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The Rudolf Steiner Archive

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Anthroposophy and Science
GA 324

Lecture III

18 March 1921, Stuttgart

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.