The Rudolf Steiner Archive

I pointed out yesterday in my introductory lecture that we can observe a transition from the ordinary knowledge of the world around us to mathematical knowledge, and that this is the beginning of a path of knowledge. This path when continued will lead to an understanding of the spiritual scientific method, as we mean it here, and ultimately to acceptance of it. It will be my special effort in these lectures to characterize the spiritual scientific method in such a way as to completely justify it. To accomplish this task will take the remaining seven lectures.

Today, once again, I would like to consider in greater depth the first stage. I would like to place before you today something which as normal scientific thinking appears here and there in fragments. As these fragments are not always found in the same place and are not seen as a whole, we have the situation that it is not possible to rise in a methodical way from a science that is free of mathematics to one that includes it. We will also have difficultly following in an entirely methodical way the transition from a mathematical penetration of the objective world to a spiritual-scientific penetration into reality. I shall also, as I have already mentioned, try to reach this last phase in a methodical way. We will start today by observing the human being as he experiences himself when he looks at the outer world.

You will know from my lectures, also my book Riddles of the Soul,¹ that one cannot reach a comprehensive observation of man without splitting the entire human organization into three distinctly different members. Naturally we have eventually to deal with the complete human being. This complete man is however a most complicated organism and its members have a certain independence. Finally we will see how what is contained independently in these members combines into a whole.

First we have to look at what I have named in Riddles of the Soul as the nerve-sense man: The member of the human organism that has its primary expression in the head, although from there it extends over the entire organism. Despite this extension we can clearly differentiate this member from the rest of the organism. This physical member is the mediator of our conceptual life. As human beings we make mental pictures and we are able to take the life of these mental pictures to ourselves through our sense organs. From the senses it flows toward our inner organism.

The way we are connected with our life of feeling is similar to the way our mental pictures are related to our nervous system. The present-day psychological approach to these things is quite inexact. Our feeling life is not directly connected to our nerve-sense system, only indirectly. It is directly connected to what we call the rhythmic system in the human organism, consisting mainly of breathing, pulse, and blood circulation. The mistaken idea that the life of feeling, as part of the soul life, is directly connected to our nervous system originates from the fact that what we experience as feeling is always accompanied by mental pictures. The physical expression of this is that the rhythmic system is connected throughout the organism with the nerve-sense system. The fact that our life of feeling is always accompanied by a mental picture of some kind is related organically to the fact that the rhythmic system works back onto the nervous system. This can give the appearance that the life of feeling is directly connected to the nerve-sense system. I have pointed out in Riddles of the Soul that if one studies what occurs in us when we listen to music, one can see the relationship correctly between feeling and the forming of mental pictures.

Besides these two systems, the nerve-sense system which provides the mental image, and the rhythmic System which mediates the life of feeling, we have the metabolic system. Every function of the human organism is contained in these three systems. The metabolic system is the expression of the will, and the real connection between willing and the human organism will become clear only if you study how a metabolic transformative action comes about in us when there is an act of will or even an impulse of will. Every metabolic activity is consciously or unconsciously the physical basis of some act of will or impulse of will. Our capacity for movement is also connected with our will activity and therefore is connected with some kind of metabolic activity. One must be clear about the fact that when we complete a movement in space, this is a primitive activity of the will. To use a saying of Goethe, the “ur-phenomenal” activity of the will can be seen as expressed by the physical transformations that occur in the organism. And, as in the case of feeling, the will activities are indirectly connected with the nerve-sense system through our following our will activities with mental pictures. So we can say, to start with, that our soul life and also our physical life can be divided in three ways organically as well as into three soul aspects.

Let us try today to look at man from a certain point of view so that we may see how these three members of our physical organism and our soul organization relate to one another. We must also go into some detail to achieve our task of showing that spiritual science is a continuation of the familiar scientific way of considering things. First of all, let us consider what I have named the nerve-sense organism. This nerve-sense organism is contained mainly in the head, as I have already mentioned, but from there it extends over the rest of the organism, in a certain way impregnating it. This is not obvious if one looks at just the outer form of a human being, but it does in fact extend inwardly through the whole organism. Take the sense of warmth as an example, which extends over the entire organism. This can be seen as a part of our nerve-sense organization that for the most part is concentrated in the head, in the life of the senses, and yet is extended over the whole organism, making the whole human being into a kind of head in regard to this particular sense of warmth.

For most people it is distasteful nowadays to try to understand this kind of problem. Because we have become so used to an outer way of considering things, the three members of the human organism are considered spatially, as separate from one another. There is a professor of anatomy who takes this view, who has asserted that anthroposophy separates the human organism spatially into head system, chest system, and abdominal system. This is clearly erroneous. It is of course not what we have said; we wish to approach these things precisely, not in dilettante fashion. One must know these things correctly, especially if one also wants to understand how three elements flow into one another and compose the threefold social organism.

To begin with it is empirically evident that it is the head organization that has most to do with cognition, at least mathematical cognition, as it approaches man in the outer world. In relation to this head organizatiion we can now empirically establish that what we can call “dimensionality” confronts us initially as a kind of intimation. You will see best what I mean if we consider the three modes of human activity.

The first of these I would like to call the total act of seeing, observation of the world with our own two eyes. Secondly, I would mention man's arms and hands. Even though they are attached to man's trunk and are therefore in a certain way connected with the metabolic system, they also have an inner relationship to the rhythmic system. Through their attachment near the rhythmic system, they are influenced by the life and functioning of this system. The fact that they are located beside the rhythmic system, which is more hidden, allows them to reveal the nature of what would normally be hidden. Please listen carefully; I repeat: The arms and hands, because of their specific location on the human body and through their life functions, can be seen as belonging to the rhythmic system. The most obvious demonstration of this connection is the way they are used freely in gestures to express feelings. When they are used in this way, they are lifted to a higher function than serving merely the body. In the case of animals, the corresponding members, the legs, are used only to serve the body, but in human beings the arms are freed for a higher function. Through the fact that they are used for gestures in connection with speech, they have the higher function of making the invisible aspects of speech visible.

The third mode is the activity of walking, an activity primarily of the limb system. Let us consider the activities of seeing, arm movement, and walking from a scientific point of view. In general, what you see with both eyes presents itself to you in two dimensions and these dimensions are independent of any mental activity. I can represent these two dimensions by these perpendicular coordinates. I will draw these as dotted lines for the purpose of later references I wish to make. With these dotted lines representing two dimensions, I want to express the fact that our mental activity of comprehension is not really involved when we look only at these two dimensions.

The third dimension is in sharp contrast to this. The third dimension of depth does not stand ready-made before our soul independent of any mental activity. It confronts us as something we undergo as an inner operation of the mind when we supplement what we normally see as the surface of things with the depth dimension and thus obtain a three-dimensional body. Roughly speaking, what we actually do in this case is not brought to consciousness. But when we enter into the activity more precisely, we see that one experiences the depth dimension in a different way from width and height dimensions. We can become aware, for instance, how we are able to guess how distant something is from us. In ordinary observation something is added to the mere observation of the eyes when we progress from a surface-picture consciousness to a full-bodied three-dimensional consciousness. So long as we remain within our consciousness, we cannot say how height perception and width perception are achieved. We simply have to accept the height and width dimensions; for the activity of seeing they are simply given. This is not true of the depth dimension. For this reason I will draw it in perspective; I will draw a solid line to represent the difference. In this third dimension of depth, we are able to have the act of perceiving enter our consciousness in a slightly conscious way. Thus we recognize when we examine the act of seeing, that the height and width dimensions are given to us purely in thought; that is, if we penetrate the act of seeing with our thoughts. The depth dimension, however, is based an an activation of consciousness, a kind of half-conscious mental operation. Therefore, what you may already have heard as the physiological and anatomical interpretation of the total act of seeing must be accepted only in reference to the physical components of the act of seeing, to that aspect which does not involve an operation of the mind; only the perception of surface can be attributed to the act of seeing. In contrast, when considering the depth dimension, it is not sufficient to merely consider the activity of the corpora quadrigemina, the organ in the human body upon which the visualizing activity of the eyes depends, the bodily aspect of seeing—here the cerebrum must serve a mediating function, the cerebrum being that part of the brain to which are attributed the anatomical-physiological aspects of the volitional operation of the intellect.

Thus we can grasp this depth dimension when we examine it carefully, using both analytical and synthetic means. The matter of depth perception belongs into the realm of what I would like to call “conscious activation through the human head.”

When we turn our attention from the act of seeing to that activity which may be seen externally through the movement of the arms and hands, we immerse ourselves in an element that is very difficult to grasp consciously. Even so, we can follow what takes place in our life of feeling when we gesture with our arms and hands, which are free for this kind of activity, and we can become aware of the way this action is related to depth perception with our two eyes. What is it really that depth perception mediates to us? It is the exact position of the left and the right eye. It is the convergence of the left axis and right axis of sight. The mental judgment of the distance of some object from us depends upon the distance at which the lines of sight cross each other. Very little of this convergence activity of the eyes lying at the basis of the judgment of depth is outwardly perceptible.

When we turn to the activity of our arms and hands, we find we are able to distinguish more exactly, with little effort of consciousness, what is happening inwardly when we move our arms in the horizontal plane, in the dimension of right-left, in the width dimension. If we look carefully, our judgment in relation to the width dimension is connected with the feeling we have when we consciously move our arms in a horizontal gesture expressing how wide something is. We have a feeling experience of what we call symmetry. This experience takes place particularly in the width dimension, through the feeling that is mediated to us through our left and right arm movements. Through the corresponding movements of our left and right arms we can actually feel our own symmetry. Our grasping in feeling of the width dimension is translated for us chiefly through the medium of symmetry into mental pictures, and we then also evaluate symmetry in our mental life. But we must not overlook the fact that this judging of the symmetry of the width dimension is something secondary: If we only looked at the symmetry without having the accompanying feelings that correspond to the symmetrical aspects of left and right, our experience would be pale, dry and wanting in its full reality. You can understand all that symmetry shows us if you can feel the symmetry. But you can really only feel the symmetry through the delicate process of becoming conscious of the fact that the movements of the left and right arms belong together, and in the same way the movements of the hands belong together. What we experience in feeling thus supports everything we can experience in relation to the width dimension.

But also what we have called the depth dimension in relation to the act of seeing enters our consciousness through something to be found in the activity of our arms. The way the axes of our vision intersect is similar to the way our arms can intersect. When our arms intersect, we have a certain equivalent to the act of seeing. When we cross our arms, first close to us and then farther away, if we follow the points of intersection we can get a sense of depth dimension by trying to experience what is going on in our arms. In these moments we don't experience the width dimension as fully as we do—with no effort on our part—in the act of seeing. But if I would represent symbolically what is expressed in relation to the dimensions by the arms and hands, I would have to sketch the width dimension and the depth dimension as full lines and the height dimension as a dotted line. That is all that I can experience through my arms. The height dimension remains unconscious to us when we make gestures, because we connect our gestures consciously with a surface which is made up of depth and width dimensions.

When does the third dimension show itself in a distinct, conscious way? Actually, it only appears to our consciousness in the act of walking. When we move from one place to another, then the line which is this third, vertical dimension changes continually, and although our consciousness of this third dimension while we walk is almost imperceptible, we must not overlook it. In fact, the half-conscious intellectual awareness we can experience is related to this height dimension.

Therefore, when we examine the act of seeing, which obviously belongs to the head organization, we realize that in the act of seeing there is given ready-made a two-dimensional activity, and in addition we must establish an activity that creates the third dimension—depth. In the action which we have described as representative of the rhythmic system, namely, the free movement of the arms and hands, we can have an inner experience of two spatial dimensions. The third spatial dimension—height—is given to our consciousness in the same way that width and breadth are given for the head organization in the act of seeing. Only in the metabolic-limb system (the connection between these two is only recognized when we study the metabolic activity in the act of walking) is everything open to our consciousness that gives us the full measure of three dimensions.

If you consider the following, you will have something extraordinarily important. The only content of our fully alert consciousness is the life of mental pictures. In contrast to this, our life of feeling does not come into our consciousness with the same clarity. As we shall see later, our feelings by themselves have no greater intensity in our consciousness than our dreams. Dreams are rendered from the clear content of daily life, from the fully alert life of mental pictures; in this way they become distinct mental pictures in our consciousness. In the same way, our feelings in daily life are continually accompanied by the mental pictures representing them during our waking hours. In this way our feelings, which otherwise only possess the intensity of dream life, are brought to the distinct, fully conscious life of mental pictures.

The will-movements remain completely in the subconscious. How do we know anything of the will? Basically, in our everyday consciousness we know nothing of the real nature of the will. This is made clear in the psychology of Theodor Ziehen, for instance, who in his Physiological Psychology speaks only of the life of mental pictures or the representational life of the mind. He says: As psychologists we can only follow the life of mental images, but we find certain mental images to be tinged with feeling. The fact that the life of feeling, as I explained to you just now, is bound up with the rhythmic system and only shines up into the life of mental pictures, this is unknown to Theodor Ziehen. In his view, feelings are only an aspect of the life of mental pictures. This psychologist simply has no insight into the actual organization of the human being, which I have now to describe to you.

Because feelings are bound up with the rhythmic system, they remain in the half-conscious realm of dreaming. And the will activity remains completely unconscious. That's the reason why the average psychologist does not write about it. Just read Theodor Ziehen's strange explanations concerning the activity of the will, and you will see that its real nature is completely missed by such psychologists.

When we observe the result of an act of will, this is only something we are able to look at externally. We do not know what has happened inwardly when a will impulse moves our arm. We only see the arm move; that is, we observe the outer happening afterward. Thus we accompany the manifestations of our will with mental images; they are mediated organically through the metabolic system and the limb system related to it. So it is only in part of the human organism, in the metabolic system—which is the bodily aspect of the soul's will activity—that we experience the reality of all three dimensions of space. In our ordinary process of knowing the reality of the three dimensions cannot be grasped. It cannot be grasped, as we will see, until we are able to look with the same clarity into our will activity as we normally do into our mental activity. It cannot come about in our ordinary way of knowing but only with spiritual-scientific knowledge. It is through the activation of the entire man, of the entire limb-and-metabolic system, that our subconscious experience of the three dimensions comes about. What happens is that what is contained in the metabolic-limb system is lifted into the rhythmic system. There it is experienced in its two-dimensional aspect, not in its total reality. When experienced in two dimensions, the height dimension has already become abstract. Only in the subconscious do we normally experience the height dimension.

You can see how reality becomes an abstraction in the human organization through the human activity itself. In the working of the human organization, the height or vertical dimension already becomes an abstraction, appearing as a mere line, a mere thought in the region of the rhythmic system. Following this up into the nerve-sense system, what occurs? Both height and width become abstraction. We can no longer experience them; they can only be thought by the intellect as we approach the subject afterward. So in the head, the region of our ordinary knowledge, we only have the possibility of expressing the two dimensions abstractly. It is only the depth dimension for which we still have a faint consciousness in the head. So you can see, it is only due to a delicate perception of the depth dimension that we are able to know anything at all in our normal consciousness of the spatial dimensions. Please now consider: With our present constitution, what if depth perception should become equally abstract? Then we would be left with just three abstract lines—and it would never even occur to us to search for the realities represented by those abstract lines.

In this way I have pointed you toward reality. In Kantianism this reality appears in an unreal form. Kantianism speaks of the three dimensions being contained a priori in the human organization, and of the human organization transposing its subjective experience out into space. How is it that Kant came to this one-sided view? He arrived at this because he did not know that what is brought into consciousness in the delicate experience of the depth dimension, and otherwise abstractly, is experienced in its reality in our subconscious. As it is pushed up into consciousness, it is made into an abstraction, with only a small remainder in the case of depth dimension. We experience the reality of the three dimensions through our individual human organization. The reality is present in actuality in the realm of the will, and physiologically in the metabolic-limb system. Initially in this system we are unconscious of reality in our ordinary mind, but we become conscious of it, at first in the thought abstractions of mathematical-geometrical space.

With this subject of the three dimensions I wished to give an example of the ways and means by which spiritual science can penetrate human activity. We don't have to remain on the abstract level—where, for example, Kant regards space and time as a priori—but we can progress to a discovery of the concrete aspects of the reality of the human being. I wanted to use this particular example of the actual meaning of space because it will be useful in the future in leading us to an exact understanding of the mathematical facts from all sides. We will speak further of this tomorrow.

• 1. See The Case for Anthroposophy, Anthroposophic Press.

In yesterday's lecture I tried to consider what the origin is, in the human being, of the mental images of the three dimensions. For the moment I would like to leave this subject alone. When trying to illuminate physical facts with spiritual-scientific reflections, it is best to view things from many sides and I wish to do this in these lectures. Today I want to add something to yesterday's view, in order to bring these separate considerations together. We will then raise the whole to the level of a spiritual-scientific point of view.

The objection is often heard that spiritual-scientific considerations interest only those who can relate to such ideas. In a certain way one may admit this, but only in a very narrow sense can one have such a feeling. The important question is whether or not it is possible for the results of spiritual-scientific investigation to be understood without special capacities of higher vision. It is precisely this question that I would like to answer in the affirmative. The results of spiritual-scientific investigation are indeed intelligible to a sound human understanding. The only essential element is an openness to what spiritual science has to say, justifying itself from various points of view.

One of the attempted refutations of spiritual science, which cannot really stand, is this: that the natural world around us, just as given to us in outer experience, can be explained completely out of itself and there is no possibility of rising from this self-explanatory condition to some more satisfactory explanation. From a certain point of view I would be the first to emphasize that the outer sense world is explicable in itself. On one occasion I tried to make this clear, using an admittedly trivial comparison. I said: when someone examines the mechanism of a clock, he has no need for explanation originating from the world outside the clock if his desire is only to understand the mechanism itself. The clock is from a certain point of view explicable in itself. But of course this does not prevent us from wishing for complete clarity from some other point of view, such as knowledge about the clockmaker and other such things. Naturally these other aspects are outside the mechanism of the clock. Some things cannot be learnt so quickly as is sometimes thought—and for this reason: if one wishes to judge the real inner nature of spiritual-scientific investigation, it is necessary to venture into specifics. One must be willing to observe the way this science actually obtains results originating in the super-sensible realm and applies them in the field of ordinary sensory observation. I would like to speak to you today an this very subject.

It must first become clear that real investigation in the field of spiritual science leads to a different kind of knowledge—I might also say a different condition of soul in relation to reality—than is normally present in everyday life, or in ordinary scientific life. The first level of this super-sensible knowledge I have named the imaginative level. Later I will describe the way in which this imaginative level of knowledge is reached through certain work performed in the soul. Today I would like to develop an understanding of what this imaginative level of cognition actually is. For this we must return to an earlier explanation of the nature of mathematical thinking.

I attempted to characterize the difference in consciousness between an absorption in something which the external sense world presents to us, which we then penetrate with our intellectual activity (and of course with feeling and will impulses also), and on the other hand the absorption in mathematical thought. We can see that what takes place in the soul in the observation of the sense world is—if expressed purely externally—a kind of interaction, an immediate interaction between the human being and some form or other of the outer world. Please take what I am saying quite literally. It is not my intention to put forward some hypothesis—to speak of some reality hidden behind the phenomena. For the moment I wish only to indicate what is there as content of our completely ordinary consciousness when we confront the world on this level of knowing. There would be absolutely no meaning to this ordinary type of knowledge if we did not assume an immediate relationship to some sort of external world.

In contrast to this, in mathematical thought, in the activity of pure mathematical thinking, things are different. The difference is there when we dwell in geometrical, arithmetical, or algebraic regions without any concern for external, concrete sense content. What we bring to inner clarity in this domain, whether it is in some elementary area such as the Pythagorean theorem or in some advanced theory of functions, is something that lives entirely within the creative activity of the soul. What is experienced is the continuity of the activity and the visualization of one's own activity.

This “high” mathematical thinking—if I may call it that—which takes place entirely within the soul, is then found in today's mathematically-oriented science being applied to the outer world. What had been a process of inner work experienced purely inwardly, is then applied to our outer sense world. This should indicate that our mathematics can be characterized as purely pictorial. One can say: what we experience mathematically has as such no content, it has none of the content that we observe in our natural surroundings. In this regard, mathematical thinking is devoid of content, it is mere image. Yesterday, when we spoke of the spatial dimensions, I showed how what mathematical thinking only makes images of, is actually real and full of content; but mathematical thinking itself is merely imagery. If this were not so, we could not apply it as we do today to natural science. If this thinking were not just something pictorial, some reality would have to merge into the act of cognition. And the fact that something real does not merge with the act of cognition becomes conscious experience for us if we really enact this act of cognition.

As we recognize the pictorial character of mathematical thought, we can realize that we experience these mathematical pictures vividly as a content of consciousness. In fact, we are able to experience this content so vividly just because we see that certain things are hidden there which we must assume to exist from the evidence of our senses, in contrast to what we experience as the mathematical thinking itself.

In mathematical thinking we are right inside what actually takes place; we can say that we are entirely bound up with what takes place. This, along with the pictorial character of mathematical activity, permits us to have a clear consciousness of what we are actually experiencing. That is why we really know that when we work in mathematics we are in a realm where certainties of knowledge hold sway. Someone may have noticed the difference in the experience one has studying external sense realities or if one is active in the field of pure mathematics.

Most important is the fact that in the process of mathematical thinking, one is assured of continually following everything one does with full, clear consciousness. I believe I am not exaggerating when I say that clarity of consciousness can be measured against mathematical thought, its highest standard. In fact, when we engage in mathematical thinking, there is no possibility to doubt that each single manipulation we perform is accompanied by our inner conscious activity—for each is inwardly visible. We have ourselves in complete control, so to speak, when we think mathematically.

And, dear friends, the condition of consciousness present in mathematical thinking is in fact what a person strives for who strives toward what I call imaginative knowledge. When we think mathematically, what is really the content of our soul? It is the numerical world, the spatial world, and so on. I will speak of this later. Thus we have in our soul the content of a particular field with a certain pictorial representation. To work in a similar condition of soul but toward another pictorial content, is what constitutes the development of imaginative cognition. And this brings me to the following.

When we apply mathematics to outer nature (at first we can hardly do otherwise if we are accustomed to this approach), we apply it to only one part of nature, which we call the mineral world. In the mineral world we are presented with something that in a certain way is fully suited to a pure mathematical approach. But the moment we rise from the merely mineral to the plant or other kingdoms of nature, then the mathematical approach to which we are accustomed is of no use to us. A person who strives to rise to the imaginative level of knowledge desires to gain something more in his soul life than geometrical constructs or numerical relationships. He would like to gain forms that will live in his soul in exactly the same way as these mathematical forms, but which go beyond the mathematical in their content. He would like to gain forms that he can apply in the same way to the plant kingdom as he applies purely mathematical forms to the mineral kingdom. I will speak later concerning exact methods which lead in the direction of imaginative forms. Our first concern must be that everything that leads to an imaginative level of knowledge shall take place in a condition of soul that is absolutely equivalent to mathematical cognition. Actually, the best preparation for the development of imaginative cognition is to have dealt as much as possible with mathematics—not so much in order to reach particular mathematical insights as to be able to experience clearly what the human soul does when it moves in the realm of mathematical structures. This activity of the human soul, this fully conscious activity, is now to be applied to another area. It is to be applied in such a way that out of our inner constructs—if I may use the expression in a wider sense—we form further constructs which enable us to penetrate plant life in the same way that we penetrate mineral nature, chemical-physical nature with mathematical constructs.

I must raise all this into particularly sharp relief because of the way the word “clairvoyance” is normally used, and the way this incorrect usage is applied to the supersensory vision exercised in spiritual science. Frequently, what can quite correctly be designated as clairvoyance is confused with phenomena that can arise in the human constitution when conscious functions are suppressed so that they fall below the level of everyday consciousness—as in hypnosis, under the influence of suggestive mental images, and so forth. This suppression of consciousness, this entering into a subconscious realm, has absolutely nothing to do with what is meant here by the attainment of imagination. For in the case of imagination we have an enhancement of consciousness, we go in exactly the opposite direction from what is often called clairvoyance when the term is used in a trivial sense. As it is commonly used, the word is not given its correct meaning (“clear vision,” or “seeing in the light”), but rather “a reduced vision” or “dim vision.” At the risk of being misunderstood, it would not be incorrect to describe the upward striving toward imaginative knowledge as a striving toward clairvoyance. From the few words I have said on this subject, the difference should be clear to you between “dim vision” and a truly “clear vision.”

Everything we encounter in a state of soul more or less inclined toward mediumship, shows us a reduction of consciousness. It may entail an artificial lowering of the consciousness, or it may be that the human being was somewhat feeble-minded in the first place, making his consciousness easily suppressible. In no case is it ever what you could compare to an inner state as luminous and clear as a mathematically-attuned state should be. What is widely called clairvoyance today—no doubt you have experienced this—has extremely little to do with a striving toward a mathematical clarity of soul. Quite the contrary, what is usually found is the desire to plunge as deeply as possible into the darkness of confusion. Imaginative vision is the opposite of this, as I will now describe to you.

To begin with, imaginative vision is something that can only be present in the soul after being developed. After all, a five-year-old child is not yet a mathematician; the mathematical pictorial capacity must first be developed. It is also not strange that a development of soul from a pre-mathematical capacity to a mathematical capacity can be continued further in a certain way. That is, what has already been brought to a certain clarity of inner experience in mathematical thought can be developed further. Now, however, we must ask ourselves if someone is correct who says, "Yes, but the relationship must be established to ordinary sense-perceptible observation." In one way he is quite correct, and it is important to pursue this relationship in a detailed way.

For this purpose let us consider once again what I called yesterday the nerve-sense system of the human being. The nerve-sense system is concentrated primarily in the head, as I said yesterday, but it extends throughout the human organism. This head organization can also be looked at in the following way. As our starting point let us take something that has proved difficult for modern science for a long time. I have dealt with this in my book Riddles of Philosophy, in the chapter entitled, "The World as Illusion." For the modern way of thinking, it is difficult to establish a proper relationship between the content of sensation itself and what is actually experienced by the human being in his pictorial representation of this content or in his feeling. Indeed, this difficulty has led some to say: What takes place in the world outside us cannot become the content of our consciousness. In fact, they say, the content of our consciousness is the reaction of the soul to the impressions of the outer world; the actual impressions are beyond the perceptible. The domain of the perceptible only consists of what is a reaction of the soul to the sense-world. For quite a while people imagined the situation in a rather crude way, saying—and many still say so even today: Outside in the world are vibrations from some kind of medium, extremely rapid vibrations, and these vibrations somehow make an impression on us. Our soul then reacts to this impression and we conjure up the whole world of color out of our soul, the whole world that can be called the visual realm. What to our consciousness seems spread out all around us—the entire world of color—is in fact only the reaction of the soul to what exists out there, completely in the realm of the unknowable, as some sort of vibrations of a medium that fills space. I offer this only as an example of how such things are pictured, and I would now like to describe what at first is intended as an alternative way of looking at the matter.

Let us return to what I spoke of yesterday as the total act of seeing. This may serve as a basis for regarding the same process in the other senses. Let us consider external sense perception: what does it represent for the human being? To make this clear let us think of the realm of the eye. If we consider the eye in a descriptive way, even though it must really be regarded as a living member of a living organism, we can note processes in it that can be followed in the same way as processes in the extemal mineral world. Even though the eye is something living, we can construct a model to show how light falls into it. Through the way the eye is formed, the effect is similar to when we let light pass through a small hole in a wall and then fall on a screen, producing a picture. In short, it is possible to apply to the eye the interpretation that we feel justified in applying to the external, mechanical, mineral world. This can be carried further into the human organism. In spite of differences in the various senses, the eye can be regarded as offering an example for a series of phenomena also occurring in the other senses. You see, what takes place with our model does in fact take place in the eye and thus in our whole organism. And the question is: can we learn what really takes place in our organism? If one insists on a purely external approach, one will say something like this: Well, some sort of unknown outer world exerts an impression on the eye. In the eye something or other happens; this in turn exerts an impression on the optic nerve, and so on up to the central nerve organs. Then, inexplicably, a reaction to all this comes about in the soul. Out of our soul we conjure up the whole world of color as a reaction to this impression.

There is no doubt that such an approach leads to an abyss. Indeed, it is already openly admitted by many scientists today that with such a method of investigation, in which we simply look externally—first, at what stands before the eye, then at the process in the eye, then at processes in the nerves and further back, even in the brain—we will never get beyond material processes. The point will never be found where some reaction of a soul nature to the external stimulus occurs. With this approach we never examine our actual experience of the outer world.

For the spiritual investigator who develops in himself what I call imaginative cognition, the whole problem is transformed. He reaches a point where, when he looks at the eye, he is no longer obliged to see merely an aspect of the physical-mineral world: he can apprehend something else in the eye through his faculty of imagination. In a mathematical way of thinking we permeate the outer physical-mineral world with geometrical and arithmetical pictures, and feel that what we have imagined comes to meet the outer processes. For one who has developed imaginative cognition, it is not only what he develops mathematically that he experiences coinciding with the process in the eye, but also the imaginative images developed in accordance with imaginative cognition coincide with it. In other words, with these imaginative pictures of the eye one has additional content, so that one knows that with the faculty of imagination a reality is grasped, just as in contemplating external nature a reality is grasped when working with mathematical thought.

So now let us understand this properly: in spiritual research, initially the same methods are applied in investigating the eye as are usually applied with the help of mathematics to the external investigation of nature. However, until we have developed imaginative cognition we do not really recognize—especially in regard to the eye—that we are in possession of a reality which is lacking when we confront only the external world. For someone who has advanced to imaginative cognition, outer physical matter is not altered from what it is for ordinary consciousness. Let us keep this firmly in mind. You may have developed imaginative cognition to the highest degree, but if you have developed it correctly and if you maintain the right condition of soul during an imagination, you will not be able to claim, when looking at a physical or chemical or purely mechanical process, that you see more than anyone else who is in full possession of his senses and normal understanding. If someone claims that he sees something different in the inorganic realm from one who has not developed higher vision, then he is on a deviant path of spiritual cognition. He may see all kinds of specters, but the spiritual entities of the world will not reveal their true form to him. On the other hand, the moment one undertakes in imagination to observe the human eye, one has exactly the same experience as one has in mathematical thought when applied to external nature. In other words, when we observe the living human eye with developed imagination, we find ourselves for the first time confronting a complete reality, for now we are not only able to extend our mathematical thought to the eye but we can also extend what we have apprehended in the imaginative realm,

What follows from this? I can construct a model of the process that happens in the eye exactly similar to the process that happens in the outer world. I know that it is quite possible to reproduce this process in a darkroom or something similar in the mineral, mechanical world. But I also know that this whole domain which I can reproduce physically contains something else, which, if I want to proceed in the same manner as with mathematics in the inorganic realm, I can penetrate only with imaginative cognition. What does that mean? There is something in the eye that is not present in inorganic nature, and that is only recognized as a reality when one becomes one with it in the same way that one becomes one with inorganic nature through a mathematical approach. When one achieves this, one has reached the human etheric body. Through imaginative activity one has grasped the etheric nature of the human being, in the same way that one grasps the external inorganic world through a mathematical approach.

Thus it is possible to indicate quite exactly what one does in order to discover the etheric within a sense organ through imagination. It is not true that the idea of an etheric body is arrived at in any kind of fantastic way. One arrives at this idea by first developing imagination and then—at first for oneself—demonstrating with a suitable object that the content of imaginative cognition can unite with its object in the same way that mathematical thought unites with its object.

What light does this throw on the human constitution? Something living in us, the human etheric body, is brought into view in such a way that it joins with what is observed as outer inorganic nature. And what we can assert for the eye holds true, if slightly altered, for the other senses as well. Thus we can say: when we consider one of our senses, what we have is primarily a kind of empty space in our organism (if I may express myself crudely). In the case of the eye, the “organism” is those parts of the brain and of the face that connect with the eye. The outer world has sent “gulfs” into the organism. As the ocean creates gulfs in the Land, so the outer world makes gulfs in our organism and in these gulfs simply continues its inorganic processes. We can reconstruct the inorganic processes that take place there. It is not only outside the eye that we find the inorganic and deal with it mathematically, but we can follow these processes right into the eye. Thus with the eye we can use the same approach as we do to the inorganic realm. What we apprehend through imagination, however, reaches the boundary of the eye and goes beyond it. (I will not speak of this today.) Thus outer nature, which streams in as into a gulf, comes together with a member of the human organism, which does not consist of flesh and blood but nonetheless belongs to the organism and can be known through imaginative cognition. In the eye and the other senses our etheric organization penetrates what streams into these gulfs from the outer world. There is actually an encounter between something of a higher, super-sensible nature—allow me to use this expression; I will explain it in due course—between what can be called our etheric organization and what comes into us from the outer world. We become one with the process in our eye, which we can reconstruct purely geometrically. In the realm of our senses we actually experience the inorganic within us.

This is the significant finding to which imaginative cognition brings us. It leads to the solution of a problem that is central for modern physiology and for what is called epistemology. It is central to such investigations because it discloses the fact that we possess an etheric organism, known only through imaginative cognition, that this organism unites with what is thrust into us by the outer world and completely penetrates it. We are now able to see the problem in a new light. Imagine that the human being could direct his etheric body through a photographic apparatus: he would regard what takes place in the photographic apparatus as connected with his own being. Similarly he regards what happens in the eye as connected with his own being.

The problems dealt with in anthroposophical spiritual science are truly not fanciful ones. They are precisely the problems over which one can inwardly bleed to death—if I may express it in such a way—when one has no choice but to accept what modern science is in a position to offer in this field. Whoever has gone through all that one can inwardly go through when in striving for the truth one acknowledges the illusionary development of the outer world; whoever has suffered the uncertainty that immediately arises when one wants to comprehend—solely from one's physical understanding—what takes place in the process of sense perception: only such a person will know how strong the forces are that draw one to strive toward a higher development of our faculties of knowledge.

I have spoken today of the first stage of imaginative cognition and described its similarity to, and some of its differences from, mathematical thinking. What we experience at this level influences our view of the boundaries of knowledge that are accepted by today's science. If we really approach existence and the world conscientiously as they pose their riddles for us; if we have recognized how helpless ordinary logic and ordinary mathematics are in the face of what is taking place in us at every moment when we are seeing, hearing, and so forth; if we see how helpless we are in our usual approach to knowledge in the face of what normally confronts us in our waking consciousness, then truly a deep longing can arise to widen and deepen our knowledge. A scientist in our modern culture would certainly not claim to be a researcher in some field other than his own; he accepts what a trained investigator in another field has to say to him. The same attitude might well prevail for a while—in a limited sense—toward the spiritual researcher.

But it must be repeated again and again: above all, the world does have a right to require the spiritual scientist to tell how he arrives at his results. And this can be shown in every detail. When I look back at the way I have tried to do this for more than twenty years—to report to the world in purely anthroposophical language—I think I am justified in saying the following: If I have still not succeeded in finding a response in the world to this anthroposophical spiritual science; if again and again it has been necessary to speak for those less capable of going into detail because they are not scientifically trained; and if it has not been possible to any great extent to speak for the scientifically trained: then this, as experience has shown, is really due to the scientific schooling. Until now, the scientific community has shown small desire to hear what the spiritual investigator has to say about his methods. Let us hope that this will change in the future. For without a doubt, it is necessary that we progress through the use of deeper forces than those which have shown so clearly that they are of no value. In the last analysis it is those very forces that have led us into a cultural decline. We will speak further about this tomorrow.

Yesterday I tried to show how, by developing the ability to form imaginative vision, it is possible to gain a different kind of insight into human sense perception than can be gained when we approach it with the logic of the mind. I emphasized especially that this imaginative picturing that lives in the soul—as I said, I will describe its development in due course—has to be built up the way mathematical imagery is built up, the way mathematical constructs are developed, analyzed, and so on.

From this, the rest of what I said will also be clear: how we apply the results of our inner mathematical activity to the outer mineral-physical realm; and how in a similar way we apply our imaginative activity to the human senses. In this way we may know what takes place in those "gulfs"—as I called them yesterday—which the physical sense world sends into the human organism. The fact is that with the development of such an imaginative faculty and of knowledge of the real nature of the senses—of what is mainly the head organization—we also gain something else. We become able, for example, to form mental pictures of the plant kingdom. I indicated this yesterday. When we use only spatial and algebraic mathematics to approach plant growth and plant formation, we do not find that this mathematical form of consciousness is able to penetrate into the plant kingdom as it can penetrate into the mineral kingdom.

When on the other hand we have developed imaginative cognition, at first just inwardly, then we become able to form mental images applicable to the plant kingdom just as we found it possible with the mineral kingdom.

At this point, however, something peculiar appears: we now approach the plant world in such a way that the individual plant appears to us as only part of a great whole. In this way, for the first time we have a clear picture of what the plant nature in the earthly world really is. The picture we receive allows us to see the entire plant kingdom of the earth forming a complete unity with the earth-world. This is given purely empirically to the imaginative view. Of course, with our physical make-up we cannot possibly hold more than part of the earth's plant life in our consciousness. We observe only the plant world of a particular territory. Even if we are botanists, our practical knowledge of the plant world will always remain incomplete in the face of the entire plant world of the earth. This we know by the most simple thought. We know we do not have a whole, we have only part of the whole, something that belongs together with the rest. The impression we have in looking at the partial plant world is very much like being confronted by someone who is completely hidden from view except for a single arm and hand. We know that what is before us is not a complete whole, but just part of a whole, and that this part can only exist by virtue of being connected with the whole. At the same time we arrive at a concept that is completely unlike that of the physicist, mineralogist, or geologist: we see that the forces in the plant world are just as integral a part of the earth as those in the geological realm. Not in the sense of a vague analogy but as a directly perceived truth, the earth becomes a kind of organic being for us—an organic being that has cast off the mineral kingdom in the course of its various stages of development, and has in turn differentiated the plant kingdom.

The thoughts I am developing here for you can, of course, be arrived at very easily by mere analogy, as we see happening in the case of Gustav Theodor Fechner. Such conclusions arrived at by analogy have no value for the spiritual science intended here—what we value is direct perception. For this reason it must always be emphasized that in order to speak of the earth as an organism, for example, one must first speak of imaginative mental pictures. For the earth as an integral being reveals itself only to the imaginative faculty, not to the logical intellect with its analogies.

There is something else that one acquires in this process, and I wish especially to mention it because it would be most useful to students as regards methodology. In present-day discussions on the subject of thinking and also on how we apprehend the world in general, there is a great lack of clarity. Let us take an example. A crystal is held up to view—a cubic salt crystal, for instance—with the idea of illustrating something or other: perhaps something about its relation to human knowledge, its position in nature as a whole, or something similar. Now it could happen that in the same way that the salt cube is used, a single rose is held up for illustration. The person who holds up the rose feels it is acceptable to ascribe objective life to the rose in the same way as to the salt cube. To someone who does not strive for just a kind of formal knowledge, but who aspires to an experience of reality, it is clear that there is a difference. It is clear that the salt cube has an existence within its own limits. The plucked rose, on the other hand, even on its stem is not living its life as a rose. For it cannot develop independently to the same degree (please note the word) as the salt does. It must develop on the rosebush. The whole bush belongs to the development of the rose; separated from the bush, the rose is not quite real. An isolated rose only appears to have life.

I say all this in an effort to be clear. In all observations that we make, we must take care not to theorize about the observations before we have grasped them in their totality. It is only to the entire rosebush that we can attribute an independent existence in the same sense as to the salt cube. When we rise to imaginative mental Images, we acquire the ability to experience reality in a certain completeness.Then what I have just said about the plant world can be accepted. We see it as a whole only if our consciousness is able to apprehend it as a whole, if we can regard everything confronting us separately—all the different families and species—as part of the entire plant organism which covers the earth, or better said, which grows out of the earth.

Thus through imaginative mental images one not only gains understanding of the sense world, one also has important inner experiences of knowledge. I would like to speak of these inner experiences of knowledge in purely empirical terms.

As human beings we are in a position to look back with our ordinary memory to what took place in our waking life, back to a certain year in our childhood; with our power of memory we can call up one or another event in pictorial form out of the stream of our experiences. Still, we are clearly aware that to do this we must exert a distinct effort to raise individual pictures out of the past stream of time. As this imaginative vision develops further, however, we arrive gradually at a point where time takes on the quality of space. This comes about very gradually. It should not be imagined that the results of something like imaginative vision come all at once. It is pointless to think that the acquisition of the imaginative method is easier than the methods employed in the clinic, the observatory, and so on. Both require years of work: one, mental work; the other, inner work in the soul. The result of this inner work is that the individual pictorial experiences join one another. At this point, time—which we usually experience as “running” when we look over the course of our experiences and draw up one or another memory experience—now time, at least to some extent, becomes spatial to us. All that we have lived through in life—almost from birth—comes together in a meaningful memory picture. Through this exertion of imaginative life, of “looking back,” of remembering back, individual moments appear before the soul. These moments are more than a mere remembering. We have a subjective experience of viewing our life lived here on earth. This, as I said, is a practical result of imaginative mental imaging.

What kind of inner experience arises parallel to this inner viewing, this panorama of our experiences? We are quite clear that the strength of our soul which brings these memory pictures to consciousness is related to our ordinary bright, clear power of understanding. It is not itself the power of understanding, but it is related to it.

One can say: What we have been striving to attain—that our consciousness will be illuminated by this imaginative cognition in all our activities as it is in mathematical activity—happens for us when we come to these memory pictures. We have images and we hold them as tightly as we hold the content of our intellect. Thereby we come to a definite kind of self-knowledge, a knowledge of how the power of understanding works. For we do not merely look back at our life: our life presents itself to us in mirror images. It shows itself in such a way that this comparison with a mirror really holds true. We can extend the comparison and speak of understanding reflected images in a mirror by applying optical laws. Similarly, when we come to inner imaginative perceptions, we can recognize the power of the soul that we usually think of as our mental capacity becoming enhanced, so that we experience our intellect creating not only abstract pictures but concrete pictures of our experiences.

At first a kind of subjective difficulty arises, but once we understand it we can proceed. We experience clarity as in mathematics when we experience these pictures. But the feeling of being free—not in a behavioral sense, but in one's intellectual activity—is not present in this kind of imagining. Please do not misunderstand me. The entire imaginative activity is just as voluntary as our ordinary intellectual activity. The difference is that in intellectual activity one always has a subjective experience (I say "experience" because it is more than a mere sensation), one is really in a realm of imagery, a realm that means nothing from the point of view of the outer world. We do not have this feeling in relation to the content of the imaginative world. We have the very definite experience that what we are producing in the form of imaginations is at the same time really there. We find ourselves living and weaving in a reality. To be sure, at first this is a reality which does not have an especially strong grip on us and yet we can really feel it.

What we can gather from this reality, what we become aware of as we think back from our life panorama to the inner activity that created it, acquaints us inwardly, "mathematically," with something that is similar to the formative force of the human being. Just as mathematical mental images match and explain outer physical-mineral reality, so this something coincides with what is contained in the human formative force or growth force. (It also coincides with the formative force of other living beings, but I will not speak of that now.) We begin to see a certain inner relation between something that lives purely in the soul—namely, imagination—and something that weaves through the human being as the force of growth, the force that makes a child grow into an adult, that makes limbs grow larger, that permeates the human being as an organizing power. In short, we experience what is really active in the growth principle of the human being. This insight appears first in one definite area: namely, the nerves. The life panorama and the experiences described in connection with it give us insight at first into the growth principle in the human nerve organism—that is, the creative principle which continues inward in the nerve-sense organism. We receive a mental picture of an imaginative kind that enables us to begin to understand what our sense organs actually represent. This also gives us the possibility of seeing the entire nervous system as a synthetic sense organ that is in the process of becoming, and as embracing the present sense organs. We learn to realize that at birth, though our sense organs are not fully mature, they are complete with regard to their inner forces; this may be evident from the way I spoke about the relation of imagination to the sense world. At the same time we can see that what lives in our nerve organism is permeated by the same force as are the sense organs, but that it is in the process of becoming. It is really one large sense organ in the process of becoming. This image comes to us as a real perception. The different senses as they open outward and continue inward in the nerve organism—during our whole life up to a certain age—are organized by the power we have come to know in imagination.

You see what we are striving to accomplish. We wish to make transparent the forces that work in the human being which would otherwise remain spiritually opaque. For what does the human being know of the way in which these forces are active within him? Something that cannot be mastered by ordinary knowledge, something that can be characterized as ordinarily opaque to the soul and spirit, now begins to be clear. One has the possibility, through a higher kind of qualitative mathematics—if I may use such a phrase—of penetrating the world of the senses and the world of our nerve organism. One might think that when we reach this point we would become arrogant or immodest, but just the contrary, we learn true modesty through knowledge of the human being. For what I have described to you in a very few words is really acquired over a long period of time. For one, the knowledge comes quickly; for another, much more slowly. And often someone who applies the methods of spiritual research with patient inner work is surprised by the extraordinary results. The results that such inner work brings to light, if they are properly described, can be grasped by a healthy human understanding. But to draw these results forth from the recesses of the soul requires persistent and energetic soul work. And what especially teaches us modesty is the recognition that after much hard work, the results of imaginative cognition acquaint us only with our nerve-sense organism. We can realize how shrouded in darkness is the rest of the human organism.

Then, however, to reach beyond mere self-knowledge regarding the nerve-sense system, we must attain a higher level of knowledge. (The word "higher" is of course just a term.) Above all I must emphasize (I will go into it in more detail later) that the attainment of imaginative knowledge is based on meditation—not a confused, but a clear methodically-exercised meditation (to repeat the phrase I used in my book Knowledge of the Higher Worlds and its Attainment), in which over and over again we set before our soul easily surveyable images. What is essential is that they shall be easy to view as a well-defined whole, not some vague memories, reminiscences or the like. Vague memories would lead us away from a clear mathematical type of experience. Easily pictured mental images are required, and preferably symbolic images, for these are most easily viewed as a whole. The important thing is what we experience in our soul through these images. We seek to bring them into clear consciousness in such a manner that they are like a clear memory image. Thus through voluntary activity mental images we have evoked are taken into our soul in the same way that we take memory images into the soul. In a way, we imitate what happens in our activity of remembering. In remembering, certain experiences are continually being made into pictures. Our aim is to get behind this activity of the human soul; how we do this, I will describe in due course. In our effort to get behind the way remembering takes place, we gain the ability to hold easily-surveyable images in our consciousness (just as we hold memory images) for a certain length of time. As we become used to this activity, we are able to extend the time from a few seconds to minutes. The particular images themselves are of no importance. What is important is that through the effort of holding these self-chosen images, we develop a certain inner power of soul. We can compare the development of the muscles of the arm through exertion to the way certain soul forces are strengthened when mental images (of the kind I have described) are repeatedly held in our consciousness by voluntary effort. The soul must really exert itself to bring this about, and it is this exertion of soul that is crucial. As we practice on the mental images we ourselves have made, something begins to appear in us that is the power of imagination. This power is developed similarly to the power of memory, but it is not to be confused with the power of memory. We will come to see that what we conceive of as imaginations (we have already partly described this) are in fact outer realities, and not just our own experiences as is the case with memory images. That is the basic difference between imaginations and memory images. Memory images reproduce our own experiences in pictorial form, while imaginations, although they arise in the same way as memory images, show through their content that they do not refer merely to our own experiences but can refer to phenomena in the world that are completely objective. So you see, through the further development of the memory capacity, we form the imaginative power of the soul.

And now, just as the power of remembering can be further developed, so it is also possible to develop another capacity. It will seem almost comical to you when I name it—but the further development of this capacity is more difficult than that of memory. In ordinary life there are certain powers by which we remember, but also by which we forget. It seems sometimes that we do not need to exert ourselves in order to forget. But the situation changes when we have developed the power of memory in meditation. For oddly enough, this power to hold onto certain imaginations brings it about that the imaginations want to remain in our consciousness. Once there, they are not so easily got rid of—they assert themselves. This fact is connected with what I said earlier, that in this situation we have to deal with actually dwelling in a reality. The reality makes itself felt; it asserts itself and wishes to remain. We succeeded in forming the power of imagination (in a manner modeled on mathematical thought); now through further exertion we must be able voluntarily to throw these imaginative pictures out of our consciousness. This capacity of the voluntarily developed "enhanced forgetting" must be especially cultivated.

In the forming of these inner cognitive powers—enhanced memory and enhanced forgetting—we must be careful to avoid causing actual harm to the soul. However, just to point out the dangers involved would be like forbidding certain experiments in a laboratory for the reason that something might explode someday. I myself once had a professor of chemistry at the university who had lost an eye while conducting an experiment. Happenings of this nature are of course not a valid reason for preventing the development of certain methods. I think I can correctly say that if all the precautionary measures are applied which I have described in my books regarding the inner development of soul forces, then dangers cannot arise for the soul life. To continue—if we do not develop the capacity to obliterate the imaginative pictures again, then there is a real danger that we could be tethered to what we have given rise to in our meditations. If this happened, we would not be able to go further. The development of enhanced forgetting is really necessary for the next stage.

There is a certain way in which we can help ourselves achieve this enhanced power of forgetting. Perhaps those who are involved in any of the present-day epistemological studies will find this discussion quite dilettante and I am fully aware of all the objections, but I am obliged to present the facts as they happen to be. So—to continue—one can gain help in enhancing the power of forgetting if we further develop, through self-discipline, a quality which appears in ordinary life as the ability to love. Naturally it can be said: love is not a cognitive power, it does not concern knowledge. Perhaps this is true today because of the way cognition is understood. But here it is not a matter of keeping the power of love just as it appears in ordinary life. Here the power to love is to be developed further through work an oneself. We can achieve this by keeping the following in mind.

Is it not so?—living our lives as human beings, we must admit that with each passing year we have actually become a slightly different person. When we compare ourselves at a certain age with what we were, say, ten years earlier—if we are honest—we are sure to find that certain things have changed in the course of time. The content of our soul life has changed—not just the particular form of our thoughts, feelings, or life of will, but the whole make-up of our soul life. We have become a different person “inside.” And if we search for the factors through which we have changed inwardly, we will find the following: We may notice first of all what has happened to our physical organism—for this is always changing. In the first half of life it changes progressively through growth; in the second half it is changing through regression. Then we must look at our outer experiences: what confronts us as our own mental world; all those things that leave pain, suffering, pleasure, and joy in the soul; the forces we have tried to develop in our will life. These are the things that make us a different person again and again in the course of life. If we want to be honest about what is really taking place, we have to say we are just swimming along in the current of life. But whoever wishes to become a spiritual scientist must take his development in hand through a certain self-discipline. He might, for instance, take a habit—little habits are sometimes of tremendous importance—and within a certain time transform it through conscious work. In this way we can transform ourselves in the course of our life. We are transformed through being in the current of life, as well as through the work we do on ourselves with full consciousness. Then when we observe our life panorama, we can see what has changed in our life as a result of this self-discipline. This works back in a remarkable way on our soul life. It does not have the effect of enhancing our egotism, rather it enhances our power to love. We become more and more able to embrace the outer world with love, to enter deeply into the outer world. Only someone who has made efforts in such self-discipline can judge what this means. If one has made such efforts, one can appreciate what it means to have the thoughts we form about some process or some thing accompanied by the results of such self-discipline. We enter with a much stronger personal involvement into whatever our thoughts penetrate. We even enter into the physical-mineral world with a certain power of love—that world which if approached only mathematically leaves us indifferent. We feel clearly the difference between penetrating the world with just our weak power of mental imaging, and penetrating it with a developed power of love.

You may take offense at what I am saying about the developed power of love: you may want to assert that the power of love has no place in a quest for knowledge of the outer world, that the only correct objective knowledge is that which is obtained by logical intellectual activity. Certainly there is need for a faculty that can penetrate the phenomena of the outer world by means of the bare sober intellect alone, excluding all other powers of the soul. But the outer world will not give us its all if we try to get it in this manner. The world will only give us its all if we approach it with a power of love that strengthens the mind's mental activity. After all, it is not a matter of commanding and expecting that nature will unveil herself to us through certain theories of knowledge. What is really important is to ask: How will nature reveal herself to us? How will she yield her secrets to us? Nature will reveal herself only if we permeate our mental powers with the forces of love.

Let me return to the enhancement of forgetting: with the power of love the exercises in forgetting can be practiced with greater force, and the results will be more sure, than without it. By practicing self-discipline, which gives us a greater capacity for love, we are able to experience an enhanced faculty of forgetting, just as surely a part of our volition as the enhanced faculty of remembering. We gain the ability to put something definite, something of positive soul content, in the place of what is normally the end of an experience. Normally when we forget something, this marks the end of some sequence of experiences. Thus in place of what would normally be nothing, we are able to put something positive. In the enhanced power of forgetting, we develop actively what otherwise runs its course passively.

When we have come this far, it is as if we had crossed an abyss within ourselves and reached a region of experience through which a new existence flows toward us. And it is really so. Up to this point we have had our imaginations. If in these imaginations we remain human beings equipped with a mathematical attitude of soul, and are not fools, we will see quite clearly that in this imaginative world we have pictures. The physiologists may argue whether or not what our senses give us are pictures or reality. (I have dealt with this question in my Riddles of Philosophy.) The fact is, we are well aware that these are pictures, pictures that point to a reality, but still they are just pictures. Indeed, to achieve a healthy experience in this region we must know that they are pictures—images—confronting us. However, at the moment when we experience something of the enhanced power of forgetting, these images fill with something coming from the other side of life, so to say. They fill with spiritual reality. And we go to meet this reality. We begin, as it were, to have perceptions of the other side of life. Just as through our senses we perceive one side of life, the physical-sensible side, so we learn to look toward the other side and become aware of a spiritual reality flowing into the images of imaginative life. This flowing of spiritual reality into the depth of our soul this is what in my book Knowledge of the Higher Worlds and its Attainment I have called “inspiration.” Please do not take exception to the name—just listen to how the word is being used. Do not try to remember instances where you have met the word before. We have to find words for what we want to say, and often we must use words that already have older meanings. So for the phenomenon just described, I have chosen the word inspiration.

Through developing inspiration we finally gain insight into the human rhythmic system, which is bound up in a certain way with the realm of feeling. This leads us to something I must emphasize: the method leading to inspiration which I have just described can actually be followed only by modern man. In earlier periods of human evolution, this faculty was developed more instinctively—for example, in the Indian yoga system. This, however, is not renewable in our age. It goes against the stream of history. And in the spiritual-scientific sense, one could be called a dilettante if one wanted to renew the yoga system in these modern times. Yoga set into motion certain human forces that were appropriate only for an earlier stage of human evolution. It had to do with the development of certain rhythmic processes, with conscious respiratory processes. By breathing in a certain manner, the yogi worked to develop in a physical way what modern man must develop in a soul-spiritual way—as I have described. Nevertheless, there is something similar in the instinctive inspiration we find running through the Vedanta philosophy and what we achieve through fully conscious inspiration. The way we choose to achieve this, leads us through what I have described.

As modern human beings, we approach this from above downwards, so to say. Purely through soul-spiritual exercises we work to develop the power within us that then finds its way in to the rhythmic system as inspiration. The Indian worked to find his way into the rhythmic system directly through yoga breathing. He took the physical organism as his starting-point; we take the soul-spiritual being as ours. Both ways aim to affect the human being in his middle system, the rhythmic system. We shall see how what we are given in imaginative cognition (which combines the sense system and nervous system) is in fact enhanced when we penetrate the rhythmic system through inspiration. We shall also see how the ancient, more childlike, instinctive forms of higher knowledge (for example, yoga) come to new life in the present day in the consciously free human being.

Next time I will speak further on the relation of the earlier yoga development of the rhythmic system and the modern approach which leads through inner soul-spiritual work to inspiration.

I have tried to show how it is possible to rise to supersensory modes of cognition, how through them we gain access to new realms of experience—realms that are completely accessible only to a super-sensory approach. I spoke of the development of imaginative cognition—how by means of it we can understand what takes place in the activity of the human senses, and also understand the nature of the plant world. We learn these things through imaginative cognition as we understand the physical-mineral phenomena of the world through a mathematical approach. Further, I pointed out that through a continuation of these exercises we can attain to a higher form of knowledge—namely, inspired cognition. This opens the way to certain realms of experience through which we can begin to understand what I have called the human rhythmic system.

I would like to look at the whole problem once again from a certain angle. When one tries to gain a real understanding of what is included in the sphere of human rhythmic activity, one sees—if one is honest—that the processes taking place here elude the kind of comprehension by which physical processes are understood through mathematics. Nor will one find that they can be comprehended through what I have called imaginative cognition. Everything that has to do with the senses and which is developed in the nervous system in the course of life as I have described—thus also providing a basis for the experience of the life panorama when imaginative cognition has been developed: all of this only clarifies the term, nerve-sense organization.

In fact, our sensory organization can only be fully understood when this capacity of imaginative cognition has been acquired by us. Even external natural science has noticed that it is not really possible to understand a particular human sense when it is explained in terms of the general human organization. You will find, if you study what individual scientists have to say in this regard, that the facts themselves—in external phylogeny, or embryology, or ontology—simply point to the necessity of accepting the eye, for instance, as being formed from without. The structure of the eye cannot be understood in terms of the rest of the human organism—as, for example, the structure of the liver or the stomach. It can only be understood as brought about through outer influences, through action from without. But how do we grasp this process of "in-forming from without" in the human organism? Only imaginative cognition makes it comprehensible to us, as a mathematical approach makes physical phenomena comprehensible.

From all this you may now begin to see why external science gives us essentially a deficient physiology of the senses. Before I myself was able through imaginative cognition to develop a physiology of the senses, something in me always resisted any wish to subject the realm of the human senses to the sort of measures applied by conventional physiology and psychology. I always found that what they offered to explain the senses was incomplete for the sense of hearing or sight, for example. Particularly the psychological explanations are deficient in this respect. Basically they always start by asking: how are the human senses constructed in general? Then, having given a general characterization, they proceed to specialize for the various senses. But it never occurs to them that their customary descriptions, particularly in the psychology text books, are really only applicable to the sense of touch. There is always something in their theories that does not fit when one tries to apply them unchanged to any other sense. We can understand this when we remember that the physiologies and psychologies use exclusively the ordinary logic of the intellect to put together the facts which external research presents. However, for someone who is examining the question carefully, it is simply impossible to do justice to the sensory phenomena by only the putting together of physical facts. When we apprehend each separate sense with imaginative cognition (when doing this, I was forced to extend the number of senses to twelve) and not just intellectually, we arrive at their true individual forms. We see that each separate sense is built into the human being from certain entities, certain qualities of the outer world. This reveals again—to one who will see it—the bridge that is thrown across from what I have called clairvoyant research to what is given by empirical observation.

Certainly it can be said that a person endowed with healthy human understanding may still have no inclination to give up a certain point of view, and therefore may find no reason to be interested in clairvoyant research. But there really is an objection to this. When we subject the facts to a thorough analysis, there is a point at which we reach an impasse when we apply only sense observation and the ordinary logic of the intellect. We simply cannot clear up the problems. They leave an unsolved remainder. For this reason we must develop our logical thinking further to imaginative perception. Part of what imaginative perception discloses to us is the individual forms of the various human senses, as well as the gradual formation of the human nervous system.

There is something to add to this—I will explain with a short story. Once I was at a meeting of the society that at that time called itself the Giordano Bruno Association. The first to speak at the meeting was a stalwart materialist who elaborated on the physiology of the brain; by this he believed he had given sufficient explanation for the association of mental images and in fact for everything that takes place in mental life. He made drawings for the different parts of the brain and showed how they are assigned different functions—one to seeing, another to hearing, and so on. Then he tried to show how it might be possible, following the neurologist Meynert, to see the connecting paths as physical formations responsible for connecting the individual sensory impressions, the individual mental pictures, and so on. Whoever wishes to learn about this can read about these extremely interesting investigations by the important neurologist Meynert, for they are still significant even for the present day. Well, after this materialistically tinged but still quite ingenious explanation, in which the brain was presented not as the mediator but as the producer of mental life, another man stepped forward, just as stalwart an Herbartian as the man before him was a materialist. This man said the following:

This is in fact a characteristic experience in the field of knowledge, because when one tries to illustrate mental pictures symbolically through diagrams, as Herbart did (it can also be done in other ways), one actually arrives at something very similar to what one gets when one sketches processes and parts of the brain. How does this happen? This is something that becomes clear only to imaginative cognition, when we see in the retrospective life panorama how the independence of the soul life develops. We see how the etheric body actually organizes—and, in fact, has already at birth to some extent organized—the brain. It permeates the brain in its organization. Then we are not surprised to find out that the brain grows similar in formation to the entity which permeates it. But we do not come to real insight in the matter until we are able to perceive that there is an activity of soul working on the organization of the brain. This is similar to when someone paints a picture and what he paints resembles what he is copying. It is similar because the image he has in his mind works on in his painting and brings about the similarity. In the same way, what is found in the brain—actually in the entire nervous system—as the consequence of a forming activity on the part of the soul, will be similar to the soul's forming activity, or to the soul content itself. But if we wish to understand the activity that works itself into the nervous system, we must simply say: in its origin and development, the whole nervous system is an expression of a reality that may only be viewed imaginatively.

The brain and the entire nervous system are, of course, external physical formations. But we do not really grasp them unless we comprehend them as imaginations that have become physical. Thus what the spiritual investigator generally calls imagination is not, as one might suppose, absent from the phenomenal world—it is indeed present, but in its physical image. This fact occasionally makes itself manifest in a striking way, as in the case of those two men, the one a physiologist, the other a philosopher, who portrayed two different things in the same way.

But this has still another aspect. I have already referred to the research of the psychiatrist, physiologist, and psychologist Theodor Ziehen. Theodor Ziehen undertook to explain mental life in such a way that he replaced it by brain activity in every particular. His explanation is essentially the following: he contemplates mental life; he then considers the brain and nervous system anatomically and physiologically (to the extent that present empirical research permits) and shows which processes, in his opinion, are present in the brain for a particular mental activity (including memory). I have pointed out, however, that his explanation—which is truly valuable for the study of mental life and brain activity—is forced to come to a standstill before our life of feeling and our life of will. You will find this in Ziehen's Physiologische Psychologie (Physiological Psychology). There is, however, a shortcoming in this psychology. Although he makes everything so enticing by explaining mental life in terms of processes in the brain, in the end he does not completely account for such things as the forms that are present in the brain. To do this it is necessary to bring in an artistic principle; and this again is nothing else than the outward expression of imaginative cognition. Were Ziehen to consider this, his explanation of mental life through brain processes would not be fully satisfying to him either. When he wants to move on to the realm of feeling, he finds himself completely at sea. He is not able to account for feelings at all. So he tacks a “feeling coloration” onto the mental images. This is nothing but a word; when one cannot go any further, one makes do with a word. He says: Yes, in certain cases we are dealing not just with mental images, but with feeling-tinged mental images. He comes to this because he is unable to fit feeling into the brain, where it might enter into mental life. Also he does not find an organic basis for feeling that would permit him to make a link to mental life similar to that of the brain and nerves.

In the case of brain and nerve activity it is easier because researchers like Theodor Ziehen are—most of them—extremely clever when it comes to an intellectual or mathematical understanding of the entire natural realm. I mean that exactly—without irony. In science these days an extraordinary amount of intellectual acumen has been applied in this direction. If you should decide to become better acquainted with the whole anthroposophical movement, it would become clear to you that in no way do I favor dilettante talk about abstruse nebulous anthroposophical conceptions while arrogantly disputing what present-day science presents, or that I approve when a speaker does not know present-day science well enough to acknowledge it in all its proper significance. I hold firmly to the standpoint that one can pass judgment on present-day science from an anthroposophical point of view only if one is really familiar with this science. I have had to suffer continually from the actions of anthroposophists who, without having an idea of the importance and task of contemporary science, talk loosely about it. They think a few fine anthroposophical phrases they have learned entitle them to pass judgment on what has been achieved through years of painstaking, conscientious, and methodical work. This stage we must of course leave behind us.

Now, to continue, what actually happens is this: one arrives at the point of finding the relation between mental life and nerve-sense activity. But something is always left unexplained. Something always eludes one's attention. One swims slowly from the point of view of rational, logical, mathematical construction into a realm where things become unclear. One examines the senses and sees their continuation in the nervous system—and that is where one should take the next step into imaginative thought. But to some degree every human being has a dim feeling of the transformation of well-defined mathematically constructible figures into something that cannot be grasped mathematically and yet manifests itself clearly in the brain and nervous system. As a result of this feeling it is said that someday we shall also succeed in penetrating those parts of sensory life and nerve life that evade direct, purely mathematical construction. In other words, something is put off as a future ideal that is in fact attainable now if one will simply admit that it is not possible to penetrate the realm of the senses and nerves merely by rational cognition. This must be led over to something pictorial, something evoked just as consciously as a mathematical figure, but going beyond the mathematical. I mean, of course, imagination.

Perhaps for some of you it would be helpful to make an exact picture of how ordinary analytic geometry relates to so-called synthetic or projective geometry. I would like to say a few words on this subject. In analytic geometry we discuss some equation of the kind y=ƒ(x). If we stay, for instance, in the x-y coordinate system, then we say that for every x there is a y, and we look for the points of the y-coordinate, which are the results of the equation. What is actually occurring here? Here we have to say that in the way we manipulate the equation, we always have our eye on something that lies outside of what we ultimately seek, because what we are really looking for is the curve. But the curve is not contained in the equation—only the possible x and y values are contained in the equation. When we proceed in this manner, we are actually working outside the curve; and what we get as values of the y-coordinate in relation to the x-coordinate we consider as points belonging to the curve. With our analytic equation, we never really enter the curve itself, its real geometric form. This fact has significant implication as regards human knowledge.

When we do analytic geometry, we perform operations which we subsequently look for spatially; but in all our figuring we actually remain outside of a direct contemplation of geometrical forms. It is important to grasp this because when we consider projective geometry, we arrive at a very different picture of what we are doing. Here, as most of you know, we don't calculate, we really only deal with the intersection of lines and the projection of forms. In this manner we get away from merely calculating around the geometrical forms, and we enter—at least to some degree—the geometrical forms themselves. This becomes evident, for example, when you see how projective geometry goes about proving that a straight line does not have two, but only one point at infinity. If we set off in a straight line in front of us, we will come back from behind us (this is easily understood from a geometrical point of view), and we can show that we travel through exactly one point at infinity on this line. Similarly, a plane has only one line at infinity, and the whole of three-dimensional space has only one plane at infinity.

These ideas—which I am only mentioning here—cannot be arrived at by analytical means. It is not possible. If we already have projective-geometric ideas, we may imagine we can do it; but we cannot really. However, projective geometry does show us that we can enter into the geometrical forms, which is not possible for analytic geometry. With projective geometry it is really possible. When we move out of mere analytic geometry into projective geometry, we get a sense of how the curve contains in itself the elements of bending, or rounding, which analytic geometry describes only externally. Thus we penetrate from the environment of the line, the surroundings of the spatial form, into its inner configuration. This gives us the possibility of taking a first step along the way from purely mathematical thinking—of which analytic geometry is the prime representative—to imagination. To be sure, with projective geometry, we do not actually have imagination yet, but we approach it. When we go through the processes inwardly, it is a tremendously important experience—an experience which can actually be decisive in leading us to an acknowledgment of the imaginative element. Also, this experience leads us to affirm the path of spiritual research, inasmuch as we can form a real mental picture of what the imaginative element is. When I was reading the memoirs of Moriz Benedict—a good natural scientist and physician of our day—I found them in general to be unpleasant, blase and arrogant, but at one point I felt real sympathy. There he says something which seems to me quite correct; he finds that medical doctors lack the preparation that the study of mathematics can give. Of course, it would be a very good thing indeed if physicians had more mathematical preparation, but in this regard we must just register the shortcomings in contemporary training. From my point of view, however, while reading his memoirs, I could not help feeling: No matter how good their mathematical conceptions, doctors would still not be in a position with them to properly account for the kinds of forms that exist, for example, in the sense and nervous systems. There one can only succeed by transforming mathematical knowledge and advancing to imaginative knowledge. Only then does the specific nerve or sense structure reveal itself to us in a similar manner as a physical-mineral structure reveals itself to the mathematical representation.

Matters such as these allow you to see how, in every area, the doors stand open for contemporary science to enter into what spiritual research wishes to give. In the coming days, if we manage to enter, even a little bit, into medical-therapeutic aspects, you will see how wide open the doors really are for spiritual research to enter and throw light on all that cannot be revealed through the usual methods of investigation. Let us now suppose we proceed on this path, but we do not wish to proceed any further than imagination, which I will describe further tomorrow. Let us suppose we do not wish to move forward to inspiration. We will then not have the slightest possibility of even recognizing something in the human organism as the approximate image or bodily realization of a soul-spiritual nature—so that two men with completely opposite ways of thinking will draw these structures similarly. Only through inspired cognition will we have our first opportunity to become aware in the human being of the rhythmic system, encompassing primarily the processes of respiration and blood circulation. Only at this point are we able to tolerate—if I may express it thus—the outer lack of similarity between the physical structures and the soul-spiritual. The life of feeling does in fact belong directly to the rhythmic system in the same way as the life of mental representation belongs to the nervous system. The nerve-sense system, however, is a kind of external physical image of mental life, while the rhythmic system—what is accessible to external sense-empirical investigation—shows hardly any resemblance to what takes place in the soul as feeling. Just because this is so, external research never discovers that this similarity exists; it only reveals itself when we come to another kind of cognition than that of imagination. With this step, as I indicated yesterday, we approach a path of knowledge which was followed in a more primitive, or instinctive way in the practice of yoga in ancient India.

Those who practiced the yoga system, (as already pointed out, to try to renew this yoga would be wrong, because it is not suited to the changed constitution of modern man) tried for short periods of time to replace the ordinary, normal, but largely unconscious respiratory process with a more consciously regulated respiration. They inhaled differently from the way we ordinarily do in our normal, unconscious breathing. The breath was then held, to bring to awareness of how long it was held and then it was exhaled in a particular manner. At best, such a method of breathing could give additional support to present spiritual life. In India, however, this process was done by those who wanted to reach the awe-inspiring Vedanta philosophy or the philosophical foundation of the Vedas. This is no longer possible todäy. In fact, it would contradict what the human constitution actually is today. Nevertheless, much can be learned from this way in which a rhythmic process is willfully made conscious by an alteration of normal breathing. What otherwise takes place quite naturally in the course of living is lifted into the domain of conscious will. Thus respiration—all that takes place in the human life-process during breathing—is carried out consciously. Because it is carried out consciously, the entire content of human consciousness changes. In breathing we draw what is in the environment into our own organization. In the kind of consciously structured breathing process I have described, something of a soul-spiritual nature is also drawn into the human organization.

Now consider the following. When we contemplate the human organization as a whole, if we are not satisfied with abstraction but want to move on to reality, then we cannot really say: We are only what is within our skin. We have within us the respiratory process, it may be about to begin, or it may be proceeding with the transformation of oxygen and so on. But what is in us now was outside us before and it belonged to the world. And, what is in us now, when exhaled, will again belong to the world. As soon as we approach the rhythmic system, we do not find ourselves individualized organically in the same way as we picture ourself when we consider only what is not of an aeriform nature within our skin. When the human being becomes fully aware that he exchanges his aeriform organization quite rapidly—now the air is without, now it is within—he cannot help but appear to himself as a self-conscious finger would appear to itself, as a part of our organism. The finger could not say: I am independent—it could only feel part of the whole human organism. As a breathing organism, we must feel the same way. We are members of our cosmic surroundings precisely by virtue of the respiratory organism and the only reason we do not pay attention to the fact that we are a part of it is because we perform this rhythmical organizing activity naturally, almost unconsciously.

When, on the other hand, this fact is raised to consciousness through the yoga process, one notices that, in fact, it is not just material air that is inhaled and combined with one's self, but along with the air something of a soul-spiritual nature is inhaled and assimilated. When exhaling, something of a soul-spiritual nature is returned to the outer world. One comes to know not only one's material connection with the cosmic surroundings; one also comes to know one's soul-spiritual connection with the cosmic surroundings. The entire rhythmic process is metamorphosed so that a soul-spiritual element can incorporate itself.

Just as the cosmic environment integrates itself into the process of mental representation, so into the breathing process (which otherwise is an inner physical-organic process), something of a soul-spiritual nature is incorporated. In this way the transformed yoga breathing becomes a more pantheistically-tinged way of knowing, in which the separate entities are less individualized. Thus in the Indian, a different consciousness takes shape from the ordinary one. He experiences himself in another state of consciousness in which he is, as it were, surrendered to the world. At the same time, this has the effect of leading him into an objective relationship with his accustomed mental world as he moves down, as it were, with his consciousness into the respiratory-rhythmic system. Before this, his conscious life was in the nerve-sense system, in the form of the sum total of his mentally-viewed images. Now he experiences himself, precisely what he experiences he doesn't know, but as soon as it becomes objective it comes into inner view, and through this he learns to recognize the true nature of his accustomed image world. He now experiences himself one level lower, so to speak, in the rhythmic system. When we become acquainted with this inner process of experience, then we can understand in a new way what is breathing through the Vedas. The Vedanta philosophy is not only something that has taken a different form than it takes in the west; it grows out of something immediately experienced—from the experience that is simply given in a consciousness displaced into the breathing process.

There is still a further experience when we descend into this respiratory process. Before I mention it, however, I would like to review more precisely what I indicated the day before yesterday. I said that the yoga-process is not for us any more, and the human constitution has advanced since then. In our age we are no longer capable of entering into the yoga process, simply because our intellectual organization is so strong today; because our mental images are so inwardly “hardened”—this is just meant figuratively—that we would send much more power into the respiratory system than did the Indian with his “softer” mental life. Today the human being would be inwardly numbed or he would disturb his rhythmic system in some other way if he proceeded as the Indian did in the yoga process. As I have pointed out—and as I will describe later in greater detail, we are in a position to advance from a further development of the memory faculty to a development of the process of forgetting. By entering into the depth of the forgetting process, we take hold of respiration from above, and can leave it as it is. We do not need to change it. The right way for modern man is to let it be. With an artificially enhanced forgetting, we shine down, as it were, into the respiratory system. We transfer our consciousness into this region. But now it is possible to do this in a more fully conscious way, with greater penetration of the will than the ancient Indian could use.

In this way, we now have the possibility to recognize the rhythmic system in its association with human feeling life. When we gain the ability to retain a mental imaging capacity in this region, when it becomes possible for us to have inspired mental images, we no longer feel the need for the sense-perceptible structure to be similar to the soul structure—as is the case where the brain structure is similar to the connections between mental images. In fact, the external, sensory structure can be so different from the related soul element that it completely escapes the notice of conventional physiology, as in Theodor Ziehen's case. Looking at the world in a more spiritual way, looking at it purely spiritually, we find that in fact it is the feeling life that enables us to penetrate consciously into the rhythmic system. Thus we begin to see why in earlier times (the Indians, after all, are simply representative of what came from the earlier stages of human development), when human beings strove to go beyond an ordinary everyday understanding of the world, their path to knowledge led them down into the life of feeling. Cognition remained an activity of mental picturing, but it penetrated into the feeling life, it was suffused with feeling. Modern research only speaks of a coloration of feeling. What the yogi of old, and human beings in general in older cultures experienced, was a sinking down into the realm of feeling. Yet this was without the vagueness typical of this realm. The full clarity of conscious mental life remained, and yet not only was feeling not extinguished, but it appeared more intense than in ordinary everyday life, thereby suffusing everything that normally had a sober, prosaic character. At the same time the mental images, in going through a metamorphosis, a deepening, took on other forms. These transformed mental images were so suffused with feeling that the will was directly stimulated. What this human being of earlier times then did was something that we do today in a more abstract way, when we take something we are carrying in our soul and use it as a subject for drawing or painting. What was experienced in yoga in this way was so intense that the mere drawing or painting of it would not have been enough. It was an entirely natural step to transform it into an external symbolism embodied in external objects.

Here you have the psychological origin of all that appeared in the form of rituals in ancient culture. To find the motive for these rituals, one must look at their inner nature. It was not out of some form of childishness, but out of his way of experiencing knowledge that the human being of old came to perform ritualistic ceremonies and to regard them as something real. For he knew that what he molded into his ritual was something inward put into outer form, something rooted in a cognition from which he was not estranged, but which connected him with reality. What he impressed into his ritual was what the world had first impressed into him. When he had reached this state of knowledge, he said to himself: Just as the physical breath from the surrounding cosmos lives within me, now the spiritual essence of the world lives in my transformed consciousness. And when I in turn make an outer structure, when I build into the objects and rituals what first formed itself in me out of the spiritual cosmos, I am performing an act that has a direct connection with the spiritual content of the cosmos.

Thus for the human being of an ancient culture, the outward cultic objects stood before him symbolically in such a way that through them he felt again the original connection with the spiritual entities he had first experienced through ordinary knowledge. He knew that in the elements of the ritual something is concentrated in an outer visible form. This something does not exhaust itself in the outward expression I see before me, for the soul-spiritual powers that live in the cosmos are alive in the ritual while it takes place.

What I am relating to you is what went on in the souls of those human beings who as a result of their inner experiences gave form to the rituals. One reaches a psychological understanding of such rituals when one is willing to accept the idea of inspired cognition. These things simply cannot be explained in the usual external way. One must enter deeply into man's being and must consider how the various functions of the entire human race developed in sequence—how, for instance, in a certain epoch particular rituals developed. The religious ceremonies of today are actually rernnants of something that took form in ancient times and then stood still afterward. This is why it is becoming so difficult for a person today to understand the reason for the religious ritual, for he feels it is no longer a justifiable way of relating to the outer world.

Furthermore, we can see another aspect of how the soul works in the course of mankind's development. Deep knowledge, as I have described, underlies the creation of a ritual or the carrying out of a ritual. But humanity has developed further and another factor has entered in, which still lives more or less in the unconscious. What shows itself most clearly when we reach imaginative cognition is that the nervous system is formed out of our soul-spiritual powers. This too has developed in the course of human history. Particularly since the middle of the fifteenth century, humanity in all its various groups has developed in such a way that this instinctive incorporation of the soul-spiritual powers into the nervous system has become stronger than it was formerly. We simply have a stronger intellect today. This is obvious when one studies Plato and Aristotle. Our intellect is organized differently. In my Riddles of Philosophy I have demonstrated this from the history of philosophy itself. Our intellectual functioning is different. We simply overwork that element of the soul which has grown stronger in the course of human development. And this element which has grown stronger has also become more independent. The increasing independence of our intellect from the nervous system simply has not reached the attention of the philosophers—or of mankind in general. Because the human being has grown stronger on the inside, so to say—because he has penetrated his nervous system with a stronger organizing power from the soul-spiritual realm, he feels the need to make use of this intensified intellectual activity in the outer world. In ancient times, knowledge attained inwardly was used in the creation and the exercise of rituals; there was a striving to carry over what had been originally experienced inwardly as knowledge into what was performed outwardly. In the same way today, the longing arises to satisfy our stronger, more independent intellect in the outer world. The intellect wants a counterpart that corresponds to the ritual.

What is the result of such a wish? Please accept the paradox, for psychologically it is so: Where inner experience is expelled, as it were; where the intellect alone wishes to arrange a procedure so that it can live in the object just as cosmic life was once intended to live in the “object” of the ritual: what results from this is the scientific device, serving the experiment. Experiment is the way the modern human being satisfies his now stronger intellect. Thereby he lives of the opposite pole from the time when man satisfied his relation to the cosmos through the cultic object and ritual ceremony. These are the two opposite poles. In an ancient culture of instinctive clairvoyance, the impulse was to give outer presence to inner cosmic experience in what could be called ritualistic exercise. Our intensified modern intellect, on the other hand, is such that it wishes to externalize itself in controlled movements that are devoid of all inwardness, in which nothing subjective lives—and yet the experiment is controlled just precisely through the subjective attainments of our intellect. It may seem strange to you that the same underlying impulse gives rise on the one hand to the ritual, and on the other to the experiment, but one can understand these polarities if one considers the human being as a whole.

Starting with this as a foundation, we will continue our discussion tomorrow.

In the lectures so far, I have spoken of the capacities for supersensory knowledge and I have named them Imagination and Inspiration. Today I would like to say something about acquiring these capacities. At the moment I can only mention a few details. In my book Knowledge of the Higher Worlds and Its Attainment, you will find this presented in greater depth. Today, however, I would point out what is important in the context I have chosen for the present lecture. I have indicated that what I call Imagination with regard to knowledge of the world is attained through a development modeled on the memory process, only on another level. The importance of the memory process is that it retains in picture form what the human being encounters in outer experience.

Our first task will be to understand certain characteristics of the ordinary memory process, and then we must distill out what can be called pure memory in the true sense, also in ordinary life. One of the peculiarities of memory is that it tends to alter to a certain degree what has been experienced. Perhaps it is unnecessary to go into detail here, since most of you will be quite familiar with the fact that at times you can despair when you are relating something, and you hear from your own telling what has become of your experience by its passing through your memory. Even in ordinary life a certain self-education is necessary if we wish to come closer to pure memory, to the capacity to have these pictures ready at hand so that they faithfully render our experience. We can distinguish what happens with memory. On the one hand there is an activity of fantasy, quite justified, that goes on in an artistic direction. On the other hand there is a falsification of our experience. It should suffice for the moment to point out the difference between the fantasy tendency and the falsifying tendency, and that we must be able to experience this to maintain a healthy soul life. Certainly we must be aware of how memory is transformed by our fantasy, and how, when it is not subjected to such arbitrary action, when it is allowed to proceed according to a kind of natural similarity in the soul, it becomes increasingly faithful and true. In any case, both from the good tendency to artistic fantasy, as well as from the forces active in falsifying the memories—when we study it psychologically, we can recognize what is alive in the memory forces.

And out of these forces, something can take form that is no longer just memory. For example, one can point to certain mystical teachings that are in fact essentially falsified memory images; and yet we can profit from studying 'such images that have taken the form of earnest mystical experience. What concerns us at this moment, however, is what I have already indicated, that we can attain a power of the soul which is alive in the memory which can be metamorphosed into something else. This must happen in such a way that the original power of memory is led in the direction of inner faithfulness and truth, and not toward falsification. As I have said, when we repeatedly evoke easily surveyable mental images, which we intentionally combine out of their separate elements and then view as a whole, just as easily as the mathematical images: when we call up such images, hold them in our consciousness and dwell upon them, not so that we are fascinated by them, but so that at each moment we continue to hold them through an inner act of will—then gradually we succeed in transforming the memory process into something different, something of which we were previously unaware. The details are contained in the book I named, and also in Occult Science, an Outline.

If we continue long enough with such exercises (how long depends on the individual) and if we are in a position to expend sufficient soul energy on them, then we come to a point where we simply begin to experience pictures. The form of these pictures in the life of the soul is like that of memories. Gradually we win the capacity to live in such imaginations of our own making, although in their content they are not of our making. The exercise of this capacity results in imaginations rising up in the soul, and if we maintain a “mathematical” attitude of soul, we can make sure at any time whether we are being fooled by a suggestion or auto-suggestion, or are really living in that attitude of soul voluntarily. We begin to have mental images with the characteristic form of memory pictures but with a greater degree of intensity. Let me emphasize: at first these imaginations have the character of memory pictures. Only through inspiration do they become permeated with a more intense experience. At first they have the character of memory pictures, but of such a kind that we know their meaning does not relate to any experiences we have lived through externally since our birth. They do, however, express something just as pictorially as memory pictures express pictorially our personal experiences. They refer to something objective, yet we know that this objective something is not contained in the sphere which is surveyed by our memory. We are conscious that these imaginations contain a strong inner reality, yet at the same time we are aware that we are dealing with just images—just pictures of the reality. It is a matter of being able to distinguish these pictures from those of memory, in order that these imaginations remain pure, so that no foreign elements slip into them.

I will describe the outer process, but of course in just a few lectures one cannot go into any great detail. We may form a mental picture of an outer experience and we can see how in a sense the outer experience passes over into our organism, and—expressed abstractly—it then leads a further existence there, and can be drawn forth again as a memory picture. We notice that there is a certain dependence between what lives in the memory and the physical condition of the human organism. The memory is really dependent on our human organism right into the physical condition. In a way we pass on what we have experienced to our organism. It is even possible to give a detailed account of the continuation of the various pictures of our experience in the human organism. But this would be an entire spiritual-scientific chapter in itself. For our memories to remain pure and true, no matter how much our organism may participate in what lives on in the memory process, this involvement may not add anything of real content. Once mental pictures of an experience have been formed, nothing further should flow into the content of the memories.

If we are clear about this fact of memory life, we are then in a position to ascertain what it means when pictures appear in our consciousness that have the familiar character of memory pictures, but a content which does not relate to anything in our personal experience. In the process of experiencing imagination we realize the necessity of continually increasing the power of our soul. For what is it that we must really do? Normally our organism takes over the mental pictures we have formed from life and provides memory. Thereby the mental pictures do not just sink down into an abyss, if I may so express it, but are caught and held by our organism so that they can be reflected back again at any necessary moment. With imaginative pictures, this is just what should not be the case; we must be in a position to hold them through inner soul forces alone. Therefore it is necessary for us to acquire something that will make us stronger than we are ordinarily in receiving and retaining mental images. There are of course many ways to do this; I have described them in the books already named. I wish to mention just one of them. From what I now tell you, you will be able to see the relation between various demands of life which spring from anthroposophical spiritual science and their connection with the foundation of anthroposophical research.

Whoever uses his intellect to spin all kinds of theories about what he confronts as phenomena in the world (which of course can be extraordinarily interesting at times) will hardly find the power for imaginative activity. In this respect, certain developments in the intellectual life of the present day seem specifically suited to suppress the imaginative force. If we go further than simply taking the outer phenomena of the mineral-physical realm and connecting them with one another through the power of our intellect; if we begin to search for things that are supposed to be concealed behind the visible phenomena, with which we can make mental constructions, we will actually destroy our imaginative capacity.

Perhaps I may make a comparison. No doubt you have had some dealings with what could be called phenomenalism in the sense of a Goethean world view. In arranging experiments and observations, Goethe used the intellect differently from the way it is used in recent phases of modern thought. Goethe used the intellect as we use it in reading. When we read, we form a whole out of the individual letters. For instance, when we have a row of letters and succeed in inwardly grasping the whole, then we have solved a certain riddle posed by this row of individual letters. We would not think of saying: Here is a b, an r, an e, an a and a d—I will look at the b. As such, this isolated b tells me nothing in particular, so I have to penetrate further for what really lies behind the b. Then one could say: Behind this b there is concealed some mysterious “beyond,” a “beyond” that makes an impression on me and explains the b to me. Of course, I do not do this; I simply take a look at the succession of letters in front of me and out of them form a whole: I read bread. Goethe proceeds in the same way in regard to the individual phenomena of the outer world. For instance, he does not take some light phenomenon and begins to philosophize about it, wondering what states of vibration lie behind this phenomenon in some sort of “beyond.” He does not use his intellect to speculate what might be hiding behind the phenomenon; rather, he uses his intellect as we do when we “think” the letters together into a word. Similarly he uses the intellect solely as a medium in which phenomena are grouped—grouped in such a way that in their relation to one another they let themselves be “read.” So we can see that regarding the external physical-mineral phenomenological world, Goethe employs the intellect as what I would call a cosmic reading tool.

He never speaks of a Kantian “thing in itself” that must be sought behind the phenomena, something Kant supposed existed there. And so Goethe comes to a true understanding of phenomena—of what might be called the “letters” in the mineral-physical world. He starts with the archetypal or “Ur”-phenomenon, and then proceeds to more complex phenomena which he seeks either in observation or in experiments which he contrives. He "reads" what is spread out in space and time, not looking behind the phenomena, but observing them in such a way that they cast light on one another, expressing themselves as a whole. His other use of the intellect is to arrange experimental situations that can be “read”—to arrange experimental situations and then see what is expressed by them. When we adopt such a way of viewing phenomena and make it more and more our own, proceeding even further than Goethe, we acquire a certain feeling of kinship with the phenomena. We experience a belonging-together with the phenomena. We enter into the phenomena with intensity, in contrast to the way the intellect is used to pierce through the phenomena and seek for all kinds of things behind them—things which fundamentally are only spun-out theories. Naturally, what I have just said is aimed only at this theoretical activity.

We need to educate ourselves in phenomenology, to reach a “growing together with” the phenomena of the world around us. Next in importance is to acquire the ability to recall a fully detailed picture of the phenomena. In our present culture, most people's memories consist of verbal images. There comes a moment when we should not be dependent on verbal images: these only fill the memory so that the last memory connection is pushed up out of the subconscious into consciousness. We should progress toward a remembering that is really pictorial. We can remember, for instance, that as young rascals we were up to some prank or other—we can have a vivid picture of ourselves giving another fellow punches, taking him by the ear, cuffing him, and so on. When these pictures arise not just as faded memories, but in sharp outline, then we have strengthened the power we need to hold the imaginations firmly in our consciousness. We are related to these pictures in inner freedom just as we are to our ordinary memories. With this strengthened remembering, we grow increasingly interested in the outer world, and as a result the ultimate "living together with" all the various details of the outer world penetrates into our consciousness. Our memories take on the quality of being really objective, as any outer experience is, and we have the feeling that we could affectionately stroke them. Or one could say: These memory pictures become so lively that they could even make us angry. Please bear with me as I describe these things to you! It is the only thing I can do with our present language.

Then comes the next step: we must practice again and again eliminating these imaginations so that we can dive down again and again into an empty consciousness. If we bring such pictures into our consciousness at will and then eliminate them again in a kind of inner rhythm—meditating, concentrating, creating images, and then freeing ourselves of them—this will quicken powerfully the feeling of inner freedom in us. In this way we develop a great inner mobility of soul—exactly the opposite of the condition prevailing in psychopaths of various kinds. It really: is the exact opposite, and those who parallel what I have just described here with any kind of psychopathic state show that they simply have no idea of what I am talking about.

When we finally succeed in strengthening our forgetting—the activity which normally is a kind of involuntary activity—when now we control this activity with our will, we notice that what we knew before as an image of reality, as imagination, fills with content. This content shows us that what appears there in pictorial form is indeed reality, spiritual reality. At this point we have come to the edge of an abyss where, in a certain sense, spiritual reality shines across to us from the other side of existence. This spiritual reality is present in all physical sense reality. It is essential to develop a proper sense for the external world in order to have a correct relationship to these imaginations. Whoever wishes just to speculate about phenomena, to pierce them through, as it were, hoping to see what is behind them as some kind of ultimate reality—whoever does this, weakens his power to retain and deal with imaginations.

When we have attained a life of inspiration—that is, experiencing the reality of the spiritual world just as ordinarily we experience the physical world through our external senses—then we can say: now I finally understand what the process of remembering means. Remembering means (I will make a kind of comparison) that the mental images we have gained from our experiences sink down into our organism and act there as a mirror. The pictures we form in our minds are retained by the organism, in contrast to a mirror which just has to reflect, give back again what is before it. Thus we have the possibility of transforming a strictly reflective process into a voluntary process—in other words, what we have entrusted to memory can be reflected back from the entire organism and particularly from the nervous system. Through this process, what has been taken up by the organism in the form of mental pictures is held in such a way that we too cannot see “behind the mirror.” Looking inward upon our memories, we must admit that having the faculty of memory prevents us from having an inner view of ourself. We cannot get into our interior any more than we can get behind the reflective surface of a mirror.

Of course what I am telling you is expressed by way of comparisons, but these comparisons do portray the fact of the matter. We realize this when inspiration reveals these imaginations to us as pictures of a spiritual reality. At this moment the mirror falls away with regard to the imaginations. When this happens we have the possibility of true insight into ourselves, and our inner being appears to us for the first time in what is actually its spiritual aspect. But what do we really learn here?

By reading such mystics as Saint Theresa or Mechtild of Magdeburg, beautiful images are evoked, and from a certain point of view this is justified. One can enter into a truly devotional mood before these images. For someone who begins to understand what I have just described to you, precisely this kind of mystical visions cease to be what they very often are for the nebulous types of mystic: When someone comes to real inner vision, not in an abnormal way (as is the case with such mystics) but by the development of his cognitive faculty as I have described it, then he learns not only to describe a momentary aspect as Mechtild of Magdeburg, Saint Theresa and others do, but he learns to recognize what the real interior of the human organization is. If one wants to have real knowledge and not mystical intoxication, one must strive toward the truth and put it in place of their mist-shrouded images. (Of course, this may seem prosaic to the nebulous mystic.) When this is accomplished, the mirror drops away and one gains a knowledge, an inner vision of the lungs, diaphragm, liver, and stomach. One learns to experience the human organization inwardly. It is clear that Mechtild of Magdeburg and Saint Theresa also viewed the interior, but in their case this happened through certain abnormal conditions and their vision of the human interior was shrouded in all manner of mists. What they describe is the fog which the true spiritual investigator penetrates.

To a person who is incapable of accepting such things, it would naturally be a shock if, let's say hypothetically, a lofty chapter out of Mechtild were read and the spiritual researcher then told him: Yes, that is really what one sees when one comes to an inner vision of the liver or the kidneys. It is really so. For anyone who would rather it were otherwise, I can only say: That is the way it happens to be. On the other hand, for someone who has gained insight into the whole matter, this is for him the beginning of a true relation to the secrets of world existence. For now he learns the origin of what constitutes our human organization and at what depths they are to be recognized. He clearly recognizes how little we know of the human liver, the human kidneys, not to speak of other organs, when we merely cut open a corpse—or for that matter, when we cut open the living human organism in an operation—and get just the one-sided view of our organism.

There is the possibility not just to understand the human organism from the external, material side, but to see and understand it from the inside. We then have spiritual entities in our consciousness, and such entities show us that a human being is not so isolated as we might think—not just shut up inside his skin. On the contrary! Just as the oxygen I have in me now was first outside and is now working within me, in the same way—though extended over a long period of time—what is now working in me as my inner organization (liver, kidneys, and so on) is formed out of the cosmos. It is connected with the cosmos. I must look toward the cosmos and how it is constituted if I want to understand what is living in the liver, kidneys, stomach, and so on; just as I must look toward the cosmos and the make-up of the air if I want to understand what the substance is that is now working in my lungs, that continues to work on in the blood stream. You see, in true spiritual research we are not limited to separate pictures of separate organs but we come to know the connections between the human organism and the whole cosmos.

Not to be overlooked is the simple symbolic picture which we have already mentioned of the senses. We can in a way visualize our senses as “gulfs,” through which the outer world and its happenings flow into us. At the same time our senses continue inward as I have described them. Little by little we can see this activity from an inner point of view—the forming and molding activity that has worked on our nervous system since our birth. I have described the subjective experience of this activity as a life review, a life panorama, and we discover in the configuration of the nervous system an external pictorial form of what is really soul-spiritual. It can also be said that first we experience imaginations and then we see how these imaginations work in the formation of nerve substance. Of course this should not be taken in too broad a sense, since, as we know, nerve substance is also worked on before birth. I shall come back to this tomorrow. But essentially what I have said holds true. We can say: here is where the activity continues toward the inside; you can see exactly how it goes farther. It is the same activity, in a certain sense, that "engraves" itself into the nervous system. For the parts of the nervous system that are formed completely, this "engraving" activity can be seen streaming through the nerve paths. In childhood, however, for the parts that are still in the-process of being formed, this “engraving” acts as a real modeling force, a structuring proceeding out of imaginations. This leaves the rest of the human organism, about which we will speak shortly—what underlies the muscles, bones, and so on, also the physical basis of the nervous system—in fact, all of the organic tissue. At this point I should relate to you a certain experience I had; it will make this all a bit clearer.

I spoke once before the Theosophical Society about a subject I called “anthroposophy.” I simply set forth at that time as much of this anthroposophy as had revealed itself to my spiritual research. There was a request for these lectures to be printed and I set about doing this. In the process of writing them down, they turned into something different. Not that anything that had first been said was changed, but it became necessary to add to what was said by way of further explanation. It was also necessary to state the facts more precisely. This task would require a whole year. Now came another opportunity. There was again a general meeting of the Society and there was a request that the lectures should be ready for sale. So they had to get finished. I sent the first signature (16 pages) of the book Anthroposophy to the printer. The printing was rapidly done and I thought I would be able to continue writing. I did continue writing but more and more it became necessary to explain things more accurately. So a whole number of pages were printed. Then it happened that one signature was only filled up to page thirteen or fourteen and I had to continue writing to fill up all sixteen pages. In the meantime I became aware that in order to get this matter done the way I wanted to would require a more accurate, detailed development of certain mental processes, a very specific working out of imaginative, of inspirational cognition and then to apply these modes of cognition to these anthroposophical issues. And so I had to take a negative step, I dropped the whole idea of writing on Anthroposophy. It is still lying there today as it lay then—many pages.¹ For my intention was to make further investigations. Thus I became thoroughly acquainted with what I want to describe to you now. I can only describe it schematically at this time, but it is a sum total of many inner experiences that are really a cognitive method of investigating the human being.

It became increasingly clear to me that before one could finish the book called “Anthroposophy,” in the form intended at that time, one must have certain experiences of inner vision. One must first be able to take what one perceives as soul-spiritual activity working in the nervous system and carry it further inward, until one comes to the point where one sees the entire soul-spiritual activity—which one grasps in imagination and inspiration—crossing itself. This crossing point is really a line, in a vertical direction if looked at schematically. For certain phenomena the point lies farther up, for others farther down. In these lectures I can't describe this in detail, I just wanted to make a kind of cross section through the whole of it. Now because of this crossing, one is no longer free in exercising this activity. In fact, one was not altogether free before, as I have shown; now one is even less free. The whole situation undergoes a change. One is now being held strongly in an imaginative-inspired state. Expressed concretely, if one comes to an imagination of the eye by taking hold of visual sense-perception and the continuation into mental processes with imaginative-inspired cognition, then this activity proceeds inwardly and one comes to a kind of crossing, and with the activity first encompassing the eye another organ is encompassed, and that is the kidney.

The same applies to the other organs. In each case, when one carries one's imaginative-inspired activity into the body, one finds various relatively complete organs—complete at least in their basic form from birth—and one comes to a real inner view of the human organism. This kind of research is very demanding; and as I was not obliged at that moment to finish the book, and had to give another lecture cycle, which also demanded research efforts, you can imagine that it was not easy to continue to work out the method which I had developed at that time—of course, it was quite a few years ago that this occurred.

I mention this only to show you some of the difficulties—how one is continually held back by various demands. To continue in this, one must hold one's inner forces firmly together if one is to accomplish it. One must, in fact, repeatedly resolve to intensify one's thinking ability, the force of one's inner soul work—to strengthen it through love of external nature. Otherwise one simply cannot proceed. One goes consciously into oneself, but again and again one is thrown back, and instead of what I would call an inner view, one gets something not right. One must overcome the inward counterblow that develops.

I wanted to tell you all this so that you could see that the spiritual investigator has moments when he must wrestle with certain problems of spiritual research. Unfortunately, in the years that followed the event I have just described to you, my time was so filled with everything imaginable, particularly in recent years, that the needful—indeed, indispensable—activity for finishing my Anthroposophy could not take place.

You see, something that is inwardly understood, something we spoke of above rather abstractly, is in fact what is spun into an enveloping form of an organ, something quite concrete. If you picture this to yourselves, you will realize that such an insight into the human being can also build a bridge to practical activities. These activities must of course be founded on a vision of the human being and his relation to the world. I have already indicated in another connection how through developing imagination we gain knowledge not only of the sensory realm and its continuation into the nervous system, but also of the plant world. When we advance to inspiration, we become acquainted with the whole realm of forces that are at work in the animal world. At the same time we become aware of other things of which the animal world is only the outer expression. We now recognize the nature of the respiratory system, we can understand the external forms of the respiratory system through this relationship. The external form of the respiratory and circulatory system is not directly similar in its outer shape to its inner counterpart, as is the case with the outer form of the nervous system and the inner mental life. I showed this yesterday—how in the case of the nervous system two people, representing very different points of view, were able to draw similar pictures. In a parallel manner we become acquainted with the outer world and its kingdoms and the inner aspect of the human being.

Tomorrow I will consider what this inwardly experienced knowledge adds to our insight into the nature of the human being and his relation to his environment. Naturally, a great deal is revealed to us about specific relationships between the human being and his environment. It is possible to perceive the nature of a specific human organ and its connection to what exists in the outer natural realm. Thereby we discover in a rational way the transition from a spiritualized physiology to a true therapy. What once was won through instinctive inner vision is now possible to be renewed. I have mentioned yoga, and I could name even older systems which made it possible to perceive in an instinctive, childlike way the connection between the human being and the world around him. Many of today's therapeutic measures come from this older time—perhaps in somewhat different form, but they are still among the most fruitful today. Only on this spiritual path can therapy be developed that is suited to meet the real needs of today. Through insight into the connection of the human organs with the cosmos, a medicine will be developed based an inner perceptions, not just external experiment.

I set this before you just as an example of how spiritual science must fructify the various specialized branches of science. That this is needed is obvious when one looks at external research efforts, which have been very active and are magnificent in their own way—but which abound with questions. Take, for example, outer physiology or outer pathology: questions are everywhere. Whoever studies these things today and is fully awake will find the questions there—questions that beg for answers. In the last analysis, spiritual science recognizes there are great questions in outer life, and that they require answers. It does not overlook what is great and triumphant in the other sciences. At the same time, it wishes to study what questions result from this; it wishes to find a way to solutions to these questions in just as exact a manner as can be taught in the other sciences. In the end, the questions can be found (even for sense-bound empirical investigation) only through spiritual investigation. We will speak more about this tomorrow.

• 1. Published in German as Anthroposophie—Ein Fragment, Bibl. Nr. 45; English translation in preparation by Mercury Press.

Unfortunately our time together is so short that I have only been able to deal with our theme in a broad way, just intimating its development. The intention was to present a few ideas that lie, one might say, at the entrance of an anthroposophical spiritual science. From what has been presented, you will surely feel that everything we have touched upon needs further elaboration.

I have spoken of various ways of knowing that through inner soul work can follow as further steps from our everyday kind of knowing and from ordinary scientific cognition. I have already mentioned the first two of these further steps and called them imaginative cognition and inspired cognition. Yesterday I showed how, when imaginative and inspired cognition work together, and when we take account of a certain experience that I described yesterday as an inner crossing in the consciousness, a knowledge of the human being can arise in conjunction with a knowledge of the surrounding world. When this experience that we have in inspired-imaginative cognition is developed further, through certain exercises found in my books, something arises which has a similar name in ordinary life—that is, intuition. In ordinary life intuition refers to a kind of knowing that is not sharply delineated, to something more in the realm of feeling. This dimly experienced knowledge is not what the spiritual researcher means when he speaks of intuition and yet there are good reasons for thinking of the undeveloped, dim experiences of ordinary intuition as a kind of early stage of real intuition. Real intuition is a kind of knowing, a condition of the soul that is just as suffused with clarity of consciousness as is mathematical thinking. This intuition is reached through a continuation of what I have called exercises for the attainment of forgetting. These exercises must be continued in such a way that one really forgets oneself. When these exercises have been carried on in a precise and systematic way, then arises what the spiritual investigator calls intuition in the higher sense. This is the natural form of cognition into which inspired imaginations flow.

Before I go on with my discussion, I would like to stress one thing, to avoid possible misunderstanding. I can easily imagine that someone might raise a certain objection to what I described at the end of yesterday's lecture. First let me assure you that the conscientious spiritual investigator is the first to make various objections for himself. This is inherent in the process of spiritual research. With every step one must be aware from what possible angle objections may come, and how they can be met. To be specific, someone could raise an objection about what I said yesterday concerning the experiencing of a “crossing” that arises in the process of looking within, embracing our own inner organization. It could be said: This is an illusion. The fact is that especially the spiritual investigator (as is meant here) is not allowed to be a dilettante in external science; he is sure to know a thing or two about the inner organization of the human being from conventional anatomy and physiology. One might suspect that the investigator yields to a sort of self-deception, taking what he knows of external science and incorporating this into his inner vision. The spiritual researcher fully reckons with the possibility of self-deception along his path. One can settle the objections that have been raised by noting that what is perceived in the human organism during this inner viewing is totally different from anything one could possibly get from external anatomy or physiology. This perception of the inner organization could really be called a perception of the spiritual aspect of the human interior. The only help ordinary anatomy and physiology can render is the establishment of something like a mathematical reference point—a reference point for what has been spiritually perceived in the soul by inner vision, a definite content of perception at this level of cognition. For example, when we spiritually perceive the inner nature of what corresponds to the lung, it will be easier to connect this with the lung if we are already familiar with it through outer anatomy and physiology than if we knew nothing of it.

These two aspects—an inner vision of the lung, and what we know in an outer way through anatomy and physiology—are two completely different contents that must be reconciled later. At this level of cognition there is only a repetition of the kind of relationship that we experience between what is inwardly grasped in mathematical thinking and what is directly visible in the physical-mineral realm. The difference that exists between what we grasp inwardly in mathematical thought and what we find given in outer observation is very similar to the difference between what we grasp in inspired-imaginative activity and what we can learn through external research. Inner clarity of consciousness throughout is, of course, a basic requirement.

When we rise from inspired imagination to intuition, we encounter a situation similar to the one we described at the beginning of these lectures. We said: The outer world and its phenomena enter into us through our senses as through “gulfs.” Mathematical lines and forms which we construct influence our perception of the outer forms of the world. So with respect to our bodily nature there is a jutting in, a really essential penetration of the outer world into our spatial-bodily condition. We have a similar experience when all that I have described comes into us through intuition. Through this experience we become aware of one thing particularly: that what has been experienced within the human being is inexplicable of itself—or perhaps better said, it is something essentially unfinished. When we come to know ourselves through intuition, as long as we remain within the experience of self-knowledge we are basically dissatisfied. In contrast to this, with inspired imagination, when we apply it to knowledge of the self we feel a certain satisfaction. We learn what the human rhythmic system really is. This is a difficult process of knowledge. It is a process that can really never be completed, because it leads into endless further developments. In this type of knowledge you are learning to know yourself in connection with the world, as I showed yesterday. One can arrive at concrete insights concerning the connection of the healthy organism with its cosmic environment also the connection of the ailing organism with the cosmic environment. In this way the very interior of the human being can be penetrated.

At this point I would like to speak of something I described in the previous lecture course.¹ We are able to perceive through our inspired imagination how the human organism must relate itself to receiving something like a sense organ. It is, in fact, predisposed toward the sense organs. It opens itself outward so as to send a certain force system—if I may use such an expression—toward each separate sense. Beyond the interaction of the force system with our regular senses, one can discover abnormal cases of such tendencies arising in other places. A normal organization for the development of a sense can appear in a wrong place. Such a force system can be inserted into some organ not meant to be a sense organ, whose normal function is something else. The appearance of a metamorphosed force system in a place not right for it causes abnormalities in the human organism. A consequence of the particular abnormality just mentioned is the formation of a tumor where the displaced force system occurs. What we find here in the human organism is a more complex version of what Goethe in his teachings on metamorphosis always looked for, under simpler circumstances. We come to realize that a system of forces correctly associated with growth, when directed differently and in a metamorphosed form, can become the cause of illness. When inspired-imaginative cognition is directed to the whole matter of how man's sensory organization is related to the kingdoms of nature—to his whole environment—one discovers important relationships. These relationships lead us to remedies in our environment that can be used against pathological forms of forces.

Now you may see the vistas that are opened up by what I have described. This is not just fantasizing into the blue—nor is it nebulous mysticism to evoke satisfaction in the soul. Either would be completely foreign to what is meant here by anthroposophically-oriented spiritual science. This spiritual science wishes to penetrate into the real nature of the world in a serious and exact manner. At the same time, it must be admitted that much of what can be achieved in this way is still in its infancy today. And yet a fair amount of what I presented last spring in the course for physicians and medical students (which I plan to continue shortly) on pathology and therapy, made—I believe—a favorable impression on the listeners. Its view of the essential being of nature and the world, of the inner relationships, gave rise to the impression that here is something that can fertilize and complement outer observation and experiment. The contemporary world should see that here is at least an attempt to find out what it is that is creating the questions of external science, when there is no sign of any possibility in the scientific field of finding satisfactory answers to the questions.

As we advance along this path of knowledge (keeping always to what is spiritually real and concrete and avoiding abstraction), we have an experience on the other side of the human organization, of something similar to the "jutting" of the outer world into our sensory life. I said earlier that when we come to self-knowledge through intuition, it proves inevitably to be unfinished. We understand this now, for we see that here on the other side we have the reverse relationship to that of the sense organs. The senses are “gulfs” into which the outer world flows. On the other hand, we discover that the entire human being, becoming a sense organ in intuition, now reaches into the spiritual world. On the one hand, the outer world reaches into the human being; on the other, the human being reaches into the spiritual “outer world.” As I mentioned earlier in connection with the eye organization, the human being has a certain active relation to the depth dimension; with intuition he has (as long as he remains with intuition in the realm of self-knowledge) a certain relation to the vertical dimension. Thus something very similar to sense perception takes place, except that it is reversed.

We find that through intuition the human being places himself with his entire being in the spiritual world. Just as through the senses the external sense world projects inward, through intuition one consciously places oneself in the spiritual world. In this conscious projection into the spiritual world through intuition, the human being has a similar feeling to the feeling he has toward the outer world through perception. The feeling of being in the spiritual world, a kind of dim feeling of standing within the spiritual world, in ordinary life we call intuition. But this intuition is suffused with bright clarity when the stage of cognition is striven for which I have described. Thus you can realize that perception is just one side of our human relation to the outer world. In perception we have something indefinite, something that first must be inwardly worked upon. As perception is worked upon by our intellect and we discover laws at work in this perception, there is at the same time something corresponding to this that initially has just as indefinite a relation to us as does perception. It must be penetrated by inner knowledge that has been achieved, in the same way that perceptions must be penetrated by mathematical thinking. In short, our ordinary experience must be penetrated by our inwardly achieved knowledge.

In ordinary experience we call this kind of intuition belief or faith. Just as the human being faces the outer sense world and has the experience of perception, so, participating in a dim way in the spiritual world, he has the experience of belief. And just as perception can be illumined by the intellect or reason, so the content of this indefinite dim experience of belief can be illumined by our steadily increasing knowledge. This dim experience of faith becomes one of scientific knowledge just as perception attains scientific value through the addition of the intellect. You see how the things relate. What I am describing to you is truly a progression through inner spiritual work to transform the ordinary experience of faith into an experience of clear knowledge. When we rise into these regions, transforming faith into an experience of knowledge, we find this similar to the process of subjecting our perceptions to what has been worked out mathematically or logically. What is inherent here is not some artificial construction, it is a description of something a human being can experience—just as, for instance, one experiences what develops from early childhood when the intellect is not yet useable to a later time when the intellect and reason are in full use.

There are other experiences bound up with these—for example, the following: The moment we advance to inspired cognition, we have already had what I have described as the life panorama, which extends back to early childhood and, at times, even to birth. With this we have gained an inner kind of perception. It is only with the attainment of inspired cognition, however, that a kind of enhanced faculty of forgetting comes about which I must characterize as a complete extinguishing of the surroundings that up to this point were given through sense perception. In other words, a state of consciousness arises in which our own inner life, indeed our inner life in time up to birth, becomes the object of our consciousness. At this time one has the subjective feeling that one is inwardly empty, that one is in the outer world with one's consciousness, not within one's body. When we have succeeded in reaching this enhanced forgetting whereby the outer sense-perceptible world is really extinguished for a moment, then something appears through this experience being combined with what is attained intuitively. I must describe this in the following way.

We have already discussed imagination and we know it does in fact relate to reality, although at first it appears to have pictorial character. It relates to a reality, but at first we have only pictures in our consciousness. When we experience inspiration, we advance from the pictorial to the corresponding spiritual reality. When we reach the moment in which external sense perception is completely extinguished through inspiration, a new content appears for the first time. The content that appears corresponds to our existence before conception. We learn to look into our soul-spiritual being as it was before it took possession of a physical organism arising out of the stream of heredity. Thus this imagination fills itself with a real spiritual content that represents our pre-birth existence. Characterized in this way, this may still seem paradoxical to many people of our time. One can only indicate the exact point in the cognitive process where such a view of the human soul-spiritual self enters in, and where what we call the question of immortality takes on real meaning. At the same time we gain a more exact view of the other pole of the human organization. When we penetrate what we have at first only as intuitive belief and raise this to knowledge, the possibility arises to relate imaginations—although in another way than in the case just described—to the conditions after death. In short, we have a view of what one can call the eternal in man and I will only just mention the following. When intuition has developed further, to the point it is really capable of reaching, we develop our true “I” for the first time. And within the true “I” there appears to inner vision what in anthroposophical spiritual science is referred to as knowledge of repeated earth-lives. The knowledge that we were a soul-spiritual being before conception and that we will continue to be after death: this is really experienced in inspired imagination. The knowledge of repeated earth-lives is added to this only in intuition.

When we have reached this area, we first begin to discover the full significance of waking up and falling asleep, and the condition of sleep as such. Through a deepening of the cognition related to the pole of perception, we discover the experience of falling asleep, which otherwise remains unconscious. At the other pole of intuitive thought, we discover the experience of waking up. Between these two is the experience of sleep, which I would like just to characterize as follows: when the human being falls asleep in ordinary consciousness, he is in a condition in which his consciousness is completely dimmed. This empty consciousness in which the human being lives between falling asleep and awakening, is a state which he cannot know from his own subjective point of view. The inspired-imaginative condition is very similar. In this condition the will impulses are silenced just as in sleep the senses are silenced. The subjective human activity is silent in both sleep and inspired imagination. The major difference is this: in sleep the consciousness is empty. In the condition of inspired imagination one's consciousness is filled; one's inner experiences are independent of sense perception and will impulses; in a certain sense one is awake while one is asleep. One has therefore the possibility of studying the life of sleep.

I would like to return to something that I spoke of this morning in the history seminar. The historical problems we spoke of take on new meaning when seen in connection with the experiences we have just been speaking of. At one time or another you may have reflected upon such historians as Herodotus. He and others were really precursors of what we call history in the modern scientific sense. The way history is written today developed with the intellectual culture that finds special satisfaction in experiment. In other words, those who find special satisfaction in experiment also find satisfaction in the external aspect of history. This science of history proceeds empirically, and rightly so from its own point of view. It collects data, and from this data it pieces together a picture of the course of history. One can, however, object that this way of interpreting empirical data easily allows that history could have developed differently. As I put it this morning, one could hypothesize that Dante somehow died as a boy. We would then be faced with the possibility that what we experience as coming through Dante would be absent, at least it would be absent as manifested in the person of Dante. In the study of history one will meet with great difficulties in reaching true insight, unless one is satisfied with the ready-made scholarly harangues.

Let us take another example. Historians set out to study the Reformation, using the available facts of external history. (We cannot go into detail here; you can research this yourself if you are interested.) For instance, if the monk Luther had died young, I would really like to know what would have been recorded as derived purely from the external historical method! Certainly something quite different from what is recorded today. Quite serious difficulties arise when one wants truly to characterize historical knowledge. One may say if one focuses on the philosophy of history, one can follow the observable outer events from the point of view of some abstract element of necessity, or one may want to find an element of purpose shaping the events as Strindberg did. The fact that the other reforms would not have been there either if Luther had died as a boy, would not affect this theoretical finding of purpose or necessity, in whatever might have taken place instead of the Reformation. If Luther had died, the other reformers would not have been there either.

One must be very careful in coming to conclusions when one is working in the field of external historical observation. However, the course of human development reveals something quite different when it is observed from the level of knowledge that I have been describing to you. Let me give you a concrete example. One would see that there were certain forces at work in European civilization around the fourth century between the time of Constantine and Julian the Apostate. The outer aspect of this world would appear differently if records existed of a personality so impressive as, for instance, Dante. There really is a problem here, and I confess I am not finished with it yet but must pursue it a bit further. The problem is a most concrete one. I am not yet finished in that I cannot tell you whether important documents, important evidence concerning an important figure around the period of 340 or 350 A.D. somehow disappeared from the view of external history, or whether he died in his youth—or somehow perished in those turbulent, war-filled times. It is a fact, however, that one sees forces at work in this period that cannot be traced in external history today. These forces would only be accessible to external history through some stroke of luck, like the chance discovery of written documents in some monastery. It is beyond any doubt for the spiritual investigator, however, that these forces are active. The spiritual investigator can truly establish what otherwise would be seen as forces abstracted from outer circumstances.

Now suppose we would wish to look back on the life of Dante and acquaint ourselves with him. We would try to make him come to life in our soul, really to try to know him inwardly. We would also familiarize ourselves with the forces active in the time of Dante. This is an external approach to knowledge. Naturally, the knowledge that the spiritual scientist gains of the Dantean period will look somewhat different from what can be found in external documents—for example, in the Divine Comedy. One could of course object that the spiritual scientist might confuse what he has learned through external perception with what he has obtained through inner vision. When, however, inner vision operates in such a way that we know beyond any doubt that in a particular age—as in this one just named—the outer events do not correspond to the inner happenings, we know that spiritual powers are really at work. Under these circumstances it is possible to present history as I did recently for a small circle, by looking exclusively at the forces seen inwardly. We come to the point where we have inwardly observed these forces; they penetrate us, they live within us. It would really be a miracle if, for instance, one could just fantasize about the forces at work in Julian the Apostate at the time in question. Those times can only be truly explored spiritually.

The level of historical observation achieved here can be described as a direct viewing of the original spiritual forces that are active in the historical process. Thereby one receives a satisfactory explanation for precisely the parts of history where external facts are missing—because documents are missing, or men and women did not have a chance to live their lives out normally. In such cases what is viewed inwardly can help external history. Examples of the result of such inner knowledge, pointing to the forces behind historical events, are given in my little book, The Spiritual Guidance of Mankind. What is presented there must naturally be preceded by the inner vision of the missing aspects of external history, as I have mentioned. It is only at this point, assuming we intend to be inwardly responsible in our relation to knowledge, that we can feel justified in saying: It is possible simply on the foundation of sound human understanding to rise (as I have repeatedly described) to a level where such real forces are active.

But, you may object, no one could speak of the beings I described in The Spiritual Guidance of Mankind who has not yet advanced to such vision. This is of course true; to speak with this degree of emphasis, one must have a certain level of cognition. But one may take something else into consideration. If we are honest in approaching the facts of history and if we are sufficiently schooled in philosophy to be aware of the riddles and doubts the usual study of history presents, we can still have an inner experience of a certain kind. This experience is similar to the one that the astronomer had when on the basis of certain gravitational forces he predicted the as-yet-unseen planet of Neptune. The discovery of the spiritual laws and essential nature of history is really a very similar process in the spiritual domain to the calculations employed by LeVerrier to predict the existence of Neptune. LeVerrier did not somehow piece together a scientific result as is done in external history—with a positive or skeptical slant, simply avoiding connections: he followed the facts according to their truth. He said to himself: Something must be at work here. This is similar to what the astronomer before him said concerning Uranus. Uranus doesn't follow the course which it ought to according to the forces I already know, so there must be something exercising an influence on these known forces. The conscientious investigator also recognizes certain forces at work. He sees the intervention of these forces much as someone who on finding a limestone or silica shell-form in a rock formation looks for the active forces. From the way the silica fossil looks, he surely does not say: This silica form has somehow crystallized out of its mineral surroundings. Rather he says: At one time this form was filled out with something; it was made by some kind of animal and one can have a mental picture of this animal. If some being were to arrive who had lived at the time the animal was alive in that shell, and he described the animal, such an eyewitness could be likened to the spiritual investigator. The finder of the shell bearing the imprint of the animal is not necessarily the one who uses his sound human understanding to deduce from the outer configuration what must have been there to form the shell. What the living facts were is something only the spiritual investigator can say. The person who is willing to bring a sound sense of logic, a logical view of facts, and healthy human understanding, can follow and inwardly test what the spiritual researcher tells him about the forms in front of him.

It is not necessary to have a blind belief in the spiritual investigator. Naturally, the actual discovery of such things as are presented in The Spiritual Guidance of Mankind requires spiritual research. When the spiritual researcher has presented what he wishes to tell in terms of what he calls higher beings, he will also readily agree to be tested for this vision by those gathering outer facts. His attitude is this: I invite you to rap my knuckles if you discover anything whatever that contradicts the outer order of events predicted by my inner vision.

Something similar appeared in our circle, in connection with interpretations of the gospels which had been worked out in a purely spiritual manner. It has also occurred in such cases as the one given this morning. I am busy with a variety of literature, yet to this day the author was unknown to me of the work Dr. Stein cited this morning giving the date of Christ's death. I have never seen it. Naturally, this is not the sort of evidence that one can accept objectively—I mention this only parenthetically. Nevertheless, such things have occurred within our circle. Verifications have appeared that must be accepted objectively. Through a living involvement in spiritual-scientific work, many of our friends have a real personal conviction; it does not rest on blind faith, but precisely on their experience of the life that goes on in spiritual science. This explains why those who have been involved in the activities of spiritual science for many years can speak in a different tone from those for whom spiritual science is just a theory.

I believe we can show in the context of the evolution of humanity the connections between the state of science today and the state of knowledge today. Naturally, everything has earlier stages; scientific experimentation is no exception. Given this, however, the experimentation of the past, up to the most recent times, cannot help but seem primitive compared to what we have today. When our fully developed experiment is experienced inwardly, it really calls for something more. From what has been combined by the intellect in the actual activity of experimentation something is released in the soul. What is released requires spiritual knowledge to balance it. We have shifted our understanding from mere observation to experimentation. Something happens when we discover the real difference between what is experienced in mere observation and what is experienced in the activity of experimentation: the urge arises in us to rise to a higher level of self-knowledge from the ordinary kind. This higher knowledge is what I have recently been describing. These two things are related. The urge for a higher knowledge, which is natural to human beings striving for knowledge today, has developed quite naturally in the course of history out of an elementary interest in experimentation itself. The scientific data that we have gained in regard to outer nature are, in many respects, really related to questions. The important thing is that if the formulation of the questions is correct, then a correct answer is possible.

What natural science has given us recently is really in large measure no more than a statement of questions for the spiritual researcher. Whether we look at recent astronomy or the views of modern chemistry, when we grasp what is in them, the question arises: how is what is described related to what goes on in the human being himself? Questions arise about man's relation to the world precisely through the scientific results that have come from our shifting from observation over to the experimental realm. So we can see that for someone who really experiences modern science and does not theorize about it, this science is full of spiritual-scientific questions. From the nature of these questions, there simply is no choice but to go to spiritual science for answers. In the year 1859 Darwin came to a conclusion of what he had studied so meticulously; but for someone who studies these results afterwards, in spite of what Darwin took to be scientific conclusions, they appear as questions.

We are helped by the kind of experience we have in experimenting but at the same time we recognize the essentially independent nature of mathematics. When we seek for the realm in which mathematics is applicable, where it will result in an inner satisfying knowledge, then we see a merging of observation and of mathematical thinking, of the results of mathematical thinking, into an understanding of nature. But we may ask, what underlies what we experience in experiment; what is really happening when we feel the necessity for a form of knowledge that can even venture into historical knowledge? Where does this lead? We tend to look for connections everywhere for which the threads are simply not to be found in the material of contemporary science. Once we have grasped what it is that brings order into the connections between the facts, and in all spheres of knowledge—from the study of nature up to the study of history, we sense higher beings revealing themselves, purely soul-spiritual beings. If we come this far, then the door is open to a contemplation of an independent spiritual world.

My honored guests! I know just how much these lectures must seem unsatisfying to you, due to their sketchy and aphoristic nature. But rather than lecture on a narrowly defined subject, I chose to give a wide overview, even though in the particulars it could not be filled in. My intention was that you might learn something of the procedures involved in spiritual-scientific knowledge as it is meant here. I hoped you would get a feeling for the aims toward which it aspires. It aims for the greatest possible exactness and not some sort of fanciful or dilettante activity. For even in mathematics, what makes it so exact is the fact that we have an inner experience of it. In the Platonic age it was known why the words “God geometrizes” were inscribed as a motto on the school; it was clear that all who entered would receive a training in geometry and mathematics. In a similar way modern science of the spirit knows that to attain its goal it must have inner mathematical clarity. I hope you have received the impression, particularly as regards its methods, that the orientation of spiritual science is worthwhile. Perhaps on reflection you may come to ask the question: Can this not indeed lead to a fructification of our other sciences—not to belittle them, but to raise them to their true value? If I have achieved this to some degree, aphoristic and in some ways insufficient as these lectures have been, then my intention have been fulfilled.

• 1. The Boundaries of Natural Science, Bibl.-Nr. 322, eight lectures, Dornach 1920, Anthroposophic Press.

Now we have come to the end of our university courses. We have heard lectures from various individuals who have worked in our anthroposophical spiritual science for some time. We have also had a number of seminars which were intended to fill out what the lectures only sketched as a framework. In spite of the fact that all the participants in these lectures have worked hard, we must also consider the quality of the time spent together given the nature of such an event. All we were able to do was to let some light come in, as through individual windows in a building—that light which we believe is present in our anthroposophical spiritual science. Please consider what is contained in this room, the openings into which we are describing symbolically as windows of the spiritual-scientific movement. The contents of the room are various subjects that are just at their beginning; a richer work will exist ultimately. If you take this into account, you can understand why we could present only a small amount of what we might hope to give in such courses on similar occasions.

With such an event we hoped to draw students from all directions, and to our joy they have in fact appeared in great numbers. It is very gratifying to us and meaningful for the movement. For first and foremost, we would like to show, no matter how sketchily, that a genuine scientific attitude prevails in the anthroposophical movement. No doubt there are other spiritual intentions at work also, but these will have to be shown in other ways. Above all, these lectures are meant to demonstrate at the very least the will to strive toward real scientific knowledge. However, considering present-day conditions, anyone who understands the situation must feel: If we speak of a scientific attitude, a scientific spirit that plays directly into the living conditions of the modern human being, then it must be able to prove itself in the social sphere.

It is really necessary that the scientific spirit of our day shall give rise to ideas that can bring strength and healing into our social life. It is not enough today to have a scientific spirit that calls the human being into an existence estranged from life. We need a scientific spirit that will give us real health in our social life. The social situation confronts us full of riddles and urgent demands, even in a certain way threatening. If we have a feeling for these times, we can sense the need for real solutions—solutions that can be found only by those who grasp the social life with scientific understanding. We believe we are able to recognize this necessity from the most significant signs of this time. It is out of this recognition that our anthroposophical movement is artistically, scientifically and culturally conceived; this includes the building in Dornach called the Goetheanum, the Free University for Spiritual Science. Our wish is that out of a genuine scientific attitude these impulses can come to life in us and become really socially active.

We have attempted in the very structure of our lectures and seminars to make possible a recognition of the truly scientific spirit to which we aspire in our anthroposophical movement. Attacks from various directions accuse us of sectarianism or the desire to found a religion, but they come from those who don't know us, or—in some cases—from a malicious desire to slander us. The scientific spirit cannot of course be seen in the factual content of what is presented. Whoever would exclude empirical content, whether physical or super-sensible, shows that he himself is not imbued with the scientific spirit. It can only be seen in the treatment of the facts, in the striving to follow a definite method. And the real test of its validity—whether its results originated from sensory or supersensory experience—is based on the nature of this striving. Do we strive toward the scientific spirit that rules in the recognized sciences?

Is this striving demonstrated in our methodology, in our thinking with scientific accuracy? This is a justifiable question. It is also a worthwhile point of discussion inasmuch as this scientific spirit, as it prevails among us, is in need of improvement. One can determine whether our movement is scientific or not, not on the content we present but by how we proceed. Let it be shown in any instance that we have proceeded illogically, unscientifically, or in a dilettante fashion and—since we are serious about the correct development of our spiritual-scientific endeavors—we will make the necessary improvements without argument. We do not wish to deny this principle of progress in any way. So, enough about the underlying elements for discussing the scientific status of our endeavors.

We have striven to prove in the social realm, in life itself, what results from our knowledge of the world. In our discussions we have tried to present what we believe to be the truth regarding knowledge of the human being and the world. In the seminars we showed how the Waldorf School movement arose out of the anthroposophical movement. The lively manner of teaching in the Waldorf schools raises the question whether what is found in spiritual science will also prove itself in the shaping of today's young people. We don't want to exhaust ourselves in fruitless theoretical discussion: we want to let reality itself test what we believe is the truth toward which we should strive. Goethe said, “What is fruitful, that alone is true.” Even those far removed from modern philosophical pragmatism or the “as if” school must have their truth proven by its fruitfulness. We can declare ourselves in full agreement with the Goethean principle that only what is fruitful yields proof of its truth before reality—particularly where social truths are concerned. If what flows livingly out of spiritual science can return again into life, and if life can show that the result of recognized truth, or supposed truth, can send a human being out into life with ability, vigor, sureness, and enthusiasm and strength for work, then this is a proof of the truth which has been striven for. At the same time we have attempted something else, but it is really still too much in its infancy to be outwardly demonstrated.

In Der Kommende Tag, in Futura, we have put forth economic ideas which are intended to show that what is derived in a spiritual way, out of reality, also enables us to see the affairs of practical life in the right light. The time has not yet come when we can speak of these things becoming manifest, of fulfilling the conditions for a real proof. However, even in the economic realm, one may grant us the fact that we have not been afraid to extend something that was won purely in the spiritual out into practical life. This is actual testimony that we do not shy away from the tests of reality. How things develop in this region is perhaps not fully within our own will to determine. In such cases, even more than in the field of education, one is dependent on the practicalities of life, as well as how one is understood by the world and one's own circle.

In this way, we try to take into account the signs of the times. We have recently seen in some of our lectures that these signs point directly to spiritual-scientific demands; they also confront us with great social questions. But above all we seek to take into account the inner soul needs of the human being. For someone who is familiar with one area, for example the natural sciences, it is very easy to believe that we are already in possession of an infallible scientific method. Ultimately, however, what arises as science can only be fruitful for the whole evolution of humanity if it joins human evolution in a way that sustains the life of man. With this essential condition in mind, I ask you: Isn't there something in today's universities or in similar circumstances that can cause the soul to come somewhat into error? One can, of course, enter a laboratory and work in the dissection room, believing that one is working with a correct method and that one has an overview of all factors involved, grasping them in accord with present conditions and the level of humanity's evolution. But for humanity's evolution something else is necessary. Something is necessary which perhaps occurs very rarely, and the significance of which is not properly appreciated. It would be necessary that someone who has worked seriously and conscientiously with scientific spirit in the chemistry lab, observatory, or clinic, could then step into a history or aesthetics classroom and hear something there that would live in inner conformity with what he had learned in his technical courses. Such unity is needed—for the simple reason that regardless to what degree individuals may specialize, ultimately the things achieved in separate disciplines must work together in the process of general human evolution, and must spring from a common source.

We believe it is impossible today to experience a unity directly between, for instance, present historical pronouncements and the teachings of natural science. For this reason we strive toward what stands behind all scientific endeavors: the spiritual reality, the source that is common to them all. The aim of our striving is to come to know this spiritual reality. With our feeble powers we are striving to establish the validity of such knowledge of the spirit and its right to exist. In this lecture series and similar events, we have striven to show you what we are doing and how we do it, and we are grateful that you joined us.

May I touch on one additional subject: A short time ago, a coworker of long standing in our movement spoke with me. He knew that for spiritual-scientific reasons I must speak about two Jesus children. Until recently he hadn't told me of his intentions to follow this matter up in a conscientious manner studying the external aspect. His recent conversation with me was after he had finished his investigations. He said that he had compared the gospels thoroughly with one another, and had discovered that they don't begin to make sense until they are regarded from this spiritual-scientific viewpoint.

May research proceed thus in all realms! If it does, we know that our spiritual science will be able to stand fast. We do not fear the testing, no matter how detailed the examination may be. We have no fear of the request to verify. We only worry if someone opposes our viewpoint without proof, proof of all the individual details. The more carefully our spiritual research is tested, the more at ease we can be about it. This consciousness we bear deep within us. It is with such awareness that we have taken the responsibility of calling you all here, you who are striving to build a life of science and of scientific spirit. Today, my honored students, it is impossible to offer you the things of the outer world. In the places where this is done, our efforts are sometimes rejected in a surprising manner. Even so, your appearing here allows us to feel we are correct in saying that there are still souls among today's youth whose concern is the truth and striving toward the truth. Therefore we wish to say—I speak from the fullness of my heart, and I know I am also speaking for the coworkers of these courses we have truly enjoyed working with you. This is particularly gratifying because at the same time from other quarters attacks are raining down on us from ill-will, and we are called upon again and again to refute these attacks. We do as much as we can to make the refutations—as much as time permits. But really, the burden of proof lies with the one who makes an assertion; he should bring evidence of its truth. Otherwise, one could blithely throw assertions at anyone, leaving him to refute everything.

I only wish to indicate how the opposition operates toward us, personally attacking us rather than attempting to understand our ideas by discussing matters seriously with us.

What is most strongly held against us is that in one important area we have to insist upon setting ourselves against the well-intended strivings of the times. We cannot just go along with the general attitude to take what traditional science represents in the various fields and simply let it be carried in a popular way throughout the world. Rather, from our own knowledge we believe there is another need. Something must be brought into those quarters which consider themselves infallible these days. It is generally believed that such authority is held in those quarters that their ideas can be taken unaltered and be disseminated among the masses.

We believe, however, that certain scientific elements still lacking must enter those quarters to fructify their scientific work. The fact that we do not merely want the scientific spirit disseminated from certain quarters into the wide world but also want to bring a different spirit into science—this, I believe, is why we are confronted by such frightful opposition. It would be good if these matters were considered in a calm and objective way. For we must not hide the fact that we are in serious need of the collaboration of wider circles, even though every one of us is convinced of the scientific value of our endeavors. What worries us most is that we have so few coworkers who can really stand their ground. This is why it means so much to us that you, the university youth, have been coming to us now for some time. We have faith in you young students. We believe that what we need can sprout out of your youthful energy. Therefore, my honored fellow students, we would particularly like to work together with you in our field, as far as time and conditions permit.

It is with this spirit that we sought to permeate the work in these courses. Perhaps you can carry away with you the conviction that it has at least been our aspiration to work in this direction. I began today by comparing what we are offering to a closed room, opening out through windows to the surrounding world of spiritual science. Through these windows we have wanted to let fragments shine in of a world of knowledge, which we want to apply in a spiritual-scientific way. Now we are at the end of the course, and I wish to say a heartfelt “goodbye till we meet again” in similar circumstances.

But I would still like to return to the comparison with which I began the course. It is not generally my habit to pay homage to fine phrases, even when they are time-honored; rather, I like to return to just a simple expression of truth. In our cultural literature, a high-sounding phrase is often quoted as being Goethe's dying words, “Light, more light!” Well, Goethe lay in a tiny room in a dark corner when he was dying, and the shutters on the opposite window were closed. From my knowledge of Goethe I have every reason to believe that in truth his words were simply: “Open the shutters!” Now that I have dealt with that lofty phrase of my beloved and revered Goethe in an heretical manner, I would like to use my version of it as we end our work. My honored students! As we feel ourselves together in the room whose windows open out to spiritual knowledge, windows through which we have sought in a fragmentary way to let in what we believe to be light, I call to you out of the spirit that led us to invite you here: I call out to you, “Open the shutters!”

If you are disappointed about what you are about to hear, I would like to say in advance that today I want to discuss very elementary things [about the fourth dimension]. Those who want to delve deeper into this question should be very familiar with the higher concepts of mathematics. I would like to give you some very elementary and general concepts. One must distinguish between the possibility of thinking in a four-dimensional space and reality. Whoever is able to make observations there is dealing with a reality that extends far beyond what we know as the sensual-real. You have to do thought transformations when you go there. You have to let things play into mathematics a little, find your way into the way of thinking of the mathematician.

You have to realize that the mathematician does not take a step without accounting for what arrives at his conclusions. But we must also realize when we deal with mathematics that even the mathematician cannot penetrate a single step [into reality], that he cannot draw any conclusions [that go beyond what is merely possible in thought]. First of all, it is about simple things, but they become more complicated when one wants to arrive at the concept of the fourth dimension. We must be clear about what we mean by dimensions. It is best to examine the various spatial structures in terms of their dimensionality. They lead to considerations that were only tackled in the 19th century by great mathematicians such as Bolyai, Gauss and Riemann.

The simplest spatial size is the point. It has no extension at all; it must be conceived. It is the fixation of an extension in space. It has no dimension. The first dimension is the line. The straight line has one dimension, length. If we move the line, which has no thickness, ourselves, we step out of the one dimension, and the line becomes a surface. This has two dimensions, a length and a width. If we move the surface, we step out of these two dimensions and we get the body. It has three dimensions: height, width, depth (Figure 1).

If you move the body itself, if you move a cube around in space, you will again only get a spatial body. You cannot move space out of itself.

We need to turn to a few other concepts. If you look at a straight line, it has two boundaries, two endpoints A and B (Figure 2).

Let's imagine that we want A and B to touch. But if they are to touch, we have to curve the line. What happens? You cannot possibly remain within the [one-dimensional] line if you want to make A and B coincide. To connect points A and B, we have to step out of the straight line itself, we have to step out of the first dimension and into the second dimension, the plane. In this way, the straight line becomes a closed curve (that is, in the simplest case, a circle) by bringing its endpoints into alignment (Figure 3).

It is therefore necessary to go beyond the first dimension; you cannot remain within it. Only in this way can the circle be created. You can perform the same operation with a surface. However, this only works if you do not remain within the two dimensions. You have to enter the third dimension and then you can turn the surface into a tube, a cylinder. This operation is done in a very similar way to the way we brought two points into coincidence earlier, thereby moving out of the first dimension. Here, in order to bring two boundaries of the surface into coincidence, we have to move into the third dimension (Figure 4).

Is it conceivable that a similar operation could be carried out with a spatial structure that already has three dimensions itself? If you have two congruent cubes, you can slide one into the other. [Now imagine two congruent cubes as the boundaries of a three-dimensional prismatic body.] If you try to make one cube, which is colored red on one side [and blue on the opposite side], fit exactly over the other cube, which is otherwise [geometrically] identical but with the red and blue colors swapped, then you cannot make them fit except by rotating the cube (Figure 5).

Let us consider another spatial structure. If you take the left-hand glove, it is impossible for you to pull the left-hand glove over the right hand. But if you look at the two [mirror-symmetrical] gloves together, like the straight line with the end points A and B, you have something that belongs together. It is then a single entity, with a boundary [that is, with a mirror plane] in the middle. It is very similar with the two symmetrical halves of the human outer skin. 2

How can we now make two [mirror] symmetrical three-dimensional structures coincide? Only if we go beyond the third dimension, as we did with the first and second. We can also put the right or left glove over the left or right hand, respectively, when we walk through four-dimensional space.

[When constructing the third dimension (depth dimension) of the visualization space, we align the image of the right eye with that of the left eye and place it over it.

We now look at an example from Zöllner. We have a circle and a point P outside of it. How can we bring the point P into the circle without crossing the circle? This is not possible if we remain within the plane. Just as one has to go from the second dimension into the third when moving from a square to a cube, we also have to go out of the second dimension here. With a sphere, there is also no possibility of entering [into the interior] without [piercing the surface of the sphere or] going beyond the third dimension.

These are possibilities for thought, but they have a practical significance for the theory of knowledge, [in particular for the problem of the objectivity of the content of perception]. If we realize how we actually perceive, we will come to the following view. Let us first ask ourselves: How do we gain knowledge of bodies through our senses? We see a color. Without eyes, we would not perceive it. The physicist then says: Out there in space is not what we call color, but purely spatial forms of movement; they penetrate through our eye, are captured by the optic nerve, transmitted to the brain, and there, for example, the red arises. One may now ask: Is the red also present when there is no sensation?

Red could not be perceived without the eye. The ringing of a bell could not be perceived without the ear. All our sensations depend on the transformation of forms of motion by our physical and mental apparatus. However, the matter becomes even more complicated when we ask ourselves: Where is the red, this peculiar quality, actually located? Is it in the body? Is it a process of vibration? Outside there is a process of movement, and this continues right into the eye and into the brain itself. There are vibrational [and nervous] processes everywhere, but red is nowhere to be found. Even if you examine the eye, you would not find red anywhere. It is not outside, but it is also not in the brain. We only have red when we, as a subject, confront these processes of movement. So do we have no possibility at all to talk about how the red meets the eye, how a c sharp meets the ear?

The question is, what is this inner [representation], where does it arise? In the philosophical literature of the 19th century, you will find that this question runs through everything. Schopenhauer, in particular, has provided the following definition: The world is our representation. But what then remains for the external body? [Just as a color representation can be “created” by movements, so can] movement can arise in our inner self through something that is basically not moved. Let us consider twelve snapshots of a [moving] horse figure on [the inside of] a [cylinder] surface, [which is provided with twelve fine slits in the spaces between. If we look at the rotating cylinder from the side,] we will have the impression that it is always the same horse and that only its feet are moving. So [the impression of] movement can also arise through our [physical organization] when something is not moving at all [in reality]. This is how we arrive at a complete dissolution of what we call movement.

But what then is matter? If you subtract color, movement [shape, etc., i.e. what is conveyed by sensory perception] from matter, then nothing remains. If we already have the [secondary, i.e. “subjective” sensations [color, sound, warmth, taste, smell] within us, we must also place [the primary sensations, that is, shape and movement,] within us, and with that the external world completely disappears. However, this results in major difficulties [for the theory of knowledge].

Let us assume that everything is outside, how then do the properties of the object outside come into us? Where is the point [where the outside merges into the inside]? If we subtract all [sensory perceptions], there is no outside anymore. In this way, epistemology puts itself in the position of Münchhausen, who wants to pull himself up by his own hair. But only if we assume that there is an outside, only then can we come to [an explanation of] the sensations inside. How can something from the outside enter our inside and appear as our imagination?

We need to pose the question differently. Let us look at some analogies first. You will not be able to find a relationship [between the outside world and the sensation inside] unless you resort to the following. We return to the consideration of the straight line with endpoints A and B. We have to go beyond the first dimension, curve the line, to make the endpoints coincide (Figure 7).

Now imagine the left endpoint A [of this straight line] brought together with the right endpoint B so that they touch at the bottom, so that we are able to return to the starting point [via the coinciding endpoints]. If the line is small, the corresponding circle is also small. If I turn the [initially given] line into a circle and then turn larger and larger lines into circles, the point at which the endpoints meet moves further and further away from the [original] line and goes to infinity.

of the [original] line and goes to infinity. Only at infinity do the [increasingly large] circle lines have their endpoint. The curvature becomes weaker and weaker, and eventually we will not be able to distinguish the circle line from the straight line with the naked eye (Figure 8).

In the same way, when we walk on the Earth, it appears to us as a straight piece, although it is round. If we imagine that the two halves of the straight line extend to infinity, the circle actually coincides with the straight line.

The straight line can be conceived as a circle whose diameter is infinite.

Now, instead of a [geometric] line, imagine something that is real and that connects to a reality. Let us imagine that as the point C [on the circumference of the circle] progresses, cooling occurs, that the point becomes colder and colder the further it moves away [from its starting point] (Figure 9). Let us leave the point within the circle for the time being, and, as it becomes colder and colder, let it reach the lower limit A, B. When it returns on the other side, the temperature increases again. So on the way back, the opposite condition to the one on the way there occurs. The warming increases until the temperature at C is reached again, from which we started. No matter how extended the circle is, it is always the same process: a flow of heat out and a flow of heat in. Let us also imagine this with the [infinitely extended straight] line: as the temperature [on one side increasingly] dissipates, it can rise on the other side. We have here a state that dissipates on one side while it rebuilds on the other.

In this way, we bring life and movement into the world and approach what, in a higher sense, we can call an understanding of the world. We have here two states that are interdependent and interrelated. However, for everything you can observe [sensually], the process that goes, say, to the right has nothing to do with the one that comes back from the left, and yet they are mutually dependent.

We now compare the body of the external world with the state of cooling and, in contrast, our inner sensation with the state of warming. [Although the external world and inner sensation have nothing directly perceptible in common,] they are related to each other, mutually dependent [in an analogous way to the processes described above]. This results in a connection between the external world [and our internal world] that we can support with an image: [through the relationship between] the seal and the sealing wax. The seal leaves behind an exact imprint, an exact reproduction of the seal in the sealing wax, without the seal remaining in the sealing wax [and without any material from the seal being transferred to the sealing wax]. So in the sealing wax there remains a faithful reproduction of the seal. It is quite the same with the connection between the outside world and inner sensations. Only the essential is transferred. One state determines the other, but nothing (material) is transferred.

If we imagine that this is the case with [the connection between the] outside world and our impressions, we come to the following. [Geometric] mirror images in space behave like gloves from the left and right hand. [In order to relate these directly and continuously to each other,] we have to use a new dimension of space to help us. [Now the outside world and the inner impression behave analogously to geometric mirror images and can therefore only be directly related to each other through an additional dimension.] In order to establish a relationship between the outside world and inner impressions, we must therefore go through a fourth dimension and be in a third element. We can only seek the common ground [of the outside world and inner impressions] where we [are one] with them. [One can imagine these mirror images as] floating in a sea, within which we can align the mirror images. And so we come [initially in thought] to something that transcends three-dimensional space and yet has a reality. We must therefore bring our spatial ideas to life.

Oskar Simony has tried to represent these animated spatial structures with models. [As we have seen, one comes] from the consideration of the zero-dimensional [step by step] to the possibility of imagining four-dimensional space. [On the basis of the consideration of mirror-symmetrical bodies, that is, with the help of] symmetries, we can first [most easily] recognize this space. [Another way to study the peculiarities of empirical three-dimensional space in relation to four-dimensional space is to study the knotting of curves and ribbons.] What are symmetry conditions? By intertwining spatial structures, we cause certain complications. [These complications are peculiar to three-dimensional space; they do not occur in four-dimensional spaces.]

Let's do some practical thinking exercises. If we cut a band ring in the middle, we get two such rings. If we now cut a band whose ends have been twisted by 180° and then glued, we get a single twisted ring that does not disintegrate. If we twist the ends of the tape 360° before gluing them together, then when we cut it, we get two intertwined rings. Finally, if we twist the tape ends 720°, the same process results in a knot.

Anyone who reflects on natural processes knows that such convolutions occur in nature; [in reality,] such intertwined spatial structures are endowed with forces. Take, for example, the movement of the Earth around the Sun, and then the movement of the Moon around the Earth. It is said that the Moon describes a circle around the Earth, but [if you look more closely] it is a line that is wrapped around [a circle, the orbit of the Earth], thus a helix around a circular line. And then we have the sun, which rushes through space so fast that the moon makes an additional spiral movement around it. So there are very complicated lines of force extending in space. We have to realize that we are dealing with complicated concepts of space that we can only grasp if we do not let them become rigid, if we have them in a fluid state.

Let us recall what has been said: the zero-dimensional is the point, the one-dimensional is the line, the two-dimensional the surface and the three-dimensional the body. How do these concepts of space relate to each other?

Imagine you are a creature that can only move along a straight line. What would the spatial perceptions of such a being, which itself is only one-dimensional, be like? It would not perceive its own one-dimensionality, but would only imagine points. This is because, if we want to draw something on a straight line, there are only points on the straight line. A two-dimensional being could encounter lines, and thus distinguish one-dimensional beings. A three-dimensional being, such as a cube, would perceive the two-dimensional beings. Man, then, can perceive three dimensions. If we reason correctly, we must say to ourselves: Just as a one-dimensional being can only perceive points, as a two-dimensional being can only perceive one dimension, and a three-dimensional being can only perceive two dimensions, so a being that perceives three dimensions can only be a four-dimensional being. The fact that a human being can define external beings in three dimensions, can [deal with] spaces of three dimensions, means that he must be four-dimensional. And just as a cube can only perceive two dimensions and not its third, it is true that the human being cannot perceive the fourth dimension in which he lives.

Today I want to discuss some elementary aspects of the idea of multidimensional space [among other things, in connection with the] spirited Hinton.

You will recall how we arrived at the concept of multi-dimensional space, having considered the zeroth dimension [last time]. I would like to briefly repeat the ideas of how we can move from two- to three-dimensional space.

What do we mean by a symmetrical behavior? How do I align a red and a blue [flat figure, which are mirror images of each other]?

With two halves of a circle, I can do this relatively easily by sliding the red [half] circle into the blue one (Figure 10).

This is not so easy in the following [mirror]symmetrical figure (Figure 11). I cannot make the red and blue parts coincide [in the plane], no matter how I try to slide the red into the blue.

But there is a way [to achieve this anyway]: if you step out of the board, that is, out of the second dimension [and use the third dimension, in other words, if you] place the blue figure on the red one [by rotating it through the space around the mirror axis].

The same applies to a pair of gloves: I cannot match one with the other without stepping out of [three-dimensional] space. You have to go through the fourth dimension.

Last time I said that in order to develop an understanding of the fourth dimension, you have to make [the relationships in] space fluid, thereby creating conditions similar to those you have when moving from the second to the third dimension. In the last lesson, we created spatial structures out of paper strips that intertwined. Such interweaving causes certain complications. This is not a game, but such inter-weavings occur in nature all the time. Anyone who reflects on natural processes knows that such inter-weavings really do occur in nature. Material bodies move in such intertwined spatial structures. These movements are endowed with forces, so that the forces also intertwine. Take the movement of the earth around the sun and then the movement of the moon around the earth. The moon moves in an orbit that is itself wound around the earth's orbit around the sun. It thus describes a spiral around a circular line. Because of the movement of the sun, the moon describes another spiral around this. The result is very complicated lines of force that extend through the whole space.

The heavenly bodies behave in relation to each other like the intertwined strips of paper [by Simony, which we looked at last time]. We have to keep in mind that we are dealing with complicated spatial concepts that we can only understand if we do not let them become rigid. If we want to grasp space [in its essence], [we must first conceive it as rigid, but then] make it completely fluid again. [You have to go as far as zero]; the [living] point can be found in it.

Let us once again visualize the structure of the dimensions]. The point is zero-dimensional, the line is one-dimensional, the surface is two-dimensional and the body is three-dimensional. The cube has the three dimensions: height, width and depth. How do the spatial structures [of different dimensions] relate to each other? Imagine that you are a straight line, that you have only one dimension, that you can only move along a straight line. If such beings existed, what would their concept of space be like? Such beings would not perceive one-dimensionality in themselves, but would only be able to imagine points wherever they went. Because in a straight line, if we want to draw something in it, there are only points. A two-dimensional being would only encounter lines, so it would only perceive one-dimensional beings. [A three-dimensional being like] the cube would perceive two-dimensional beings, but could not perceive its [own] three dimensions.

Now, humans can perceive their three dimensions. If we reason correctly, we must say to ourselves: Just as a one-dimensional being can only perceive points, a two-dimensional being only straight lines, and a three-dimensional being only surfaces, so a being that perceives three dimensions must itself be a four-dimensional being. The fact that humans can define external beings in terms of three dimensions, can [deal with] spaces of three dimensions, means that they must be four-dimensional. And just as a cube can perceive only two dimensions and not its third, so it is clear that man cannot perceive the fourth dimension in which he lives. Thus we have shown [that man must be a four-dimensional being]. We swim in the sea [of the fourth dimension, like ice in water].

Let us return once more to the consideration of mirror images (Figure 11). This vertical line represents the cross-section of a mirror. The mirror reflects an image [of the figure on the left]. The process of reflection points beyond the two dimensions into the third dimension. [To understand the direct and continuous connection between the mirror image and the original, we have to add a third dimension to the two.

[Now let us consider the relationship between external space and internal representation.] The cube here apart from me [appears as] an idea in me (Figure 12). The idea [of the cube] is related to the cube like a' mirror image to the original. Our sensory apparatus [creates an imagined image of the cube. If you want to align this with the original cube, you have to go through the fourth dimension. Just as the third dimension has to be transitioned to (during the continuous execution of the two-dimensional) mirroring process, our sensory apparatus has to be four-dimensional if it is to be able to establish a [direct] connection [between the imagined image and the external object].

If you only imagined [two-dimensionally], you would [only] have a dream image in front of you, but you would have no idea that there is an object outside. Our imagination is a direct inversion of our ability to imagine [external objects by means of] four-dimensional space.

The human being in the astral state [during earlier stages of human evolution] was only a dreamer, he had only such ascending dream images.” He then passed from the astral realm to physical space. Thus we have mathematically defined the transition from the astral to the [physical-] material being. Before this transition occurred, the astral human being was a three-dimensional being and therefore could not extend his [two-dimensional] ideas to the objective [three-dimensional physical-material] world. But when he [himself] became physical-material, he still acquired the fourth dimension [and could therefore also experience three-dimensionally].

Due to the peculiar design of our sensory apparatus, we are able to align our perceptions with external objects. By relating our perceptions to external things, we pass through four-dimensional space, imposing the perception on the external object.

How would things appear if we could see from the other side, if we could enter into things and see them from there? To do that, we would have to pass through the fourth dimension.

The astral world itself is not a world of four dimensions. But the astral world together with its reflection in the physical world is four-dimensional. Anyone who is able to see the astral world and the physical world at the same time lives in four-dimensional space. The relationship of our physical world to the astral world is a four-dimensional one.

One must learn to understand the difference between a point and a sphere. In reality, this point would not be passive, but a point radiating light in all directions (Figure 13).

What would be the opposite of such a point? Just as there is an opposite to a line that goes from left to right, namely a line that goes from right to left, there is also an opposite to the point. We imagine an enormous sphere, in reality of infinite size, that radiates darkness from all sides, but now inwards (Figure 14). This sphere is the opposite of the point.

These are two real opposites: the point radiating light and infinite space, which is not a neutral dark entity, but one that floods space with darkness from all sides. [As a contrast, this results in] a source of darkness and a source of light. We know that a straight line that extends to infinity returns to the same point from the other side. Likewise, it is with a point that radiates light in all directions. This light comes back [from infinity] as its opposite, as darkness.

Now let us consider the opposite case. Take the point as the source of darkness. The opposite is a space that radiates light from all sides.

As was recently demonstrated [in the previous lecture], the point behaves in this way; it does not disappear [into infinity, it returns from the other side] (Figure 15).

[Similarly, when a point expands or radiates out, it does not lose itself in infinity; it returns from infinity as a sphere.] The sphere, the spherical, is the opposite of the point. Space lives in the point. The point is the opposite of space.

What is the opposite of a cube? Nothing other than the whole of infinite space, except for the piece that is cut out here [by the cube]. So we have to imagine the [total] cube as infinite space plus its opposite. We cannot do without polarities if we want to imagine the world as powerfully dynamic. [Only in this way] do we have things in their life.

If the occultist were to imagine the cube as red, the space around it would be green, because red is the complementary color of green. The occultist not only has simple ideas for himself, he has vivid ideas, not abstract, dead ideas. The occultist must enter into things from within himself. Our ideas are dead, while the things in the world are alive. We do not live with our abstract ideas in the things themselves. So we have to imagine the infinite space in the corresponding complementary color to the radiating star. By doing such exercises, you can train your thinking and gain confidence in how to imagine dimensions.

You know that the square is a two-dimensional spatial quantity. A square composed of four red- and blue-shaded sub-squares is a surface that radiates differently in different directions (Figure 16). The ability to radiate differently in different directions is a three-dimensional ability. So here we have the three dimensions of length, width and radiance.

What we did here with the surface, we also think of as being done for the cube. Just as the square above was made up of four sub-squares, we can imagine the cube as being made up of eight sub-cubes (Figure 17). This initially gives us the three dimensions of height, width and depth. Within each sub-cube, we can then distinguish a specific light-emitting capacity, which results in a further dimension in addition to height, width and depth: the radiation capacity.

You can imagine a square made up of four sub-squares, a cube made up of eight different sub-cubes. And now imagine a body that is not a cube, but has a fourth dimension. We have created the possibility of understanding this through radiative capacity. If each [of the eight partial cubes] has a different radiating power, then if I have only the one cube that radiates only in one direction, if I want to obtain the cube that radiates in all directions, I have to add another one on the left, doubling it with an opposite one, I have to put it together out of 16 cubes.

Next lesson we will have the opportunity to consider how we can think of a multidimensional space.

My dear friends, today I will continue with the difficult chapter we have undertaken to take on. In doing so, it will be necessary to refer to the various things that I have already mentioned in the last two lectures. Then today I would also like to create the basic lines and basic concepts in order to [the more exact geometrical relationships as well as] the interesting practical aspects of theosophy, to make them our own.

You know that we have tried to imagine four-dimensional space in its potentiality for the very reason that we can at least create some kind of concept about the so-called astral realm as well as about the higher realms, about higher existence in general. I have already indicated that entering the astral space, the astral world, is initially something tremendously confusing for the secret disciple. For those who have not studied these things in detail, who have not even studied them theoretically, who have not even studied Theosophy theoretically, it is extremely difficult to even begin to form an idea of the very different nature of the things and entities that confront us in the so-called astral world. Let us once again point out how great this diversity is.

As the simplest thing, I mentioned that we have to learn to read every number symmetrically. The secret student, who is only accustomed to reading numbers as they are read here in the physical world, will not be able to find his way through the labyrinth of the astral. If you have a number in the astral, for example 467, you have to read it as 764. You have to get used to reading everything symmetrically, to seeing everything symmetrically (in a mirror image). That is the basic condition. This is still easy as long as we are dealing with spatial structures or numbers. It becomes more difficult when we come to time relationships. When we come to time relationships, the matter also becomes symmetrical in the astral, in such a way that what comes later appears to us first and what comes earlier appears later. So when you observe astral processes, you also have to be able to read backwards from front to back. These things can only be hinted at, because they sometimes seem quite grotesque to those who have never had an idea of them. In the astral, the son is there first and then the father; in the physical, the egg is there first and then the chicken. In the physical, it is different. In the physical, birth comes first, and then the birth is an emergence of a new thing from an old one. In the astral, it is the other way around. There, the old emerges from the new. In the astral, what is paternal or maternal nature devours what is filial or daughterly nature for the appearance.

In Greek, you have a pretty allegory. The three gods Uranus, Kronos and Zeus symbolize the three worlds. Uranus represents the heavenly world: Devachan; Kronos represents the astral; Zeus the physical. Kronos is said to devour his children.” So in the astral, one does not give birth, but is consumed.

But things get very complicated when we look at the moral aspect of the astral plane. This also appears in a kind of reversal or mirror image. And that is why you can imagine how differently things appear when we interpret things as we are accustomed to interpreting them in the physical. In the astral, for example, we see a wild animal approaching us. This is not to be understood in the same way as in the physical. The wild animal is choking us. This is the appearance that someone who is accustomed to reading things in the same way as external events has. But the wild animal is in truth something that exists within ourselves, that lives in our own astral body and that is choking us. What approaches you as a strangler is rooted in your own desire. So you can experience that when you have a thought of revenge, this thought of revenge appears to you as a strangling angel that approaches you from outside and harasses you.

In truth, everything radiates from us [in the astral realm]. We must regard everything that we see approaching us in the astral as emanating from us (Figure 18). It comes from the sphere, from all sides, as if from infinite space, it penetrates into us. But in reality it is nothing other than what our own astral body sends out.

We only really read the astral [and only then] find the truth when we are able to bring the peripheral into the center, to see and interpret the peripheral as the central. The astral seems to come at you from all sides. Think of it this way: in reality, it is something that radiates out from you in all directions.

I would like to familiarize you with a term that is very important in occult training. It appears in a wide variety of works on occult research, but is rarely understood correctly. Those who have reached a certain level of occult development must learn to see everything that is still karmically predisposed in them – joy, lust, pain, and so on – in the astral outside world. If you think theosophically in the right sense, you will realize that the outer life, our body, in the present age is nothing more than a result, an average of two currents coming from opposite directions and merging into each other .

Imagine a current coming from the past and one coming from the future, and you have two currents that merge and actually intersect at every point (Figure 19). Imagine a red current in one direction and a blue current in the other direction. And now imagine, for example, four different points in this intersection. [Then, at each of these four points, we have] an interaction of these red and blue currents. [This is an image for the interaction of] four successive incarnations, where in each incarnation something comes towards us from one side [and something from the other]. You can always say to yourself, there is a current that comes towards you and a current that you bring with you. Man flows together out of these two currents.

You get an idea of it if you think of it this way. Today you sit here with different experiences, tomorrow at the same hour you will have a different set of events around you. Imagine the events that you will have by tomorrow are already all there. It would then be the same experience as if you were looking at a panorama. It would be as if you were approaching these events, as if these events were coming towards you spatially. So imagine that the stream that is coming towards you from the future brings you these events, then you have the events between today and tomorrow in this stream. You allow the future flowing towards you to be carried by the past.

In every period of time, your life is an intersection of two currents, one from the future to the present and the other from the present to the future. Where the currents meet, a congestion occurs. Everything that a person still has ahead of him must be seen emerging as an astral phenomenon. This is something that speaks an incredibly impressive language.

Imagine that the secret disciple [comes to the point in his development where he] is supposed to look into the astral world, where the senses are opened to him so that he would see emerging around him as outer phenomena in the astral world that which he would still have to experience before the end of the present period. This is a sight that is very powerful for every human being. We must therefore say that it is an important step in the course of occult training for the human being to be confronted with the astral panorama, the astral phenomenon, of what he still has to experience until the middle of the sixth root race, because that is how long our incarnations will last. The path opens up before him. No secret disciple will experience it differently, except that he sees as an external phenomenon what he still has to face in the near future up to the sixth root race.

When the disciple has advanced to the threshold, the question arises: Do you want to live through all this in the shortest conceivable time? Because that is what it is about for the one who wants to receive the initiation. If you think about it, you have your own future life in front of you as an external panorama in a moment. That, in turn, is what characterizes our view of the astral. For one person, it is something that makes them say, “No, I'm not going in there.” For another, on the other hand, it is something that makes them say, “I have to go in there.” This point in the process of development is called the 'threshold', the decision, and the phenomenon that one has there, oneself with everything that one still has to experience and live through, is called the 'guardian of the threshold'. The guardian of the threshold is therefore nothing other than our own future life. It is ourselves. Our own future life lies behind the threshold.

You see in this another peculiarity of the astral world of appearance, namely, that when the astral world is suddenly opened to someone through some event – and such events do occur in life – that person must first face something incomprehensible. It is a terrible sight, which could not be more confusing for those people upon whom, unprepared, the astral world suddenly breaks in through some event. It is therefore eminently good to know what we have now discussed, so that in the event of the astral world breaking in, one knows what to do. It may be a pathological event, a loosening between the physical body and the etheric body or between the etheric body and the astral body. Through such events, a person may be unexpectedly transported into the astral world and gain insights into astral life. If this happens, the person will come and say that he sees this or that apparition. He sees it and does not know how to read it, because he does not know that he has to read symmetrically, that he has to understand every wild animal that approaches him as a reflection of what lies within himself. Indeed, the astral powers and passions of man appear in Kamaloka in the most diverse forms of the animal world.

It is not a particularly beautiful sight to see people in Kamaloka who have just been reaped. At that moment they still have all their passions, urges, desires and cravings. Such a person in Kamaloka no longer has his physical body or etheric body, but in his astral body he still has everything that connected him to the physical world, that can only be satisfied through the physical body. Imagine an average citizen of the present day who has achieved nothing special in his past life and has not made any effort to achieve anything, who has never done much for his religious development, who may not have abandoned religion in theory, but practically, that is, in his feelings and attitudes, has thrown it overboard. In that case it is not a living element in him. What then is in his astral body? There are only things that can be satisfied through the physical organism. For example, he craves palate enjoyment. But the palate would have to be there for that, so that this desire can be satisfied. Or man craves for other pleasures, which can only be satisfied by setting his physical body in motion. Suppose he had such a craving, but the body was gone. Then all this lives in his astral body. This is the situation in which man finds himself when he has died without astral purification and cleansing. He still has the desire for the pleasures of the palate and the other things, but not the possibility of satisfying them. This is what causes the torment and horror of the life in Kamaloka. Therefore, the desire must be laid aside in Kamaloka if man dies without astral purification. Only when this astral body has learned that it can no longer satisfy its desires and wishes, that it must unlearn them, is it freed.

[In the astral world] the instincts and passions take on animal forms. As long as the person is embodied in the physical body, the shape of their astral body is somewhat based on this physical body. But when the outer body is gone, then the instincts, desires and passions, as they are in their animal [nature], come into their own in their own form. So in the astral world, a person is an image of their instincts and passions.

Because these astral beings can make use of other bodies, it is dangerous to let mediums enter into a trance when there is no clairvoyant is present to avert evil.

In the physical world, the lion is a plastic expression of certain passions, the tiger is an expression of other passions, and the cat is an expression of yet other passions. It is interesting to see how each animal is the plastic expression of a passion, of an urge.

In the astral, in Kamaloka, man is therefore approximately similar to [animal nature] through his passions. This is the source of the misunderstanding regarding the doctrine of transmigration of souls that has been attributed to Egyptian and Indian priests and teachers of wisdom. You should live in such a way that you do not incarnate as an animal, says this teaching. But this teaching never speaks of the physical life, but of the higher life, and its only aim was to persuade people on earth to lead such a life that after death in Kamaloka they would not have to develop their animal form. Those who develop the characteristics of a cat will appear in Kamaloka as a cat. The fact that one also appears as a human being in Kamaloka is the meaning of the rules of the doctrine of the transmigration of souls. The true teachings have not been understood by the scholars; they only have an absurd idea of them.

Thus we have to deal with a complete mirror image of what we actually think and do here in the physical world in every area – in the areas of number, time and moral life – when we enter the astral realm. We must get used to reading symmetrically, because we must be able to do so when we enter the astral space.

The easiest way for a person to get used to reading symmetrically is to build on such elementary mathematical ideas as we have hinted at in the previous lecture and as we will get to know more and more in the following discussions. I would like to start with a very simple idea, namely the idea of a square. Imagine a square as you are accustomed to seeing it (Figure 20). I will draw the square so that the four sides are drawn in four different colors.

This is the physical appearance of the square. Now I would like to draw the devachan aspect of the square on the board. It is not possible to do this exactly, but I would like to give you an approximate idea of what a square would look like in the mind. The mental counter-image [of a square] is approximately like a cross (Figure 21).

We are dealing here mainly with two perpendicular intersecting axes. Two lines that pass through each other, and that's it. The physical counter-image is created by drawing perpendicular lines on each of these axes. The physical counter-image of a mental square can best be imagined as a congestion [of two mutually intersecting currents]. Let us imagine these perpendicular axis lines as currents, as forces that act outwards from the point of intersection, and let us imagine countercurrents to these currents, only now in the direction from outside to inside (Figure 22). A square then enters into the physical world by imagining these two types of currents or forces - one from the inside, the other from the outside - as accumulating against each other. The currents of force are thus limited by accumulations.

With this, I have given a picture of how everything mental relates to the physical. Likewise, you can construct the mental counterpart for any physical thing. The square here is only the simplest of examples.

If you could construct a correlative for every physical thing that corresponds to the physical world in the same way that two perpendicular lines correspond to a square, then you would obtain the devachan or mental image for every physical thing. With other things, it is of course much more complicated.

Now imagine a cube instead of a square. The cube is very similar to the square. The cube is a body that is bounded by six squares. Mr. Schouten made these six squares that bound the cube specially. Now, instead of the four bounding lines that are present in the square, imagine six bounding surfaces. Imagine that instead of vertical lines we have vertical surfaces as a kind of congestion, and then assume that you have not two but three axes standing on one another [vertically], and you have the boundary of the cube. Now you can also imagine what the mental correlate of the cube is. You have again two things that challenge each other reciprocally. The cube has three perpendicular axes and three surface directions; we have to think of congestion effects in these three surface directions (Figure 23). We cannot imagine the three axes and the six surfaces, as before the two axes and four lines, in any other relationship than by thinking of a certain contrast.

Anyone who reflects on this will have to admit that we cannot imagine this without forming a certain concept of the opposition, namely the opposition of activity and an obstruction, a counter-activity. You have to introduce the concept of opposition here. The matter is still simple here. By entwining ourselves around geometric concepts, we will be able to construct the mental counter-images of more complicated things in an appropriate way. Then we will find the way and to some extent reach higher knowledge. But you can already imagine the colossal complexity that arises when you think of another body and look for its mental counter-image. Many complicated things come to light. And if you were to imagine another person and their mental counterpart, with all their spatial forms and their activity, you can imagine the complicated mental structure that this produces. In my book 'Theosophy', I was only able to give a rough idea of what mental counter-images look like.

We have three dimensions, three axes in the cube. On each axis we have the corresponding perpendicular planes on both sides. So you must now be clear about the fact that the contrast I have spoken of is to be understood in such a way that you imagine each face of the cube as having come into being in a way similar to the way I described human life earlier, as the intersection of two currents. You can imagine currents emanating from the center point. Imagine space in one axial direction, flowing outwards from the center, and in the other direction, flowing in from infinity, another current. And this [imagine] flowing in two colors, one red, the other blue. At the moment they meet, they will flow into a surface, a surface will arise, so that we can assume the surface of the cube to be the meeting point of two opposing currents in a surface. This gives a vivid idea of what a cube is.

The cube is therefore an intersection of three currents acting on each other. If you think about it, you are not dealing with three, but with six directions: forward-backward, up-down, right-left. So you have six directions. And indeed, that is the case. Then the matter becomes even more complicated by the fact that you have two types of currents: One in the direction of a point, the other coming from infinity. This will give you a perspective on the practical application of the higher, theoretical theosophy. I have conceived every direction in space as two opposing currents. And if you then imagine a physical body, then you have in that physical body the result of these two currents running into each other.

Let us now denote these six currents, these six directions, with six letters a, b, c, d, e, f. If you could visualize these six directions or currents — we will come to being able to do this next time — and you would imagine the first and last, a and f, erased, then you would be left with four. And that is what I now ask you to take into account: these four that remain are the four that you can perceive when you see the astral world alone.

I have tried to give you an idea of the three [ordinary dimensions] and of three [further] dimensions that actually behave in the opposite way. It is through the interaction of these dimensions and their counteraction that physical bodies arise. But if you think a little way away from the physical [dimension] and a little way away from the mental on the other side, you are left with four dimensions. These then represent the astral world existing between the physical and mental worlds.

The theosophist's view of the world is such that it necessarily has to work with a higher sense of geometry that goes beyond ordinary geometry. The ordinary geometer describes the cube as bounded by six squares. We must understand the cube as the result of six currents running into each other, that is, as the result of a movement and its reversal, of the interaction of opposing forces.

I would like to show you another such concept outside in nature, where a real contrast has taken place that contains a deep secret of the world's development before the eyes of man. In the “Fairytale of the Snake and the Lily”, Goethe speaks of the “revealed secret”, and that is one of the truest and wisest words that can be spoken at all. It is true, there are secrets in nature that can be grasped with hands, but are not seen by people. We are dealing with reversal processes in nature in many cases. I would like to show you one such reversal process.

Let us compare humans with plants. When compared to plants, humans behave as follows. What I am about to say is not a game, even if it initially seems like one. It is something that points to a deep mystery. What does a plant have in the ground? Its roots. And upwards it develops stems, leaves, flowers and fruit. The main part of the plant, the root, is in the earth, and the organs of reproduction it develops upwards, towards the sun, which we can call the chaste way of reproducing. Imagine the whole plant turned upside down, with the root becoming the head of a human being. Then you have the opposite of the plant in the human being, who has his head at the top and his reproductive organs at the bottom. And the animal is in the middle of it all, as a stowage. If you turn the plant upside down, you get a human being. That is why the occultists of all times draw this with three lines (Figure 24).

One [line] as the symbol of the plant, one as the [symbol] of the human being, and one in the opposite direction as the [symbol] of the animal – three lines that together form the cross. The animal has the transverse position, it thus crosses what we have in common with the plant.

You know that we speak of an all-soul, of which Plato says that it is crucified to the cosmic body, that it is chained to the cross of the cosmic body.? Imagine the world soul as plant, animal and human being, and you have the cross. By living in these three realms, the world soul is chained to this cross. As a result, you will find the concept of congestion expanded. You will find it expanded by something in nature. Two complementary, diverging, but interlocking currents form plants and humans, with congestion being the animal. Thus, the animal actually places itself between an upward and a downward current. In this way, the Kamaloka [astral sphere] interposes itself between Devachan and the physical world. Thus, something interposes itself between these two symmetrical worlds, between Devachan and the physical world, and acts between them, acting on both sides like a dam. The outer expression of this Kamaloka world is the animal world.

Those who already have organs for this world, which must be grasped with strength, will recognize what we see in the three kingdoms in their mutual relationship to one another. If you understand the animal kingdom as emerging from a congestion, if you understand the three kingdoms as mutual congestion, then you will find the position that the plant kingdom has to the animal kingdom and the animal kingdom to the human kingdom. The animal is perpendicular to the other two directions, and the other two are two complementary currents that merge into each other. The lower realm serves the higher realm as food. This is something that allows a small glimpse of the very different kind of relationship between humans and plants and between animals and humans. Those who feed on animals are therefore related to a congestion.

The real effect consists in the encounter of opposing currents. This is the beginning of a series of thoughts that you may later see in a strange and very different way.

We have seen that the square is created when two axes are intersected by lines. The cube is created by intersecting three axes through surfaces. Can you now imagine four axes intersecting through something? The cube is the boundary of the spatial structure that is created when four axes are intersected.

The square limits the three-dimensional cube. Next time, we will see whose boundary the cube itself is. The cube bounds a four-dimensional structure.

Answering Questions

[What does it mean to] imagine six currents, of which two must be imagined as having been extinguished, and so on?

The six currents must be thought of as two times three currents: three acting from the inside out according to the three axial directions, and the other three as flowing towards these from infinity. For each axial direction, there are thus two types, one going from the inside out, the other coming from the outside in the opposite direction. If we call the two categories positive and negative, plus and minus, we have:

math figur

And of this [in order to get to the astral space, we have to] imagine an entire direction, [for example the] inner and outer flow, erased, so for example +a and -a.