve of Cassini—these curves are so named after their discoverer. The particular form assumed by the curve is determined by the ratio between the constant magnitudes which appear in the equation characterizing the curve. In the equation, we have only these two constant magnitudes, b and a, and the form of the curve depends on the ratio between them.

Then the third case is possible, that b ˂ a. If b ˂ a, we can still find values for the curve. We can always solve the equation and obtain values for the curve, ordinates and abscissae, even when b is smaller than a, only the curve then undergoes yet another metamorphosis. For when b ˂ a, we find two branches of the curve, which look something like this (Fig. 7). We have a discontinuous curve. And here we come to the point where the mathematics itself confronts us with what I called the “palpably impalpable”, something that is difficult to grasp in space. For in the sense of the mathematical equation, this is not two curves, but one; it is a single curve in exactly the same way as all these are single curves (Figs. 3 through 5). In this one (the lemniscate) there is already a transition. The point which describes the curve takes this path, goes round underneath, cuts its previous path here and continues on here (Fig. 7). Here, we must picture the following: If we let the point M move along this line, it does not simply cross over from one side to the other,—it does not do this. It runs along the path just as in the other curves, describes a curve here, but then manages to turn up again here (Fig. 7) You see, that which carries the point along the line disappears here in the middle. If you want to understand the curve you can only imagine that it disappears in the middle. If you try to form a continuous mental picture of this curve, what must you do?

It is quite easy, is it not, to imagine curves such as thes. (I only say this in parenthesis for the ordinary philistine!) You can go on imagining points along the curve and you do not find that the picture breaks off. Here (in the lemniscate) admittedly, you have to modify the comfortable way of simply going round and round, but still it goes on continuously. You can keep hold of the mental picture. But now, when you come to this curve (Fig. 7), which is not so commonplace, and you want to image it, then, in order to keep the continuity of the idea you will have to say: Space no longer gives me a point of support. In crossing over to the other branch in my imagination, unless I break the continuity and regard the one branch as independent of the other, I must go out of space; I cannot remain in space. So you see, Mathematics itself provides us with facts which oblige us to go out of space, if we would preserve the continuity of the idea. The reality itself demands of us that in our ideas we go out of space. Even in Mathematics therefore we are confronted with something which shows us that in some way we must leave space behind, if the pure idea is to follow its right path. Having ourselves and going the idea is beginning to think the process through, we must go on thinking in such a way that space is no longer of any help to us. If this were not so, we should not be able to calculate all possibilities in the equation.

In pursuing similar line of thought, we meet with other instances of this kind. I will only draw your attention to the next step, which ensures if one things as follows. The ellipse is the locus of the constant sum,—it is defined by the fact that is is the curve of constant sum. The hyperbola is the curve of constant difference. The curve of Cassini in its various forms is the curve of constant product. There must then be a curve of constant quotient also, if we have here A, here B, here a point M, and then a constant quotient to be formed through the division of BM by AM. We must be able to find different points, M 1, M 2, etc., for which

etc. are equal to one another and always equal to a constant number. This curve is, in fact, the Circle. If we look for the points M1, M2 etc. we find a circle which has this particular relationship to thee points A and B (Fig. 8). So that we can say: Besides the usual, simple definition of a circle,—namely, that it is the locus of a point whose distance from a fixed point remains constant,—there is another definition. The circle is that curve, very point of which fulfills the condition that its distances from two fixed points maintain a constant quotient.

Now, in considering the circle in this way there is something else to be observed. For you see, if we express this

(it could of course be expressed in some other way), we always obtain corresponding values in the equation, and we can find the circle. In doing this we find different forms of the circle (that is, different proportions between the radius of the circle and the length of the straight line AB), according to the proportion of m to n. These different forms of the circle behave in such a way that their curvature becomes less and less. When \(n\) is much greater than m, we find a circle with a very strong curvature; when n is not so much greater, the curvature is less. The circle becomes larger and larger the smaller the difference between n and m. And if we follow this proportion of m to n still further, the circle gradually passes over into a straight line. You can follow this in the equation. It passes over into the ordinate axis itself. The circle becomes the ordinate axis when \(m=n\), that is, when the quotient \(m/n=1\). In this way the circle gradually changes into the ordinate axis, into a straight line.

You need not be particularly astonished at this. It is quite possible to imagine. But something very different happens it we wish to follow the process still further. The circle has flattened more and more, and through becoming flatter from within, as it were, it changes into a straight line. It does this because the constant ratio in the equation undergoes a change. Through this the circle becomes a straight line. But this constant ratio can of course grow beyond \(1\), so that the arcs of the circles appear here (on the left of the \(y\)-axis). What must we do, however, if we try to follow it in our imagination? We have to do something quite peculiar. We have, in fact, to think of a circle which is not curved towards the inside, but is curved towards the outside. Of course, I cannot draw this circle, but it is possible to think of a circle which is curved towards the outside.¹ In an ordinary circle the curvature is towards the inside, it is not? If we follow the line round it returns into itself. But defining the circle in this other way, if we use the necessary constant, we obtain a straight line. The curvature is still on this side (right of the \(y\)-axis). But it now makes things not nearly so comfortable for us as before! Previously, the curvature always turned towards the center of the circle, while now (in the case of the straight line), we are shown that the center is somewhere in the infinite distance, as one says. Following on from this, there arises for us the idea of a circle which is curved towards the outside. Its curvature is then no longer as it is here (Fig. 9a)—that would be the ordinary, commonplace, philistine circle,—but its curvature is here (Fig. 9b). Therefore, the inside of this circle is not here; this is the outside; the inside of this circle (Fig. 9c) is to the right.

Now compare what I have just put before you. I have described the curve of Cassini, with its various forms, the lemniscate and the form in which there are two branches. And now we have pictured the circle in such a way that at one time it is curved in the familiar way, with the inside here and the outside here; while in a second form of circle (in drawing it we are only indicating what is meant) we find that the curvature is this way round, with an inside here and an outside here. Comparing it with the Cassini curve, the first form of the circle would correspond to the closed forms, as far as the lemniscate. After this we have another kind of circle, which must be thought of in the other direction, being curved this way, with the inside here and the outside here. You see, when we are concerned with the constant product we find forms of the curve of Cassini where, it is true, we are thrown out of space, yet we can still draw the other branch on the other side. The other branch is once more in space, although in order to pass from the one to the other we are thrown out of space. Here, in the case of the circle, however, the matter becomes still more difficult. In the transition from circle to straight line we are, indeed, thrown out of space, and moreover, we can no longer draw a self-contained form at all. This we are unable to do. In passing over from the curve of constant product to the curve of constant quotient, we are only just able to indicate the thought spatially.

It is extraordinarily important that we concern ourselves with the creating of ideas which, as it were, will still slip into such curve-forms. I am convinced that most people who concern themselves with mathematics take note of such discontinuities, but then make the thought more comfortable by simply holding to the formula and not passing on to what should accompany the mathematical formula in true continuity of thought. I have also never seen that in the treatment of Mathematics as subject matter for education any great value is laid upon the forming of such thoughts in imagination.—I do not know,—I ask the mathematicians present, Herr Blümel, Herr Baravalle, if this is so; whether in modern University education any importance is attached to this? (Dr. Unger here mentioned the use of the cinema.) Yes, but that is a pretense. It is only possible to represent such things within empirical space by means of the cinema or in similar ways, it some sort of deception is introduced. It cannot be pictured fully in real space without the effect being achieved through some form of deception. The point is, whether there is anywhere in the sphere of reality something which obliges us to think realistically in terms of such curves. This is the question I am now asking. Before passing on, however, to describe what might perhaps correspond to these things in the realm of reality, I should like to add something which may perhaps make it easier for you to pass transition from these abstract ideas to the reality. It is the following.

You can set another problem in the sphere of theoretical Astronomy, theoretical Physics. You can say: Let us suppose that here as \(A\), is a source of light, and this source of light in a illumines a point \(M\) (Fig. 10). The strength of the light shining from \(M\) is observed from \(B\). That is, with the necessary optical instruments, observation is made from \(B\) of the strength of the light shining from the point \(M\), which is illumined from \(A\). And of course, the strength of the light would vary, according to the distance between \(B\) and \(M\). But there is a path which could be described by the point \(M\), such that, being illumined from A, it always shines back to \(B\) with the same intensity. There is such a path; and we can therefore ask: What must be the locus of a point, illumined from a fixed point \(A\), such that, seen from another fixed point \(B\), its light is always of the same intensity? This curve—the curve in which such a point would have to move—is the curve of Cassini! From this you see that something which takes on a qualitative nature is set into spatial connection, fitting into a complicated curve. The quality that we must see in the beam of light—for the intensity of light is a quality—depends in this case on the element of form in the spatial relationships.

I only wished to bring this forward for you to see that there is at least some way of leading over from what can be grasped in geometrical form to what is qualitative. This way is a long one, and what we will now discuss is something to which I want to draw your attention, although it would take months to present in all detail. You must be fully aware that I only intend to give you guiding lines; it is left to you to develop them further and to go into all the details which would testify to the truth of what is said. For you see, the connection which must be formed between spiritual science and empirical sciences of today demands very far-reaching and extensive work. But when lines of direction are once given, this work can to some extent be undertaken and carried forward. It is at all events possible. One must only be able in a quite definite way to penetrate into the empirical phenomena.

If we now tackle the problem from quite another angle,—we have sought to some degree to understand it from the mathematical aspect, then, to anyone who is studying the human organism, there is something which cannot escape unnoticed, something which has often been brought forward in our circle, especially in the talks which accompanied the course of lectures on Medicine in Dornach in the spring of 1920. It is not to be overlooked that certain relationships exist between the organisation of the head and the rest of the human organisation, for example the metabolism. There is indeed a connection, indefinable to begin with, between what takes place in the third system of the human being—in all the organs of metabolism—and what takes place in the head. The relationship is there, but it is hard to formulate. Clearly as it emerges in various phenomena,—for example, it is obvious that certain illnesses are connected with skull or head deformities and the like, and these things can easily be traced by one who tries to follow them with biological reasoning,—it nevertheless difficult to grasp this relationship in imagination. People do not usually get beyond the point of saying that there must be some sort of connection between what takes place in the head, for instance, and in the rest of the human organism. It is a picture which is difficult to form, just because it is so very hard for people to make the transition from the quantitative aspect to the qualitative. If we are not educated through spiritual-scientific methods to find this transition, quite independently of what outer experience offers,—to extend to what is qualitative the kind of thought we use for what is quantitative, if we do not methodically train ourselves to do this, then, my dear friends, there will always be an apparent limit to our understanding of the external phenomena.

Let me indicate but one way in which you can train yourselves methodologically to think the qualitative in a similar way as you think the quantitative. You are all acquainted with the phenomenon of the solar spectrum, the usual continuous spectrum. You know that we have there the transition of colour from red to violet. You know, too, that Goethe wrestled with the problem of how this spectrum is in a sense the reverse of what must arise if darkness be allowed to pass through the prism in the same way as is usually done with light. The result is a kind of inverted spectrum, and as you know Goethe arranged this experiment also. In the ordinary spectrum, the green passes over on the one side towards the violet and on the other towards the red; whereas in the spectrum obtained by Goethe in applying a strip of darkness to the prism there is peach-blossom in the middle and then again red on the one side and violet on the other (Fig. 11). The two colour bands are obtained, the centres of which are opposite to one another, qualitatively opposite, and both bands seem to stretch away as it were into infinity. But now, one can imagine that this axis, the longitudinal axis of the ordinary spectrum, is not simply a straight line, but a circle, as indeed every straight line is a circle. If this straight line is a circle, it returns into itself, and we can consider the point where the peach-blossom appears to be the same point as the one in which the violet, stretching to the right, meets the red, which stretches to the left. They meet in the infinite distance to the right and left. If we were to succeed—maybe you know that one of the first experiments to be made in our newly established physical laboratory is to be in this direction—if we were to succeed in bending the spectrum in a certain way into itself, then even those who are not willing to grasp the matter to begin with in pure thought will be able to see that we are here concerned with something real and of a qualitative nature.

We come to certain limiting ideas in Mathematics, where—as in Synthetic Geometry—we are obliged to regard the straight line as a circle in a quite real though inner sense; where we are obliged to admit of the infinitely distant point of a straight line as being only one point; or to understand as bounding a plane, not some line above and then again below, but a single straight line; or to think of the boundary of infinite space, not in the nature of something spherical, but as a plane. Such ideas, however, also become, in a way, limiting ideas for sense-perceptible empirical reality, and we are made to realise it if we insist on restricting ourselves to sense-perceptible reality.

This brings us to something which would otherwise always remain perpetually in the dark. I have already mentioned it. It invites us really to think-through the thought-pictures to which we come when we allow the lemniscate-form of the Cassini curve to pass over into the double-branched form,—the form with the two branches for which we must go out of space,—and them compare this with what confronts us in the empirical reality.

You are indeed already doing this, my dear friends, when you apply Mathematics in one way or another to the empirical reality. You call a triangle a triangle, because you have first constructed it mathematically. You apply to the outer form what has been evolved in an inner constructive way within you. The process I have just described is only more complicated, but it is the same process when you think of the two branches of that particular form of the Cassini curve as one. Apply this thought to the correspondence between the human head and the rest of the human organism and you will have to realise that in the head there is a connection with the remaining organism of precisely such a character as is expressed by the equation which requires, not a continuous curve, but a discontinuous one. This cannot be followed anatomically; you must go out beyond what the body comprises physically, if you would find the connection of what comes to expression in the head with what comes to expression in the metabolic system. It is essential to approach the human organism with thoughts which are quite unattainable if for every element of the thought you insist on an entire correspondence within the sense-perceptible empirical realm. We must reach out to something else, beyond the sense-perceptible empirical realm, if we are to find what this relationship really is within the human being.

Such a study, if one really gives oneself up to it and carried it out methodically, is extraordinarily rich in its results. The human organisation is of such a nature that it cannot be embraced by the anatomical approach alone. Just as we are driven out of space in the Cassini curve, so in the study of man we are driven out of the body, by the method of study itself. You see, it is quite possible to understand in the first place in thought, that in a study of the whole man we are driven out of the realm of what can be grasped in a physical-empirical sense. To put forward such things is no offence against scientific principles. Such ideas are far removed from the purely hypothetical fantasies which are often entertained in connection with natural phenomena, for they refer to the whole way in which man is membered into the universe. You are not looking for something which is otherwise non-existent, but rather for something which is exactly the same as what is expressed in the relationship between a man thinking mathematically and the empirical reality.

It is not a question of looking for hypotheses which in the end are unjustifiable; it is a question, since the reality is obviously complicated, of looking for other cognitive relations to the inner reality, in addition to the simple relation of mathematical man to empirical reality. When once you have accepted such thoughts, you will also be led to ask whether what takes place outside the human being in other domains besides the astronomical,—for example, in those phenomena which we call the chemical and physical,—whether those same phenomena, which we regard as chemical phenomena outside of man, take the same course within man, when he is alive, as they do outside him, or whether here, too, a transition is necessary which leads in some way out of space.

Now consider the important question arising out of this. Suppose we have here some kind of chemical phenomena and here the boundary leading over to the inside of the human being (Fig. 13). Supposing that this chemical phenomenon were able to call forth another, so that the human being reacted here (inside); then, if we remain in the field of the empirical, space would of course be the mediator. If, however, the continuance of this phenomenon within the human being comes about by virtue of the fact, say, that the human being is nourished by food, and the processes already taking place outside him continue inside him, then the question arises: Does the force which is at work in the chemical process remain in the same space when it taking place within man as when it is taking its course outside him? Or must we perhaps go out of space?

And there you have what is analogous to the circle which changes over into a straight line. If you look for its other form, where what is usually turned outward is now turned inward, you are entirely outside of space.

The question is, whether we do not need such ideas as these, thought-pictures which, while remaining continuous, go right out of space,—when we follow the course of what happens outwardly, outside of man, into the interior of the human being. The only thing to be said against such things, my dear friends, is that they certainly impose greater demands on the human capacity of understanding than the ideas with which he phenomena are approached today. They might therefore be rather awkward in University education. They are, no doubt, thoroughly awkward, for they imply that before approaching the phenomena we must awaken in ourselves what will enable us to understand them. Nothing like this exists in our educational system today; but it must come, it must certainly come, otherwise simply in speaking of a phenomenon we get into the greatest disparities, without in any way seeing the reality. Just think what happens when someone observes the circle as it curves to this side (Fig. 9a), and then sees how it curves to this side (Fig. 9b), but then remains a philistine and simple does not conceive that the circle now curves towards the other side. He says: This is impossible, the circle cannot curve this way; I must put the curvature this way round, I must simply place myself on the other side. What he is speaking about seems to be one and the same thing; but he has changed his point of view.

In this way today we make matters simple, in describing what is within the human being in comparison with what takes place in Nature outside him. We say: What is within man does not exist at all; I must simply place myself within man and say that the curvature is facing this way (Fig. 9c). I will then consider what is inside, without taking into account that I have reversed the curvature. I will make the interior of the human being into an outer Nature. I simply imagine outer Nature to continue through the skin into the interior. I turn myself round, because I am not willing to admit the other form of curvature, and then I theorise. That is the trick which is performed today, only in order to adhere to more comfortable motions. There is no desire to accent what is real; in order not to have to do so, we simply turn ourselves round, and—this is now a comparison—instead of looking at the human from in front, we look at Nature from behind and thus arrive in this way at all the various theories concerning man.

We will continue, then, tomorrow.

• 1. If it were drawn it would look like an ordinary circle, only one would have to bear in mind that “outside” and “inside” had changed places. (Editor's note.)