The Rudolf Steiner Archive

My dear friends,

Today it is my object by giving you a few indications to bring these observations to a close for the time being.

It is indeed obvious that what we have sought for in the former course and in this one can only come out fully when we are in a position to extend our treatment of the subject further. Today I will have a few remarks to make on this phase of the matter, at the conclusion of the lecture.

Let me first give a general summary of what we have taken under consideration in connection with heat and the matter related to it. Out of the array of concepts you have got, I will draw your attention to certain ones. They are the following. When we bring before our eyes the realms of reality that we are able to distinguish in physics, we may list them as follows:

The solid realm, which was have called \(Z'\)
The fluid realm, which we have called \(Y'\)
The gaseous or aeriform world, denoted by \(X'\)
The realm of chemical effects, which we call \(Y\)

And lastly, by \(Z\) we have denoted the life activity realm (see Table at end.) Moreover, we considered yesterday very definite conditions obtaining in regard to the heat state when we pass from X to \(X'\) and from \(Y\) to \(Y'\). We tried for example to bring before you the facts which showed how chemical effects could make themselves felt in the fluid element. One who strives to comprehend chemical processes finds the following: Wherever chemical processes are taking place, wherever chemical combinations and chemical dissociations occur, all that has a certain relation to the fluid element must enter in its own particular way into the solid or gaseous realms in order for the chemical effects to manifest themselves there. Thus when we consider our terrestrial chemistry we must keep before our eyes an interpenetration, and with this interpenetration, a kind of mutual binding of chemical effects and the fluid realm. Our terrestrial chemistry presents to us, as it were, the fluid element animated by chemical effects.

But now, you will readily see that when we consider these various realms of reality it is impossible for us to think that this working of one realm in another is limited to the activity of heat in the gaseous realm. The other realms also work within each other. These call forth their appropriate effects in this or that field of action. We can indeed say the following: although chemical effects work primarily in the fluid medium since they have an inner relationship to is, we have also to visualize the working of the chemical on X′, that is to say a direct working on the chemical or gaseous or aeriform bodies. When I say “chemical effect” you must not think of that which comes to clear manifestation and is penetrated with an inner spirituality in the blue-violet portion of the spectrum. Here we have the chemical effect standing, as it were, by itself in a certain independence over against the material realm. When, however, we speak of chemical processes, we are really dealing with this effect as it interpenetrates physical bodies. We must conceive of something here in this chemical realm that, at the outset, has nothing to do with ponderable matter, but interpenetrates it, and in particular does it interpenetrate the fluid element owing to an inner relationship that I showed you yesterday. But let us now ask ourselves the question: What happens when the chemical effect picks out (figuratively speaking) the next realm, the gaseous, or its activities? Then it must happen, considering the matter simply from the external point of view, that something takes its rise in the gaseous which shows an inner relationship to the manifestation of this effect in fluids, which can be compared to this manifestation. In the fluid, the chemical effect seizes upon the material, as it were, and brings this material into such a condition that a mutual interaction sets in. When we put the fluid element before us in thought, we must conceive of it as in mutual reaction with the chemical effect. Let us assume, however, that the action does not go so far as to admit of this seizing of the chemical effect on the matter itself, but let us assume that it works on the matter from the outside only, that it is a stage removed from it as compared to its action on the fluid. Then we have as in the gaseous, a process in which the chemical effect accompanies the material, in one stage removed as compared to its action in fluids. Then there comes about a certain wide independence of the imponderable as compared to the material carrier. In chemical processes proper, the imponderable seizes definitely on the material. Here, however, we come upon a realm where there is not this definite linkage where the imponderable does not definitely insert itself into matter. This is the case in the acoustical realm, in the effect of tone; while in chemical processes in matter we have a complete submergence of the imponderable in matter, in tone we have a persistence of the imponderable as such, a preservation of it in gaseous or aeriform matter. This leads us to something further. It leads us to the point when we have to say: There must be some reason why in fluids the imponderable seizes directly on the material, while in tone effects in the gaseous realm, the imponderable is less able to do this. If we observe chemical activity and have a feeling for what is to be seen within the physically visible, then we will as a matter of course, understand that it belongs to the nature of matter that chemical phenomena go as they do. That is to say: the imponderable is there as something which is a characteristic of matter. It is not possible otherwise than in this way, that when we are dealing with terrestrial matter the seizing upon the imponderable matter takes place through the earth. By means of the forces of the earth, the chemical effect is, so to speak, seized upon and works within the fluids. You see the forces of form stretched out over the whole terrestrial realm and active by virtue of the fact that these forces of form get hold of the interpenetrating chemical effect. When we really understand correctly that we have here the forces of the earth, then we have understood something further, if we will grasp the meaning of tone in the air, namely that an opposite kind of force is involved in tone. That is, we have to think as active in tone a force passing into the earth in all directions from the cosmos, a tendency overcoming the earth forces, and thus striving to separate the imponderable from the earth. This is the peculiarity of the tone world. It is this which gives a certain characteristic to the physics of tone, of acoustics. For in this realm we can on the one hand study the material processes and on the other hand we can live in the world of tone by means of our sensations without paying the slightest attention to the acoustical side. What does acoustics matter to us perceiving men, when we live in tone with our sensations? Acoustics is a beautiful science; it reveals for us striking inner laws and an inner order, but that which lies before us as a subjective experience of tone is far, far removed from the physics of the tone as it is expressed in the material world.

And this is really due to the fact that tone manifestation preserves a certain individuality. It takes its origin from the periphery of the cosmos, while such a process as we observe in the chemical forces active in fluids, for instance, proceeds from the earth as a center.

Now there is one relation brought out also yesterday in Dr. Kolisko's lecture which shows itself only when we rise, as it were, to a universal point of view. This is that we can conceive of the periodic arrangement of the elements as octaves. In this we have an analogy between the inner laws of tone and the whole nature of matter as it demonstrates itself in chemical processes.

Thus is established the fact that we may conceive of all the combinations and breaking down of material compounds as an outer reflection of an inner world music. This inner world music reveals itself to us outwardly as such in only one particular form, namely in our terrestrial music. Music should never be so conceived that we merely say, what is tone within us, subjectively, is only vibrating air outside of us. This must be looked upon as nonsense.

It is to be considered just as nonsensical as if we were to say the following: What you are outwardly as a physical body that you are inwardly as a soul; such a statement leaves out the subject. Likewise we leave out the subject when we consider tone in its inner nature as identical with the condensations and rarefactions of the air that constitute, in the aerial medium, the carrier of tone. Now if you get a correct conception of this matter, you will see that we have in chemical processes to do with a certain relationship between \(Y\) and \(Y'\), and in tone we have to do with a certain relationship between \(Y\) and \(X'\) (See Table.)

I have already indicated to you that when we stand within this or that realm, what we become aware of in the outer world always pertains to difference in level or potential differences. Please endeavor now, to trace what is similar to potential difference in this realm we are dealing with. Let us try to trace what is similar to the potential difference which becomes active in the case where gravity is used to furnish a driving force for a wheel through the falling water. Let us make clear to ourselves that we have differences in level involved in temperature, heat, tone and in the equalization of electric strains. Everywhere are potential differences, we meet them wherever we study forces. But what do we have, then? We have an inner relationship between what we perceive in the spectrum and liquid matter; and that which presents itself to us as chemical process is nothing but the result of the difference between chemical effects and the forces that are in the fluid. It is a \(Y-Y'\) potential difference. And in tone, a lower \(Y-X'\) potential difference is manifesting.

Thus we can say: In relating a chemical process to the world of reality we are dealing with a potential difference between chemical effects and fluid forces. In the manifestation of tone and sound in the air, we are dealing with a potential difference between what is working formatively into chemical effects, what starts from the periphery into the world and the material of the gas, the aeriform body. Furthermore, what shows itself in this realm of reality manifests through potential differences. The matter rests on these differences in potential even though we remain in one element, in warmth, or even in gas or in water. But especially when we perceive distinctions between realms, do we deal with potential differences in the effects of these realms.

Taking all of this together you come to the following: from a consideration of fluids and their boundary surfaces we are obliged to attribute the form of solids to earth forces. The extent to which gravity and the energies of configuration, to borrow a term from modern physics, are related, has been brought before you in past lectures. If we proceed from the forces that manifest in gravity, to those which result in liquid surfaces, apparently plane surfaces on account of the great size of the earth, we find we are really dealing with a sphere. Obviously the liquid levels of all the terrestrial bodies of water taken together constitute a sphere. Now you see, when we pass outwards from the center of the earth toward the surface of the sphere we meet successively certain sets of conditions. For terrestrial relations, within the solid realm we have forces which tend to close in, to delimit. Fluid forces, however, may perhaps be represented in their configuration by a line or plane tangential to the surface of the sphere. If we go further and observe the sphere from without we must put the matter in this way: beneath the sphere of liquid we have to deal with the formative forces of solids. In these formative forces which delimit solids we are dealing with a single body if we consider the earth as a whole.

The many single bodies together form a single form like the fluid element of the earth. How must we then conceive of these various conditions? For we have passed beyond the formed, beyond what is shaped from within as the solid bodies are. How must we picture this to ourselves? Well, we must conceive of it as the opposite condition. Within the sphere we have solids filled with matter, and without we must think of space filled with negative matter. Within we have filled space (see figure). We must become accustomed to thinking of an emptying of space. The earth is indeed not influenced only by what happens on it, but by the other effects from all sides. If this were not so, the terrestrial phenomena themselves would be different. This can only be mentioned today; later we will go into it more thoroughly. For instance, it would not be possible for us to have a separations of continents from bodies of water, or a north and a south pole, if in the environment of the earth there were not empty spaces. These “matterless” spaces must work in from various directions. If we search for them we find them in what the older cosmic systems designated as the planets, to which we must add also the sun.

Thus we are forced from the realm of the earth into the realm of the cosmos, and we are obliged to find the transition from the one condition of space to the opposite condition. We must learn to pass from a space filled positively with matter to one filled negatively with matter and this condition of negativity filled space so far as it acts on our earth we must think of as localized in the planets around the earth. Thus there is active at the point where terrestrial phenomena are going on a mutual interaction of the terrestrial proper and the cosmic, and this is due to the fact that from the negatively filled spaces, a suction-like action is going on while the formative forces are expressing themselves as pressures. This mutual interaction meets us in that particular force-configuration ordinarily sought for in molecular forces and attractions. We should conceive of these things as they were thought of by the intuitive knowledge of former times. Manifestations in matter, which are always accompanied by the imponderable, were then thought of as influenced by the whole cosmos instead of being misinterpreted fantastically as due to certain theoretical inner configurations. What the stars, like giants, do in the cosmos is reflected in the terrestrial dwarfs, the atoms and molecules.

This indeed, is what we have to do; we must know that when we represent a terrestrial process or perform calculations on it, we are dealing with a picture of extra-terrestrial effects, with a mutual action of the terrestrial and the cosmic.

Now you see here we have the force that fills space with matter (see drawing.) Also, here we still have this force that fills space with matter, but this force is attenuated. Ultimately we come to the condition where there is negative matter. There must be a region between where, so to speak, space is torn apart.

We can put the matter in this way. Our space as it surrounds us constitutes a kind of vessel for physical manifestations, and has an inner relationship to these forces. Something in it corresponds to them. But when we go from the ponderable to the imponderable, space is torn apart. And in this tearing apart, something enters that was not there before it happened.

Let us assume that we tear apart the three dimensional space. What is it that enters through the rift? When I cut my finger, blood comes out—it is a manifestation in three dimensional space. But when I tear apart space itself that which comes through is something that is otherwise non-spatial.

Note how modern physical thinking is lost in the woods. Is it not true that when we make electrical experiments in the school room, our apparatus must be painstakingly dried, we must make it a good insulator, or our experiments will fail. If it is moist, the experiment will fail. But I have often called attention to the fact that the inner friction of clouds which are certainly moist is supposed to give rise to electricity which in turn produced lightning and thunder. This is one of the most impossible ideas that can be conceived.

Now on the other hand, if we bring together these things we have considered as necessary for a real understanding, then we can see that space is torn apart the moment the flash appears. At that moment, what fills space as non-dimensional entity, intensively, comes forth like the blood when I cut my hand. This is indeed always the case when light appears accompanied by heat. Space is torn apart. Space reveals to us what dwells within, while it shows us only its exterior in the usual three dimensions that we have before us. Space then shows us its inner content.

We may thus say: when we proceed from the ponderable to the imponderable and have to pass through the realm of heat as we go, we find heat welling out wherever we make the transition from the pressure effects of ponderable matter to the suction effects of the imponderable. At all such points of transition heat wells out.

Now you will see that when we are constructing ideas about the processes which we spoke of several days ago as processes of conduction of heat, you have to relate to them the concept that the heat is bound to the ponderable matter. This is quite the opposite condition to that which we have considered as existing in radiating heat itself. This heat we find as the entity welling out when matter is torn apart. How will it affect matter? It will work from the intensive condition to the extensive. It will, so to speak, work from the inner portion of space into its outer portions. When heat and a material body mutually react on one another we see a certain thing occurring. What occurs is that the characteristic tendency of the heat is transformed. The suction effect is transformed into a pressure effect so that the cosmic tendency of the heat opposes the individualizing tendency of the material which, in solids, is the force that gives form.

We thus have in heat, in phenomena of warmth, insofar as these manifest a conductivity, to seek, not for rays, but for a tendency to spread in all directions. We must look for a mirroring of the imponderable matter, or for the presence of the imponderable in the ponderable. Bodies that conduct heat bring it into manifestation by an intensive reflection of the impinging imponderable heat on their material portion This is in contracts to the extensive reflection characteristic of light.

Now I wish to ask you to work over in your minds such concepts as we are accustomed to entertain and to work them over in the way we do here so that they become saturated with reality, as it were. Let me give you a picture in closing to recapitulate and show you how much reality-saturated concepts can lead us into a vital grasp of the being of the cosmos.

I have already called your attention to the basis upon which rests the perception, the subjective experiences of temperature. We really experience the difference between our own temperature and the temperature of the environment, which, indeed, is what the thermometer does—I have drawn this to your attention. But perception depends precisely on this that we have within us a certain condition and that which lies outside this condition constitutes our perception. We cannot be a thing and perceive it at the same time. But we must always be other than the conditions we are experiencing. Suppose we consider tone. Insofar as we are tone, we cannot experience tone. If we would answer without prejudice the question: what are we as experiencers of tone, we come to the conclusion that we simply experience one potential difference while we are the other potential difference. We experience the \(Y-X'\) difference; we do not experience the \(Y-Y'\) difference because that is part of our being in time. It accompanies our perception of tone. It is an orderly inner chemical process in our fluid nature and is a part of our being. What causes chemical effects within us produces certain orderly effects in the world itself. It is by no means without interest to picture the following to yourselves. You know well that the human body consists only of a small degree of solid constituents. More than 90 percent of it is water, what plays through us as a delicate chemical process while we listen to a symphony is an inner continually phosphorescent marvel in this fluid nature. We are in our inner nature what these chemical processes reflect from tone. And we become aware of the tone world through the fact that we are chemically the tone world in the sense I have presented to you.

Our understanding of man himself is really much broadened, you see, if we bring an understanding of physical problems to bear on the human body. But the thing we must strive for is not to form abstract concepts of which physics is so fond today Rather, we must force our way through the concepts really woven into the world, the objective world. Fundamentally everything that spiritual science is striving to bring into the conceptual world and especially what it is striving to do to promote a certain way of thinking, has for its object to bring back into human development thought permeated with reality. And it is indeed necessary for this to happen. For this reason we must prosecute vigorously such studies as have been presented here during the last few days.

You can see, my friends, how everywhere around you something old is dying out. Is it not possible from examination of physical concepts, to see that something old is really dying out, for little is to be done with them? The very fact that we can build up a new physical concept even when we attempt it in such a limited way—for we can only give indications now—this fact shows that we stand today at a turning point in human development.,

We must, my friends, give thought to certain things. We must push forward the varied lines of endeavor which Dr. Baravalle, Dr. Blumel, Mr. Strakesch, and Dr. Kolisko have presented to you in order to give a new impulse to the development hitherto consummated by the human race. Thus we will lay foundations for progress.

You must see that people the world over are asking for an extension of these things. We must found schools. What is happening in the world outside? People are encouraging schools, the Danish school movement is an example. What is characteristic of the old schools is being carried into the new ones. But nothing new will come of this. The whole people will simply have fastened on them the thing that up to now has been fastened on the learned.

There is nothing sadder than to contemplate a future where the manner of thinking which has devastated the heads of the learned men in the fashion we have seen will be transmitted to the people of the whole earth through the school system. If we would found schools for the people, we must be sure that there will be something available to teach in them, something whose inner configuration represents an advance. We need first the science that can be given in these schools. People wish always to remain superficial, considering only what is obvious. Consequently, in a spiritual movement, they do not wish to do anything radical toward renewing their manner of thinking, but simply to bring to people the old, the disappearing. It is just in regard to physical facts that this tendency is most noticeable.

You will certainly find many things in these lectures that are unsatisfactory, for they can only be suggestive at best. One thing however, is shown, and that is the necessity to build anew our whole physical, chemical, physiological and biological thought world. It must be rebuilt from the fundamental up. We will naturally accomplish this when we have reconstructed not only the schools, but also the science itself. And until we have succeeded in so arranging things that the academic side has been renewed along the lines started in these last few days, only then will we reach that which will and must be reached if European civilization is not to perish in a spiritual sense.

Only consider the shocking trend in the modern academic world. We have long controversial papers read, completely divorced from real life. People sit in fine lecture halls and each reads his paper, but the others do not listen. For it is a noteworthy fact that one man is a specialist in one line, another man is a specialist in a different line. The mathematician reads but the medical man does not listen. And when the medical man reads the thoughts of the mathematician are busy elsewhere. This is indeed a well known sign. Something new must be injected. And this something must have its center in a spiritual striving. We must see this point. Therefore, one can say: if we can but bring together this striving towards a new kind of reality with a building up of the way of thinking in our schools, then we will attain what must be attained.

You can see there is much to be done. We really learn how such is to be done only when we begin to go into details.

For this reason it is so pathetic that people today who cling to the old way of thinking, for it has become old, it has had its day—coin phrases and accumulate great amounts of money to perpetuate their academic system in the world. It is especially difficult because we must become fundamentally convinced that a genuine new world is necessary. We must not deceive ourselves and simply say, “build schools.” We must live in reality and say, “first it is necessary to have something to teach in these schools for the people.” And I would like to say that while fruitful technological results have flowed from science, a still more fruitful technology will flow from a popularizing of science of such a nature as we have tried to indicate here in the realm of physics.

We have in every case tried to emerge from the old theoretical point of view and enter into a point of view that is real, so that our concepts will be saturated with reality. This will yield technical results quite different from those attained up to the present. Practice and theory hang together inwardly. And when we see in any one case what reform is needed as in the case of physics, for instance, we can understand what must happen. Since the time has come when we must separate, I wish to emphasize that I have only indicated to you in these lectures what you are to see, to stimulate you to develop these things further. You will be able to develop them. Our mathematical physicists, whom we have among our number will be able to give new life to the old formulae. And they will find, when they apply to these old formulae the ideas I have indicated to you, that certain transformations can be made that are real metamorphoses. From these will grow much that will be of enormous importance technically for the further development of mankind. This is, of course, something which cannot be gone into in detail, but only can be indicated at this time.

But these observations must now be brought to a close and their further progress will depend on your own work. It is this that I wish you to take especially to heart, for the things are now extremely pressing that have to be accomplished in the three paths of human endeavor. These things have become urgent in our era and there is no time to lose because chaos stands before the door. A second thing to remember is this: The end can only be attained satisfactorily through an orderly human working together. Thus we must try to work out further within ourselves the things that have been stimulated, and you will also find something arising in the work of the Waldorf School. The moment you really try to utilize in pedagogy the definite and valid ideas we have set forth here, they will be taken up at once, and you will also discover that they will go well if you find it necessary to apply them in the conduct of life. We could wish that one did not always have to speak about science to a public which while it takes in much, is always exposed to the opinions of “rigorous scientific thinkers,” to “authorities.” These authorities have no inkling that all we observe is very definitely shot through with the play of something else. We can see this even from language.

Note that in language we have everything mutually related. We speak of an impact. Now it is only because we have ourselves brought about an impact and given a name to the phenomenon that we speak of an impact in a space free of human activity, and vice versa we speak of things that happen within us in words drawn from the outer world. But we do not realize that we should look into the outer world, that is the planetary world, if we will understand the terrestrial bodies, and because we not know this we cannot learn what is happening in the embryos of plants and animals or in any tiny cell upon which we turn our microscopes. We discover all sorts of interesting things, but the source of all this, the thing we long to know, we will only be able to see when we understand macroscopically these processes microscopically observed. We must see that the fertilization and the fruiting of outer nature takes place in a mutual interaction with the outer cosmos. We must study how to conceive of the planets as points of departure for the working of the imponderable in the physical world, as if we are to grasp the relation of the cosmos to plant and animal germ cells.

If we can learn to see all these things on a grand scale without, these things that today we look for under the microscope where they are not really present, if we try to see these things in that which surrounds us (in the cosmos) then we will make progress.

The way is now clear before us. Human prejudice makes for us a very, very serious barricade. This prejudice is hard to overcome. It is for us to do all that we can to overcome it.

Let us hope that we can at some future time continue again these discussions.

It must be answered, not to meet a human “need to know” but to meet man's universal need to become fully human. And in just what way one can strive for an answer, in what way the ignorabimus can be overcome to fulfil the demands of human evolution—this shall be the theme of our course of lectures as it proceeds.

To those who demand of a cycle of lectures with a title such as ours that nothing be introduced that might interfere with the objective presentation of ideas, I would like, since today I shall have to mention certain personalities, to say the following. The moment one begins to represent the results of human judgment in their relationship to life, to full human existence, it becomes inevitable that one indicate the personalities with whom the judgments originated. Even in a scientific presentation, one must remain within the sphere in which the judgment arises, within the realm of human struggling and striving toward such a judgment. And especially since the question we want above all to answer is: what can be gleaned from modern scientific theories that can become a vital social thinking able to transform thought into impulses for life?—then one must realize that the series of considerations one undertakes is no longer confined to the study and the lecture halls but Stands rather within the living evolution of humanity.

Behind everything with which I commenced yesterday, the modern striving for a mathematical-mechanical world view and the dissolution of that world view, behind that which came to a climax in 1872 in the famous speech by the physiologist, du Bois-Reymond, concerning the limits of natural science, there stands something even more important. It is something that begins to impress itself upon us the moment we want to begin to speak in a living way about the limits of natural science.

A personality of extraordinary philosophical stature still looks over to us with a certain vitality out of the first half of the nineteenth century: Hegel. Only in the last few years has Hegel begun to be mentioned in the lecture halls and in the philosophical literature with somewhat more respect than in the recent past. In the last third of the nineteenth century the academic world attacked Hegel outright, yet one could demonstrate irrefutably that Eduard von Hartmann had been quite right in claiming that during the 1880s only two university lecturers in all of Germany had actually read him. The academics opposed Hegel but not on philosophical grounds, for as a philosopher they hardly knew him. Yet they knew him in a different way, in a way in which we still know him today. Few know Hegel as he is contained, or perhaps better said, as his world view is contained, in the many volumes that sit in the libraries. Those who know Hegel in this original form so peculiar to him are few indeed. Yet in certain modified forms he has become in a sense the most popular philosopher the world has ever known. Anyone who participates in a workers' meeting today or, even better, anyone who had participated in one during the last few decades and had heard what was discussed there; anyone with any sense for the source of the mode of thinking that had entered into these workers' meetings, who really knew the development of modern thought, could see that this mode of thinking had originated with Hegel and flowed through certain channels out into the broadest masses. And whoever investigated the literature and philosophy of Eastern Europe in this regard would find that the Hegelian mode of thinking had permeated to the farthest reaches of Russian cultural life. One thus could say that, anonymously, as it were, Hegel has become within the last few decades perhaps one of the most influential philosophers in human history. On the other hand, however, when one perceives what has come to be recognized by the broadest spectrum of humanity as Hegelianism, one is reminded of the portrait of a rather ugly man that a kind artist painted in such a way as to please the man's family. As one of the younger sons, who had previously paid little attention to the portrait, grew older and really observed it for the first time, he said: “But father, how you have changed!” And when one sees what has become of Hegel one might well say: “Dear philosopher, how you have changed!” To be sure, something extraordinary has happened regarding this Hegelian world view.

Hardly had Hegel himself departed when his school fell apart. And one could see how this Hegelian school appropriated precisely the form of one of our new parliaments. There was a left wing and a right wing, an extreme left and an extreme right, an ultra-radical wing and an ultra-conservative wing. There were men with radical scientific and social views, who felt themselves to be Hegel's true spiritual heirs, and on the other side there were devout, positive theologians who wanted just as much to base their extreme theological conservatism on Hegel. There was a center for Hegelian studies headed by the amiable philosopher, Karl Rosenkranz, and each of these personalities, every one of them, insisted that he was Hegel's true heir.

What is this remarkable phenomenon in the evolution of human knowledge? What happened was that a philosopher once sought to raise humanity into the highest realms of thought. Even if one is opposed to Hegel, it cannot be denied that he dared attempt to call forth the world within the soul in the purest thought-forms. Hegel raised humanity into ethereal heights of thinking, but strangely enough, humanity then fell right back down out of those heights. It drew on the one hand certain materialistic and on the other hand certain positive theological conclusions from Hegel's thought. And even if one considers the Hegelian center headed by the amiable Rosenkranz, even there one cannot find Hegel's philosophy as Hegel himself had conceived it. In Hegel's philosophy one finds a grand attempt to pursue the scientific method right up into the highest heights. Afterward, however, when his followers sought to work through Hegel's thoughts themselves, they found that one could arrive thereby at the most contrary points of view.

Now, one can argue about world views in the study, one can argue within the academies, and one can even argue in the academic literature, so long as worthless gossip and Barren cliques do not result. These offspring of Hegelian philosophy, however, cannot be carried out of the lecture halls and the study into life as social impulses. One can argue conceptually about contrary world views, but within life itself these contrary world views do not fight so peaceably. One must use just such a paradoxical expression in describing such a phenomenon. And thus there stands before us in the first half of the nineteenth century an alarming factor in the evolution of human cognition, something that has proved itself to be socially useless in the highest degree. With this in mind we must then raise the question: how can we find a mode of thinking that can be useful in social life? In two phenomena above all we notice the uselessness of Hegelianism for social life.

One of those who studied Hegel most intensively, who brought Hegel fully to life within himself, was Karl Marx. And what is it that we find in Marx? A remarkable Hegelianism indeed! Hegel up upon the highest peak of the conceptual world—Hegel upon the highest peak of Idealism—and the faithful student, Karl Marx, immediately transforming the whole into its direct opposite, using what he believed to be Hegel's method to carry Hegel's truths to their logical conclusions. And thereby arises historical materialism, which is to be for the masses the one world view that can enter into social life. We thus are confronted in the first half of the nineteenth century with the great Idealist, Hegel, who lived only in the Spirit, only in his ideas, and in the second half of the nineteenth century with his student, Karl Marx, who contemplated and recognized the reality of matter alone, who saw in everything ideal only ideology. If one but takes up into one's feeling this turnabout of conceptions of world and life in the course of the nineteenth century, one feels with all one's soul the need to achieve an understanding of nature that will serve as a basis for judgments that are socially viable.

Now, if we turn on the other hand to consider something that is not so obviously descended from Hegel but can be traced back to Hegel nonetheless, we find still within the first half of the nineteenth century, but carrying over into the second half, the “philosopher of the ego,” Max Stirner. While Karl Marx occupies one of the two poles of human experience mentioned yesterday, the pole of matter upon which he bares all his considerations, Stirner, the philosopher of the ego, proceeds from the opposite pole, that of consciousness. And just as the modern world view, gravitating toward the pole of matter, becomes unable to discover consciousness within that element (as we saw yesterday in the example of du Bois-Reymond), a person who gravitates to the opposite pole of consciousness will not be able to find the material world. And so it is with Max Stirner. For Max Stirner, no material universe with natural laws actually exists. Stirner sees the world as populated solely by human egos, by human consciousnesses that want only to indulge themselves to the full. “I have built my thing on nothing”—that is one of Max Stirner's maxims. And on these grounds Stirner opposes even the notion of Providence. He says for example: certain moralists demand that we should not perform any deed out of egoism, but rather that we should perform it because it is pleasing to God. In acting, we should look to God, to that which pleases Him, that which He commands. Why, thinks Max Stirner, should I, who have built only upon the foundation of ego-consciousness, have to admit that God is after all the greater egoist Who can demand of man and the world that all should be performed as it suits Him? I will not surrender my own egoism for the sake of a greater egoism. I will do what pleases me. What do I care for a God when I have myself?

One thus becomes entangled and confused within a consciousness out of which one can no longer find the way. Yesterday I remarked how on the one hand we can arrive at clear ideas by awakening in the experience of ideas when we descend into our consciousness. These dreamlike ideas manifest themselves like drives from which we cannot then escape. One would say that Karl Marx achieved clear ideas—if anything his ideas are too clear. That was the secret of his success. Despite their complexity, Marx's ideas are so clear that, if properly garnished, they remain comprehensible to the widest circles. Here clarity has been the means to popularity. And until it realizes that within such a clarity humanity is lost, humanity, as long as it seeks logical consequences, will not let go of these clear ideas.

If one is inclined by temperament to the other extreme, to the pole of consciousness, one passes over onto Stirner's side of the scale. Then one despises this clarity: one feels that, applied to social thinking, this clarity makes man into a cog in a social order modeled on mathematics or mechanics—but into that only, into a mere cog. And if one does not feel oneself cut out for just that, then the will that is active in the depths of human consciousness revolts. Then one comes radically to oppose all clarity. One mocks all clarity, as Stirner did. One says to oneself: what do I care about anything else? What do I care even about nature? I shall project my own ego out of myself and see what happens. We shall see that the appearance of such extremes in the nineteenth century is in the highest degree characteristic of the whole of recent human evolution, for these extremes are the distant thunder that preceded the storm of social chaos we are now experiencing. One must understand this connection if one wants at all to speak about cognition today.

Yesterday we arrived at an indication of what happens when we begin to correlate our consciousness to an external natural world of the senses. Our consciousness awakens to clear concepts but loses itself. It loses itself to the extent that one can only posit empty concepts such as “matter,” concepts that then become enigmatic. Only by thus losing ourselves, however, can we achieve the clear conceptual thinking we need to become fully human. In a certain sense we must first lose ourselves in order to find ourselves again out of ourselves. Yet now the time has come when we should learn something from these phenomena. And what can one learn from these phenomena? One can learn that, although clarity of conceptual thinking and perspicuity of mental representation can be won by man in his interaction with the world of sense, this clarity of conceptual thinking becomes useless the moment we strive scientifically for something more than a mere empiricism. It becomes useless the moment we try to proceed toward the kind of phenomenalism that Goethe the scientist cultivated, the moment we want something more than natural science, namely Goetheanism.

What does this imply? In establishing a correlation between our inner life and the external physical world of the senses we can use the concepts we form in interaction with nature in such a way that we try not to remain within the natural phenomena but to think on beyond them. We are doing this if we do more than simply say: within the spectrum there appears the color yellow next to the color green, and on the other side the blues. We are doing this if we do not simply interrelate the phenomena with the help of our concepts but seek instead, as it were, to pierce the veil of the senses and construct something more behind it with the aid of our concepts. We are doing this if we say: out of the clear concepts I have achieved I shall construct atoms, molecules—all the movements of matter that are supposed to ex-ist behind natural phenomena. Thereby something extraordinary happens. What happens is that when I as a human being confront the world of nature [see illustration], I use my concepts not only to create for myself a conceptual order within the realm of the senses but also to break through the boundary of sense and construct behind it atoms and the like I cannot bring my lucid thinking to a halt within the realm of the senses. I take my lesson from inert matter, which continues to roll on even when the propulsive force has ceased. My knowledge reaches the world of sense, and I remain inert. I have a certain inertia, and I roll with my concepts on beyond the realm of the senses to construct there a world the existence of which I can begin to doubt when I notice that my thinking has only been borne along by inertia.

It is interesting to note that a great proportion of the philosophy that does not remain within phenomena is actually nothing other than just such an inert rolling-on beyond what really exists within the world. One simply cannot come to a halt. One wants to think ever farther and farther beyond and construct atoms and molecules—under certain circumstances other things as well that philosophers have assembled there. No wonder, then, that this web one has woven in a world created by the inertia of thinking must eventually unravel itself again.

Goethe rebelled against this law of inertia. He did not want to roll onward thus with his thinking but rather to come strictly to a halt at this limit [see illustration: heavy line] and to apply concepts within the realm of the senses. He thus would say to himself: within the spectrum appear to me yellow, blue, red, indigo, violet. If, however, I permeate these appearances of color with my world of concepts while remaining within the phenomena, then the phenomena order themselves of their own accord, and the phenomenon of the spectrum teaches me that when the darker colors or anything dark is placed behind the lighter colors or anything light, there appear the colors which lie toward the blue end of the spectrum. And conversely, if I place light behind dark, there appear the colors which lie toward the red end of the spectrum.

What was it that Goethe was actually seeking to do? Goethe wanted to find simple phenomena within the complex but above all such phenomena as allowed him to remain within this limit [see illustration], by means of which he did not roll on into a realm that one reaches only through a certain mental inertia. Goethe wanted to adhere to a strict phenomenalism. If we remain within phenomena and if we strive with our thinking to come to a halt there rather than allow ourselves to be carried onward by inertia, the old question arises in a new way. What meaning does the phenomenal world have when I consider it thus? What is the meaning of the mechanics and mathematics, of the number, weight, measure, or temporal relation that I import into this world? What is the meaning of this?

You know, perhaps, that the modern world conception has sought to characterize the phenomena of tone, color, warmth, etc. as only subjective, whereas it characterizes the so-called primary qualities, the qualities of weight, space, and time, as something not subjective but objective and inherent in things. This conception can be traced back principally to the English philosopher, John Locke, and it has to a considerable extent determined the philosophical basis of modern scientific thought. But the real question is: what place within our systematic science of nature as a whole do mathematics, do mechanics—these webs we weave within ourselves, or so it seems at first—what place do these occupy? We shall have to return to this question to consider the specific form it takes in Kantianism. Yet without going into the whole history of this development one can nonetheless emphasize our instinctive conviction that measuring or counting or weighing external objects is essentially different from ascribing to them any other qualities.

It certainly cannot be denied that light, tones, colors, and sensations of taste are related to us differently from that which we could represent as subject to mathematical-mechanical laws. For it really is a remarkable fact,a fact worthy of our consideration: you know that honey tastes sweet, but to a man with jaundice it tastes bitter—so we can say that we stand in a curious relationship to the qualities within this realm—while on the other hand we could hardly maintain that any normal man would see a triangle as a triangle, but a man with jaundice would see it as a square! Certain differentiations thus do exist, and one must be cognizant of them; on the other hand, one must not draw absurd conclusions from them. And to this very day philosophical thinking has failed in the most extraordinary way to come to grips with this most fundamental epistemological question. We thus see how a contemporary philosopher, Koppelmann, overtrumps even Kant by saying, for example—you can read this on page 33 of his Philosophical Inquiries [Weltanschauungsfragen]: everything that relates to space and time we must first construct within by means of the understanding, whereas we are able to assimilate colors and tastes directly. We construct the icosahedron, the dodecahedron, etc.: we are able to construct the standard regular solids only because of the organization of our understanding. No wonder, then, claims Koppelmann, that we find in the world only those regular solids we can construct with our understanding. One thus can find Koppelmann saying almost literally that it is impossible for a geologist to come to a geometer with a crystal bounded by seven equilateral triangles precisely because—so Koppelmann claims—such a crystal would have a form that simply would not fit into our heads. That is out-Kanting Kant. And thus he would say that in the realm of the thing-in-itself crystals could exist that are bounded by seven regular triangles, but they cannot enter our head, and thus we pass them by; they do not exist for us.

Such thinkers forget but one thing: they forget—and it is just this that we want to indicate in the course of these lectures with all the forceful proofs we can muster—that the natural order governing the construction of our head also governs the construction of the regular polyhedrons, and it is for just this reason that our head constructs no other polyhedrons than those that actually confront us in the external world. For that, you see, is one of the basic differences between the so-called subjective qualities of tone, color, warmth, as well as the different qualities of touch, and that which confronts us in the mechanical-mathematical view of the world. That is the basic difference: tone and color leave us outside of ourselves; we must first take them in; we must first perceive them. As human beings we stand outside tone, color, warmth, etc. This is not entirely the case as regards warmth—I shall discuss that tomorrow—but to a certain extent this is true even of warmth. These qualities leave us initially outside ourselves, and we must perceive them. In formal, spatial, and temporal relationships and regarding weight this is not the case. We perceive objects in space but stand ourselves within the same space and the same lawfulness as the objects external to us. We stand within time just as do the external objects. Our physical existence begins and ends at a definite point in time. We stand within space and time in such a way that these things permeate us without our first perceiving them. The other things we must first perceive. Regarding weight, well, ladies and gentlemen, you will readily admit that this has little to do with perception, which is somewhat open to arbitrariness: otherwise many people who attain an undesired corpulence would be able to avoid this by perception alone, merely by having the faculty of perception. No, ladies and gentlemen, regarding weight we are bound up with the world entirely objectively, and the organization by means of which we stand within color, tone, warmth, etc. is powerless against that objectivity.

So now we must above all pose the question: how is it that we arrive at any mathematical-mechanical judgment? How do we arrive at a science of mathematics, at a science of mechanics? How is it, then, that this mathematics, this mechanics, is applicable to the external world of nature, and how is it that there is a difference between the mathematical-mechanical qualities of external objects and those that confront us as the so-called subjective qualities of sensation, tone, color, warmth, etc.?

At the one extreme, then, we are confronted with this fundamental question. Tomorrow we shall discuss another such question. Then we shall have two starting-points from which we can proceed to investigate the nature of science. Thence we shall proceed to the other extreme to investigate the formation of social judgments.

Yesterday I attempted to show the methods employed by Eastern spirituality for approaching the spiritual world and pointed out how anybody who wished to pursue this path into the super-sensible more or less dispensed with the bridge linking him with his fellow men. He chose a path different from that which establishes communication within society by means of language, thought, and perception of the ego. And I showed how it was initially attempted not to understand through the word what one's fellow man wished to say, what one wants to understand from him, but to live within the words. This process of living within the word was enhanced by forming the words into certain aphorisms. One lived in these and repeated them, so that the forces accrued in the soul by this process were strengthened further by repetition. And I showed how something was achieved in the condition of the soul that might be called a state of Inspiration, in the sense in which I have used the word, except that the sages of the ancient East were, of course, members of their race: their ego-consciousness was much less developed than in later epochs of human evolution. They thus entered into the spiritual world in a more instinctive manner, and because the whole thing was instinctive and thus resulted, in a sense, from a healthy drive within human nature, in the earliest times it could not lead to the pathological afflictions of which we have also spoken. In later times steps were taken by the so-called Mysteries to guard against the rise of such afflictions as I have described to you. I said that those Westerners who desire to gain knowledge of the spiritual world must approach this in another way. Humanity has progressed in the interim. Different soul faculties have evolved, so that one cannot simply renew the ancient Eastern path of spiritual development. Within the realm of spiritual life one cannot long to return in a reactionary manner to prehistoric or earlier historical periods of human evolution. For Western civilization, the path leading into the spiritual worlds is that of Imagination. This faculty of Imagination, however, must be integrated organically into the life of the soul as a whole. This can come about in the most varied ways, just as the Eastern path of development was not unequivocally predetermined but could take numerous different courses. Today I would like to describe the path into the spiritual world that conforms to the needs of Western civilization and is particularly suited to anyone immersed in the scientific life of the West.

In my book, Knowledge of the Higher Worlds and Its Attainment, I have described an entirely safe path leading to the super-sensible, but I describe it in such a way that it applies for everybody, above all for those who have not devoted their lives to science. Today I shall describe a path into the super-sensible that is much more for the scientist. All my experience has taught me that for such a scientist a kind of precondition for this cognitional striving is to take up what is presented in my book, Philosophy of Freedom. I will explain what I mean by this. This book, Philosophy of Freedom, was not written with the same intent as most books written today. Nowadays books are written simply in order to inform the reader of the book's subject matter, so that the reader learns the book's contents in accordance with his education, his scientific training, or the special knowledge he already possesses. This was not my primary Intention in writing Philosophy of Freedom, and thus it will not be popular with those who read books only to acquire Information. The purpose of the book is to make the reader directly engage his thinking activity on every page.

In a sense, the book is only a kind of musical score that one must read with inner thought activity in order to progress, as the result of one's own efforts, from one thought to the next. The book constantly presupposes the mental collaboration of the reader. Moreover, the book presupposes that which the soul becomes in the process of such mental exertion. Anyone who has really worked through this book with his own inner thinking activity and cannot confess that he has come to know himself in a part of his inner life in which he had not known himself previously has not read Philosophy of Freedom properly. One should feel that one is being lifted out of one's usual thinking [Vorstellen] into a thinking independent of the senses [ein sinnlichkeitsfreies Denken], in which one is fully immersed, so that one feels free of the conditions of physical existence. Whoever cannot confess this to himself has actually misunderstood the book. One should be able to say to oneself: now I know, as a result of the inner thought activity I myself have expended, what pure thinking actually is.

The strange thing is that most Western philosophers totally deny the reality of the very thing that my Philosophy of Freedom seeks to awaken as something real in the soul of the reader. Countless philosophers have expounded the view that pure thinking does not exist but is bound to contain traces, however diluted, of sense perception. A strong impression is left that philosophers who maintain this have never really studied mathematics or gone into the difference between analytical and empirical mechanics. Specialization, however, has already grown to such an extent that nowadays philosophy is often pursued by people totally lacking any knowledge of mathematical thinking. The pursuit of philosophy is actually impossible without a grasp of at least the spirit of mathematical thinking. We have seen what Goethe's attitude was toward this spirit of mathematical thinking, even though he made no claim himself to any special training in mathematics. Many thus would deny the existence of the very faculty I would like those who study The Philosophy of Freedom to acquire.

And now let us imagine a reader who simply sets about working through The Philosophy of Freedom within the context of his ordinary consciousness in the way I have described: he will, of course, not be able to claim that he has been transported into a super-sensible world. For I intentionally wrote The Philosophy of Freedom in the way that I did so that it would present itself to the world initially as a purely philosophical work. Just think what a disservice would have been accorded anthroposophically oriented spiritual science if I had begun immediately with spiritual scientific writings! These writings would, of course, have been disregarded by all trained philosophers as the worst kind of dilettantism, as the efforts of an amateur. To begin with I had to write purely philosophically. I had to present the world with something thought out philosophically in the strict sense, though it transcended the normal bounds of philosophy. At some point, however, the transition had to be made from a merely philosophical and scientific kind of writing to a spiritual scientific writing. This occurred at a time when I was invited to write a special chapter about Goethe's scientific writings for a German biography of Goethe. This was at the end of the last century, in the 1890s. And so I was to write the chapter on Goethe's scientific writings: I had, in fact, finished it and sent it to the publisher when there appeared another work of mine, called Mysticism at the Dawn of the Modern Age. The book was a bridge between pure philosophy and an anthroposophical orientation. When this work came out, my manuscript was returned to me by the publisher, who had enclosed nothing but my fee so that I would not make a fuss, for thereby the legal obligations had been met. Among the learned pedants, there was obviously no interest in anything—not even a single chapter devoted to the development of Goethe's attitude toward natural science written by one who had authored this book on mysticism.

I will now assume that The Philosophy of Freedom has been worked through already with one's ordinary consciousness in the way described. Now we are in the right frame of mind for our souls to undertake in a healthy way what I described yesterday, if only very briefly, as the path leading into Imagination. It is possible to pursue this path in a way consonant with Western life if we attempt to surrender ourselves completely to the world of outer phenomena, so that we allow them to work upon us without thinking about them but still perceiving them. In ordinary waking life, you will agree, we are constantly perceiving, but actually in the very process of doing so we are continually saturating our percepts with concepts; in scientific thinking we interweave percepts and concepts entirely systematically, building up systems of concepts and so on. By having acquired the capacity for the kind of thinking that gradually emerges from The Philosophy of Freedom, one can become capable of such acute inner activity that one can exclude and suppress conceptual thinking from the process of perception and surrender oneself to bare percepts. But there is something else we can do in order to strengthen the forces of the soul and absorb percepts unelaborated by concepts. One can, moreover, refrain from formulating the judgments that arise when these percepts are joined to concepts and create instead symbolic images, or images of another sort, alongside the images seen by the eye, heard by the ear, and rendered by the senses of warmth, touch, and so on. If we thus bring our activity of perception into a state of flux, infusing it with life and movement, not as we do when forming concepts but by elaborating perception symbolically or artistically, we will develop much sooner the power of allowing the percepts to permeate us as such. An excellent preparation for this kind of cognition is to school oneself rigorously in what I have characterized as phenomenalism, as elaboration of phenomena. If one has really striven not to allow inertia to carry one through the veil of sense perception upon reaching the boundary of the material world, in order to look for all kinds of metaphysical explanations in terms of atoms and molecules, but has instead used concepts to set the phenomena in order and follow them through to the archetypal phenomena, one has already undergone a training that enables one to isolate the phenomena from everything conceptual. And if one still symbolizes the phenomena, turns them into images, one acquires a potent soul forte enabling one to absorb the external world free from concepts.

Obviously we cannot expect to achieve this quickly. Spiritual research demands of us far more than research in a laboratory or observatory. It demands above all an intense effort of the individual will. If one has practiced such an inner representation of symbolic images for a certain length of time and striven in addition to dwell contemplatively upon images that one keeps present in the soul in a way analogous to the mental representation of phenomena, images that otherwise only pass away when we race from sensation to sensation, from experience to experience; if one has accustomed oneself to dwell contemplatively for longer and longer periods of time upon an image that one has fully understood, that one has formed oneself or taken at somebody else's suggestion so that it cannot be a reminiscence, and if one repeats this process again and again, one strengthens one's inner soul forces and finally realizes that one experiences something of which one previously had no inkling. The only way to obtain even an approximate idea of such an experience, which takes place only in one's inner being—one must be very careful not to misunderstand this—is to recall particularly lively dream-images. One must keep in mind, however, that dream-images are always reminiscences that can never be related directly to anything external and are thus a sort of reaction coming toward one out of one's own inner self. If one experiences to the full the images formed in the way described above, this is something entirely real, and one begins to understand that one is encountering within oneself the spiritual element that actuates the processes of growth, that is the power of growth. One realizes that one has entered into apart of one's human constitution, something within one; something that unites itself with one; something that is active within but that one previously had experienced only unconsciously. Experienced unconsciously in what way?

I have told you that from birth until the change of teeth a soul-spiritual entity is at work structuring the human being and that this then emancipates itself to an extent. Later, between the change of teeth and puberty, another such soul-spiritual entity, which dips down in a way into the physical body, awakens the erotic drives and much else as well. All this occurs unconsciously. If, however, we use fully consciously such measures of soul as I have described to observe this permeation of the physical organism by the soul-spiritual, one sees how such processes work within man and how man is actually given over to the external world continually, from birth onward. Nowadays this giving-over of oneself to the external world is held to be nothing but abstract perception or abstract cognition. This is not so. We are surrounded by a world of color, sound, and warmth and by all kinds of sense impressions, By elaborating these with our concepts we create yet further impressions that have an effect on us. By experiencing all this consciously we come to see that in the unconscious experience of color- and sound-impressions that we have from childhood onward there is something spiritual that suffuses our organization. And when, for example, we take up the sense of love between the change of teeth and puberty, this is not something originating in the physical body but rather something that the cosmos gives us through the colors, sounds, and streaming warmth that reach us. Warmth is something other than warmth; light something other than light in the physical sense; sound is something other than physical sound. Through our sense impressions we are conscious only of what I would term external sound and external color. And when we surrender ourselves to nature, we do not encounter the ether-waves, atoms, and so on of which modern physics and physiology dream; rather, it is spiritual forces that are at work, forces that fashion us between birth and death into what we are as human beings. Once we tread the path of knowledge I have described, we become aware that it is the external world that forms us. We become best able to observe consciously what lives and embodies itself within us when we acquire above all a clear sense that spirit is at work in the external world. lt is of all things phenomenology that enables us to perceive how spirit works within the external world. It is through phenomenology, and not abstract metaphysics, that we attain knowledge of the spirit by consciously observing, by raising to consciousness, what otherwise we would do unconsciously, by observing how, through the sense world, spiritual forces enter our being and work formatively upon it.

Yesterday I pointed out to you that the Eastern sage in a way disregards the significance of Speech, thought, and the perception of the ego. He experiences these things differently and cultivates a different attitude of soul toward these things, because language, perception of thoughts, and perception of the ego initially tend to lead us away from the spiritual world into social contact with other human beings. In everyday physical existence we purchase our social life at the price of listening right through language, looking through thoughts, and feeling our way right through the perception of the ego. The Eastern sage took upon himself not to listen right through the word but to live within it. He took upon himself not to look right through the thought but to live within the thought, and so forth. We in the West have as our task more to contemplate man himself in following the path into super-sensible worlds.

At this point it must be remembered that man bears a certain kind of sensory organization within as well. I have already described the three inner senses through which he becomes aware of his inner being, just as he perceives what goes on outside him. We have a sense of balance by means of which we sense the spatial orientation appropriate to us as human beings and are thereby able to work inside it with our will. We have a sense of movement by means of which we know that we are moving even in the dark: we know this from an inner sensing and not merely because we perceive our changing relationship to other objects we pass. We have an actual inner sense of movement. And we have a sense of life, by means of which we can perceive our general state of well-being, the constant changes in the inner condition of our life forces. These three inner senses work together with the will during man's first seven years. We are guided by our sense of balance, and a being who initially cannot move at all and later can only crawl is transformed into one who can stand upright and walk. This ability to walk upright is effected by the sense of balance, which places us into the world. The sense of movement and the sense of life likewise contribute toward the development of our full humanity. Anybody who is capable of applying the standards of objective observation employed in the scientist's laboratory to the development of man's physical body and his soul-spirit will soon discover how the forces that worked formatively upon man principally during the fast seven years emancipate themselves and begin to assume a different aspect from the time of the change of teeth onward. By this time a person is less intensively connected to that within than he was as a child. A child is closely bound up inwardly with human equilibrium, movement, and life. Something else, however, is evolving simultaneously during this emancipation of balance, movement, and life. There takes place a certain adjustment of the three other senses: the senses of smell, taste, and touch. It is extremely interesting to observe in detail the way in which a child gradually finds his way into life, orienting himself by means of the senses of taste, smell, and touch. Of course, this can be seen most obviously in early life, but anybody trained to do so can see it clearly enough later on as well. In a certain way, the child pushes out of himself balance, movement, and life but at the same time draws more into himself the qualities of the sense of smell, the sense of taste, and the sense of touch. In the course of an extended phase of development the one is, so to speak, exhaled and the other inhaled, so that the forces of balance, movement, and life, which press from within outward, and the qualitative orientations of smell, taste, and touch, which press from without inward, meet within our organism. This is effected by the interpenetration of the two sense-triads. As a result of this interpenetration, there arises within man a firm sense of self; in this way man First experiences himself as a true ego. Now we are cut off from the spirituality of the external world by speech and by our faculties of perceiving thoughts and perceiving the egos of others—and rightly so, for if it were otherwise we could never in this physical life become social beings—in just the same way, inasmuch as the qualities of smell, taste, and touch encounter balance, movement, and life, we are inwardly cut off from the triad life, movement, and balance, which would otherwise reveal itself to us directly. The experiences of the senses of smell, taste, and touch place themselves, as it were, in front of what we would otherwise experience through our sense of balance, our sense of movement, and our sense of life. And the result of this development toward Imagination of which I have spoken consists in this: the Oriental comes to a halt at language in order to live within it; he halts at the thought in order to live there; he halts at the perception of the ego in order to live within it. By these means he makes his way outward into the spiritual world. The Oriental comes to a halt within these; we, by striving for Imagination, by a kind of absorption of external percepts devoid of concepts, engage in an activity that is in a way the opposite of that in which the Oriental engages with regard to language, perception of thoughts, and perception of the ego. The Oriental comes to a halt at these and enters into them. In striving for Imagination, however, one wends one's way through the sensations of smell, taste, and touch, penetrating into the inner realm so that, by one's remaining undisturbed by sensations of smell, taste, and touch, the experiences stemming from balance, movement, and life come forth to meet one.

It is a great moment when one has penetrated through what I have described as the sense-triad of taste, smell, and touch, and one confronts the naked essence of movement, balance, and life.

With such a preparation behind us, it is interesting to study what Western mysticism often sets forth. Most certainly, I am very far from decrying the elements of poetry, beauty, and imaginative expression in the writings of many mystics. I most certainly admire what, for instance, St. Theresa, Mechthild of Magdeburg, and others have to tell us, and indeed Meister Eckhart and Johannes Tauler. But all that arises in this way reveals itself to the true spiritual scientist as something that arises when one traverses the inward-leading path yet does not penetrate beyond the region of smell, taste, and touch. Read what has been written by individuals who have described with particular clarity what they have experienced in this way. They speak of a tasting of that within, of a tasting regarding what exists as soul-spirit in man's inner being; they also speak of a smelling and, in a certain sense, of a touching. And anybody who knows how to read Mechthild of Magdeburg, for instance, or St. Theresa, in the right way will see that they follow this inward path but never penetrate right through taste, smell, and touch. They use beautiful poetic imagery for their descriptions, but they are speaking only of how one can touch, savor, and sniff oneself inwardly.

For it is far less agreeable to see the true nature of reality with senses that are developed truly spiritually than to read the accounts given by voluptuous mysticism—the only term for it—which in the final analysis only gratifies a refined, inward-looking egotism of soul. As I say, much as this mysticism is to be admired—and I do admire it—the true spiritual scientist must realize that it stops halfway: what is manifest in the splendid poetic imagery of Mechthild of Magdeburg, St. Theresa, and the others is really only what is smelt, tasted, and touched before breaking through into the actual inner realm. Truth is occasionally unpleasant, and at times perhaps even cruel, but modern humanity has no business becoming rickety in soul by following a nebulous, imperfect mysticism. What is required today is to penetrate into man's true inner nature with strength of spirit, with the same strength we have achieved in a much more disciplined way for the external world by pursuing natural science. And it is not in vain that we have achieved this. Natural science must not be undervalued! Indeed, we must seek to acquire the disciplined and methodical side of natural science. And it is precisely when one has assimilated this scientific method that one appreciates the achievements of a nebulous mysticism at their true worth, but one also knows that this nebulous mysticism is not what spiritual science must foster. On the contrary, the task of spiritual science is to seek clear comprehension of man's own inner being, whereby a clear, spiritual understanding of the external world is made possible in turn.

I know that if I did not speak in the way that truth demands I could enjoy the support of every nebulous, blathering mystic who takes up mysticism in order to satisfy his voluptuous soul. That cannot be our concern here, however; rather, we must seek forces that can be used for life, spiritual forces that are capable of informing our scientific and social life.

When one has penetrated as far as that which lives in the sense of balance, the sense of life, and the sense of movement, one has reached something that one experiences initially as the true inner being of man because of its transparency. The very nature of the thing shows us that we cannot penetrate any deeper. But then again one has more than enough at this initial stage, for what we discover is not the stuff of nebulous, mystical dreams. What one finds is a true organology, and above all one finds within oneself the essence of that which is within equilibrium, of that which is in movement, of that which is suffused with life. One finds this within oneself.

Then, after experiencing this, something entirely extraordinary has occurred. Then, at the appropriate moment, one begins to notice something. An essential prerequisite is, as I have said, to have thought through The Philosophy of Freedom beforehand. This is then left, so to speak, to one side, while pursuing the inner path of contemplation, of meditation. One has advanced as far as balance, movement, and life. One lives within this life, this movement, this balance. Entirely parallel with our pursuit of the way of contemplation and meditation but without any other activity on our part, our thinking regarding The Philosophy of Freedom has undergone a transformation. What can be experienced in such a philosophy of freedom in pure thinking has, as a result of our having worked inwardly on our souls in another sphere, become something utterly different. lt has become fuller, richer in content. While on the one hand we have penetrated into our inner being and have deepened our power of Imagination, on the other hand we have raised what resulted from our mental work on The Philosophy of Freedom up out of ordinary consciousness. Thoughts that formerly had floated more or less abstractly within pure thinking have been transformed into substantial forces that are alive in our consciousness: what once was pure thought is now Inspiration. We have developed Imagination, and pure thinking has become Inspiration. Following this path further, we become able to keep apart what we have gained following two paths that must be sharply differentiated: on the one hand, what we have obtained as Inspiration from pure thinking—the life that at a lower level is thinking, and then becomes a thinking raised to Inspiration—and on the other hand what we experience as conditions of equilibrium, movement, and life. Now we can bring these modes of experience together. We can unite the inner with the outer. The fusion of Imagination and Inspiration brings us in turn to Intuition. What have we accomplished now? Well, I would like to answer this question by approaching it from another side. First of all I must draw attention to the steps taken by the Oriental who wishes to rise further after having schooled himself by means of the mantras, after having lived within the language, within the word. He now learns not only to live in the rhythms of language but also in a certain way to experience breathing consciously, in a certain way to experience breathing artificially by altering it in the most varied ways. For him this is the next highest step—but again not something that can be taken over directly by the West. What does the Eastern student of yoga attain by surrendering himself to conscious, regulated, varied breathing? Oh, he experiences something quite extraordinary when he inhales. When inhaling he experiences a quality of air that is not found when we experience air as a purely physical substance but only when we unite ourselves with the air and thus comprehend it spiritually. As he breathes in, a genuine student of yoga experiences something that works formatively upon his whole being, that works spiritually; something that does not expend itself in the life between birth and death, but, entering into us through the spirituality of the outer air, engenders in us something that passes with us through the portal of death. To experience the breathing process consciously means taking part in something that persists when we have laid aside the physical body. For to experience the breathing process consciously is to experience the reaction of our inner being to inhalation. In experiencing this we experience something that preceded birth in our existence as soul-spirit—or let us say preceded our conception—something that had already cooperated in shaping us as embryos and then continued to work within our organism in childhood. To grasp the breathing process consciously means to comprehend ourselves beyond birth and death. The advance from an experience of the aphorism and the word to an experience of the breathing process represented a further penetration into an inspired comprehension of the eternal in man. We Westerners must experience much the same thing—but in a different sphere.

What, in fact, is the process of perception? It is nothing but a modified process of inhalation. As we breathe in, the air presses upon our diaphragm and upon the whole of our being. Cerebral fluid is forced up through the spinal column into the brain. In this way a connection is established between breathing and cerebral activity. And the part of the breathing that can be discerned as active within the brain works upon our sense activity as perception. Perception is thus a kind of branch of inhalation. In exhalation, on the other hand, cerebral fluid descends and exerts pressure on the circulation of the blood. The descent of cerebral fluid is bound up with the activity of the will and also of exhalation. Anybody who really studies The Philosophy of Freedom, however, will discover that when we achieve pure thinking, thinking and willing coincide. Pure thinking is fundamentally an expression of will. Thus pure thinking turns out to be related to what the Oriental experienced in the process of exhalation. Pure thinking is related to exhalation just as perception is related to inhalation. We have to go through the same process as the yogi but in a way that is, so to speak, pushed back more into the inner life. Yoga depends upon a regulation of the breathing, both inhalation and exhalation, and in this way comes into contact with the eternal in man. What can Western man do? He can raise into clear soul experiences perception on the one hand and thinking on the other. He can unite in his inner experience perception and thinking, which are otherwise united only abstractly, formally, and passively, so that inwardly, in his soul-spirit, he has the same experience as he has physically in breathing in and out. Inhalation and exhalation are physical experiences: when they are harmonized, one consciously experiences the eternal. In everyday life we experience thinking and perception. By bringing mobility into the life of the soul, one experiences the pendulum, the rhythm, the continual interpenetrating vibration of perception and thinking. A higher reality evolves for the Oriental in the process of inhalation and exhalation; the Westerner achieves a kind of breathing of the soul-spirit in place of the physical breathing of the yogi. He achieves this by developing within himself the living process of modified inhalation in perception and modified exhalation in pure thinking, by weaving together concept, thinking, and perceiving. And gradually, by means of this rhythmic pulse, by means of this rhythmic breathing process in perception and thinking, he struggles to rise up to spiritual reality in Imagination, Inspiration, and Intuition. And when I indicated in my book The Philosophy of Freedom, at first only philosophically, that reality arises out of the interpenetration of perception and thinking, I intended, because the book was meant as a schooling for the soul, to show what Western man can do in order to enter the spiritual world itself. The Oriental says: systole, diastole; inhalation, exhalation. In place of these the Westerner must put perception and thinking. Where the Oriental speaks of the development of physical breathing, we in the West say: development of a breathing of the soul-spirit within the cognitional process through perception and thinking.

All this had to be contrasted with what can be experienced as a kind of dead end in Western spiritual evolution. Let me explain what I mean. In 1841 Michelet, the Berlin philosopher, published posthumously Hegel's works on natural philosophy. Hegel had worked at the end of the eighteenth century, together with Schelling, at laying the foundations of a system of natural philosophy. Schelling, as a young firebrand, had constructed his natural philosophy in a remarkable way out of what he called “intellectual Intuition” [intellektuale Anschauung]. He reached a point, however, where he could make no further progress. He immersed himself in the mystics at a certain point. His work, Bruno, or Concerning the Divine and Natural Principle in Things, and his fine treatise on human freedom and the origin of evil testify so wonderfully to this immersion. But for all this he could make no progress and began to hold back from expressing himself at all. He kept promising to follow up with a philosophy that would reveal the true nature of those hidden forces at which his earlier natural philosophy had only hinted. When Michelet published Hegel's natural philosophy in 1841, Schelling's long-expected and oft-promised “philosophy of revelation” had still not been vouchsafed to the public. He was summoned to Berlin. What he h ad to offer, however, was not the actual spirit that was to permeate the natural philosophy he had founded. He had striven for an intellectual intuition. He ground to a halt at this point, because he was unable to use Imagination to enter the sphere of which I spoke to you today. And so he was stuck there. Hegel, who had a more rational intellect, had taken over Schelling's thoughts and carried them further by applying pure thinking to the observation of nature. That was the origin of Hegel's natural philosophy. And so one had Schelling's unfulfilled promise to bring forth nature out of the spirit, and then one had Hegel's natural philosophy, which was discarded by science in the second half of the nineteenth century. It was misunderstood, to be sure, but it was bound to remain so, because it was impossible to gain any kind of connection to the ideas contained in Hegel's natural philosophy with regard to phenomenology, the true observation of nature. It is a kind of wonderful incident: Schelling traveling from Munich to Berlin, where great things are expected of him, and it turns out that he has nothing to say. It was a disappointment for all who believed that through Hegel's natural philosophy revelations about nature would emerge from pure thinking. Thus it was in a way demonstrated historically, in that Schelling had attained the level of intellectual intuition but not that of genuine Imagination and in that Hegel showed as well that if pure thinking does not lead on to Imagination or to Inspiration—that is, to the level of nature's secrets ... it was shown that the evolution of the West had thereby run up against a dead end. There was as yet nothing to counter what had come over from the Orient and engendered skepticism; one could counter with nothing that was suffused with the spirit. And anyone who had immersed himself lovingly in Schelling and Hegel and has thus been able to see, with love in his heart, the limitations of Western philosophy, had to strive for anthroposophy. He had to strive to bring about an anthroposophically oriented spiritual science for the West, so that we will possess something that works creatively in the spirit, just as the East had worked in the spirit through systole and diastole in their interaction. We in the West can allow perception and thinking to resound through one another in the soul-spirit [das geistig-seelische Ineinanderklingenlassen], through which we can rise to something more than a merely abstract science. It opens the way to a living science, which is the only kind of science that enables us to dwell within the element of truth. After all the failures of the Kantian, Schellingian, and Hegelian philosophies, we need a philosophy that, by revealing the way of the spirit, can show the real relationship between truth and science, a spiritualized science, in which truth can really live to the great benefit of future human evolution.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

We will continue, then, tomorrow.

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

What we are doing, as you will have seen, is to bring together the diverse elements by means of which in the last resort we shall be able to determine the forms of movement of the heavenly bodies, and—in addition to the forms of movement—what may perhaps be described as their mutual positions. A comprehensive view of our system of heavenly bodies will only be gained when we are able to determine first the curve-forms (inasmuch as forms of movement are called curves), i.e. the true geometrical figures, and then the centres of observation. Such is the task before us along our present lines of study, which I have formed as I have done for very definite reasons.

The greatest errors that are made in scientific life consist in this: they try to make syntheses and comprehensive theories when they have not yet established the conditions of true synthesis. They are impatient to set up theories—to gain a conclusive view of the thing in question,—they do not want to wait till the conditions are fulfilled, subject to which alone theories can properly be made. Our scientific life and practice needs this infusion badly,—needs to acquire a feeling of the fact that you ought not to try and answer questions when the conditions for an intelligent answer are not yet achieved. I know that many people (present company of course excepted) would be better pleased if one presented them with curves all ready made, for planetary or other movements. For they would then be in possession of tangible answers. What they are asking is in effect to be told how such and such things are in the Universe, in terms of the ideas and concepts they already have. What if the real questions are such as cannot be answered at all with the existing ideas and concepts? In that case, theoretic talk will be to no purpose. One's question may be set at rest, but the satisfaction is illusionary. Hence, in respect to scientific education, I have attempted to form these lectures as I have done.

The results we have gained so far have shown that we must make careful distinctions if we wish to find true forms of curves for the celestial movements. Such things as these, for instance, we must differentiate: the apparent movements seen in the paths of Venus and of Mars respectively,—Venus making a loop when in conjunction, Mars when in opposition to the Sun. We came to this conclusion when trying to perceive how diverse are the forms of curves that arise in man himself through the forces that build and form him. We ascertained quite different forms of curve in the region of the head-nature and in the organization of the metabolism and the limbs. The two types of form are none the less related, but the transition from one to the other must be sought for outside of space,—at least beyond the bounds of rigid Euclidean space.

Then comes a further transition, which still remains for us to find. We have to pass from what we thus discover in our own human frame, to what is there outside in Universal Space, which only looks to us plainly Euclidean. We think it nicely there, a rigid space, but that is mere appearance. As to this question, we only gain an answer by persevering with the same method we have so far developed. Namely we have to seek the real connection of what goes on in man himself and what goes on outside in Universal Space, in the movements of the celestial bodies. Then we are bound to put this fundamental question: What relation is there, as to cognition itself, between those movements that may legitimately be considered relative and those that may not? We know that amid the forming and shaping forces of the human body we have two kinds: those that work radially and those which we must think of as working spherically. The question now is, with regard to outer movements: How, with our human cognition do we apprehend that element of movement which takes its course purely within the Sphere, and how do we apprehend that element which takes its course along the Radius?

A beginning has been made in Science as you know, even experimentally, in respect of these two kinds of spatial movement. The movements of a heavenly body upon the Sphere can of course be seen and traced visually. Spectrum analysis however also enables us to detect those movements that are along the line of sight, spectrum analysis enables us to recognise the fact. Interesting results have for example been arrived at with double stars that move around each other. The movement was only recognizable by tackling the problem with the help of Doppler's principle,—that is the experimental method to which I am referring.

For us, the question now is whether the method which includes man in the whole cosmic system will give us any criterion—I express myself with caution—any criterion to tell whether a movement may perhaps only be apparent or whether we must conclude that it is real. Is there anything to indicate that a given movement must be a real one? I have already spoken of this. We must distinguish between movements that may quite well be merely relative and on the other hand such movements as the “rotating, shearing and deforming movements” (so we described them), the very character of which will indicate that they cannot be taken in a merely relative sense. We must look for a criterion of true movement. We shall gain it in no other way than by envisaging the inner conditions of what is moving. We cannot possibly confine ourselves to the mere outer relations of position.

A trite example I have often given is of two men whom I see side by side at 9 am and again at 3 in the afternoon. The only difference is, one of them stayed there while the other went on an errand lasting six hours. I was away in the meantime and did not see what happened. At 3 pm I see them side by side again. Merely observing where they are outwardly in space, will never tell me the true fact. Only by seeing that one is more tired than the other—taking account of an inner condition therefore—shall I be able to tell, which of them has been moving. This is the point. If we would characterize any movement as an inherent and not a merely relative movement, we must perceive what the thing moved has undergone in some more inward sense. For this, a further factor will be needed, of which tomorrow. Today we will at least approach the problem.

We must in fact get hold of it from quite another angle. If we in our time study the form and formation of the human body and look for some connection with what is there in cosmic space, the most we can do to begin with is in some outward sense to see that the connection is there. Man is today very largely independent of the movements of cosmic space; everything points to the fact that this is so. For all that comes to expression in his immediate experience, man has emancipated himself from the phenomena of the Universe. We therefore have to look back into the time when what he underwent depended less upon his conscious life of soul than in his ordinary, by which I mean, post-natal life on Earth. We must look back into the time when he was an embryo. In the embryo the forming and development of man does indeed take place in harmony with cosmic forces. What afterwards remains is only what is carried forward, so to speak. Implanted in the whole human organization during the embryonal life it then persists. We cannot say it is "inherited" in the customary sense, for in fact nothing is inherited, but we must think of some such process, where entities derived from an earlier period of development stay on.

We must now look for an answer to the question: Is there still anything in the ordinary life we lead after our birth—after full consciousness has been attained—is there still any hint of our connection with the cosmic forces? Let us consider the human alternation of waking and sleeping. Even the civilized man of today still has to let this alternation happen. In its main periodicity, if he would stay in good health, it still has to follow the natural alternation of day and night. Yet as you know very well, man of today does lift if out of its natural course. In city life we no longer make it coincide with Nature. Only the country folk do so still. Nay, just because they do so, their state of soul is different. They sleep at night and wake by day. When days are longer and nights shorter they sleep less; when nights are longer the sleep longer. These aspects however can at most lead to vague comparisons; no clear perception can be derived from them. To recognize how the great cosmic conditions interpenetrate the subjective conditions of man, we must go into the question more deeply. So shall we find in the inner life of man some indication of what are absolute movements in the great Universe.

I will now draw your attention to something you can very well observe if only you are prepared to extend your observation to wider fields. Namely, however easily man may emancipate himself from the Universe in the alternation of sleeping and waking as regards time, he cannot with impunity emancipate himself as regards spatial position. Sophisticated folk—for such there are—may turn night into day, day into night, but even they, when they do go to sleep, must adopt a position other than the upright one of waking life. They must, as it were, bring the line of their spine into the same direction as the animal's. One might investigate a thing like this in greater detail. For instance, it is a physiological fact that there are people who in conditions of illness cannot sleep properly when horizontal but have to sit more upright. Precisely these deviations from the normal association of sleep with the horizontal posture will help to indicate the underlying law. A careful study of these exceptions—due as they are to more or less palpable diseases (as in the case of asthmatic subjects for example)—will be indicative of the true laws in the domain. Taking the facts together, you can quite truly put it in this way: To go to sleep, man must adopt a position whereby his life is enabled in some respects to take a similar course, while he is sleeping, to that of animal life. You will find further confirmation in a careful study of those animals whose spinal axis is not exactly parallel to the Earth's surface.

Here again I can only give you guiding lines. For the most part, these things have not been studied in detail; the facts have not been looked at in this manner, or not exhaustively. I know they have never been gone into thoroughly. The necessary researches have not been undertaken.

And now another thing: You know that what is trivially called “fatigue” represents a highly complex sequence of events. It can come about by our moving deliberately. When we move deliberately, we move our centre of gravity in a direction paralleled to the surface of the Earth. In a sense, we move about a surface parallel to the Earth's surface. The process which accompanies our outward and deliberate movements takes its course in such a surface. Now here again we can discover what belongs together. On the one hand we have our movement and mobility parallel to the surface of the earth, and our fatigue,—becoming tired. Now we go further in our line of thought. This movement parallel to the surface of the Earth, finding its symptomatic expression in fatigue, involves a metabolic process—an expenditure of metabolism. Underlying the horizontal movement there is therefore a recognizable inner process in the human body.

Now the human being is so constituted that he cannot well do without such movement—including all the concomitant phenomena, the metabolic expenditure of substance and so on. He needs all this for bodily well-being. If you're a postman, your calling sees to it that you move about horizontally; if you are not a postman you take a walk. Hence the relationship, highly significant for Economics, between the use and value of that mobility of man which enters into economic life and that which stays outside it—as in athletics, games and the like. Physiological and economic aspects meet in reality. In my critique of the economic concept of Labour, you may remember I have often mentioned this. It is at this point that the relation emerges between a purely social science and the science of physiology, nor can we truly study economics if we disregard it. For us however at the present moment, the important thing is to observe this parallelism of movement in a horizontal surface with a certain kind of metabolic process.

Now the same metabolic process can also be looked for along another line. We think once more of the alternation of sleeping and waking. But there is this essential difference. The metabolic transformation, when it takes place with our deliberate movements, makes itself felt at once as an external process, even apart from what goes on inside the human being. If I may put it so, something is then going on, for which the surface of the human body is no exclusive frontier. Substance is being transformed, yet so that the transformation takes place as it were in the absolute; the importance of it is not only for the inside of man's body. (The world “absolute” must of course again be taken relatively!)

That we get tired is, as I said, a symptomatic concomitant of movement and of the metabolic process it involves. Yet we also get tired if we have only lived the life-long day while doing nothing. Therefore the same entities which are at work when we move about with a will, are also at work in the human being in his daily life simply by virtue of his internal organization. The metabolic transformation must also be taking place when we just get tired, without our bringing it about by any deliberate action.

We put ourselves into the horizontal posture so as to bring about the same metabolism which takes place when we are not acting deliberately,—which takes place simply with the lapse of time, if I may so express it. We put ourselves into the horizontal posture during sleep, so that in this horizontal position our body may be able to carry out what it also carries out when we are moving deliberately in waking life. You see from this that the horizontal position as such is of great significance. It is not a matter of indifference, whether or not we get into this position. To let our inner organism carry out a certain process without our doing anything to the purpose, we must bring ourselves into the horizontal position in which there happens in our body something that also happens when we are moving by our deliberate will.

A movement must therefore be going on in our body, which we do not bring about by our deliberate will. A movement which we do not bring about by our deliberate will must be of significance for our body. Try to observe and interpret the given facts and you will come to the following conclusion, although again—for lack of time—in saying this I must leave out many connecting links. Human movement, as we said just now, involves an absolute metabolic process or change of substance, so that what then goes on in our metabolism has, so to speak, real chemical or physical significance, for which the limits of our skin are in some sense non-existent;—so that the human being in this process belongs to the whole Cosmos. And now the very same metabolic change of substance is brought about in sleep, only that then its significance remains inside the human body. The change of substance that takes place in our deliberate movement takes place also in our sleep, but the outcome of it is then carried from one part of our body to another. During sleep, in effect, we are supplying our own head. We are then carrying out or rather, letting the inside of our body carry out for us—a metabolic process of transformation for which the human skin is an effective frontier. The transmutation so takes place that the final process to which it leads has its significance within the bodily organization of man.

Once more then, we may truly say: We move of our own will, and a metabolic process (a transformation of substance) is taking place. We let the Cosmos move us; a transformation of substance is taking place once more. But the latter process goes on in such a way that the outcome of it—which in the former metabolic process takes its course, so to speak, in the external world—turns inward to make itself felt as such within the human head. It turns back and does not go flowing outward and away. Yet to enable it to turn back, nay to enable it to be there at all, we have to bring ourselves into the horizontal posture. We must therefore study the connection between those processes in the human body that take place when we move deliberately and those that take place when we are sleeping. And from the very fact that we are obliged to do this at a certain stage of our present studies, you may divine how much is implied when in the general Anthroposophical lectures I emphasize—as indeed I must do, time and gain,—that our life of will, bound as it is to our metabolism, is to our life of thought and indeation even as sleeping is to waking.

In the unfolding of our will, as I have said again and again, we are always asleep. Here now you have the more exact determination of it. Moving of his own will and in a horizontal surface, man does precisely the same as in sleep. He sleeps by virtue of his will. Sleep, and deliberate or wilful movement, are in this relation. When we are sleeping in the horizontal posture, only the outcome is different. Namely, what scatters and is dispersed in the external world when we are moving deliberately, is received and assimilated, made further use of, by our own head-organisation when we are asleep.

We have then these two processes, clearly to be distinguished from one another:—the outward dispersal of the metabolic process when we move about deliberately in day-waking life, and the inward assimilation of the metabolic process by all that happens in our head when we are sleeping. And if we now relate this to the animal kingdom, we may divine how much it signifies that the animal spends its whole life in the horizontal posture. This turning-inward of the metabolism to provide the head must be quite different in the animal. Also deliberate movement must be quite different in the animal from what it is in man.

This is the kind of thing so much neglected in the Science of today. They only speak of what presents itself externally, failing to see that the same external process may stand for something different in the one creature and in the other. For example—quite apart now from any religious implication—man dies and the animal dies. It does not follow that this is psychologically the same in either case. A scientist who takes it to be the same and bases his research on this assumption is like a man who would pick up a razor and declare: This is a kind of knife, therefore the same function as any other knife; so I will use it to cut my dumpling. Put on this simple level, you may answer: No-one would be so silly. Yet have a care, for this is just what happens in the most advanced researches.

This then is what we are led to see. In our deliberate movements we have a process finding its characteristic expression in curves that run parallel to the surface of the Earth; we cannot but make curves of this direction. What have we taken as fundamental now, in this whole line of thought? We began with an inner process which takes its course in man. In sleep this is the given thing, yet on the other hand we ourselves bring a like process about by our own action. Through what we do ourselves, we can therefore define the other. The possibility is given, logically. What is done to our bodily nature from out of cosmic space when are sleeping, this we can treat as the thing to be defined,—the nature of which we seek to know. And we can use as the defining concept what we ourselves do in the outer world—what is therefore well-known to as to its spatial relations. This is the kind of thing we have to look for altogether, in scientific method: Not to define phenomena by means of abstract concepts, but to define phenomena by means of other phenomena. Of course it presupposes that we do really understand the phenomena in question, for only then can we define them by one-another. This characteristic of Anthroposophical scientific endeavour. It seeks to reach a true Phenomenalism,—to explain phenomena by phenomena instead of making abstract concepts to explain them. Nor does it want a mere blunt description of phenomena, leaving them just as they are in the chance distributions of empirical fact and circumstance, where they may long be standing side by side without explaining one-another.

I may digress a moment at this point, to indicate the far-reaching possibilities of this “phenomenological” direction in research. The empirical data are at hand, for us to reach the right idea. There is enough and to spare to empirical data. What we are lacking in is quite another thing, namely the power to synthesize them,—in other words, to explain one phenomenon by another. Once more, we have to understand the phenomena before w can explain them by each other. Hence we must first have the will to proceed as we are now trying to do,—to learn to penetrate the phenomenon before us. This is so often neglected. In our Research Institute we shall not want to go on experimenting in the first place with the old ways and methods, which have produced enough and to spare of empirical data. (I speak here not from the point of view of technical applications but of the inner synthesis which is needed.) There is no call for us to go on experimenting in the old ways. As I said in the lectures on Heat last winter, we have to arrange experiments in quite new ways. We need not only the usual instruments from the optical instrument makers; we must devise our own, so as to get quite different kinds of experiments, in which phenomena are so presented that the one sheds light on the other. Hence we shall have to work from the bottom upward. If we do so, we shall find an abundance of material for fresh enlightenment. With the existing instruments our contemporaries can do all that is necessary; they have acquired admirable skill in using them in their one-sided way. We need experiments along new lines, as you must see, for with the old kind of experiment we should never get beyond certain limits. Nor on the other hand will it do for us merely to take our start from the old results and then indulge in speculation. Again and again we need fresh experimental results, to bring us back to the facts when we have gone too far afield. We must be always ready to find ways of means, when we have reached a certain point in our experimental researches, not just to go on theorising but to pass on to some fresh observation which will help elucidate the former one. Otherwise we shall not get beyond certain limits, transient though they are, in the development of Science.

I will here draw attention to one such limit, which, though not felt to be insurmountable by our contemporaries, will in fact only be surmounted when fresh kinds of experiment are made. I mean the problem of the constitution of the Sun. Careful and conscientious observations have of course been made by all the scientific methods hitherto available, and with this outcome: First they distinguish the inner most part of the Sun; what it is, is quite unclear to them. They call it the solar nucleus, but none can tell us what it is; the methods of research do not reach thus far. To say this is no unfriendly criticism; everyone admits it. They then suppose the Sun's nucleus to be surrounded by the so-called photo-sphere, the atmosphere, the chromosphere and the corona. From the photosphere onward they begin to have definite ideas abut it. Thus they are able to form some idea about the atmosphere, the chromosphere. Suppose for instance that they are trying to imagine how Sun-spots arise. Incidentally, this strange phenomenon does not happen quite at random; it shows a certain rhythm, with maxima and minima in periods of about eleven years. Examine the Sun-spot phenomena, and you will find they must in some way be related to processes that take place outside the actual body of the Sun. In trying to imagine what these processes are like, our scientists are apt to speak of explosions or analogous conditions. The point is that when thinking in this way they always take their start from premisses derived from the earthly field. Indeed, this is almost bound to be so if one has not first made the effort to widen out one's range of concepts,—as we did for instance when we imagined curves going out of space. If one has not done something of this kind for one' s own inner training, one has no other possibility than to interpret on the analogy of earthly conditions such observations as are available of a celestial body that is far beyond this earthly world.

Nay, what could be more natural—with the existing range of thought—than to imagine the processes of the solar life analogous to the terrestial, but for the obvious modifications. Yet in so doing one soon encounters almost insuperable obstacles. That which is commonly thought of as the physical constitution of the Sun can never really be understood with the ideas we derive from earthly life. We must of course begin with the results of simple observation, which are indeed eloquent up to a point; then however we must try to penetrate them with ideas that are true to their real nature. And in this effort we shall have to come to terms with a principle which I may characterize as follows.

It is so, is it not? Given some outer fact or distribution which we are able thoroughly to illumina with a truth of pre Geometry we say to ourselves: how well it fits: we build it up purely by geometrical thinking and now the outer reality accords with it. It hinges-in, so to speak. We feel more at one with outer reality when we thus find again and recognize what we ourselves first constructed, (yet the delight of it should not be carried too far. Somehow or other, one must admit, it always “hinges-in” even for those theorists who get a little unhinged themselves in the process: They too are always finding the ideas they first developed in their mind in excellent agreement with the external reality. The principle is valid, none the less.)

The following attempt must now be made. We may begin by imagining some process that takes place in earthly life. We follow the direction of it outward from some central point. It takes its course therefore in a radial direction. It may be a kind of outbreak, such for example as a volcanic eruption, or the tendency of deformation in an earthquake or the like. We follow such a process upon Earth in the direction of a line that goes outward from the given centre. And now in contrast to this you may conceive the inside of the Sun, as we are want to call it, to be of such a nature that its phenomena are not thrust outward from the centre, but on the contrary; they take their course from the corona inward, via the chromosphere, atmosphere and photosphere,—not from within outward therefore, but from without inward. You are to conceive , once more,—if this (Fig. 2) is the photosphere, this the atmosphere, this the chromosphere and this the corona,—that the processes go inward and, so to speak, gradually lose themselves towards the central point to which they tend just as phenomena that issue from the Earth lose themselves outward in expanding spheres, into the wide expanse. You will thus gain a mental picture which will enable you to bring some kind of synthesis and order into the empirical results. Speaking more concretely, you would have to say: If causes on the Earth are such as to bring about the upward outbreak for example of an active crater, the cause on the Sun will be such that if there is anything analogous to such an outbreak, it will happen from without inward. The whole nature of the phenomenon holds it together in quite another way. While on the Earth it tends apart, dispersing far and wide, here this will tend together, striving towards the centre.

You see, then what is necessary. First you must penetrate the phenomena and understand them truly. Only then can you explain them by one-another. And only when we enter thus into the qualitative aspect,—only when we are prepared, in the widest sense of the word, to unfold a kind of qualitative mathematics,—shall we make essential progress. Of this we shall speak more tomorrow. Here I should only like to add that there is a possibility, notably for pure mathematicians, to find the transition to a qualitative mathematics. Indeed this possibility is there in a high degree, especially in our time. We need only consider Analytical Geometry, with all its manifold results, in relation to Synthetic Geometry—to the real inner experience of Projective Geometry. True, this will only give us the beginning, but it is a very, very good beginning. You will be able to confirm this if you once begin along this pathway,—if for example you really enter into the thought and make it clear to yourself that a line has not two infinitely distant points (one in the one and one in the opposite direction) but only one,—fact of which there is no doubt. You will then find truer and more realistic concepts in this field, and from this starting-point you will find your way into a qualitative form of mathematics.

This will enable you to conceive the polarities of Nature no longer merely in the sense of outwardly opposite directions, where all the time the inner quality would be the same; whereas in fact the inner quality, the inner sense and direction, is not the same. The phenomena at the anode and the cathode for example have not the same inner direction; an inherent difference underlies them, and to discover what the difference is, we must take this pathway. We must not allow ourselves to think of a real line as though it had two ends. We should be clear in our mind that a real line in its totality must be conceived not with two ends but with one. Simple by virtue of the real conditions, the other end goes on into a continuation, which must be somewhere. Please do not underestimate the scope and bearing of these lines of thought. For they lead deep into many a riddle of Nature, which, when approached without such preparation, will after all only be taken in such a way that our thoughts remain outside the phenomena and fail to penetrate.

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.

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.[1]

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.[5] 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,[7] 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.[8] 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].[9]

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.[10] 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. [12]

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. [13]

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[14] 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.[15]]

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 interweavings occur in nature all the time. Anyone who reflects on natural processes knows that such interweavings 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.