On the Dimensions of Space

On the Dimensions of Space

On the Dimensions of Space.

LECTURE BY RUDOLF STEINER.

Dornach, 24th June, 1922.

My dear Friends,

The things I shall have to explain to-day may be apparently a little far removed from our more concrete studies of Anthroposophy. They are however a necessary foundation for many other perceptions which we need — a foundation on which we shall afterwards have to build in our more intimate considerations.

There is a certain inherent difficulty for our human power of knowledge and understanding when we speak of the physical bodily nature of man on the one hand, and the soul-and-spirit on the other. Man can gain ideas about the physical and bodily with comparative ease, for it is given to him through the senses. It comes out to meet him, as it were, from his environment on all sides, without his having to do very much for it himself — at any rate so far as his consciousness is concerned. But it is very different when we come to speak of the soul-and-spirit. True, if he is open-minded enough, man is distinctly aware of the fact that such a thing exists. Men have always received into their language designations, words and phrases referring to the soul-and-spirit. The very existence of such words and phrases shews after all, for an open-minded consciousness, that something does exist to draw man's attention to the reality of soul-and-spirit.

But the difficulties begin at once when man endeavours to relate the world of things physical and bodily with the world of soul and spirit. Indeed for those who try to grapple with such questions philosophically, shall we say, the search for this relationship gives rise to the greatest imaginable difficulties. They know that the physical and bodily is extended in space. They can even represent it spatially. Man forms his ideas of it comparatively easily. He can use all that space with its three dimensions gives to him, in forming his ideas about things physical and bodily. But the spiritual as such is nowhere to be found in space.

Some people, who imagine they are not materialistically minded — though in reality they are all the more so — try to conceive the things of the soul and spirit in the world of space. Thus they are led to the well-known spiritualistic aberrations. These aberrations are in reality materialistic, for they are an effort to bring the soul and spirit perforce into space.

But quite apart from all that, the fact is that man is conscious of his own soul-and-spirit. He is well aware of how it works, for he is aware that when he resolves to move about in space his thought is translated into movement through his will. The movement is in space, but of the thought no open-minded, unbiased thinking person can assert that it is in space. In this way the greatest difficulties have arisen, especially for philosophic thinking.

People ask: How can the soul-and-spirit in man — to which the Ego itself belongs — work upon the physical and bodily which is in space? How can something essentially unspatial work upon something spatial?

Diverse theories have arisen on this point, but they all of them labour more or less under the difficulty of bringing the soul-and-spirit, which is unspatial, into relation with the physical and bodily, which is spatial. Some people say: In the will, the soul-and-spirit works upon the bodily nature. But in the first place, with ordinary consciousness, no one can say how the thought flows into the will, or how it can be that the will, which is itself a kind of spiritual essence, manifests itself in outer forms of movement, in outer activities.

On the other hand the processes which are called forth by the physical world in our senses — i.e., in the bodily nature — are also processes extended in space. Yet inasmuch as they become an experience in soul and spirit, they are transformed into something non-spatial. Man cannot say out of his ordinary consciousness, how the physical and spatial process which takes place in sense-perception can influence the non-spatial, the soul-and-spirit.

In recent times, it is true, men have sought refuge in the conception, to which I have often referred, of ‘psychophysical parallelism.’ It really amounts to a confession that we can say nothing of the relation of the physical and bodily to the soul-and-spirit. It says, for example: The human being walks, he moves his legs, he changes his position in external space. This is a spatial, a physical-bodily process. Simultaneously, while this is taking place in his body, a process of soul-and-spirit is enacted — a process of thought, feeling and will. All that we know is that when the physical and bodily process takes place in space and time, the process of soul and spirit also takes place. But we have no concrete idea of how the one works upon the other. We have psycho-physical parallelism: a psychical process takes its course simultaneously with the bodily process. But we still do not get behind the secret — whose existence is thus expressed — that the two processes run parallel to one another. We gain no notion of how they work on one another. And so it is invariably, when men try to form a conception of the existence of the soul-and-spirit.

In the 19th Century, when the ideas of men were so thoroughly saturated with materialism, even this question could arise: — Where do the souls sojourn in universal space when they have left the body? There were even men who tried to refute spiritualism by proving that when so and so many men are dying and so and so many are already dead, there can be no room in the whole world of space for all these souls to find a place of abode! This absurd line of thought actually arose more than once during the 19th Century. People said, Man cannot be immortal, for all the spaces of the world would already have been filled with their immortal souls.

All these things indicate what difficulties arise when we seek the relation between the bodily and physical, clearly spread out as it is in space, and the soul and spirit which we cannot in the first place assign to the spatial universe.

Things have gradually come to this pass; our purely intellectualistic thinking has placed the bodily-physical and the soul-and-spirit sharply and crudely side by side. For the modern consciousness they stand side by side, without any intermediary. Nor is there any possibility of finding a relation on the lines along which people think of them to-day. The man of to-day conceives the spatial and physical in such a way that the soul has no conceivable place in it. Again, he is driven to conceive the soul-qualities so sharply separated from the physical and bodily, that the absolutely unspatial soul-and-spirit, as he conceives it, cannot possibly impinge at any point upon the physical. ...

This sharp contrast and division was however only developed in the course of time. We must now begin again from an altogether different angle of approach, which is only made possible once more by taking our start from what anthroposophical spiritual science has to say.

In the first place, anthroposophical science must consider the nature of the will. To begin with, straightforward observation shews undoubtedly that the will of man follows his movements everywhere. Moreover, the movements man accomplishes externally in space when he moves about, and those too which take place within him in the fulfilment of his everyday functions of life, in a word, all the activities of man in the physical world-are in the three dimensions of space. Hence the will must also go everywhere, wherever the three dimensions extend. Of this there can be no doubt.

Thus if we are speaking of the will as of an element of soul-and-spirit, there can be no question but that the will — albeit a thing of soul and spirit — is three-dimensional. It has a three-dimensional configuration.

We cannot but think of it in this way: — When we carry out a movement through our will, the will adapts itself and enters into all the spatial positions which are traced, for example, by the arm and hand. The will goes with it everywhere, wherever the movement of a limb takes place. Thus after all we must speak of the will as of a quality of soul which can assume a three-dimensional configuration.

Now the question is, do all the soul-qualities assume this three-dimensional configuration? Let us pass from the Will to the world of Feeling. To begin with, we can make the same kind of observation. Considering the matter with the ordinary everyday consciousness, man will say to himself, for example: ‘If I am pricked by a needle on the right-hand side of my head, I feel it; if I am pricked on the left-hand side I feel it also.’ In the everyday consciousness he can, therefore, be of opinion that his Feeling is spread out over his whole body. He will then speak of Feeling as having a three-dimensional configuration in the same sense as the Will. But in so doing he gives himself up to an illusion. It is not really so. The fact is, at this point there are certain experiences which every man can have in his own nature, and from these we must take our start today. Our considerations will have to be somewhat subtle, but spiritual science cannot really be understood without subtlety of thought.

Consider for a moment what it is like when you touch your own left hand with your right. You have a perception of yourself thereby. Just as in other cases you perceive an outer object, so do you perceive yourself when you touch your right hand with your left hand-say with the several fingers one by one.

The fact to which I am referring appears still more distinctly when you consider that you have two eyes. To focus an object with both eyes you have to exert your will to some extent. We often do not think of this exertion of the will. It comes out more strongly when you try to focus a very near object. You then endeavour to turn your left eye towards the right and your right eye towards the left. You focus an object by bringing the lines of vision into contact, just as you bring your right and left hands into contact when you touch yourself. From these examples you can see that it is of some importance for man, with respect to his orientation in the world, to bring his left and right into a certain mutual relation. By the contact of the hands or the crossing of the lines of vision we can thus become aware of an underlying fact which is of deep significance. Though the everyday consciousness does not generally go farther than this, it is possible to continue very much farther along this line of study.

Suppose we are pricked by a needle on the right-hand side of our body. We feel the prick. But we cannot really say so simply ‘where’ we feel the prick-meaning by ‘where’ some portion of the surface of our body. For unless the several members of our organism stood in a living mutual relationship to one-another, — unless they were working one upon the other — our human nature, body and soul together, would not be what it is. Even when our body is pricked, let us say, on the right-hand side, there is always a connection established from the right-hand side to the central plane of symmetry. For any feeling or sensation to be brought about, the left half of the body must always enter into relation with the right.

It is comparatively easy to realise — if this be the plane of symmetry, seen from in front — that when the right hand touches the left the mutual feeling of the two hands is brought about in the plane of symmetry. It is comparatively easy to speak of the crossing of the lines of vision from the two eyes. But there is always a connecting line in every case — whenever we are pricked, for example, on the right-hand side; — the left half of the body crosses with the connecting line from the right. Without this process, the sensation would never come about. In all the surging waves of feeling and sensation, the fact that we have a right and a left half of the body — the fact that we are built symmetrically — plays an immense part. We always relate to the left-hand side what happens to us on the right. In a vague groping way something reaches over in us from the left, to cross with what is flowing from the right.

Only so does Feeling come about. Feeling never comes about in space, but only in the plane. Thus the world of Feeling is in reality spread out, not three-dimensionally, but two-dimensionally. Man experiences it only in the plane which as a plane of section would divide him into two symmetrical halves.

The life of Feeling is really like a painting on a canvas — but we are painting it not only from the one side but from both. Imagine that I here erect a canvas, which I paint from right to left and from left to right, and observe the interweaving of what I have painted from the one side and the other. The picture is only in two dimensions. Everything three-dimensionalis projected, so to speak, into the two dimensions.

You can arrive at the same idea in a somewhat different way. Suppose you were able to project on to a flat surface shadow-pictures of objects on the right-hand side and on the left. On the flat expanded wall you then have shadows of left- and right-hand objects. So it is with our world of Feeling. It is two-dimensional, not three-dimensional. Man is a painter working from two sides. He does not simply feel his way into space. Through his three-dimensional will he projects on to a plane in shadow-forms, in pictures, the influences of feeling which meet him in the world of space. In his life of feeling, man lives in a picture drawn two-dimensionally through his body-only it is for ever being painted from both sides. Thus if we would seek the transition from Will to Feeling in ourselves — as human beings in the life of soul — we must pass from the three-dimensional into the two-dimensional.

But this will already give you a different spatial relationship of the soul-quality which is expressed in feeling, than if you merely say of the soul-life that it is unspatial. The plane has two dimensions, but it has no ‘space.’ Take any plane in the outer world — the blackboard for example. In reality it is a solid body, it has a certain thickness. But an actual plane, though it is in space, is not in itself spatial. ‘Space’ must always be of three dimensions; and only our Will enters into this three-dimensional space. Feeling does not enter into the three dimensions of space. Feeling is two-dimensional. Nevertheless it has its own relations to space, just as a shadow-picture has. In saying this, I am drawing your attention at the same time to a fact of very great importance, which is not at all easy to penetrate with clear perception, because with his everyday consciousness man has little inclination as a rule to perceive the peculiar nature of his world of Feeling.

The fact is that the world of Feeling is always permeated by the Will. Think only for a moment of this: If you really receive on the right-hand side of your body the prick or sting of which we spoke just now, you do not immediately sever the Feeling from the Will. You will certainly not patiently receive the sting. Quite apart from the fact that you will probably reach out in a very tangible way, striking out pretty intensely with your Will into the three dimensions of space ; inwardly too there will be a defensive movement which does not appear externally but shews itself in all manner of delicate disturbances of the blood and the breathing. The defensive movement which we make, when, stung by a gnat, we reach out with our hand, is only the crudest and most external aspect. Of the finer aspect — the inner defensive movement which we perform in the motion of the blood and breathing and many another inward process — we are generally unaware. Hence we do not distinguish what the Will contributes from the content of Feeling as such.

The real content of Feeling is in fact far too shy, far too elusive. We can only get at it by very careful meditation. If however you can exclude, from the Feeling as such, all that belongs to the Will, then as it were you shrink together from the right and left and you become the plane in the middle. And when you are the central plane, and like a conscious painter you record your inner experiences on this plane, then you begin to understand why the real world of Feeling is so very different from our ordinary, everyday experience.

We can indeed experience this plane-quality, this surface-quality of Feeling. But it needs to be experienced meditatively. We must feel all the shadow-likeness of our feelings as against the robust outer experiences in three-dimensional space. We must first prepare ourselves for this experience, but if we do so we can really have it, and then we gradually come near the truth that Feeling takes its course in two dimensions.

How shall we characterise Thinking? To begin with we must admit with open and unbiased mind how impossible it is to speak of a thought as if it were in space. A thought is really nowhere there in space. Nevertheless the thought must have some relation to space, for undoubtedly the brain — if not the instrument — is at least the foundation of our Thinking. Without the brain we cannot think. Thus our Thinking takes its course in connection with the activity of the brain. If Thinking had nothing to do with space, we should get the following curious result: If you were able to think well as a child of 12, your head having now grown beyond the position in which it was when you were 12 years old, you would have grown out of your Thinking. But that is not the case. As we grow up, we do not leave our Thinking behind. The very fact of growth will serve to indicate that even with our Thinking we are somehow in the world of Space.

The fact is this. Just as we can separate out the world of Feeling — the world of inner experience of our Feelings — by learning gradually to perceive our plane of symmetry, so too we can learn to experience our Thinking meditatively, as something that only has extension upward and downward. Thinking is one-dimensional. It takes its course in man in the line.

In a word, we must say: The Will takes on a three-dimensional configuration, the Feeling a two-dimensional and the Thinking a one-dimensional configuration.

When we make these inner differentiations of space, we do not arrive at the same hard-and-fast transition as the mere intellect. We are led to perceive a gradual transition. The mere intellect says : The physical is three-dimensional, spatially extended. The soul-and-Spirit has no extension at all. From this point of view no relationship can be discovered between them. For it goes without saying, there is no relationship between that which has extension and that which has none. But when once we perceive that the Will has a three-dimensional configuration, then indeed we find that the Will pours itself out everywhere into the three-dimensional world. And again, when once we know that Feeling has a two-dimensional configuration, then we must pass from the three dimensions to the two, and as we do so we are led to something which still has a relationship to space, though it is no longer spatial in itself. For the mere plane — the two-dimensional — is not spatial, but the two dimensions are there in space; they are not entirely apart from space. Lastly, when we pass from Feeling to Thinking we pass from the two dimensions to the one. Thus we still do not go right out of space. We pass over gradually from the spatial to the unspatial.

As I have often said, it is the tragedy of materialism that it fails to understand the material-the material even in its three-dimensional extension. Materialism imagines that it understands the material, substantial world, but that is precisely what it does not understand. Many things of real historic importance emerged in the 19th century, which still present an unsolved riddle to the ordinary consciousness. Think only of the great impression which Schopenhauer's philosophic system, The World as Will and Idea, made on so many thinking people. There is something unreal in the Idea, says Schopenhauer. The Will alone has reality. Why did Schopenhauer arrive at the idea that the world only consists of Will? Because even he was infected with materialism. Into the world in which matter is extended three-dimensionally, only the Will pours itself out. To place the Feelings too into this world, we must look for the relationship which obtains between the three-dimensional object and the two-dimensional image on the screen. Whatever we experience in our Feelings is a shadow-picture of something in which our Will too is living in its three-dimensional configuration. And what we experience in our Thinking consists of one-dimensional configurations. Only when we go right out of the dimensions — that is to say, when we pass to the dimensionless point, — only then do we arrive at our I or Ego. Our Ego has no extension at all. It is purely point-like, ‘punctual.’

So we may say, we pass from the three-dimensional to the two-dimensional, to the one-dimensional and to the ‘punctual.’ So long as we remain within the three-dimensional, there is our Will in the three dimensions. Our Feeling and our Thinking are also there within them, only they are not extended three-dimensionally. If we leave out the third dimension and come down to the two dimensions, we only have the shadow of outward existence, but in the shadow is extended that element of soul-and-spirit which lives in our Feeling. We are already getting more away from space. Then, when we go on to Thinking, we come away from space still more. And lastly when we pass on to the Ego, we go right out of space.

Thus we are led out of space, as it were piece by piece. Now we see that it is meaningless merely to speak of the contrast between the soul-and-spirit, and the physical and bodily. It is meaningless, for if we wish to discover the relation between the soul-and-spirit and the physical and bodily, we must ask: How are things which are extended in three-dimensional space (our own body, for example) related to the soul as a being of Will? How is the bodily and physical in man related to the soul as a being of Feeling? The bodily and physical is related to the soul as a being of Will in such a way that one would say, it is saturated by the Will on all sides, in all dimensions, just like the sponge is saturated by water. Again, the bodily and physical is related to the Feeling, like objects whose shadows are thrown upon the screen. And when we pass from Feeling to the quality of Thought, then we must indeed become strange painters — for we must paint on to a line what is otherwise existing in the two dimensions of the picture.

Ask yourselves the following question. (It will indeed make some demands on your imagination.) Suppose that you are standing face to face with the ‘Last Supper’ by Leonardo da Vinci. You have it before you in the surface. The whole thing is two-dimensional — for we need not take into account the thickness of the colours. The picture which you have before you is essentially two-dimensional.

But now imagine to yourselves a line, drawn through the middle from top to bottom of the picture. This line shall represent a one-dimensional being. Imagine that this one-dimensional being has the peculiar quality that Judas, let us say, is not indifferent to him. He feels Judas in a certain way. He feels him more where Judas inclines his head in that direction, and where Judas turns away he feels him less. Likewise this one-dimensional being feels all the other figures. He senses them differently according as the one figure is in blue and the other in a yellow colour. He feels all that is there, to the left and to the right of him. All that is present in the picture is livingly felt by this one-dimensional being.

Such in reality is our Thinking within us. Our Thinking is a one-dimensional being of this kind, and only partakes in the life of the remainder of our human being inasmuch as it is related to the picture which divides us into the left- and right-hand man. Via this two-dimensional picture, our Thinking stands in relation to the world of Will with its threefold configuration.

If we wish to gain an idea of our being of soul-and-spirit (to begin with without the Ego; only in so far as it is willing, feeling and thinking) we must conceive it not as a mere nebulous cloud. We must regard the soul and spirit, as it were diagramatically. There it appears, to begin with, as a cloud, but that is only the being of Will. It has the constant tendency to become pressed together; thereby it becomes a being of Feeling. First we see a cloud of light. Then we see the cloud of light creating itself in the centre as a plane, whereby it feels itself. And the plane in turn strives to become a line. We must conceive this constant process — cloud, plane and line as an inwardly living form. It constantly tends to be a cloud, and then to squeeze together from the cloud into the plane, and then to elongate into the line. Imagine the plane that becomes a line and then a plane again and then again a cloud in three dimensions. Cloud, plane line; line, plane, cloud, and so on. Only so can you imagine graphically what your soul is in its inner being, its inner nature and essence. An idea that remains at rest will not suffice. No idea that remains at rest within itself can reproduce the essence of the soul. You need an idea with an inner activity of its own. The soul itself, as it conceives itself, plays with the dimension of space. Letting the third dimension vanish, it loses the Will. Letting the second dimension vanish, it loses the Feeling. And the Thinking is only lost when we let the first dimension vanish. Then we arrive at the point, and then only do we pass over to the Ego.

Hence all the difficulty in gaining a knowledge of the soul. People are accustomed only to form spatial ideas. Hence they would like to have spatial ideas — however diluted — of the soul's nature. But in this form they only have the element of Will.

Unless we make our thinking inwardly alive and mobile we can reach no conception of the soul-and-spirit. If we wish to conceive a quality of soul-and-spirit, and our conception is the same in two successive instants, we shall at most have conceived a quality of Will. We must not conceive the soul-and-spirit in the same form in two successive moments. We must become alive and mobile-not by moving from one point in space to another, but rather by passing from one dimension to another. This is difficult for the modern consciousness. Hence even the most well-meaning people — well-meaning for the conception of spiritual things — have tried to escape from Space by transcending the three dimensions. They come to a fourth dimension. They pass from the three-dimensional to the four-dimensional. So long as we remain within the mathematical domain, the thoughts which we arrive at in this way are quite in order. It is all perfectly correct. But it is no longer correct when we relate it to the reality. For the peculiar thing is, that when we think the fourth dimension in its reality, it eliminates the third. Through the fourth dimension the third dimension vanishes. Moreover, through the fifth dimension the second vanishes, and through the sixth the first vanishes, and we arrive at length at the point.

When we pass in reality from the third to the fourth dimension, we come into the Spiritual. We eliminate the dimensions one by one, we do not add them, and in this way we enter more and more into the Spiritual.

Through such ideas we gain a deeper insight too into the human form and figure. For a more artistic way of feeling is it not rather crude how we generally observe a human being, as he places himself with his three dimensions into the world? That after all is not the only thing. Even in ordinary life we have a feeling for the essential symmetry between the left and right halves of the body. And when we thus comprise the human being in his central plane, we are already led beyond the three dimensions. We pass into the plane itself. And only thereafter do we gain a clear conception of the one dimension in which he grows. Artistically we do already make use of this transition, from three to two and on to one dimension. If we cultivated more intensely this artistic perception of the human form, we should find more easily the transition to the soul's life. For you would never be able to feel a being, unsymmetrically formed, as a being of united and harmonious Feeling.

Look at the star-fish. It has not this symmetrical form. It has five rays. Of course you can pass it by without any inner feeling. But if you perceive it feelingly, you could never say that the star-fish has a united feeling-life. The star-fish cannot possibly relate a right-hand to a left-hand side, or grasp a right-hand with a left-hand member. The star-fish must continually relate the one ray to one or two or three, or even to all four remaining rays. What we know as Feeling cannot live in the star-fish at all.

I beg you to follow me along this intimate line of thought. What we know as Feeling comes from the right and from the left, and finds itself at rest in the middle. We go through the world by placing ourselves with our Feeling restfully into the world. The star-fish cannot do so. Whatever the star-fish has, as influence of the world upon itself, it cannot relate it symmetrically to another side. It can only relate it to one, or two, or to the third or fourth ray. But the first influence will always be more powerful. Thus the star-fish has no Feeling-life at rest within itself. When, as it were, it turns its attention to the one side, then by the whole arrangement of its form it will experience: ‘You are raying out in that direction, thither you are sending forth a ray.’ The star-fish has no restfulness in feeling. It has the feeling of shooting forth out of itself. It feels itself as raying forth in the world.

If you develop your feelings in a more intimate way, you will be able to experience this even as you contemplate the star-fish. Observing the end-point of any one ray and relating it to the creature as a whole, in your imagination the star-fish will begin to move in the direction of this ray, as it were a streaming, wandering light. And so it is with all the other animals which are not symmetrically built, which have no real access of symmetry.

If man would only enter into this more intimate way of Feeling — instead of giving himself up entirely to the intellectual, merely because in the course of time he had to become an intellectual being, — then indeed he would find his way far more intimately into the world.

It is so also in a certain sense for the plant world, and for all things that surround us. True self-knowledge takes us ever farther and farther into the inwardness of things.