The Rudolf Steiner Archive

My dear friends,

Yesterday we carried out an experiment which brought to your attention the fact that mechanical work exerted by friction of a rotating paddle in a mass of water has changed into heat. You were shown that the water in which the paddle turned became warmer.

Today we will do just the opposite. We showed yesterday that we must in some ways seek an explanation for the coming of heat into existence upon the expenditure of work. Now let us follow the reverse process. We will first of all heat this air (see Figures at end of Chapter) using a flame, raise the pressure of the vapor, and thus bring about a mechanical effect by means of heat, in a way similar to that by which all steam engines are moved. Heat is turned into work through pressure change. By letting the pressure come through from one side we raise the bell up and by letting the vapor cool, the pressure is lessened, the bell goes down again and we have performed mechanical work, consistive in this up and down movement. We can see the condensation water which reappears when we cool, and runs into this flask. After we have let the entire process take place, after the heat that we have produced here has transformed itself into work, let us determine whether this heat has been entirely transformed into the up and down movement of the bell or whether some of it has been lost. The heat not changed into work must appear as such in the water. In case of a complete transformation the condensation water would not show any rise in temperature. If there is a rise in temperature which we can determine by noting whether the thermometer shows a temperature above the ordinary, then this temperature rise comes from the heat we have supplied. In this case, we could not say that the heat has been completely changed over into work; there would be portion remaining over. Thus we can ascertain whether the whole of the heat has gone over into work or whether some of it appears as heat in the condensate. The water is 20° and we can see whether the condensate is 20° or shows a higher temperature indicating a loss of heat to this condensate. Now we condense the vapor; the condensate water drops in the flask. A machine can be run in this way. If the experiment succeeds fully, you may determine for yourselves that the condensate shows a considerable increase in temperature. In this way we can demonstrate, when we carry out the reverse of yesterday's experiment, that it is not possible to get back as mechanical work in the form of up and down movement of the bell all the heat left over. The heat used in producing work does not change completely, but a portion always remains.

We wish first to grasp this phenomenon. Now let us consider how ordinary physics and those who use ordinary physical principles handle these things.

We have at the beginning to deal with the fact that we in fact do change heat into work and work into heat just as it is said we do. As previously stated an extension of this idea has been made. It is supposed that every form of so-called energy—heat energy, mechanical energy, and the experiment may be made with other forms—that all such energies are mutually changeable the one into the other. We will for the moment neglect the quantitative aspect of the transformation and consider only the fact. Now, the modern physicist says: It is therefore impossible for energy to arise anywhere except from energy of another sort already present. If I have a closed system of energy, let us say of a certain form, and another energy appears, then this must be considered as transformation of the energy already present in the closed system. In a closed system, energy can never appear except as a transformation product. Eduard von Hartmann, who, as I have said, expressed current physical views in the form of philosophical concepts, states the so-called first law of the mechanical theory of heat as follows: “A perpetuum mobile of the first kind is impossible.”

Now we come to the second series of phenomena illustrated for us by today's experiment. This is that in an energy system apparently closed, we have one form of energy changing over to another form. In this transformation however, it is apparent that a certain law underlies the process and this law is related to the quality of the energy. In this case of heat energy, the relation is such that it cannot go over completely to mechanical energy, but there is always a certain amount unchanged. Thus it is impossible in a closed system to transform completely all the heat energy into its mechanical equivalent. If this were possible the reverse transformation of mechanical energy completely into heat energy would also be possible. We would then have in a closed energy system one type of energy transformed into another. This law is stated, again by Eduard von Hartmann, as follows: A closed energy system in which for instance, the entire amount of heat could be changed into work, or where work could be completely changed into heat, when a cycle of complete transformation could exist, this would be a perpetuum mobile of the second type. But, says he, a perpetuum mobile of the second type is impossible. Fundamentally, these two are the principle laws of the mechanical theory of heat as this theory is understood by thinkers in the realm of physics in the 19th century and the early part of the 20th century.

“A perpetuum mobile of the first type is an impossibility.” This concept is intimately connected with the history of physics in the 19th century. The first person to call attention to this change of heat into other forms of energy or vice-versa was Julius Robert Mayer. He had observed, as a physician, that the venous blood showed a different behavior in the tropics and in the colder regions, and from this concluded that there was a different sort of physiological work involved in the human organism in the two cases. Using principally these experiences, he later presented a somewhat confused theory which as he worked it out meant little more than this, that it was possible to transform one type of energy into another. The matter was then taken up by various people, Helmholtz among others, and further developed. In the case of Helmholtz a characteristic form of physical-mechanical thinking was taken as the starting point for these things.

If we consider the most important treatise by which Helmholtz sought to support the mechanical theory of heat in the forties of the 19th century, we see that such ideas as expressed by Hartmann are really postulated as their foundation. A perpetuum mobile of the first type is impossible. Since it is impossible the various forms of energy must be transformations of each other. No form of energy can arise from nothing. The axiom from which we proceed—“a perpetuum mobile of the first type is impossible”—can be changed into another: the sum of the energy in the universe is constant. Energy never is created, never disappears, it is only transformed. The sum of the energy in the universe is constant.

These two principles fundamentally, then, mean precisely the same thing. “There is no perpetuum mobile of the first type.” “The sum of all the energy in the cosmos is constant.” Now applying the method of thinking that we have used before in all our observations, let us throw a little light on this whole point of view.

Note now, when we make an experiment with the object of transforming heat into what we call work, that some of the heat is lost so far as the transformation is concerned. Heat reappears as such and only a portion of it can be turned into the other energy form, the mechanical form. What we learn from this experiment we may apply to the cosmos. This is what the 19th century investigators did. They reasoned somewhat as follows: “In the world about us work is present and heat is present. Processes are continually going on by which heat is transformed into work. We see that heat must be present if we would produce work. Only recollect how great a part of our technical achievements rest on the fact that we produce work by the use of heat. But it always comes out that we cannot completely transform heat into work, a portion remains as heat. And since this is so, these remainders not capable of yielding work, accumulate. These non-transformable residues accumulate. And the universe approaches a condition in which all mechanical work will have been turned into heat.”

It has even been said that the universe in which we live is approaching what has been learnedly called its “warmth-death.” We will speak in coming lectures of the so-called entropy concept. For the present our interest lies in the fact that certain ideas have been drawn from experiment bearing on the fate of the universe in which we find ourselves.

Eduard von Hartmann has presented the matter very neatly. He says: physical observation shows that the world-process in the midst of which we live, exhibits two sorts of phenomena. In the end, however, all mechanical work can be produced, and the universe will have to come to an end. Thus says Eduard von Hartmann; physical phenomena shows that the world process is running down. This is the way he expresses himself about the conditions within which we live. We live in a universe whose processes preserve us, but which has a tendency to become more and more sluggish and finally to lapse into a state of complete inaction. I am merely repeating Eduard von Hartmann's own words.

Now we must make clear to ourselves the following point. Is there ever really the possibility of calling forth a series of processes in a closed system? Note well what I am saying. If I consider the totality of my experimental implements, I certainly am not myself in a vacuum, in empty space. And even when I believe myself to be standing in empty space, I am still not entirely certain but that this empty space is empty only because I am unable to perceive what is really in it. Do I therefore ever really carry out my experiments in a closed system? Is it not so that what I carry out in the simplest experiment has to be thought of as dovetailed into the world process immediately around me? Can I conceive of the matter otherwise than in this fashion, that when I do all these things it is as though I took a small needle and pricked myself here? When I prick myself here I experience pain which prevents me from having an idea that I would otherwise have had. It is quite certain indeed, that I cannot consider merely the prick of the needle and the reaction of the skin and muscles as the whole of the process. In such a case I would not be placing the whole process before my eyes. The process is not entirely contained in these factors. Imagine for a moment that I am so clumsy as to pick up a needle, prick myself and experience the pain. I will pull the needle away. What appears thus as an effect is very definitely not comprehended when I hold in mind only what goes on in the skin. The drawing back of the needle is in reality nothing other than a continuation of what I apprehend when I hold before my mind the first part of the process. If I wish to describe the whole process, I must take into account that I have not stuck the needle into my clothes, but into my organism. This organism must be considered as a regulating whole, calling forth the consequences of the needle prick.

Is it legitimate for me to speak of an experiment such as we have before our eyes in the following way: “I have produced heat, and caused mechanical work. The heat not transformed remains over in the condensation water as heat.” It is not in this way that I stand in relation to the whole thing. The production or retention of heat, the passage of it into the condensation water are related to the reaction of the whole great system as the reaction of my whole organism is to the small activity of being pricked with the needle. What must be taken into account especially is: That it is never valid for me to consider an experimental procedure as a closed system. I must keep in mind that this whole experimental procedure falls under the influence of energies that work out of this environment.

Consider along with this another fact. Suppose you have to begin with a vessel containing a liquid with its liquid surface which implies an action of forces at right angles to this surface. Suppose now that through cooling, this liquid goes over into a solid state. It is impossible for you to think of the matter otherwise than that the forces in the liquid are short through by another set of forces. For the liquid forces are such as to make it imperative that I hold this liquid, say water, in a vessel. The only form assumed by the water on its own account is the upper surface. When by solidification a definite form arises it is absolutely necessary to assume that forces are added to those formerly present. More observation convinces us of it. And it is quite absurd to think that the forces creating the form are present in some way or other in the water itself. For if they were there they would create the form in the water. They are thus added to the system, but must have come into it from the outside. If we simply take the phenomenon as it is presented to us we are obliged to say: when a form appears, it represents as a matter of fact a new creation. If we simply consider what we can determine from observation we have to think of the form as a new creation. It is simply a matter of observation that we bring about the solid state from the fluid. We see that the form arises as a new creation. And this form disappears when we change the solid back into a liquid. One simply rests on that which is given as an observable fact. What follows now from this whole process when one makes it over into a concept? It follows that the solid seeks to make itself an independent unit, that it tends to build a closed system, that it enters into a struggle with its surroundings in order to become a closed system.

I might put the matter in this way, that here in the solidification of a liquid we can actually lay our hands on nature's attempt to attain a perpetuum mobile. But the perpetuum mobile does not arise because the system is not left to itself but is worked upon by its whole environment. The view may therefore be advanced: in space as given us, there is always present the tendency for a perpetuum mobile to arise. But a counter tendency appears at once. We can therefore say that wherever the tendency arises to form a perpetuum mobile, the opposite tendency arises in the environment to prevent this. If you will orient your thinking in this way you will see that you have altered the abstract method of modern 19th century physics through and through. The latter starts from the proposition: a perpetuum mobile is impossible, therefore etc. etc. If one stands by the facts the matter has to be stated thus: a perpetuum mobile is always striving to arise. Only the constitution of the cosmos prevents it.

And the form of the solid, what is it? It is the impress of the struggle. This structure that forms itself in the solid is the impress of the struggle between the substance as individuality which strives to form a perpetuum mobile and the hindrance to its formation by the great whole in which the perpetuum mobile seeks to arise. The form of a body is the result of opposition to this striving to form a perpetuum mobile. It might be better understood in some quarters if, instead of perpetuum mobile, I spoke of a self-contained unit, carrying its own forces within itself and its own form-creating power.

Thus we arrive at a point where we have to reverse completely the entire point of view, the manner of thinking of 19th century physics. Physics itself, insofar as it rests on experiment, which deals with facts, we do not have to modify. The physical way of thinking works with concepts that are not valid and it cannot realize that nature strives universally for that which it holds as impossible. For this manner of thinking it is quite easy to consider the perpetuum mobile as impossible, but it is not impossible because of the abstract reasons advanced by the physicists. It is impossible because the instant the perpetuum mobile strives to establish itself in any given body, at that instant the environment becomes jealous, if I may borrow an expression from the realm of morals, and does not let the perpetuum mobile arise. It is impossible because of facts and not because of logic. You can appreciate how twisted a theory is that departs from reality in its very foundation postulate. If the facts are adhered to, it is not possible to get around what I presented to you yesterday in a preliminary sketchy way. We will elaborate this sketchy presentation in the next few days.

I said to you: we have, to begin with, the realm of solids. Solids are the bodies which manifest in definite forms. We have, touching on the realm of the solids as it were, the realm of fluids. Form is dissolved, disappears, when solids become liquids. In the gaseous bodies we have a striving in all directions, a complete formlessness—negative form. Now how does this negative form manifest itself? If we look in an unbiased manner on gaseous or aeriform bodies we can see in these that which may be considered as corresponding to the entity elsewhere manifested as form. Yesterday I called your attention to the realm of acoustics, the tone world. In the gas, as you know, the manifestation of tone arises through condensations and rarefactions. But when we change the temperature we also have to do with condensation and rarefaction in the body of the gas as a whole. Thus if we pass over the liquid state and seek to find in the gas what corresponds to form in the solid, we must look for it in condensation and rarefaction. In the solid we have a definite form; in the gas, condensation and rarefaction.

And now we pass to the realm next adjacent to the gaseous. Just as the fluid realm borders on the solid, and just as we know how the solid pictures the fluid, the fluid gives the foreshadowing of the gaseous, so the gas pictures the realm which we must conceive as lying next to the gaseous, i.e. the realm of heat. The realm lying next above heat, we will have to postulate for the time being and call it the X region.

If now, I seek to advance further, at first merely through analogy, I must look in this X region for something corresponding to but beyond condensation and rarefaction (this will be verified in our subsequent considerations.) I must look for something else there in the X region, passing over heat, just as we passed over the fluid state below. If you begin with a definitely formed body, then imagine it to become gaseous and by this process to have simply changed its original form into another manifesting as rarefaction and condensation and if then you think of the condensation and rarefaction as heightened in degree, what is the result? As long as condensation and rarefaction are present, obvious matter is still there. But now, if you rarefy further and further you finally pass entirely out of the realm of the material. And this extension we have spoken of must, if we are to be consistent, be made thus: a material-becoming—a spiritual-becoming. When you pass over the heat realm into the X realm you enter a region where you are obliged to speak of the condition in a certain way. Holding in mind this passage from solid to fluid and the condensation and rarefaction in gases you pass to a region of materiality and non-materiality. You cannot do other than enter the region of materiality and non-materiality. Stated otherwise: when we pass through the heat realm we actually enter a realm which is in a sense a consistent extension of what we have observed in the realms beneath it. Solids oppose heat—it cannot come to complete expression in them. Fluids are more susceptible to its action. In gases there is a thorough-going manifestation of heat—it plays through them without hindrance. They are in their material behavior a complete picture of heat. I can state it thus: the gas is in its material behavior essentially similar to the heat entity. The degree of similarity between matter and heat becomes greater and greater as I pass from solids through fluids to gases. Or, liquefaction and evaporation of matter means a becoming similar of this matter to heat. Passage through the heat realm, however, where matter becomes, so to speak, identical with heat leads to a condition where matter ceases to be. Heat thus stands between two strongly contrasted regions, essentially different from each other, the spiritual world and the material world. Between these two stands the realm of heat. This transition zone is really somewhat difficult for us. We have on the one hand to climb to a region where things appear more and more spiritualized, and on the other side to descend into what appears more and more material. Infinite extension upwards appears on the one hand and infinite extension downward on the other. (Indicated by arrows.)

But now we use another analogy that I am bringing before you today because through a general view of individual natural facts a sound science may be developed. It will perhaps be useful to array these facts before our souls. (See below.)

If you observe the usual spectrum you have red, orange, yellow, green, blue, indigo and violet.

Infra red——————————roygrbiv——————————Ultra Violet

You have the colors following each other in a series of approximately seven nuances. But you know that the spectrum does not break off at either end. If we follow it further below the red we come to a region where there is more and more heat, and finally we arrive at a region where there is no light, but only heat, the infra red region. On the other side of the violet, also, we no longer have light. We come to the ultra violet where chemical action is manifested, or in other words effects that manifest themselves in matter. But you know also that according to the color theory of Goethe, this series of colors can be bent into a circle, and arranged in such a way that one sees not only the light from which the spectrum is formed, but also the darkness from which it is formed. In this case the color in the middle is not green but the peach-blossom color, and the other colors proceed from this. When I observe darkness I obtain the negative spectrum. And if I place the two spectra together, I have 12 colors that may be definitely arranged in a circle: red, orange, yellow, green, blue, indigo, and violet. On this side the violet becomes ever more and more similar to the peach blossom and there are two nuances between. On the other side there are two nuances between peach blossom and red. You have, if I may employ the expression, 12 color conditions in all. This shows that what is usually called the spectrum can be thought of as arising in this way: I can by any suitable means bring about this circle of color and can make it larger and larger, stretching out the upper five colors (peach blossom and the two shades on each side) until they finally disappear. The lower arc becomes practically a straight line, and I obtain the ordinary spectrum array of colors, having brought about the disappearance of the upper five colors.

I finally bring these colors to the vanishing point. May it not be that the going off into infinity is somewhat similar to this thing that I have done to the spectrum? Suppose I ask what happens if that which apparently goes off into infinity is made into a circle and returns on itself. May I not be dealing here with another kind of spectrum that comprehends for me on the one hand the condition extending from heat to matter, but that I can close up into a circle as I did the color spectrum with the peach blossom color? We will consider this train of thought further tomorrow.

My dear friends,

The fact that we have spoken of the transformation of energy and force assumed by modern physics makes it necessary for us to turn our attention to the problem of indicating what really lies behind these transformations. To aid in this, I wish to perform another experiment to be ranged alongside of yesterday's. In this experiment we will perform work through the use of another type of energy than the one that is immediately evident in the work performed. We will, as it were, bring about in another sphere the same sort of thing that we did yesterday when we turned a wheel, put it in motion and thus performed work. For the turning of the wheel can be applied in any machine, and the motion utilized. We will bring about the turning of a wheel simply by pouring water on these paddle, and this water by virtue of its weight will bring the paddle wheel into motion. The force that somehow or other exists in the running water is transformed into the rotational energy of the wheel. We will let the water flow into this trough in order to permit it to form a liquid surface as it did in previous experiments. What we show is really this, that by forming a liquid surface below we make the motion of the wheel slower than it was before. Now, it will slow down in proportion to the degree to which the lower level approaches the upper level. Thus we can say: if we indicate the total height of the water from the point \(a\) here where it flows onto the wheel by \(h\) and the perpendicular distance to the liquid surface by \(h'\) then we can state the difference as \(h-h'\). We can further state that the work available for the wheel is connected in some way with the difference between the two levels. (The sense in which this is so we will seek in our further considerations.) Yesterday in our experiment we also had a kind of difference in levels, \(t-t'\). For you will recollect we denoted the heat of the surroundings at the beginning of our experiments by \(t'\) and the heat we produced in order to do work to raise and lower a bell, this we denoted by \(t\). Therefore you can say: the energy available for work depends on the difference between \(t\) and \(t'\). Here too, we have something that can be denoted as a difference in level.

I must ask you to note especially how both these experiments show that wherever we deal with what is called energy transformation, we have to take account of difference in level. The part played by this, what is really behind the phenomenon of energy transformation, this we will find only where we pursue further the train of thought of yesterday. As we do this we will illuminate so to speak, the phenomena of heat and take into account that which Eduard von Hartmann set aside before he attempted a definition of physical phenomena. In this connection we must emphasize again and again a beautiful utterance of Goethe's regarding physical phenomena. He gave utterance to this in various ways, somewhat as follows: what is all that goes on in outer physical apparatus as compared to the ear of the musician, as compared to the revelation of nature that is given us in the musician's ear itself. What Goethe wishes to emphasize by this is that we will never understand physical things if we observe them separately from man himself. According to his view, the only way to attain the goal is to consider physical phenomena in connection with the human being, the phenomena of sound in connection with the sense of hearing. But we have seen that great difficulties arise when we try in this way to bring the phenomena of heat in connection with the human being—really seek to connect heat with the being of man. Even the facts that have led to the discover of the so-called modern mechanical theory of heat support this view. Indeed, that which appears in this modern mechanical theory of heat took its origin from an observation made on the human organism by Julius Robert Mayer. Julius Robert Mayer, who was a physician, had noticed from blood-letting he was obliged to do in the tropical country of Java, that the venous blood of tropical people was redder than that of people in northern climes. He concluded correctly from this that the process involved in the coloration of blood varies, depending on whether man lives in a warmer or cooler climate, and is thus under the necessity of giving off less or more heat to his surroundings. This in turn involves a smaller or greater oxidation. Essentially he discovered that this process is less intense when the human being is not obliged to work so intensely on his environment. Thus, the human being of the tropics, since he loses less heat to his environment, is not obliged to set up so active a relation with the outer oxygen as when he gives off more heat. Consequently man, in order to maintain his life processes and exist at all on the earth in the cooler regions, is obliged to tie himself in more closely with his environment. He must take in more oxygen from the air in the colder regions where he works more intensely in connection with his environment than in the warmer zones where he labors more intensely in his inner nature.

Right here you get an insight into the inner workings of the whole human organization. You see that it has only to become warmer and the human being then works more in his inner individuality than he does when his environment is colder and he is thereby obliged to link his activities more intimately with his outer environment.

From this process in which we have represented a relation of man to his environment, there proceeded the observations that resulted in the theory of heat. These observations led Julius Robert Mayer to submit his small paper on the subject to the Poggnedorfschen Annalen. From this paper arose the entire movement in physics that we know about. This is strange enough since the paper that Mayer handed the Poggnedorfschen Annalen was returned as entirely lacking in merit. Thus we have the odd circumstance that physicists today say: we have turned physics into entirely new channels, we think entirely otherwise about physical things than they did before the year 1842. But attention has to be called to the fact that the physicists of that time, and they were the best physicists of the period, had considered Mayer's paper as entirely without merit and would not publish it in the Poggnedorfschen Annalen. Now you can see that it might be said: this paper in a certain sense brings to a conclusion the kind of view of the physical that was, as it were, incompletely expressed in Goethe's statement. After the publication of this paper, a physics arises which sees science advancing when physical facts are considered apart from man. This is indeed the principle characteristic of modern views on the subject. Many publications bring this idea forward as necessary for the advance of physics, stating that nothing must enter in which comes from man himself, which has to do with his own organic processes. But in this way we shall arrive at nothing. We will however continue our train of thought of yesterday, a train of thought drawn from the world of facts and one which will lead us to bring physical phenomena nearer to man.

I wish once more to lay before you the essential thing. We start from the realm of solids and find a common property at first manifesting as form. We then pass through the intermediate state of the fluid showing form only to the extent of making for itself a liquid surface. Then we reach the gaseous bodies, where the property corresponding to form manifests itself as condensation and rarefaction.

We then come to the region bordering on the gaseous, the heat region, which again, like the fluid, is an intermediate region, and then we come to our \(X\). Yesterday we saw that pursuing our thought further we have in \(X\) to postulate materialization and dematerialization. It is not difficult then to see that we can go beyond \(X\) to \(Y\) and \(Z\) just as, for instance, we go in the light spectrum from green to blue, from blue to violet and to ultra violet.

And now it is a question of studying the mutual relations between these different regions. In each one we see appearing what I might call definitely characteristic phenomena. In the concrete realm we see a circumscribed for; in gas a changing form, so to speak, in condensations and rarefactions. This accompanies, and I am now speaking precisely, this accompanies the tone entity, under certain conditions. When we pass through the warmth realm into \(X\) realm, we see materialization and dematerialization. The question now arising is this: how does one realm work into another?

Now I have already called your attention to the fact that when we speak of gas, the phenomena there enacted present a kind of picture of what goes on in the realm of heat. We can say therefore, in the gas we find a picture of what goes on in the heat realm. This comes about in no other manner than that we have to consider gas and heat as mutually interpenetrating each other, as so related that gaseous phenomena are seized upon in their spatial relationship by the heat entity. What is really taking place in the realm of heat expresses itself in the gas through the interpenetration of the two realms. Furthermore we can say, fluids show us a relationship of forces similar to that obtaining between gases and heat. Solids show the same sort of relationship to fluids do to gases and as gases do to heat.

What then, comes about in the realm of solids? In this realm forms appear, definite forms. Forms circumscribed within themselves. These circumscribed forms are in a relative sense pictures of what is really active in fluids. Now we can pass here to a realm \(U\), below the solid, whose existence we at the start will merely postulate; and let us try to create concepts in the realm of the observable. By extending our thinking which you can feel is rooted in reality, we can create concepts and these concepts springing from the real bring into us a bit of the real world.

What must take place if there is to be such a reality as the \(U\) realm? In this realm there must be pictured that which in solids is a manifested fact. In a manner corresponding to the other realms the \(U\) realm must give us a picture of the solids. In the world of solids we have bodies everywhere, everywhere forms. These forms are conditioned from within their own being, or at least conditioned according to their relation to the world. We will consider this further in the next few days. Forms come into being, mutually inter-related.

Let us go back for a moment to the fluid state. There we have, as it were, the fluid throwing out a surface and thus showing its relation to the entire earth. In gravity therefore, we have to recognize a force related to the creation of form in solids. In the \(U\) realm we must find something that happens in a similar manner to the form-building in the world of solids, if we are to pursue our thinking in accordance with reality. And this must parallel the picturing of the fluid world by solids. In other words: in the \(U\) world we must be able to see an action which foreshadows the solid world. We must in some way be able to see this activity. We must see how, under the influence of forms related to each other something else arises. There must come into existence as a reality what further manifests as varying forms in the solid world. We really have today only the beginning of such an insight. For, suppose you take a suitable substance, such as tourmaline, which carries in itself the principle of form. You then bring this tourmaline into such a relation that form can act on form. I refer to the inner formative tendency. You can do this by allowing light to shine through a pair of tourmaline crystals. At one time you can see through them and then the field of vision darkens. This you can bring about simply by turning one crystal. You have brought their form-creating force into a different relation. This phenomena, apparently related to the passage of light through systems of differing constitution, shows us the polarization figures. Polarization phenomena always appear when one form influences another. There we have the noteworthy fact before our eyes that we look through the solid realm into another realm related to the solid as the solid is to the liquid. Let us ask ourselves now, how come it is that under the influence of the form-building force there arises in the \(U\) realm that which we observe in the polarization figures as they are called, and which really lies in the realm beneath the solid realm? For we do, as a matter of fact, look into a realm here that underlies the world of the solids. But we see something else also.

We might look long into such a solid system, and the most varied forces might be acting there upon each other, but we would see nothing. It is necessary to have something playing through these systems, just as the U realm plays through the world of solids in order to bring out the phenomenon. And the light does this and makes the mutual inter-working of the form-building forces visible for us.

What I have here expressed, my friends, is treated by the physics of the 19th century in such a way that the light itself is supposed to give rise to the phenomenon while in reality the light only makes the phenomenon visible. Looking on these polarization figures, one must seek for their origin in an entirely different source from the light itself. What is taking place has nothing whatever to do with the light as such. The light simply penetrates the \(U\) realm and makes visible what is going on there, what is taking place there as a foreshadowing of the solid form. Thus we can say we have to do with an interpenetration of different realms which we have simply unfolded before our eyes. In reality we are dealing with an interpenetration of different realms.

And now the facts lead us to the same point which we reached, for instance, in the realm of the gaseous by means of the forces of form. Our concepts of what has been said will be better if we consider condensation and rarefaction in connection with the relation of tone to the organ of hearing. We must not feel it necessary to identify these condensations and rarefactions in a gaseous body entirely with what we are conscious of as tone. We must seek for something in the gas that uses the condensations and rarefactions as an agency when these are present in a suitable fashion. What really happens we must express as follows: that which we call tone exists in a non-manifested condition. But when we bring about in a gas certain orderly condensations and rarefactions, then there occurs what we perceive consciously as tone. Is not this way of stating the matter entirely as though I should say the following: we can imagine in the cosmos heat conditions where the temperature is very high—about 100°C. We can also imagine heat conditions where very low temperatures prevail. Between the two is a range in which human beings can maintain themselves. It is possible to say that wherever in the cosmos there is a passage from the condition of high temperature to a condition of low temperature, there obtains at some intermediate point a heat condition in which human beings may exist. The opportunity for the existence of man is there, if other necessary factors for human existence are present. But we would on no account say: man is the temperature

Variation from high to low and the reverse variation. (For here the conditions would be right again for his existence.) We would certainly not say that. In physics, however, we are always saying, tone is nothing but the condensation and rarefaction of the air; tone is a wave-motion that expresses itself as condensation and rarefaction in the air. Thus we accustom ourselves to a way of thinking that prevents us from seeing the condensations and rarefactions simply as bearers of the tone, and not constituting the tone itself. And we should conceive for the gaseous something that simply penetrates it, but belongs to another realm, finding in the realm of the gaseous the opportunity so to manifest as to form a connection between itself and our higher organs. Concepts formed in this way about physical phenomena are really valid. If however, one forms a concept in which tone is merely identified with the air vibrations, then one is naturally led to consider light merely as ether vibrations. A person thus passes from what is not accurately conceived to the creation of a world of thought-out fantasies resulting simply from loose thinking. Following the usual ideas of physics, we bury ourselves in physical concepts that are nothing more than the creation of inaccurate thinking.

But now we have to consider the fact that when we pass through the heat realm to the \(X\), \(Y\) and \(Z\) realms, we have to pass out into infinity and here from the U region we have also to step into the infinite.

Recollect now what I told you yesterday. In the case of the spectrum also, when we try to get an idea of it as it exists ordinarily, we have to go from the green through the blue to the violet and then of to the infinite, or at least to the undetermined. So likewise at the red end of the spectrum. But we can imagine the spectrum in its completeness as a series of 12 independent colors in a circle, with green below and peach-blossom above, and ranged between these the other colors. When we can imagine the circle to become larger and larger, the peach blossom disappears above and the spectrum extends on the one hand beyond the red and on the other beyond the violet. In the ordinary spectrum therefore, we really have only a part of what would be there if the entire color series could appear. Only a portion is present.

Now there is a very remarkable thing. I think, my friends, if you take as a basis the ordinary presentation of optics in the physic books and read what is there given as explanation of a special spectral phenomenon, namely the rainbow, you will be rather uneasy if you are a person who likes clear concepts. For the explanation of the rainbow is really given in such a manner that one has no foundation on which to stand. One is obliged to follow all sorts of things going on in the raindrop from the running together of extremely small reflections that are dependent on where one stands in relation to the rainbow. These reflections are said really to come from the raindrops. In brief you have in this explanation an atomistic view of something that occurs in our environment as unity. But even more perplexing is the fact that his rainbow or spectrum conjured up before us by nature herself, never occurs singly. A second rainbow is always present, although sometimes very completely hidden. Things that belong together cannot be separated. The two rainbows, of which one is clearer than the other, belong of necessity together, and if one is to explain this phenomenon, it is not possible to do so simply by explaining one strip of color. If we are to comprehend the total phenomenon we must make it clear to ourselves that something of a unique nature is in the center and that it shows two bands of color. The one band is the clearer rainbow, and the other band is the more obscure bow. We are dealing with a representation in the greatness of nature herself, which is an integral portion of the “All” and must be comprehended as a unity. Now, when we observe carefully we will see that the second rainbow, the accessory bow, shows colors in the reverse order from the first. It reflects, so to speak, the first and clearer rainbow. As soon as we go from the partial phenomenon as it appears in our environment, to a relatively more complete one, when we conceive of the whole earth in its relation to the cosmic system, we see in the rainbows a different aspect. I wish only to mention this here—we will go into it more completely in the course of our lecture. But I wish to say here that the appearance of the second bow converts the phenomenon into a closed system, so to speak. The system is only an open one so long as I limit my consideration to the special spectrum arising in the \(U\) portion of my environment. The phenomenon of the rainbow really leads me to think of the matter thus, that when I produce a spectrum experimentally, I grasp nature only at one pole, the opposite pole escapes me. Something has slipped into the unknown, and I really have to add to the seven-colored spectrum the accessory spectrum.

Now hold in mind this phenomenon and the ideas that arise from it and recollect the previous ideas that we have brought out here. We are trying to close up the band of color that stretches out indefinitely on both sides, and bring the two together. If now, we do a similar things in this other realm, what happens? (See sketch at end of Chapter) Then we will pass from solids to the U region and beyond, but as we do this we also come back from the other end of the series and the system becomes a closed one. But now, when the downward path and the upward one come together to make a closed system, what does that form for us? What happens then?

I will try as follows to lead you to an understanding of this: suppose you really go in one direction in the sense indicated in our diagrams. Let us say we go out from the sphere where, as we have explained in these lectures, gravity becomes negative. We have, let us say, arrived in one of the realms. From this realm, suppose we go downward, and imagine that we pass through first the fluid and then the solid realms. Now when we go further, we must really come back from the other side—it is difficult to show this diagrammatically. Since we come back from the other side, that which belongs to this other side has to insert itself into the realm from which we have just passed. That is to say, while I pass from the solid to the U region, if I want to represent the whole cycle I must bend what is at the other end of the series around and thrust it in here. I can picture it in this way. From the null sphere I go through the fluid into the solid and then into the U region. Returning then, I come to the same point from the other side. Or, I might say: I observe the gas, it extends to here where I have colored with blue (referring to the drawing at end of Chapter). But from the other side comes that which inserts itself, interpenetrates it from the cosmic cycle, but appearing there only as a picture. It impregnates the gas, so to speak, and manifests as a picture. The fluid in its essence interpenetrates the sphere of the solid, and attains a form. Similarly, form appears in the gas as tone and this we have indicated in our diagram. Turn over in your minds this returning and interpenetration in these world-processes. You will of necessity have to think not of a world-cycle only, but of a certain sort of world-cycle. You will have to think of a world cycle that moves from one realm to another, but in which any realm shows reflection of other realms. In this way we get a basis for thinking about these things that has a root in reality. This way of thinking will help you, for instance, to see how light arises in matter, light which belongs to an entirely different realm; but you will see that the matter is simply “overrun” by the light, as it were. And you will then, if you treat these things mathematically, have to extend your formulae somewhat.

You may, if you will, consider these things under the symbol of ancient wisdom, the snake that swallows its own tail. The ancient wisdom represented these things symbolically and we have to draw nearer to the reality. This drawing nearer is the problem we must solve.

My dear friends,

Before we continue the observations of yesterday which we have nearly brought to a conclusion, let us carry out a few experiments to give support to what we are going to say. First we will make a cylinder of light by allowing a beam to pass through this opening, and into this cylinder we will bring a sphere which is so prepared that the light passes into it, but cannot pass through. What happens we will indicate by this thermometer (see drawing Fig. 1). You will note that this cylinder of energy, let us say, passing into the sphere reveals its effect by causing the mercury column to sink. Thus we are dealing with what we have formerly brought about by expansion. And indeed, in this case we have to assume also that heat passes into the sphere, causes an expansion and this expansion makes itself evident by a depression of the column of mercury. If we placed a prism in the path of the light we would get a spectrum. We do not form a spectrum in this experiment, but we catch the light—gather it up and obtain as a result of this gathering up of what is in the bundle of light, a very market expansion. You can see the definite depression of the mercury. Now we will place in the path of the energy cylinder, an alum solution, and see what happens under the influence of this solution. You will see after a while that the mercury will come to exactly the same level in the right and left hand tubes. This shows that originally heat passed through, but under the influence of the alum solution the heat is shut off, not more goes through. The apparatus then comes only under the influence of the heat generally present in the space around it and the mercury readjusts itself to equilibrium in the two tubes. The heat is stopped as soon as I put the alum solution in the path of the energy cylinder. That is to say, from this cylinder which yields for me both light and heat, I separate out the heat and permit the light to pass through. Let us keep this firmly in mind. Something still rays through. But we see that we can so treat the light-heat mercury that the light passes on and the heat is separated by means of the alum solution.

This is one thing we must keep in mind simply as a phenomenon. There is another phenomenon to be brought to our attention before we proceed with our considerations. When we study the nature of heat we can do so by warming a body at one particular spot. We then notice that the body gets warm not only at the spot where we are applying the heat, but that one portion shares its heat with the next portion, then this with the next, etc. and that finally the heat is spread over the entire body (Fig. 2). And this is not all.

If we simply bring another body in contact with the warm body, the second body will become warmer than it formerly was. In modern physics this is ordinarily stated by saying that heat is spread by conduction. We speak of the conduction of heat. The heat is conducted from one portion of a body to another portion, and it is also conducted from one body to another in contact with the first. A very superficial observation will show you that the conduction of heat varies with different materials. If you grasp a metallic rod in your fingers by one end and hold the other end in a flame, you will soon have to drop it, since the heat travels rapidly from one end of rod to the other. Metals, it is said, are good conductors of heat. On the other hand, if you hold a wooden stick in the flame in the same way, you will not have to drop it quickly on account of the conduction of heat. Wood is a poor conductor of heat. Thus we may speak of good and poor conductors of heat. Now this can be cleared up by another experiment. And this experiment we are unfortunately unable to make today. It has again been impossible to get ice in the form we need it. At a more favorable time the experiment can be made with a lens made of ice as we would make a lens of glass. Then from a source of heat, a flame, this ice lens can be used to concentrate the heat rays just as light rays can be concentrated (to use the ordinary terminology.) A thermometer can then be used to demonstrate the concentration by the ice lens of the heat passing through it. (See Fig. 4).

Now you can see from this experiment that it is a question here of something very different from conduction even though there is a transmission of the heat, otherwise the ice lens could not remain an ice lens. What we have to consider is that the heat spreads in two ways. In one form, the bodies through which it spreads are profoundly influenced, and in the other form it is a matter of indifference what stands in the path. In this latter case we are dealing with the propagation of the real being of heat, with the spreading of heat itself. If we wish to speak accurately we must ask what is spreading, then we apply heat and see a body getting warmer gradually piece by piece, we must ask the question: is it not perhaps a very confused statement of the matter when we say that the heat itself spreads from particle to particle through the body, since we are able to determine nothing about the process except the gradual heating of the body?

You see, I must emphasize to you that we have to make for ourselves very accurate ideas and concepts. Suppose, instead of simply perceiving the heat in the metal rod, you had a large rod, heated it here, and placed on it a row of urchins. As it became warm the urchins would cry out, the first one, then the second, then the third, etc. One after another they would cry out. But it would never occur to you to say that what you heard from the first urchin was conducted to the second, the third, the fourth, etc. When the physicist applies heat at one spot, however, and then perceives it further down the rod, he says: the heat is simply conducted. He is really observing how the body reacts, one part after another, to give him the sensation of warmth, just as the urchins give a yell when they experience the heat. You cannot, however, say that the yells are transmitted.

Now we will perform also an experiment to show how the different metals we have here in the form of rods behave in respect to what we call the conduction, and about which we are striving to get valid ideas. We have hot water in this vessel (Fig. 3). By placing the ends of the rods in the water, they are warmed. Now we will see how this experiment comes out. One rod after another will get warm, and we will have a kind of graduated scale before us. We will be able to see the gradual spreading of the effect of the heat in the different substances. (The rods consisted of copper, nickel, lead, tin, zinc, iron.) The iodide of mercury on the rods (used to indicate rise in temperature) becomes red in the following order: copper, nickel, zinc, tin, iron and lead. The lead is, therefore, among these metals, the poorest conductor of heat, as it is said.

This experiment is shown to you in order to help form the general view of the subject that I have so often spoken to you about. Gradually we will rise to an understanding of what the heat entity is in its reality.

Now, from our remarks of yesterday we have seen that when we turn our attention to he realm of corporeality, we can in a certain way, set limits to the realm of the solids by following what it is essentially that takes on form. We have the fluids as an intermediate stage and then we go over to the gaseous realm. In the gaseous we have a kind of intermediate state, exactly as we would expect, namely the heat condition. We have seen why we can place it as we do in the series. Then we come, as I have said, into an X region in which we have to assume materialization and dematerialization, pass then to a Y and a Z. This is all similar to the manner in which we find in the light spectrum the transition from green through blue to violet and then apparently on to infinity. Yesterday we convinced ourselves that we have to continue below the solid realm into a U region. Thus we think of the world of corporeality as arranged in an order analogous to the arrangement in the spectrum. This is exactly what we do when we pursue our thinking in contact with reality.

Now let us further extend the ideas of yesterday. In the case of the spectrum we conceive of what disappears at the violet end and at the red end in the straight line spectrum as bent into a circle. In exactly the same way we can, in this different realm of states of aggregation, imagine that the two ends of the series do not disappear into infinity. Instead, what apparently goes off into the indefinite on the one side and what goes off into indefiniteness on the other may be considered as bending back (Fig. 1) and then we have before us a circle, or at least a line whose two ends meet.

The question now arises, what is to be found at the point of juncture? When we observe the usual spectrum, we can in that case find something at this point. In Goethe's sense you know that the spectrum considered as a whole with all its colors included shows as its middle color on one side green, when we make a bright spectrum. On the other side peach blossom which is also a middle color when we make a dark spectrum. Thus we have green, blue, violet extending to peach blossom. By closing the circle we note that at the point where it closes, there is the peach blossom color.

If we then construct a similar circle in our thinking about the realm states of aggregation, what do we find at the point of juncture? This brings us to an enormously important consideration. What must we place in the spectrum of states of aggregation which will correspond to the peach blossom of the color spectrum? The idea that arises naturally from the facts here may perhaps be easier for you to grasp if I lead you to it as follows: What do we have in reality which disappears as it were in two opposite directions—just as in the color spectrum the tones shade off on the one side into the region beyond the violet and on the other side into the region beyond the red? Ask yourselves what it is. It is nothing more or less than the whole of nature. The whole of nature is included in it. For you cannot in the whole of nature find anything not included in the form categories we have mentioned. Nature disappears from us on the one hand when we go through corporeality into heat and beyond. She disappears from us on the other when we follow form through the solid realm into the sub-solid where we saw the polarization figures as the effect of form on form. The tourmaline crystals show us now a bright field, now a dark one. By the mutual effect of one form on another there appear alternately dark and light fields.

It is essential for us to determine what we should place here when we follow nature in one direction until we meet what streams from the other side. What stands there? Man as such stands there. The human being is inserted at that point. Man, taking up what comes from both sides is placed at that point. And how does he take up what comes from the two sides? (Fig. 2) He has form. He is also formed within. When we examine his form among other formed bodies we are obliged to give him this attribute. Thus, the forces that give from elsewhere are within man. And now we must ask ourselves, are these forces to be found in the sphere of consciousness? No, they are not in the human consciousness. Think of the matter a moment. You cannot get a real understanding of the human form from what you can see in either yourselves or other men. You cannot experience it immediately in consciousness. We have a corporeality, but this form is not given in our immediate consciousness. What do we have in our immediate consciousness in the place of form?

Now, my friends, that can be experienced only when one gradually and in an unbiased manner learns to observe the physical development of man. When the human being first enters physical existence, he must be related very plastically to his formative forces. That is, he must do a great deal of body building. The nearer we approach the condition of childhood, the greater the body building, and as we take on years there is a withdrawal of the body building forces. In proportion as the body building forces withdraw, conscious reasoning comes into play. The more the formative forces withdraw the more reasoning advances. We can create ideas in regard to form in proportion as we lose the ability to create form in ourselves. This considered in a matter of fact way, is simply an obvious truth. But now you see, we can say that we experience formative forces—forces that create form outside the body can be experienced. And how do we experience them? In this way, that they become ideas within us. Now we are at the point where we can bring the formative forces to the human being. These forces are not something that can be dreamed about. Answers to the questions that nature puts to us cannot be drawn from speculation or philosophizing, but must be got from reality. And in reality we see that the formative forces show themselves where, as it were, form dissolves into ideas, where it becomes ideas. In our ideas we experience what escapes us as a force while our bodies are building.

When we place human nature before us in thought, we can state the matter as follows: man experiences as ideas the forces welling up from below. What does he experience coming down from above? What comes into consciousness from the realms of gas and heat? Here again when you look at human nature in an unprejudiced way, you have to ask yourselves: how does the will relate itself to the phenomena of heat?

You need only consider the matter physiologically to see that we go through a certain interaction with the heat being of outer nature in order to function in our will nature. Indeed heat must appear if willing is to become a reality. We have to consider will related to heat. Just as the formative forces of outer objects are related to ideas, so we have to consider what is spread abroad as heat as related to that which we find active in our wills. Heat may be thus looked upon as will, or we may say that we experience the being of heat in our will.

How can we define form what it approaches us from within-out? We see it, in this form, in any given solid body. We know that if conditions are such that this form can be seized upon by our life processes, ideas will arise. These ideas are not within the outer object. It is somewhat as if I observed the spirit separated from the body in death. When I see form in outer nature, what brings about the form is not there in the object. It is in truth not there. Just as the spirit is not within the corpse but has been in it, so is that which determines form not within the object. If I therefore turn my eyes in an unprejudiced way towards outer nature I have to say: Something works in the process of form building in objects, but in the corpse this something “has been active,” while in the object its activity is becoming. We will see that what is there active lives in our ideas.

If I experience heat in nature, then I experience what works in a certain way as my will. In the thinking and willing man we have what meets us in outer nature as form and heat respectively.

But now there are all possible intermediate stages between will and thought. A mere intellectual self-examination will soon show you that you never think without exercising the will. Exercise of the will is difficult for modern man especially. The human being is more prone to will unconsciously the course of his thoughts, he does not like to send will impulses into the realm of thought.

Entirely will-free thought content is really never present just as will not oriented by thought is likewise not present. Thus when we speak of thought and will, of ideas and will, we are dealing with extreme conditions, with what from one side builds itself as thought and from the other side builds itself as will. We can therefore say that in experiencing will permeated by thinking and thinking permeated by will, we experience truly and essentially the outer forms of nature and the outer heat being of nature. There is only one possibility for us here and that is to seek in man for essential being of what meets us in outer nature.

And now pursue these thoughts further. When you follow further the condition of corporeality on the one hand you can say that you proceed along a line into the indeterminate. The opposite must be the case here. And how can we state this? How must it be within man? We must indeed, find again here what goes off into infinity. Instead of it going off into infinity, so that we can no longer follow it, we must picture to ourselves that it moves out of space. What wells up in man from the states of aggregation we must think of as going out of space. That is, the forces that are in heat must so manifest themselves in man that they move out of space. Likewise, the forces that produce form, pass out of space when they enter man.

In other words, in man we have a point where that which appears spatially in the outer world as form and heat, leaves space. Where the impossibility arises, that that which becomes non-spatial can still be held mathematically.

I think we can see here in a very enlightening way how an observation of nature in accordance with facts obliges us to leave space when we approach man, provided we properly place him in the being of nature. We have to go to infinity above and below (the scale of that states of aggregation.) When we enter the being of man, we leave the realm of space. We cannot find a symbol which expresses spatially how the facts of nature meet us in the being of man. Nature properly conceived, shows us that when we think of her in relation to man, we must leave her. Unless we do, when we consider the content of nature in relation to man, we simply do not come to the human being.

But what does this mean mathematically? Suppose you set down the lineal series among which you are following states of aggregation to infinity. The words one after another may be considered as positive. Then what works into the nature of man must be set down as negative. If you consider this series as positive, the effects in the human being have to be made negative. What is meant by positive and negative will be cleared up I think by a lecture to be given by one of our members during the next few days. We have to conceive, however, of what comes before our eyes plainly here in this way that the essential nature of heat, insofar as this belongs to the outer world, must be made negative when we follow it into the human being, and likewise the essentiality of form becomes negative when we follow it into man. Actually then, what lives in man as ideas is related to outside form as negative numbers are to positive numbers and vice versa. Let us say, as credits and debits. What are debits on the one hand are credits on the other and vice versa. What is form in the outside world lives in man in a negative sense. If we say “there in the outside world is some sort of a body of a material nature,” we have to add: “if I think about its form the matter must be negative, in a sense, in my thinking.” How is matter characterized by me as a human being? It is characterized by its pressure effects. If I go from the pressure manifestation of matter to my ideas about form, then the negative of pressure, or suction, must come into the picture. That is, we cannot conceive of man's ideas as material in their nature if we consider materiality as symbolized by pressure. We must think of them as the opposite. We must think of something active in man which is related to matter as the negative is to the positive. We must consider this as symbolized by suction if we think of matter as symbolized by pressure. If we go beyond matter we come to nothing, to empty space. But if we go further still, we come to less-than-nothing, to that which sucks up matter. We go from pressure to suction. Then we have that which manifests in us as thinking.

And when on the other hand you observe the effects of heat, again you go over to the negative when it manifests in us. It moves out of space. It is, if I may extend the picture, sucked up by us. In us it appears as negative. This is how it manifests. Debits remain debits, although they are credits elsewhere. Even though our making external heat negative when it works within us results in reducing it to nothing, that does not alter the matter. Let me ask you again to note: we are obliged by force of the facts to conceive of man not entirely as a material entity, but we must think of something in man which not only is not matter, but is so related to matter as suction is to pressure. Human nature properly conceived must be thought of as containing that which continually sucks up and destroys matter.

Modern physics, you see, has not developed at all this idea of negative matter, related to external matter as a suction is to a pressure. That is unfortunate for modern physics. What we must learn is that the instant we approach an effect manifest in man himself all our formulae must be given another character. Will phenomena have to be given negative values in contrast to heat phenomena; and thought phenomena have to be given negative values as contrasted to the forces concerned in giving form.

My dear friends,

At this point I would like to build a bridge, as it were, between the discussions in this course and the discussion in the previous course. We will study today the light spectrum, as it is called, and its relation to the heat and chemical effects that come to us with the light. The simplest way for us to bring before our minds what we are to deal with is first to make a spectrum and learn what we can from the behavior of its various components. We will, therefore, make a spectrum by throwing light through this opening—you can see it here. (The room was darkened and the spectrum shown.) It is to be seen on this screen. Now you can see that we have something hanging here in the red portion of the spectrum. Something is to be observed on this instrument hanging here. First we wish to show you especially how heat effects arise in the red portion of the spectrum. Something is to be observed on this instrument hanging here. These effects are to be observed by this expanding action of the energy cylinder on the air contained in the instrument, which expanding action in turn pushes the alcohol column down on this side and up on this one. This depression of the alcohol column shows us that there is a considerable heat effect in this part of the spectrum. It would be interesting also to show that when the spectrum is moved so as to bring the instrument into the blue-violet portion, the heat effect is not noticeable. It is essentially characteristic of the red portion. And now, having shown the occurrence of heat effects in the red portion of the spectrum by means of the alcohol column, let us show the chemical activity of the blue-violet end. We do this by allowing the blue portion to fall on a substance which you can see is brought into a state of phosphorescence. From the previous course you know that this is a form of chemical activity. Thus you see an essential difference between the portion of the spectrum that disappears on the unknown on this side and the portion that disappears on this other side; you see how the substance glows under the influence of the chemical rays, as they are called. Moreover, we can so arrange matters that the middle portion of the spectrum, the real light portion, is cut out. We cannot do this with absolute precision, but approximately we can make the middle portion dark by simply placing the path of the light a solution of iodine in carbon disulphate. This solution has the property of stopping the light. It is possible to demonstrate the chemical effect on one side and the heat effect on the other side of this dark band. Unfortunately we cannot carry out this experiment completely, but only mention it in passing. If I place an alum solution in the path of the light the heat effect disappears and you will see that the alcohol column is no longer displaced because the alum, or the solution of alum, to speak precisely, hinders its passage. Soon you will see the column equalize, now that we have placed alum in the path, because the heat is not present. We have here a cold spectrum.

Now let us place in the light path the solution of iodine in carbon disulphate, and the middle portion of the spectrum disappears. It is very interesting that a solution of esculin will cut out the chemical effect. Unfortunately we could not get this substance. In this case, the heat effect and the light remain, but the chemical effect ceases. With the carbon disulphide you see clearly the red portion—it would not be there if the experiment were an entire success—and the violet portion, but the middle portion is dark. We have succeeded partly in our attempt to eliminate the bright portion of the spectrum. By carrying out the experiment in a suitable way as certain experimenters have done (for instance, Dreher, 50 years ago) the two bright portions you see here can be done away with. Then the temperature effect may be demonstrated on the red side, and on the other side phosphorescence shows the presence of the chemically active rays. This has not yet been fully demonstrated and it is of very great importance. It shows us how that which we think of as active in the spectrum can be conceived in its general cosmic relations.

In the course that I gave here previously I showed how a powerful magnet works on the spectral relations. The force emanating from the magnet alters certain lines, changes the picture of the spectrum itself. It is only necessary for a person to extend the thought prompted by this in order to enter the physical processes in his thinking. You know from what we have already said that there is really a complete spectrum, a collection of all possible twelve colors; that we have a circular spectrum instead of the spectrum spread out in one dimension of space. We have (in the circular spectrum) here green, peach blossom here, here violet and here red with the other shades between. Twelve shades, clearly distinguishable from one another.

Now the fact is that under the conditions obtaining on the earth such a spectrum can only exist as a mental image. When we are dealing with this spectrum we can only do so by means of a mental picture. The spectrum we actually get is the well-known linear one extending as a straight line from red through the green to the blue and violet—thus we obtain a spectrum formed from the circular one, as I have often said, by making the circle larger and larger, so that the peach blossom disappears, violet shades off into infinity on one side and red shades off on the other, with green in the middle.

We may ask the question: how does this partial spectrum, this fragmentary color band arise from the complete series of color, the twelve color series which must be possible? Imagine to yourselves that you have the circular spectrum, and suppose forces to act on it to make the circle larger and larger and finally to break at this point (see drawing). Then, when it has opened, the action of these forces would make a straight line of the circle, a line extending apparently into infinity in each direction. (Fig. 1).

Now when we come upon this straight line spectrum here under our terrestrial conditions we feel obliged to ask the question: how can it arise? It can arise only in this way, that the seven known colors are separated out. They are, as it were, cut out of the complete spectrum by the forces that work into it. But we have already come upon these forces in the earth realm. We found them when we turned our attention to the forces of form. This too is a formative activity. The circular form is made over into the straight-line form. It is a form that we meet with here. And considering the fact that the structure of the spectrum is altered by magnetic forces, it becomes quite evident that forces making our spectrum possible are everywhere active. This being the case, we have to assume that our spectrum, which we consider a primary thing, has working within it certain forces. Not only must we consider light variation in our ordinary spectrum, but we have to think ofthis ordinary spectrum as including forces which render it necessary to represent the spectrum by a straight line. This idea we must link up with another, which comes to us when we go through the series, as we have frequently done before (Fig. 2), from solids, through fluids, to condensation and rarefaction, i.e. gases, to heat and then to that state we have called X, where we have materialization and dematerialization. Here we meet a higher stage of condensation and rarefaction, beyond the heat condition, just as condensation and rarefaction proper constitute a kind of fluidity of form.

When form itself becomes fluid, when we have a changing form in a gaseous body, that is a development from form as a definite thing. And what occurs here? A development of the condensation-rarefaction condition Keep this definitely in mind, that we enter a realm where we have a development of the condensation-rarefaction state.

What do we mean by a “development of rarefaction”? Well, matter itself informs us what happens to it when it becomes more and more rarefied. When I make matter more and more dense, it comes about that a light placed behind the matter does not shine through. When the matter becomes more and more rarefied, the light does pass through. When I rarefy enough, I finally come to a point where I obtain brightness as such. Therefore, what I bring into my understanding here in the material realm is empirically found to be the genesis of brightness or luminosity as a heightening of the condition of rarefaction; and darkening has to be thought of as a condensation, not yet intense enough to produce matter, but of such an intensity as to be just on the verge of becoming material.

Now you see how I place the realm of light above the heat realm and how the heat is related to the light in an entirely natural fashion. But when you recollect how a given realm always gives a sort of picture of the realm immediately above it, then you must look in the being of heat for something that foreshadows, as it were, the conditions of luminosity and darkening. Keep in mind that we do not always find only the upper condition in the lower, but also always the lower condition in the upper. When I have a solid, it foreshadows for me the fluid. What gives it solidity may extend over into the non-solid realm. I must make it clear to myself, if I wish to keep my concepts real, that there is a mutual interpenetration of actual qualities. For the realm of heat this principle takes on a certain form; namely this, that dematerialization works down into heat from above (see arrow). From the lower side, the tendency to materialization works up into the heat realm.

Thus you see that I draw near to the heat nature when I see in it a striving for dematerialization, on the one hand, and on the other a striving for materialization. (If I wish to grasp its nature I can do it only by conceiving a life, a living weaving, manifesting itself as a tendency to materialization penetrated by a tendency to dematerialization.) Note, now, what an essential distinction exists between this conception of heat based on reality and the nature of heat as outlined by the so-called mechanical theory of heat of Clausius. In the Clausius theory we have in a closed space atoms or molecules, little spheres moving in all directions, colliding with each other and with the walls of the vessel, carrying on an outer movement. (Fig. 3) And it is positively stated: heat consists in reality in this chaotic movement, in this chance collision of particles with each other and with the walls of the vessel. A great controversy arose as to whether the particles were elastic or non-elastic. This is of importance only as the phenomena can be better explained on the assumption of elasticity or on the assumption that the particles are hard, non-elastic bodies. This has given form to the conviction that heat is purely motion in space. Heat is motion. We must now say “heat is motion,” but in an entirely different sense. It is motion, but intensified motion. Wherever heat is manifest in space, there is a motion which creates the material state striving with a motion which destroys the material state. It is no wonder, my friends, that we need heat for an organism. We need heat in our organism simply to change continuously the spatially-extended into the spatially non-extended. When I simply walk through space, my will carries out a movement in space. When I think about it, something other than the spatial is present. What makes it possible for me as a human organism to be inserted into the form relationships of the earth? When I move over the earth, I change the entire terrestrial form. I change her form continually. What makes it possible that I am in relation to the other things of the earth, and that I can form ideas, outside of space, within myself as observer, of what is manifested in space? This is what makes it possible, my being exists in the heat medium and is thus continually enabled to transform material effects, spatial effects, into non-spatial ones that no longer partake of the space nature. In myself I experience in fact what heat really is, intensified motion. Motion that continually alternates between the sphere of pressure and the sphere of suction.

Assume that you have here (Fig. 4) the border between pressure and suction forces. The forces of pressure run their course in space, but the suction forces do not, as such, act in space—they operate outside of space. For my thoughts, resting on the forces of suction, are outside of space. Here on one side of this line (see figure) I have the non-spatial. And now when I conceive of that which takes place neither in the pressure nor in the suction realms, but on the border line between the two, then I am dealing with the things that take place in the realm of heat. I have a continually maintained equilibrium tendency between pressure effects of a material sort and suction effects of a spiritual sort. It is very significant that certain physicists have had these things right under their noses but refuse to consider them. Planck, the Berlin physicist, has made the following striking statement: if we wish to get a concept of what is called ether nowadays, the first requisite is to follow the only path open to us, in view of the knowledge of modern physics, and consider the ether non-material. This from the Berlin physicist, Planck. The ether, therefore, is not to be considered as a material substance. But now, what we are finding beyond the heat region, the realm wherein the effects of light take place, that we consider so little allied to the material that we are assuming the pressure effects—characteristic of matter—to be completely absent, and only suction effects active there. Stated otherwise, we may say: we leave the realm of ponderable matter and enter a realm which is naturally everywhere active, but which manifests itself in a manner diametrically opposite to the realm of the material. Its forces we must conceive of as suction forces while material things obviously manifest through pressure forces. Thus, indeed, we come to an immediate concept of the being of heat as intensified motion, as an alternation between pressure and suction effects, but in such a way that we do not have, on the one hand, suction spatially manifested and, on the other hand, pressure spatially manifested. Instead of this, we have to think of the being of heat as a region where we entirely leave the material world and with it three-dimensional space. If the physicist expresses by formulae certain processes, and he has in these formulae forces, in the case where these forces are given the negative sign—when pressure forces are made negative—they become suction forces. Attention must be paid to the fact that in such a case one leaves space entirely. This sort of consideration of such formulae leads us into the realm of heat and light. Heat is only half included, for in this realm we have both pressure and suction forces.

These facts, my dear friends, can be given, so to speak, only theoretically today in this presentation in an auditorium. It must not be forgotten that a large part of our technical achievement has arisen under the materialistic concepts of the second half of the 19^th century. It has not had such ideas as we are presenting and therefore such ideas cannot arise in it. If you think over the fruitfulness of the one-sided concepts for technology, you can picture to yourselves how many technical consequences might flow from adding to the modern technology, knowing only pressures—the possibility of also making fruitful these suction forces. (I mean not only spatially active suction which is a manifestation of pressure, but suction forces qualitatively opposite to pressure.)

Of course, much now incorporated in the body of knowledge known as physics will have to be discarded to make room for these ideas. For instance, the usual concepts of energy must be thrown out. This concept rests on the following very crude notions: when I have heat I can change it into work, as we saw from the up and down movement of the flask in the experiment resulting from the transformation of heat. But we saw at the same time that the heat was only partly changed and that a portion remained over of the total amount at hand. This was the principle that led Eduard von Hartmann to enunciate the second important law of the modern physics of heat—a perpetuum mobile of the second type is impossible.

Another physicist, Mach, well known in connection with modern developments in this field, has done quite fundamental thinking on the subject. He has thought along lines that show him to be a shrewd investigator, but one who can only bring his thinking into action in a purely materialistic way. Behind his concepts stands the materialistic point of view. He seeks cleverly to push forward the concepts and ideas available to him. His peculiarity is that when he comes to the limit of the usual physical concepts where doubts begin to arise, he writes the doubts down at once. This leads soon to a despairing condition, because he comes quickly to the limit where doubts appear, but his way of expressing the matter is extremely interesting. Consider how things stand when a man who has the whole of physics at his command is obliged to state his views as mach states them. He says (Ernst Mach, Die Prinzipien der Warme Lehre, p. 345): “There is no meaning in expressing as work a heat quantity which cannot be transformed into work.” (We have seen that there is such a residue.) “Thus it appears that the energy principle like other concepts of substance has validity for only a limited realm of facts. The existence of these limits is a matter about which we, by habit, gladly deceive ourselves.”

Consider a physicist who, upon thinking over the phenomena lying before him, is obliged to say the following: “Heat exists, in fact, that I cannot turn into work, but there is no meaning in simply thinking of this heat as potential energy, as work not visible. However, I can perhaps speak of the changing of heat into work within a certain region—beyond this it is not valid.” And in general it is said that every energy is transformable into another, but only by virtue of a certain habit of thinking about those limits about which we gladly deceive ourselves.

It is extremely interesting to pin physics down at the very point where doubts are expressed which must arise from a straightforward consideration of the facts.

Does this not clearly reveal the manner in which physics is overcome when physicists have been obliged to make such statements? For, fundamentally, this is nothing other than the following: one can no longer hold to the energy principle put forth as gospel by Helmoltz and his colleagues. There are realms in which this energy principle does hold.

Now let us consider the following: How can one make the attempt symbolically (for fundamentally it is symbolic when we try to set the outlines of something), how can we make the attempt to symbolize what occurs in the realm of heat? When you bring together all these ideas I have developed, and through which in a real sense I have tried to attain to the being of heat, then you can get a concept of this being in the following manner.

Picture this to yourselves (Fig. 5). Here is space (blue) filled with certain effects, pressure effects. Here is the non-spatial (red) filled with suction effects. Imagine that we have projected out into space what we considered as alternately spatial and non-spatial. The red portion must be thought of as non-spatial. Using this intermediate region as an image of what is alternately spatial and non-spatial, you have in it a region where something is appearing and disappearing. Think of something represented as extended and disappearing. As substance appears, there enters in something from the other side that annihilates it, and then we have a physical-spiritual vortex continually manifesting in such a manner that what is appearing as substance is annihilated by what appears at the same time as spirit. We have a continual sucking up of what is in space by the entity which is outside of space.

What I am outlining to you here, my dear friends, you must think of as similar to a vortex. But in this vortex you should see simply in extension that which is “intensive” in its nature. In this way we approach, I might say figuratively, the being of heat. We have yet to show how this being of heat works so as to bring about such phenomena as conduction, the lowering of the melting point of an alloy below the melting point of its constituents, and what it really means that we should have heat effects at one end of the spectrum and chemical effects at the other.

We must seek the deeds of heat as Goethe sought out the deeds of light. Then we must see how knowledge of the being of heat is related to the application of mathematics and how it affects the imponderable of physics. In other words, how are real formulae to be built, applicable to heat and optics.

My dear friends,

The experiments we had anticipated carrying out today we will unfortunately have to postpone until tomorrow. At that time they will be arranged so as to show you what is necessary if I am to prove to you all that I wish to prove. Today, therefore, we will consider some things which, together with the experiments of tomorrow, will enable us to bring our observations to a conclusion the following day.

As a help toward the understanding of the being of heat, I wish to call your attention to a certain fact. This fact is one which we must take into account in developing our ideas on this subject, and it is that there is a certain difficulty in understanding what is really involved in a transparent body. I am not now speaking of transparency in connection with heat. You will see, however, when we have finished that we can get helpful ideas for understanding heat from the realm of light.

I said there was a certain difficulty in understanding what a relatively transparent body is and what an opaque body is as these reveal themselves under the influence of light. I have to express myself in a different way from that ordinarily used. The ordinary method of expression in physics would be as follows: an opaque body is one that by some peculiar property of its surface reflects the rays of light that fall on it and thus become a visible body. I cannot use this form of expression because it is not a reflection of the facts, it is a statement of a preconceived theory and is not by any means to be taken as self-evident.

For to speak of rays, of light rays, is theoretical. I have dealt with that in my former course. What we meet in reality is not light rays, but an image and it is this we must hold firmly in mind. As a matter of fact, we cannot simply say: a transparent body is one that by virtue of its inner molecular properties passes light through, and an opaque body is one that throws the light back. For how can such a theory be substantiated? Recollect what I have said to you about the relations of the various realms of reality. We have solids, fluids, gaseous bodies, heat, \(X\), \(Y\), \(Z\) and below the solid and bordering on it the U region, and you can see that the light realm must have a relation to heat and so also must the realm of chemical activity. On the other side that which we meet, so to speak, as the fluid nature in heat or in gases must have a relation to the essence of tone. For tone appears alone with the occurrence of condensation and rarefaction in gases or aeriform bodies. We may therefore suspect that where we have assumed \(X\), \(Y\), \(Z\), we will find the essence of light. Now the question is whether we have to look for the explanation of transparency of certain bodies is not to be immediately derived from the nature of light, nor from the relation of light to these bodies.

We have the \(U\) region and this \(U\) region must have a relation to the solids on the surface of the earth. We must first ask the question and seek to apply the answer to this question to our consideration of these things. What influence has the \(U\) region on solids and can we from the nature of this influence derive anything that will show use the difference between transparent bodies and the ordinary non-transparent metals? This question must be considered and the answer to it will appear when we extend further our ideas of yesterday in regard to heat by the addition of certain other conceptions.

Note now, the warmth phenomena naturally are considered as belonging to the realm of physics. Such things as conduction have been included, thought of in the way I have described to you. This spreading of heat through conduction or flow of the heat condition either through a body or from one body to another one touching it has been observed. The flow has been conceived of as though a kind of fluid were involved, and the picture is of a liquid flow. It may be compared to something readily observable in the objective world, namely the water in a brook which is at one point now, and a moment later is at a distant point. Thus is pictured the flow of heat from one spot to another when the so-called conduction of heat takes place. The phenomenon are to be found in Fourrier (other investigators might also be cited.) Let us consider these a little from our own point of view and see if we can establish their validity.

Imagine that we have a body bounded by a definite wall, say of metal (Fig. 1). Assume the wall to extend indefinitely above and below, and suppose it to consist of some sort of metal. Let us place boiling water in contact with the wall on one side holding it at a temperature \(U_1\) which in this case is 100°C. On the other side we place melting ice to hold the wall at a temperature \(U_2\) which in this special case will be 0°C.

Considering the entire phenomenon you will see that we have to do with a difference, here \(U_1\), here \(U_2\) and \(U_1\) and \(U_2\) gives us the temperature difference. Upon this difference depends the fact that we have a conduction of heat. Obviously, this transfer of heat will proceed otherwise when the difference is small, a small quantity of heat is transferred to attain equilibrium, and when the difference is great a larger quantity is transferred. Thus I may say that the quantity of heat needed to attain a certain condition depends on this temperature difference, \(U_1 - U_2\). Furthermore, it will depend not only on the difference \(U_1 - U_2\), but on the thickness of the wall which I may denote by \(L\), becoming greater when this is large and less when it is small. That is, the amount of heat transferred is inversely proportional to \(L\). I may calculate for a given area that I will call \(Q\), how much heat I will need to get a certain degree of conduction. The greater \(Q\) is, the greater will be the amount. Thus the amount of heat is directly proportional to \(Q\) and I must multiply by this factor.

Finally, the whole process is dependent upon time. A greater effect is produced by permitting a given amount of heat to act for a longer time, a smaller effect in a less time. Therefore I have to multiply by the time. Obviously then, I must multiply through by a constant representing the heat itself, by something involving heat, since none of the quantities so far mentioned include the heat and thus cannot by themselves give the quantity of heat, \(W\), which I wish to secure. This quantity of heat, \(W\), is directly proportional to \(L\). Now if you equate all the other factors with \(U_1\) and \(U_2\), you are expressing what really flows and this not a heat quantity, essentially, nor dependent directly on a heat quantity, but is a temperature fall, a difference in level. Please keep this in mind. Just as when we pour water through a sluice and turn a paddle wheel, and the motion is due to the energy arising from a different in level, so there we have to do with a drop from one level to another, and it is this we must keep our attention on.

Now we have to take up another consideration of Fourrier's to draw nearer to the being of heat. We will work over the ordinary concepts as it were so as to move nearer to reality than the physicists of the 20th century. So far I have taken into consideration only what pertains to the conducting of heat from one spot to another, but I can assume that something goes on in the body itself. Let me now ask a question. Suppose we assume that the progress of heat instead of being uniform from left to right was non-uniform, then the formula would have to apply to the inner lack of uniformity. If the irregularity in the partition of heat is present I must bring it into my considerations in some way. I must bring in the differences that reveal themselves within, that is, what takes place in the body as the temperature effects equalize themselves. As you can easily see, my formula is applicable to the process. I can say $$W=\frac{U_1-U_2}{L} t c q$$ That represents what takes place here. I will not consider the whole thickness of the wall, but deal with small portions of it, and will consider what happens in these small portions, as over the entire distance it is expressed by the factor \((U_1-U_2)/l\) It is thus a question of dealing with minute distances within the body. To do this, I employ the differential ratio \(du\) where \(du/dx\) represents an infinitesimal movement of heat. If this is considered for an instant of time, I must multiply by \(dt\), this being left out of account if I do not consider the time. Thus we have W as an expression of the quantity of heat transferred through small distance in order to equalize the temperature within the body. The following formula expresses the effects of temperature fall within the body: $$W=c•q\frac{du}{dx} dt$$ In relation to this, I will ask you please to consider what we took up yesterday in a sketchy way, which will be clearer tomorrow when we have carried out the necessary experiments. Today, I will simply mention it, since we must keep it in mind. I refer to the relation between heat, light and chemical effect in the spectrum. Yesterday, your attention was called to the following fact: when we have an ordinary terrestrial spectrum, in the middle is the light effect proper, towards one end (Fig. 2, arrow) heat effects, toward the other end the chemical effects Now we have to consider the following.

We have seen that when we construct a picture of this spectrum, we must not think of light, heat and chemical effects as stretched out in a straight line. We go toward the left to approach the warm end of the spectrum and toward the right to approach the chemically active end. (Fig. 2) thus, it is not possible to remain in the lane of the pure light effects if we wish to symbolize the heat effects; nor can we remain in this place if we wish to symbolize the chemical effects. We have to move out of this plane.

Now to visualize the whole matter, let us make clear to ourselves how we must really represent a heat quantity working within a body by means of our formula. How must we represent qualitatively the relation between it and the chemical effect? We will not do this properly until we take into account the fact that we go one way to reach the heat and the opposite way to reach the chemical effects. This fact must be kept in mind if we would orient ourselves. So when we consider W as a positive quantity here (or we might consider it negative) then we have to consider the corresponding chemical effect as: $$W=-c•q\frac{du}{dx} dt$$ The foregoing equation corresponds to the chemical effect, and this one: $$W=+c•q\frac{du}{dx} dt$$ corresponds to the heat effect.

As a matter of fact, these things demonstrate for us an important point. This point is that when we use formulae we cannot handle the mathematical quantities merely as such if we at the same time expect the formulae to express the relations within a field of actual effects, an observed realm, where heat and chemical action are manifesting themselves. In ordinary combustion, for instance, where we wish to bring heat and chemical effects into relation, we must, if we use formulae, set down as positive what represents heat and as negative what represents chemical effect.

Now if you carry your considerations further, you may make the following statement: When we think of heat as extending in one direction, so to speak, and chemical action as extending in the opposite, then we have what is essential in light left in a plane at right angles to the imagined chemical action-heat lines and between them. But if you have reserved positivity for heat and negativity for chemical action, you cannot use either of these for light effects. At this point you have to apply to the light effects a set of facts which today are only vaguely felt and not by any means explained, namely the relation between positive and negative numbers and imaginary numbers. When you are dealing with light phenomena you have to say: $$w=\sqrt{-1}•c•q•\frac{du}{dx}•dt$$ That is to say, if you wish to deal with the relation of heat, chemical action and light working in the same phenomenological field at the same time, you have to use imaginary numbers—your calculation has to involve the mathematical relations expressed in imaginary numbers. But now we have already made the following statement. The spectral band that we can produce experimentally under terrestrial conditions is to be thought of actually as a circle that has been opened out. Furthermore, the complete spectrum has the peach blossom color above. If, by the employment of a sufficiently great force, you were able to bend the spectrum into a circle, you would bring together what apparently extends off into infinity in either direction. Now you can realize that this closing up cannot simply be thought of as being carried out in a circle in one plane. For as you go out into the heat region you also go off to one side (i.e. into something qualitatively different) and, proceeding into the chemical effect region, you go off to the other side. You are then in a situation where you must go first into the infinite on one side and then into the infinite on the other side and then into the infinite on the other side. You have first the awkward problem of going into infinity in a plane in one direction and then coming back from infinity and entering the plane on the other side. This implies that you reach the same infinite point no matter what direction you take. Moreover, you are confused unless you assume that you reach the same point as you go out in one direction and then in the other and you then have to come back from two different points at infinity. The way to discovery of the peach blossom color is thus a doubly complicated one. Not only must you bend the spectrum in one plane, but at right angles with, say an electromagnet, you will have to turn the magnet. That, however, lead to another point. If the magnet would have to be turned, then none of the mathematical expressions so far given would apply entirely. We then have to call in what was put before you yesterday in the discussion following the lecture by Messrs. Blumel and Strakesch, namely the super-imaginary number. You will doubtless recollect that we have to take into account that there is controversy about these super-imaginary numbers. They are readily handled mathematically and have, so to speak, more than one meaning. Some mathematicians even question whether there is any justification for them at all. Physics does not give us a definite formulation of the super-imaginary numbers. Nevertheless we put them into the series because we are led to see that they are necessary if we wish to formulate in an orderly manner what happens in the realm of chemical activity, light, heat, and what takes place in addition when we pass out in one direction through this series and come back into it from the other direction.

One who has the organ to perceive these things finds something very peculiar. He finds something which, I believe, furnishes a real foundation for illuminating the basic facts of physical phenomena. What I mean my friends, is this. The same sort of difficulty that meets one in the consideration of super-imaginary numbers also meets one when the attempt is made to apply the science of the inorganic to the phenomena of life. It cannot be done with these concepts of the inorganic. They simply do not apply. What has been the result of this? On the one hand there are thinkers who say: “The organic things of the earth have arisen by a transformation out of the inorganic.” But with this view alone one can never enter the reality of the living. Other thinkers like Prayer, regard the organic as the source of the inorganic and come nearer the truth. They think of the earth as originally a living body and what is today inorganic they consider as something thrown off or as that which has died out of the organic. But these people do not make us an entirely satisfactory picture.

The same difficulty that meets us in the phenomena of nature considered by and for themselves is met also when we attempt a comprehensive formulation of what is present in the realms of heat, light, and chemical activity and what is come upon when we attempt to close the color band in a natural manner. We must assume, of course, that this color band can be closed somewhere although it is obvious that it cannot be done under terrestrial conditions.

It is necessary for us to recognize how the purely mathematical leads up to the problem of living. With the faculties at hand today you can handle the phenomena of light, heat and chemical action, let us say, but you cannot handle what is evidently connected with these, namely the opening up of the spectrum. This cannot be formulated in a manner corresponding to the others.

It will be helpful to us at this stage if we set up a terminology. We can base this terminology on rather definite concepts. We say: Something real is at the basis of the formula for W. Let us speak of this as heat ether. Likewise something real is involved when we change the positive signs of the heat formula to negative ones, and here we speak of the chemical ether. Where our formulae involve imaginary numbers, we speak of the light ether. You see here an interesting parallelism between thinking in mathematics and thinking within science itself. The parallelism shows how we are really dealing not so much with an objective difficulty but rather with a subjective one. For the purely mathematical difficulty arises of itself, and independently of the science of external things. No one would think that a beautifully built lecture could be delivered on the limits of mathematical thinking, similar to the one du Bois-Reymond delivered on the limits of knowledge of nature. At least the conclusions would be different. Within mathematics, unless the matter slips us because it is too complicated, in this realm of the purely mathematical it must be possible to set up a completely formulated expression. The fact that one cannot do this hangs together with our own relative lack of maturity. It is unthinkable that we have here an absolute shortcoming or limit to human knowledge. It is extremely important that you hold this before your minds as a fundamental. For this shows us how we cannot apply mathematics if we wish to enter reality unless we keep in mind certain relations. We cannot simply say with the energeticists, for instance, “a given quantity of heat changes into a certain quantity of chemical energy and vice versa.” That we cannot do, but we must bring in certain other values when a process of this kind takes place. For the necessity of the case constrains us to see as essential not the quantitative mechanical change from one energy to another but rather the qualitative aspect of the transformation. This is indeed to be found along with the quantitative.

If people turned their attention to these qualitative changes which are expressed by the numerical formulations, such ideas as the following would not be advanced: “Apparently heat is just heat because we experience it as such, mechanical energy is as we experience it, chemical energy is what we see as chemical processes; but within, these processes are all alike. Mechanical energy is manifesting everywhere and heat is nothing but a form of this energy.”

This idea of a bombardment, of collisions between molecules and atoms or between these and the wall of the vessel—this struggle for an abstract unity of all energy which makes it into a mechanical motion and nothing more—such things as these would not have arisen if it had been seen that even when we calculate we must take into account the qualitative differences between various forms of energy. It is very interesting in this connection to see how Eduard von Hartmann was obliged to find definitions for physics that excluded the qualitative. Naturally, one cannot find this in the one-sided mathematics of physics, and aside from the cases where negative quantities arise from purely mathematical relations, physicists do not like to reckon with numerical quality differences. They use positive and negative signs, but only because of purely mathematical relationships. In the ordinary theory of energy, justification would never be found for making one energy positive and another negative on the basis of qualitative differences.

My dear friends,

We will today first carry out what I had in mind yesterday because it will lead us to a more prompt conclusion of our series. Tomorrow, I will try to conclude the lecture series being given during my present visit with you. We will now demonstrate to ourselves in a completely adequate fashion that within what we call the sun's spectrum or a light spectrum, there are wrapped up heat effects, light effects and chemical effects. Yesterday, also, we saw that the forces involved in the phenomena of life as well were hidden away here; only we are not able to bring these life-effects into the field of our investigations in the same manner as we can the chemical, light and heat effects. For, there is not a simple experimental method by which the reality of the twelve-fold spectrum can be shown in its objectivity. Just this thing will be the task of a Research Institute, working entirely within our movement. Such investigations will not only be undertaken but they must be followed out in detail.

Now I would like to call your attention to something. When we consider the hypothetical inclusion of life effects or the fact that our series , as we think of it at least, has hidden away in it life, heat, light and chemical effects, an important realm escapes us. This realm is physically more definitely manifested than the ones we have named. The realm that escapes us in the acoustical realm. The realm of acoustics is manifested strikingly in the movements of the air, that is, in the movement of the gaseous or aeriform body. And now comes up an important fundamental question.

How do we come in the one direction through the heat, light and chemical spectra to the life forces and on the other side to the acoustic forces?

This is the question that presents itself when we look over the whole field of phenomena and about which we can teach according to Goethe's views of the physical world, as we have done heretofore rather than simply theorizing about it.

Now let us show our first experiment. When we place a solution of alum in the path of a light cylinder made into a spectrum by passage through a prism we remove the heat effects. Let us permit the thermometer to rise in consequence of the action of the spectrum. When we place the solution of alum in the path of the spectrum, we have to look for a fall in the column of the thermometer. (the thermometer that had been going up rapidly, rose more slowly and then stopped.) The effect is shown by the fact that the thermometer rises more slowly. Therefore, the alum solution removes heat from the spectrum. We may consider this as proven—it has been done times without number and is a well-known fact.

The second experiment we will make is to insert into the light cylinder a solution of iodine in carbon disulphide. You will see, the central portion of the spectrum is thereby entirely blotted out and the other portions considerably weakened. From the previous course you will remember that we have to consider this central portion as the light-portion proper. Thus, the light-portion of this spectrum is stopped by the solution of iodine in carbon disulphide just as the heat portion is stopped by the solution of alum. The thermometer now rises rapidly because the heat effect is present again. The third thing we will do is to place a solution of esculin in the path of light. This has the peculiarity of stopping the chemical effect leaving the heat and light effects unchanged.

We can, thus, so handle the spectrum that we can remove the heat effect by means of an alum solution, the light portion by a solution of iodine in carbon disulphide, and the chemical part by an esculin solution. We will establish the facts in regard to the chemical effect by showing that when the chemical portion is there, the phosphorescent body glows. You can see that this body has been in the light cylinder, because when I shut off the light momentarily, with my hand, it slows. Now we will place it again in the spectrum, but this time with the light cylinder passing through the esculin solution. The action is excellent. There is no phosphorescence visible. Now, place before yourselves the fact that we have first the realm of heat, then the realms of light and chemical action. From our considerations taken in their entirety, you can conclude with a fair degree of certainty, at least, that a relation must exist here similar to the ones I have in the past few days pointed out as the X and Y realms. It is in this way that we are approaching definitely the place where we can begin to identify these two realms:

Let us observe particularly the following: The heat realm, the X, Y, and Z realms, the gaseous, fluid, solid and the U realms are to be arranged as we have outlines. Recollect that there is a matter of fact a certain very loose relationship to be observed between heat effects and the phenomena manifested in a gaseous mass. We are able to observe that the gaseous body manifests in its material configuration, what is manifested otherwise in the case of heat. The nature of heat is set before us materially in the gas. Now if we will cultivate a vivid insight into what occurs in this interplay between gaseous matter and heat, we will be able to get a concept also of the difference between the realm of gases and the x-realm. We need only consider what we have many times seen in our lives. This is that light relates itself quite otherwise to gases than does heat. The gas does not follow changes in light by corresponding changes in its material configuration. When the light spreads, the gas does not do likewise, it does not show difference in pressure, etc.

Therefore when light is playing through a gas, the relationship is different from the one existing between the gas and heat playing through it. Thus, when light is active through the gas, there is a different relation involved than when heat is active through the gas. Now, in the observations made previously, we said: fluids stand between gas and solids, heat between gases and the X realm. Also the solid realm foreshadows the gaseous, and the gaseous gives a picture of heat. So likewise we can say that heat gives a picture of the X realm while heat is itself pictured in the gaseous. We have, as it were, in the gaseous, pictures of pictures of the X realm. Imagine now, these pictured pictures are really present with light passes through the air. Considering how the air relates itself in various phenomena to light, one must say that we are not dealing with a picturing of the one realm by the other, but rather that the light has an independent status in the gas. The matter may be figuratively expressed as follows: Suppose we paint a landscape and hang the picture on the wall of this room and then photograph the room. By thus changing something in the room, I alter its whole appearance and this alteration shows on the photograph. If I were accustomed always to sit on this chair when giving a lecture, and some ill-disposed person removed it while I lectured without my noticing what he was doing, I would do what many have done under similar circumstances, namely, sit on the floor. The relation of things in the room suffers real changes when I alter something in it. But whether I hand the picture in one place or another the relationship between the various figures painted upon it do not change. What exists in the picture itself in the way of relationships is not changed by alterations that go on in the room. In the same way, my experiments with light are not affected by the air in the space in which they are carried out. Experiments with heat are, on the contrary, related to the space in which they are carried out as you can convince yourselves, and indeed, you are made aware of this by the whole room becoming warm. But my light experiments have an independent being. I can think of them by themselves. Now, when I build up a concept of the action of X in a gas-filled space by analogy, I find the same relationships as if I am experimenting with light. I can identify X with light. A further extension of this train of thought leads to the identification of Y with chemical effects, and of Z with vital effects. However, as you see, there is a certain autonomy of light acting in the gaseous realm. The same sort of relationships are found when we extend a train of thought. You can do it for yourselves, it would lead us too far to do it here today. For instance, we would expect to find chemical effects in fluids, and this is in fact the case. In order to have chemical action solutions are necessary. In these solutions chemical action is related to the fluid as light is to the gas. We then have to expect to find a Z associated with the solid. This may be stated so—if I indicate the three realms by Z, Y and X, with heat as the intermediate realm and put X′ for the gas, Y′ for the fluid and Z′ for the solid, I can represent the order: $$Z, Y, X, heat, X', Y', Z'$$

X in X′ represents light in gas, Y in Y′ represents chemical effect in fluids, Z in Z′ represents the Z effect in solid bodies.

Formerly we knew these realms only as various types of manifested form. Now we meet interminglings as it were. These are representations of things that are very real in our lives. X in X′ is light-filled gas, Y in Y′ is fluid in which chemical processes are going on, Z in Z′, life acting in solids. After yesterday's talk, you can scarcely doubt that just as we proceed beyond heat to find chemical effects. This was spoken of yesterday in a preliminary way. Therefore Z in Z′ represents vital effects in solid bodies. But there is no such thing as vital effects in solid bodies. We know that under terrestrial conditions a certain degree of fluidity is necessary for life. Under terrestrial conditions life does not manifest in the purely solid state. But, these same conditions force us to set it up as a hypothesis that such a condition is not beyond the realms of possibility. For the order in which we have been able to think of these things necessarily leads to this.

We find solid bodies, we find fluid bodies, we find gas. The solids we find without vitality. Vital effects in the terrestrial sphere we discover by unfolding themselves adjacent to solid bodies, in relation with them, etc. But we do not find an immediate coupling up of what we call solids with the living. We are led to this last member of the series, Z in Z′, the living in the solid realm by analogy from Y in Y′ and X in X′. Fluid bodies have the same relation to chemical activity although not so strong as do solid bodies to life. Gases, in the realm of the terrestrial, stand in the same relation to light that solids do to the living. Now, this leads us to recognize that solids, fluids and gases in their supplementary relations to light, chemical action and vital phenomena represent, as it were, something that has died out.

These things cannot be made as obvious as people like to make most presentations of empirical facts. If you wish to make these facts really mean something to you, you must work them over within yourselves and then you will find that there is a relation between:

The solid and the living
The fluid and the chemical
The gaseous and light

That stands as it were set off by itself. These relations are not, however, under terrestrial conditions immediately active. The relations that actually exist point to something that was once there but is there no longer. Certain inner relationships of the things force us to ring time concepts into the picture. When you look at a corpse you are forced into time concepts. The corpse is there. Everything that makes possible the presence of the corpse, that gives it the appearance it has, all this you must consider as soul and spirit since the corpse has in itself no possibilities of self-determination. A human form would never arise except for the presence of soul and spirit. What the corpse presents to you, forces you to say the following: The corpse as it exists there has been abandoned by the living, the terrestrial fluid by the emanations of chemical effects and the terrestrial gaseous by the emanations of light effects. And just as we glance back from the corpse to the living, to the time when matter that is now the corpse was bound together with the soul and spirit, so we glance from the solid bodies of the earth back to a former physical condition, when the solid was bound up with the living and only occurred bound to the living; fluid existed only bound to chemical effect and gases only bound to the light. In other words, all gas had an inner glittering, or inner illumination, an illumination that showed a wave-like phosphorescence and darkening as the gas was rarefied or condensed. Fluids were not as they are today but were permeated by a continuous living chemical activity. And at the foundation of all was life, active in solidification (as it solidifies now in the horn formation in cattle, for instance) passing back again into fluid or gas, etc. In brief, we are forced by physics itself to admit a previous period of time when realms now torn apart existed together. The realms of the gaseous, the fluid and the solid are now found on the one hand, and on the other realms of light, chemical effects and vital activity. At that time they were within each other, not merely side by side, but actually within each other. Heat had an intermediate position. It did not appear to share this association of the more material and the more etheric natures. But since it occupied an intermediate position, it possessed an independence that was attributable to its not taking part in the two. If now we call the upper realm the etheric and the lower realm the region of ponderable matter, we obviously have to consider the heat realm as the equilibrium condition between them. Thus in heat we have found that which is the equilibrium condition between the etheric body and the ponderable material. It is ether and matter at the same time and indicates by its dual nature what we actually find in it, namely, a difference in level of transition. (Unless we understand this, we cannot understand or do anything in the realm of heat phenomena). If you take up this line of thinking, you will come to something much more fundamental and weighty than the so-called second law of thermodynamics: a perpetuum mobile of the second type is possible. For this second law really tears a certain realm of phenomena out of its proper connection. This realm is bound up with certain other phenomena and essentially and profoundly modified by them.

If you make it clear to yourselves that the gaseous realm and light were once united, that the fluid realm and chemical activity were once one, etc. then you will also be led to think of the two polarically opposed portions of the heat realm, namely ether and ponderable matter, as originally united. That is to say, you must conceive of heat in former ages as quite different from the heat you know now. Then you will come to say to yourselves, the things we define as physical phenomena today, the things that bear the impress of physical entities, these considerations of ours are limited in their meaning by time. Physics is not eternal. In the case of certain types of reality physics has absolutely no validity. For the reality that gas was once illumined within is an entirely different reality from the condition where gas and light are together in a relatively independent condition.

Thus, we come to see that there was a time when another type of physics was valid; and, looking forward, there will be a time when a still different type will be valid. Our modern physics must conform with the phenomena of the present time, with what is in our immediate environment. In order to avoid paradoxes, and not only these but absurdities, physics must be freed of the tendency to study terrestrial phenomena, build hypotheses based on them, and then apply these hypotheses to the whole universe. We do this, and forget that what we know as physical is time-limited on the earth. That it is space-limited, we have already seen. For the moment we move out to the sphere where gravity ceases and everything streams outward, at that moment our entire physical scheme ceases to apply.

We have to say that our earth is spatially limited as a physical body and what is more, spatially limited in its physical qualities. It is nonsensical to suppose that beyond the null-sphere the terrestrial physical laws apply. Just as nonsensical is it to apply the present laws to former ages and infer the nature of earth evolution from what is going on at a particular time.

The madness of the Kant-Laplace theory consists in the belief that it is possible to abstract something from contemporary physical phenomena and extend it without more ado backwards in time. Modern astrophysics also shows the same madness to the belief that what can be abstracted from terrestrial physical conditions can be applied to the constitution of the sun and that we can look upon the sun as governed by the laws of the earth.

But a tremendously important thing unfolds for us when we take a general view over the phenomena we have considered and bring certain series of phenomena together.

Your attention has been called to the fact that the physicists have come to a certain view so neatly expressed by Eduard von Hartmann. The second law of thermodynamics states that whenever heat is changed into mechanical work some heat remains unchanged, and thus, finally, all energy must change into heat and the earth come to a heat death. This view has been expressed by Eduard von Hartmann as follows: “The world process has the tendency to run down.”

Now suppose we assume such a running down of the world-process does take place in the direction indicated. What happens then?

When we make experiments to illustrate the second law of the mechanical theory of heat, heat appears. We see mechanical work used up and heat appearing. What we see appearing is susceptible to further change. For we can show likewise when we produce lights from heat that not all of the heat reappears as light, since heat simply reverses the mechanical process as it is understood in the sense of the second thermodynamic law of mechanical phenomena. This has, however, led us to say that we have to imagine the whole cosmic spectrum as closed into a circle. Thus if it were really true, as examination of a certain series of phenomena indicates, that the entropy of the cosmos is striving to the maximum, and that the world process is running down, provision is made for re-energizing it. It runs out here, but it runs in again here (indicating figure) on the other side, for we have to think of it as a circle. Thus even if the heat-death enters on one side, on the other side, there comes in that which re-establishes the equilibrium and which opposes the heat-death by a cosmic creating process.

Physics can orientate itself according to this fact if it will no longer observe the world process as we usually look at the spectrum, going off into infinity in the past we go from the red and again into infinity in the future as we go from the blue. Instead the world process must be symbolized as a circle. It is only thus that we can draw near to this process.

When now we have symbolized the world process as a circle then we can include in it what lies in the various realms. But we have had no opportunity in these realms to insert the acoustic phenomena. These, as it were, do not lie in the plane. In them we have something new and we will speak further of this tomorrow.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

I have brought to your notice on the one hand how problematical it is to conceive the celestial phenomena in their mathematical and geometrical aspect alone. This is now being recognized by many people and from diverse angles. Only quite unadvanced thinkers still maintain that the world-picture of Copernicus and Galileo represents downright reality. Increasingly, we hear the voice of those who find this way of thinking of the celestial phenomena useful and practical, no doubt, for purposes of calculation, yet emphasize that it represents only a certain mode of understanding, and that quite other syntheses might be conceived.

There are even those who say, somewhat as Ernst Mach used to say: In the last resort, one can uphold the Ptolemaic just as well as the Copernican world-system, and a third system might equally well be devised. These are but practical ways of correlating the observed facts. The entire realm should now be confronted with a far freer kind of outlook.

You see from this that the problematical nature of the celestial charts, described but a short time ago as replicas of the real facts, is now conceded by the widest circles. On the other hand an escape from the manifest problems and uncertainties of this realm can only be found through such views as were brought forward in outline yesterday,—views which no longer remove Man from the whole cosmic background, but on the contrary, put him into it from the outset. We have to recognize the processes within Man himself in their connection with solar phenomena, lunar phenomena and terrestrial phenomena, thus taking as a starting-point all that goes on in Man, in order to find the way to what is going on out there in the Cosmos, the latter being in some sense the cause of the processes in Man.

A path like this can of course only be trodden from the standpoint of Spiritual Science. Precisely when we try to bring Astronomy into connection with the most varied spheres of life, we shall find that we are being led through Astronomy itself into the views of Spiritual Science. Bear in mind that the visible celestial phenomena, perceptible to our senses and also to our re-inforced senses, appear at first a manifestation of something outside of man. Man confronts and, as it were, arrests with his senses whatever approaches him, introducing it into his conscious world-picture. But the impulses streaming towards us from all sides, certainly do not come to a standstill before our senses. All that goes on without being held up by man's senses and brought into consciousness, all that lives in the celestial influences that stream towards us from all sides, must be sought for within our bodily organism. The organism must in a certain way reflect it all, and it does this in the unconscious and subconscious processes which can only be raised into consciousness in more complicated ways.

We will now continue in a certain direction what we began yesterday. Only an abstraction of our earthly world is dealt with in Geology or Mineralogy; the Earth as described by Geology consists of minerals has evolved in the mineral sphere; true as it is that forces are there in the Earth by virtue of which it brings forth the minerals; yet is is equally true that all that is living in plants, animals and physical human beings also belongs to the Earth. We only see the Earth in its totality when we do not simply cast aside what lives in plant, animal and man and have in mind the mere abstraction "mineral earth ", but bring it all into our consciousness. The living beings and entities that grow up out of the Earth are also part and parcel of the whole.

Of all that belongs in this way to the Earth, let us first take the plant kingdom. We will approach it in order then to find the transition to what meets us in man. Whereas the mineral kingdom to a certain extent carries on an independent Earth-existence and is only related to the Cosmos outside the Earth in such a way as is shown, for example, in the changing of water into ice in winter, the plant kingdom retains a much greater inner connection with the cosmic surroundings of the Earth—with all that enters the Earth from the Cosmos. Through the plant-world the life of the Earth as it were opens itself to the Universe. In geographical regions where in a given season an intensive interaction is taking place between Earth and Cosmos. We must pay heed to a phenomenon like this, for it will lead us into the realm of Astronomy not only quantitatively, but qualitatively. We must be able to derive our ideas from such a thing as this, even as the astronomers of our time derive their ideas from angles, parallaxes and so on.

Then we shall say to ourselves, for example:—The plant-life, covering a given region of the Earth, is a kind of sense-organ, sensitive to all that is revealed towards the Earth out of the Cosmos. At seasons when the interplay is more intense between a portion of the Earth's surface and the Universe, it is as though a human being were opening his eyes to the outer world to receive sense-impressions. And when the interplay is less intense between the Earth and the Cosmos, the consequent decline and inward closure of the vegetative life is like a closing of the eyes to the Cosmos. It is more than a mere comparison to say that through its vegetation a given territory opens its eyes to the Universe in spring and summer and shuts its eyes in autumn and winter, and as by opening and closing of our eyes we do in a way converse with the outer world, so too it is a kind of information or revelation from the Universe which the Earth receives by the opening and closing of its eyes through the life of plants.

And to describe it a little more precisely, we may consider the vegetation of a given region of the Earth when exposed, as it were, so to speak, to the most vivid interplay with the solar life, and we may then turn our attention to the state of vegetation in this region when it is not thus exposed. The winter, I need hardly say, does not interrupt the vegetative life of the Earth. It goes without saying that the vegetative life continues through the winter. But it expresses itself in quite another way than when exposed to the intensive working of the Sun's rays—or, shall we say, of the Cosmos. Under the influence of the solar life, the vegetative life of the Earth shoots outward into form. The leaves unfold and grow more complex; flowers develop. But when this is followed by the closing of the eyes to the Universe, if we may call it so, the vegetative life goes back into itself—into the seed. Withdrawing from the outer world, it no longer shoots into outward form; it concentrates, if I may put it so, into a point; it becomes centered in itself.

We may describe this contrast truly as a law of Nature. The interplay between the earthly and the solar life reveals itself in the Earth's vegetation. Under the solar influence the vegetative life shoots outward into form; under the influence of the earthly life it closes up into a plant,—it becomes seed or germ. In all this there is a quality of expansion and contraction or gathering into a center. Here we begin to apprehend the relationships of space itself in a directly qualitative aspect. This is the very thing which we must practice in the development of our ideas, if we would attain to really fruitful notions and perceptions in this sphere.

And now we pass from plant-life to the life of man. Naturally, what comes to expression in the life of plants will find expression in man too. In what way will it do so? What we somehow perceive, my dear Friends, so outwardly and evidently in the life of plants—what we have visibly before our eyes if only we are attentive to the qualitative aspect—this we can recognize in man, properly speaking, only in the first years of childhood.

Let us then trace the interaction of the solar and terrestrial life for man in the age of childhood, as we have just been doing for the plant kingdom. The little child opens through the senses to receive the impressions of the outer world. In doing so, the human being is really opening to receive the solar life. You only need see things in the proper light to recognize that what pours in upon our senses is inherently connected with what is brought about in the terrestrial sphere by the Cosmos. You can reflect upon the special case of light. When light and darkness succeed each other in the alternation of day and night, impressions are made upon our eyes by day, and no impressions are made by night. You can apply this also to other perceptions, though it is more difficult to make it clear. You will then say that a certain effect of the daily alternations, solar and earthly, expresses itself in man's soul-life. Man has an activity of soul through what arises in the rhythm of the day. What the Sun here brings to the Earth comes to expression in the soul-life of man. But if we follow the growth of the child, particularly until the 7th year—the change of teeth—and go into all the details, we find how, notably in the first years of the child's development (less and less, the older the child becomes), it is plainly perceptible that the changing seasons, year by year, have just as much significance for human growth as for the sprouting and dying-down of the vegetation.

We will represent it diagrammatically. If, for example, we study carefully and intelligently the development of the human brain in the earliest stages from year to year, we shall find the following. We have the human skull with its brain-content. (Fig. 1)

It remodels itself, and one can follow how it remodels itself through what in the course of the changing year. Something which works formatively and creatively upon the human head, molding it from outside in a corporeal, physical sense,—we find this intimately connected with the forces playing between Earth and Sun in the course of the year. In the daily rhythm we find what enters through the senses, independent of growth, to work on the soul and spirit of man. We see how what takes place in man by reason of the Sun's activity in the daily rhythm, has an inner effect which frees itself from the external world and becomes of a soul-and-spirit nature; it is what the child learns, what it assimilates through observation, what takes place in effect, in soul and spirit. Then we see how in a totally different tempo—from a different aspect—the brain remodels itself, organizes itself, and grows. That is the other activity, the yearly activity of the solar forces. We will say nothing yet of the changes occurring in the Universe between Sun and Earth; we will consider manifestations in man himself which are united with certain changes in the solar and terrestrial life.

We consider the day and find the soul- and spirit-life of man connected with the course of the Sun. We consider the change of seasons through the year and find man's life of growth, the physical, corporeal life, connected with the course of the Sun. We can say: The change taking place between Earth and Sun in 24 hours has certain effects on the spirit and soul of man. What happens between Earth and Sun in the course of the year has certain effects on the physical, corporeal part of man. We shall have to bring these effects into connection with others and thence arrive at a world-concept which can no longer be deceptive, for it speaks to us of real processes within ourselves, no longer dependent on illusory sense-impressions or the like.

Thus we must gradually draw near to what can give us a sure basis for the astronomical world-conception. We can only take our start from what appears in man himself. So we can say: the day is something in man's connection with the Cosmos that expresses itself in soul and spirit; the year is something in man's connection with the Cosmos that expresses itself in the physical-corporeal life, as for example in growth, and so on.

Now let us look at another complex of facts, referred to yesterday. With human reproduction we must relate certain ideas referring to the life of the Cosmos. We indicated yesterday that the female organism shows in a striking manner how the monthly functions connected with the sex-life—though not, to be sure, coinciding with the Moon's phases—are yet a reflection of them in their time rhythm. The process wrests itself free from the Cosmos, as it were, but still reflects the Cosmic Moon-process in its periodic course. We have here an indication, my dear friends, of inner processes in the human organism which we can study better if we turn our attention to more familiar phenomena, such as may make these more remote phenomena easier to understand.

There is something in the soul-life which actually reproduces in miniature the organic processes to which we have just alluded. Let us say, we have an outer experience which affects us through the senses and the mind,—perhaps also through our feelings. We retain a memory of the experience. The recollection—the retention of the experience—leads to the possibility of the picture of it emerging again at a later time. Anyone who considers these facts, not on the basis of fanciful theories, but with sound qualitative observation, will have to admit that in all that arises within us by way of memory, our physical bodily organization plays a part. The remembering itself is no doubt an event in the life of soul, but it needs the inner basis of the physical body in order to come into being. The activity of remembering is directly interrelated with bodily processes; though this has not yet been investigated sufficiently by external science. Comparing what occurs in the female organism in the monthly periods (it occurs in the male organism too, only it is less evident; it can be observed more in the etheric organism and this is not usually done)—comparing this with what happens in ordinary experience when we remember something, one will certainly find a difference. Yet if with sound inner perception one recreates the process in one's consciousness, one cannot but say that the activity of remembering, this soul-occurrence arising out of the physical organism, is similar to what takes place in the monthly functions of the female organism, only is in miniature and is more drawn into the realm of soul, less impressed upon the body. From this point of view you will be able to say: Inasmuch as man individualizes himself from the Cosmos, he develops the faculty of memory; inasmuch as he still lives within the Cosmos, developing more his sub-conscious functions, something in the nature of a common experience with the Cosmos arises, connected with the Moon-processes in the Cosmos. This experience remains, just as a past experience remains in our memory, and later it emerges in an inner constitutional process, like a remembrance which has been drawn into the body and has become organic.

There is no other way, my dear friends, of understanding these matters than by thus proceeding from the simpler to the more complex. Just as it is not necessary for a recollection to coincide with a fresh outer experience, so it is not necessary for what appears in the female organism, as a memory of an earlier cosmic connection of the human organism with the phases of the Moon, to coincide in time with these phases. Nevertheless, it is connected with the Moon's phases no less essentially than is the recollection of an earlier experience with the experience itself. Here then we have an activity in the human organism, more on the psychological side and yet not unlike the effects—precipitated, as it were, into the life of time—of influences due originally to the Moon. For the organic periodicity of which we have been speaking embraces about 28 days, as you know.

Now take the following. If we consider the daily influence of the Sun, we find an inner activity of soul and spirit; if we consider the yearly influence of the Sun, then we find laws of growth belonging to the outer physical body. Thus we can say, for the Sun life:

1. Soul and Spirit: Day

2. Physical bodily nature: Year

And now we come to the Lunar activity. We pass on to consider the lunar life, the life of the Moon. What I have just described as taking place in rhythm of 28 days belongs indeed to the soul and spirit; it has only impressed itself deeply into the body. Physiologically, there is really no difference, in a finer sense, between what takes place in the body on the arising of a memory with respect to the event to which the memory refers, and what takes place in the monthly periods of the female body with respect to what the female organism experienced long ago in conjunction with the phases of the Moon. Only the latter is a stronger, a more intensive experience,—a soul spiritual experience pressed more intensively into the body. Thus, for the Lunar life:

Soul and Spirit: 28 day's activity

Let us now seek the corresponding phenomena for the physical body. What will they be? You can find it for yourselves by deduction. We will have bodily, physical effects with a 28-year period. As a day here corresponds to a year, we shall have 28 years.

Physical bodily nature: 28 year's activity

You need only remember that 28 years is the period bringing us to our full inner maturity of growth. It is then that we first cease to be in the ascending scale of growth. Just as the Sun works upon us from outside in its yearly activity, in order to complete in us an outward process corresponding to the daily process in the inner life o soul and spirit, so something works in the Cosmos in a 28-year period, organizing us from outside even as the female human being is organized inwardly. (In her it is more obvious than in the male, for in the man the corresponding daily rhythm is more withdrawn into the etheric.) Here then a 28-day period impresses itself inwardly in the realm of the soul and spirit, and we can say: As the daily Sun-life is related to the yearly Sun-life in regard to man, so the 28-day Moon-life related to the 28-year Moon-life with respect to the whole man (the former belonging, in effect, more to the human head).

You see how we place man, and rightly place him, into the whole Cosmos. We leave off speaking of Sun and Moon merely as if we stood isolated here on Earth, and only looked out with our eyes or with our telescopes to Sun and Moon. We speak of Sun and Moon as of something inwardly united with our very life, and we perceive the connection in the special configurations of our life in time. Until we place man again, my dear friends, into the picture of the doings of Sun and Moon, we shall not have evolved a firm foundation for true Astronomy.

Thus a new science of Astronomy must be built upon a spiritual-scientific basis. It must be evolved out of a more intimate knowledge of man himself. We shall only be able to find a meaning in what is taught by the external Astronomy of today, when we are in a position to base our hypotheses on man himself. We shall then be able profitably to study the rather schematic statements made in Astronomy today and we shall also be able to make essential corrections in this external Astronomy.

What follows from all this? It follows that in these processes—no matter, for the moment, what the underlying basis of them is—a universal life reveals itself. Whether it be (and we will speak of this later) that the daily and yearly rotations of the Earth underlie what I have here described as solar life with respect to the soul and spirit for the day, and to the physical bodily nature for the year; whether it be the movements of the Moon described by modern Astronomy or something very different;—we shall never reach an understanding of it merely by setting up the well-known picture taught in the Schools. But we must understand all that is expressed in this picture as being in reality a continuing, enduring universal life—a life which cannot be approached in its fullness by a mere series of diagrammatic pictures.

We will now set to work in another way. We will begin to work from the standpoint offered us in the Astronomical ideas of a man who still had very much from the past. We do not want to return to the older ideas; we must work out of new ideas This man, however, still had much of the old qualitative virtues in his ideas. I refer to Kepler. Astronomy has become more and more quantitative in modern time, and it would be a delusion to look on Astrophysics as the entry of a qualitative element into Astronomy; of an universal life that lay behind the work of Kepler. In him a feeling still persisted that behind all that is manifest to ordinary astronomical observation there lies hidden something like the gesture of a vast cosmic life—a cosmic life that here reveals its presence.

If we have a man before us and see him move a hand or an arm, we do not merely calculate the mechanics of the movement; we recognize it as the outer revelation of an inner life of soul and spirit. We understand as an expressive gesture something that can, after all, also be looked on from a purely spatial, mathematical point of view. The further back one goes in the history of man's approach to Astronomy, the more one find men conscious that the pictures they conceived of the path of the Sun or of the stars were no mere passive pictures of indifferent events but that these pictures were gestures of life and being. It is quite easy to discern in olden times this feeling of the gesture-like nature of the movements of the heavenly bodies. When my hand moves through the air I shall not merely calculate its path, but in this path I see an expression of the soul . So did the earlier observer see in the path of the Moon an expression. of a life of soul. In all the movements of the heavenly bodies he saw expressions of a soul-nature lie pictures it somewhat in this s way—If I could held an umbrella here so that only my hand were seen, my hand would make an inexplicable movement, for I am there behind the umbrella; only the hand is to be seen. Somewhat in this way the men of ancient times pictured that the movement of the Moon up in the sky was but the outer expression—a sort of terminal ‘limb’—end that the really active being stood behind it. So too in earlier times men did not speak of isolated heavenly bodies of the planets; they spoke of planetary spheres. They spoke of the several spheres, belonging to the heavenly bodies. Thus they distinguished the Moon-sphere, the Mercury-sphere, the Venus-sphere, the Sun-sphere, the Mars-sphere, the Jupiter-sphere, the Saturn-sphere, and then the eighth sphere—the Heaven of Fixed Stars They distinguished these eight spheres and saw in them something which expressed itself in outer gestures, so that a certain sphere expressed itself by lighting up now here, now there, and so on. The reality, for instance, was the sphere of the Moon. The Moon itself was not a separate entity,—only the gesture. Where the Moon appeared, the Moon-sphere was making a definite gesture I am relating this to show you the living nature of the old conceptions.

Kepler still retained in his whole consciousness a feeling for this universal life in space Only on this account was he able to draw up his three famous Laws For modern Astronomy the three famous Laws of Kepler are purely of a quantitative nature, to be regarded simply from the aspect of spatial and temporal concepts. For a man who still worked out of such a life of ideas as Kepler did, this was not the case. Let us now call to mind these Laws of Kepler. They are:

The First Law:
The Planets move in ellipses round the central body, which is situated in one of the foci of the ellipse.

The Second Law:
The Radius-vector of a Planet describes equal sectors, equal areas, in equal periods of time.

The Third Law:
The squares of the periods of revolution of the different Planets are proportional to the cubes of the major semi-axes

Now as we said, to the modern, purely quantitative view these laws too are purely quantitative To anyone like Kepler, the very expression ‘elliptical’ and the corresponding curve signified a greater livingness when it only moves in a circle, for it must use an inner impulse in order continually to alter the radius. When something simply moves in a circle it need do nothing to alter the radius. A more intense inner life must be employed in the radius-vector is continually altered. The simple. statement: “The Planets move in ellipses round the central body and the central body is not in the mid-point but in one of the foci of the ellipse”, implied an element of greater livingness than when something moves in a perfect circle.

Further: “The radius-vector describes equal sectors in equal periods of time”. We have here the transition from the line to the surface, to the plane. Please notice this.’ Inasmuch as at first only the ellipse is described, we remain in the line—the curve. When we are directed to the path that the radius-vector describes, we are led to the surface—the area. A more intensive condition in the planetary movement is disclosed, When the planet ‘rolls along’—if I may express so myself—it is not only expressing something within itself, but draws its tail after it, as it were. The whole area which the radius-vector describes belongs to it spiritually. Moreover, in equal periods of time equal areas are described, Special attention is thus drawn to the quality, the inherent character of the movement of the planets.

The third Law above all relates to the life that plays its part between the various planets. This Law assumes a more complicated form. “The squares of the periods of revolution of the Planets are in proportion to the cubes of the semi-major axes” (or of the mean distance from the central body). This Law, you see, contains a great deal if one still understands it in Kepler's living way. Newton then killed the law. He did this in a very simple fashion. Take Kepler's Third Law. You can write it thus:

or written differently:

Now write it in a somewhat different form. Write it thus:

(I might of course also have written it in the reverse order.)

What have we on the left-hand side of the equation, here in the left-hand ratio? No less than what is expressed by one half of Newton's Law, and on the other side the other half, the forces of Newton's Law. You need only write Kepler's Law thus differently and you can say: “The forces or attraction are inversely proportional to the squares of the distances.” Here then you have the Newtonian Law of Gravity deduced from the Law of Kepler. The force of gravity between the planets, the celestial bodies, is in inverse proportion to the squares of their distances apart. It is nothing else than the killing of Kepler's Third Law. In principle that is what it is.

But now take the matter actively and livingly. Do not set before yourself the dead product “force of gravity”—“the forces of attraction decrease with the squares of the distances”,—but take what is living still in Kepler's form, the squares of the periods of time. Fill out the caput mortum of the Newtonian force of attraction, which is a mere external concept, with what is implied in the square of the period of time, and you will fill with inner life of the Newtonian concept, which is really the corpse of an idea! For inner life has to do with time. And here you have before you not only time in its simple course, you have time squared—time to the second power! We shall yet have to come back to what it means to speak of ‘time squared’ But you can realize that to speak of time to the second power is to speak or something of an inward nature. It is, indeed, time which in the life of man actually represents the course of his inner soul-life. The point is that we should look right through it dead concept of the Newtonian force of attraction to that which suddenly darts into the center, bringing time into it and therewith bringing in an element of inner life.

Now look at the matter from another point of view. Notice that Kepler's first Law also has reference to the Earth. Not only does the Earth describe an ellipse, but you, since you are on the Earth, describe an ellipse together with it. What takes place outwardly is in you an inner process. Thus the arising of the ellipse from the circle, in the living way in which Kepler still conceived it, corresponds to a process in your own inner being. And inasmuch as you move in the line which is formed by the radius-vector describing equal sectors in equal times, it is you who continually relate yourself to the central body, placing yourself in relation to your own Sun. You, together with the curve, are describing a path in time, along which you are in continual relation to the Sun. If I may put it a little quaintly You must take care all the time that you do not ‘skid’ or side-slip, that you do not go too fast,—that your radius-vector does not describe too great an area. This outer point which moves in the ellipse must be continuously in the right relation to the Sun. There you have the movement you yourselves make, characterized as a pure line in space. The relation to the Sun is characterized in the Second Law.

And if we pass on to the Third Law, you have an inner experience of the relation to the other planets—your own living connection with the other planets.

Thus we not only have to find, in man himself, processes that lead us out again into the Cosmos. If we interpret rightly the mathematical pictures presented to us by the cosmic process, we also turn into an inner experience what is apparently external and quantitative. For the cosmic Mathematics indwells man. Man is himself in the midst of the living Mathematics. Of this we shall speak more tomorrow.