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.

The theme of this cycle of lectures was not chosen because it is traditional within academic or philosophical disciplines, as though we thought epistemology or the like should appear within our courses. Rather, it was chosen as the result of what I believe to be an open-minded consideration of the needs and demands of our time. The further evolution of humanity demands new concepts, new notions, and new impulses for social life generally: we need ideas which, when realized, can create social conditions offering to human beings of all stations and classes an existence that seems to them humane. Already, to be sure, it is being said in the widest circles that social renewal must begin with a renewal of our thinking.¹ Yet not everyone in these widest circles imagines something clear and distinct when speaking in this way. One does not ask: whence shall come the ideas upon which one might found a social economy offering man a humane existence? That portion of humanity which has received an education in the last three to four centuries, but particularly since the nineteenth century, has been raised with certain ideas that are outgrowths of the scientific world view or entirely schooled in it. This is particularly true of those who have undergone some academic training. Only those working in fields other than the sciences believe that natural science has had little influence on their pursuits. Yet it is easy to demonstrate that even in the newer, more progressive theology, in history and in jurisprudence—everywhere can be found scientific concepts such as those that arose from the scientific experiments of the last centuries, so that traditional concepts have in a certain way been altered to conform to the new. One need only allow the progress of the new theological developments in the nineteenth century to pass before the mind's eye. One sees, for example, how Protestant theology has arrived at its views concerning the man, Jesus, and the nature of Christ, because at every turn it had in mind certain scientific conceptions that it wanted to satisfy, against which it did not want to sin. At the same time, the old, instinctive ties within the social order began to slacken: they gradually ceased to hold human life together. In the course of the nineteenth century it became increasingly necessary to replace the instincts according to which one class subordinated itself to another, the instincts out of which the new parliamentary institutions, with all their consequences, have come with more-or-less conscious concepts. Not only in Marxism but in many other movements as well there has come about what one might call a transformation of the old social instincts into conscious concepts.

But what was this new element that had entered into social science, into this favorite son of modern thought? It was the conceptions, the new mode of thinking that had been developed in the pursuit of natural science. And today we are faced with the important question: how far shall we be able to progress within a web of social forces woven from such concepts? If we listen to the world's rumbling, if we consider all the hopeless prospects that result from the attempts that are made on the basis of these conceptions, we are confronted with a dismal picture indeed. One is then faced with the portentous question: how does it stand with those very concepts that we have acquired from natural science and now wish to apply to our lives, concepts that—this has become clearly evident in many areas already—are actually rejected by life itself? This vital question, this burning question with which our age confronts us, was the occasion of my choosing the theme, “The Boundaries of Natural Science.” Just this question requires that I treat the theme in such a way that we receive an overview of what natural science can and cannot contribute to an appropriate social order and an idea of the kind of scientific research, the kind of world view to which one would have to turn in order to confront seriously the demands made upon us by our time.

What is it we see if we consider the method according to which one thinks in scientific circles and how others have been influenced in their thinking by those circles? What do we see? We see first of all that an attempt is made to acquire data and to order it in a lucid system with the help of clear concepts. We see how an attempt is made to order the data gathered from inanimate nature by means of the various sciences—mechanics, physics, chemistry, etc.—to order them in a systematic manner but also to permeate the data with certain concepts so that they become intelligible. With regard to inanimate nature, one strives for the greatest possible clarity, for crystal-clear concepts. And a consequence of this striving for lucid concepts is that one seeks, if it is at all possible, to permeate everything that one finds in one's environment with mathematical formulae. One wants to translate data gathered from nature into clear mathematical formulae, into the transparent language of mathematics.

In the last third of the nineteenth century, scientists already believed themselves very close to being able to give a mathematical-mechanical explanation of natural phenomena that would be thoroughly transparent. It remained for them only to explain the little matter of the atom. They wanted to reduce it to a point-force [Kraftpunkt] in order to be able to express its position and momenta in mathematical formulae. They believed they would then be justified in saying: I contemplate nature, and what I contemplate there is in reality a network of interrelated forces and movements wholly intelligible in terms of mathematics. Hence there arose the ideal of the so-called “astronomical explanation of nature,” which states in essence: just as one brings to expression the relationships between the various heavenly bodies in mathematical formulae, so too should one be able to compute everything within this smallest realm, within the “little cosmos” of atoms and molecules, in terms of lucid mathematics. This was a striving that climaxed in the last third of the nineteenth century: it is now on the decline again. Over against this striving for a crystal-clear, mathematical view of the world, however, there stands something entirely different, something that is called forth the moment one tries to extend this striving into realms other than that of inanimate nature. You know that in the course of the nineteenth century the attempt was made to carry this point of view, at least to some extent, into the life sciences. And though Kant had said that a second Newton would never be found who could explain living organisms according to a causal principle similar to that used to explain inorganic nature, Haeckel could nevertheless claim that this second Newton had been found in Darwin, that Darwin had actually tried, by means of the principle of natural selection, to explain how organisms evolve in the same “transparent” terms. And one began to aim for just such a clarity, a clarity at least approaching that of mathematics, in all explanations, proceeding all the way up to the explanation of man himself. Something thereby was fulfilled which certain scientists explained by saying that man's need to understand the causes of phenomena is satisfied only when he arrives at such a transparent, lucid view of the world.

And yet over against this there stands something entirely different. One comes to see that theory upon theory has been contrived in order to construct a view of the world such as I have just described, and ever and again those who strove for such a view of the world called forth—often immediately—their own opposition. There always arose the other party, which demonstrated that such a view of the world could never produce valid explanations, that such a view of the world could never ultimately satisfy man's need to know. On the one hand it was argued how necessary it is to keep one's world view within the lucid realm of mathematics, while on the other hand it was shown that such a world view would, for example, remain entirely incapable of constructing even the simplest living organism in thought of mathematical clarity or, indeed, even of constructing a comprehensible model of organic substance. It was as though the one party continually wove a tissue of ideas in order to explain nature, and the other party—sometimes the same party—continually unraveled it.

It has been possible to follow this spectacle—for it seems just that to anyone who is able to view it with an unprejudiced eye—within the scientific work and striving of the last fifty years especially. If one has sensed the full gravity of the situation, that with regard to this important question nothing but a weaving and unraveling of theories has taken place, one can pose the question: is not the continual striving for such a conceptual explanation of phenomena perhaps superfluous? Is not the proper answer to any question that arises when one confronts phenomena perhaps that one should simply allow the facts to speak for themselves, that one should describe what occurs in nature and forgo any more detailed accounting? Is it not possible that all such explanations show only that humanity is still tied to its mother's apron strings, that humanity in its infancy sought a kind of luxury? Would not humanity, come of age, have to say to itself: we must not strive at all for such explanation; we get nowhere in that way and must simply extirpate the need to know? Why not? As we become older we outgrow the need to play; why, if we were justified in doing so, should we not simply outgrow the need for explanations?

Just such a question could already emerge in the most extraordinarily significant way when, on August 14, 1872, du Bois-Reymond stood before the Second General Meeting of the Association of German Scientists and Physicians to deliver his famous address, “The Boundaries of Natural Science” [“Grenzen des Naturerkennens”], an address still worthy of consideration today. Yet despite the amount that has been written about this address by the important physiologist, du Bois-Reymond, many still do not realize that it represents one of the important junctures in the evolution of the modern world view.

In medieval Scholasticism all of man's thinking, all of his notional activity, was determined by the view that one could explain the broad realms of nature in terms of certain concepts but that one had to draw the line upon reaching the super-sensible. The super-sensible had to be the object of revelation. They felt that man should stand in a relation to the super-sensible in such a way that he would not even wish to penetrate it with the same concepts he formed concerning the realms of nature and external human existence. A limit was set to knowledge on the side of the super-sensible, and it was strongly emphasized that such a limit had to exist, that it simply lay within human nature and the order of the universe that such a limit be recognized. This placement of a limit to knowledge was then renewed from an entirely different side by thinkers and researchers such as du Bois-Reymond. They were no longer Schoolmen, no longer theologians, but just as the medieval theologian, proceeding according to his own mode of thinking, had set a limit to knowledge at the super-sensible, so these thinkers and researchers set a limit at the sensible. The limit was meant to apply above all to the realm of external sensory data.

There were two concepts in particular that du Bois-Reymond had in mind, which to him established the limits natural science could reach but beyond which it could not proceed. Later he increased that number by five in his lecture, “The Seven Enigmas of the World,” but in the first lecture he spoke of the two concepts, “matter” and “consciousness.” He said that when contemplating nature we are forced, in thinking systematically, to apply concepts in such a way that we eventually arrive at the notion of matter. Just what this mysterious entity in space we call “matter” is, however, we can never in any way resolve. We must simply assume the concept “matter,” though it is opaque. If only we assume this opaque concept “matter,” we can apply our mathematical formulae and calculate the movements of matter in terms of the formulae. The realm of natural phenomena becomes comprehensible if only we can posit this “opaque” little point millions upon millions of times. Yet surely we must also assume that it is this same material world that first builds up our bodies and unfolds its own activity within them, so that there rises up within us, by virtue of this corporeal activity, what eventually becomes sensation and consciousness. On the one hand we confront a world of natural phenomena requiring that we construct a concept of “matter,” while on the other hand we confront ourselves, experience the fact of consciousness, observe its phenomena, and surmise that whatever it is we assume to be matter must also lie at the foundation of consciousness. But how, out of these movements of matter, out of inanimate, dead movement, there arises consciousness, or even simple sensation, is a mystery that we cannot possibly fathom. This is the other pole of all the uncertainties, all the limits to knowledge: how can we explain consciousness, or even the simplest sensation?

With regard to these two questions, then—What is matter? How does consciousness arise out of material processes?—du Bois-Reymond maintains that as researchers we must confess: ignorabimus, we shall never know. That is the modern counterpart to medieval Scholasticism. Medieval Scholasticism stood at the limit of the super-sensible world. Modern natural science stands at the limit delineated in essence by two concepts: “matter,” which is everywhere assumed within the sensory realm but nowhere to be found, and “consciousness,” which is assumed to originate within the sense world, although one can never comprehend how.

If one considers this development of modern scientific thought, must one not then say to oneself that scientific research is entangling itself in a kind of web, and only outside of this web can one find the world? For in the final analysis it is there, where matter haunts space, that the external world lies. If this is the one place into which one cannot penetrate, one has no way in which to come to terms with life. Within man one finds the fact of consciousness. Does one come at all near to it with explanations conceived in observing external nature? If in one's search for explanations one pulls up short at human life, how, then, can one arrive at notions of how to live in a way worthy of a human being? How, if one cannot understand the existence or the essence of man according to the assumptions one makes concerning that existence?

As this course of lectures progresses it shall, I believe, become evident beyond any doubt that it is the impotence of the modern scientific method that has made us so impotent in our thinking about social questions. Many today still do not perceive what an important and essential connection exists between the two. Many today still do not perceive that when in Leipzig on August 14, 1872 du Bois-Reymond spoke his ignorabimus, this same ignorabimus was spoken also with regard to all social thought. What this ignorabimus actually meant was: we stand helpless in the face of real life; we have only shadowy concepts; we have no concepts with which to grasp reality. And now, almost fifty years later, the world demands just such concepts of us. We must have them. Such concepts, such impulses, cannot come out of lecture-halls still laboring in the shadow of this ignorabimus. That is the great tragedy of our time. Here lie questions that must be answered.

We want to proceed from fundamental principles to such an answer and above all to consider the question: is there not perhaps something more intelligent that we as human beings could do than what we have done for the last fifty years, namely tried to explain nature after the fashion of ancient Penelope, by weaving theories with one hand and unraveling them with the other? Ah yes, if only we could, if only we could stand before nature entirely without thoughts! But we cannot: to the extent that we are human beings and wish to remain human beings we cannot. If we wish to comprehend nature, we must permeate it with concepts and ideas. Why must we do that?

We must do that, ladies and gentlemen, because only thereby does consciousness awake, because only thereby do we become conscious human beings. Just as each morning upon opening our eyes we achieve consciousness in our interaction with the external world, so essentially did consciousness awake within the evolution of humanity. Consciousness, as it is now, was first kindled through the interaction of the senses and thinking with the outer world. We can watch the historical development of consciousness in the interaction of man's senses with outer nature. In this process consciousness gradually was kindled out of the dull, sleepy cultural life of primordial times. Yet one must only consider with an open mind this fact of consciousness, this interaction between the senses and nature, in order to observe something extraordinary transpiring within man. We must look into our soul to see what is there, either by remaining awhile before fully awakening within that dull and dreamy consciousness or by looking back into the almost dreamlike consciousness of primordial times. If we look within our soul at what lies submerged beneath the surface consciousness arising in the interaction between senses and the outer world, we find a world of representations, faint, diluted to dream-pictures with hazy contours, each image fading into the other. Unprejudiced observation establishes this. The faintness of the representations, the haziness of the contours, the fading of one representation into another: none of this can cease unless we awake to a full interaction with external nature. In order to come to this awakening which is tantamount to becoming fully human—our senses must awake every morning to contact with nature. It was also necessary, however, for humanity as a whole to awake out of a dull, dreamlike vision of primordial worlds within the soul to achieve the present clear representations.

In this way we achieve the clarity of representation and the sharply delineated concepts that we need in order to remain awake, to remain aware of our environment with a waking soul. We need all this in order to remain human in the fullest sense of the word. But we cannot simply conjure it all up out of ourselves. We achieve it only when our senses come into contact with nature: only then do we achieve clear, sharply delineated concepts. We thereby develop something that man must develop for his own sake—otherwise consciousness would not awake. It is thus not an abstract “need for explanations,” not what du Bois-Reymond and other men like him call “the need to know the causes of things,” that drives us to seek explanations but the need to become human in the fullest sense through observing nature. We thus may not say that we can outgrow the need to explain like any other child's play, for that would mean that we would not want to become human in the fullest sense of the word—that is to say, not want to awake in the way we must awake.

Something else happens in this process, however. In coming to such concepts as we achieve in contemplating nature, we at the same time impoverish our inner conceptual life. Our concepts become clear, but their compass becomes diminished, and if we consider exactly what it is we have achieved by means of these concepts, we see that it is an external, mathematical-mechanical lucidity. Within that lucidity, however, we find nothing that allows us to comprehend life. We have, as it were, stepped out into the light but lost the very ground beneath our feet. We find no concepts that allow us to typify life, or even consciousness, in any way. In exchange for the clarity we must seek for the sake of our humanity, we have lost the content of that for which we have striven. And then we contemplate nature around us with our concepts. We formulate such complex ideas as the theory of evolution and the like. We strive for clarity. Out of this clarity we formulate a world view, but within this world view it is impossible to find ourselves, to find man. With our concepts we have moved out to the surface, where we come into contact with nature. We have achieved clarity, but along the way we have lost man. We move through nature, apply a mathematical-mechanical explanation, apply the theory of evolution, formulate all kinds of biological laws; we explain nature; we formulate a view of nature—within which man cannot be found. The abundance of content that we once had has been lost, and we are confronted with a concept that can be formed only with the clearest but at the same time most desiccated and lifeless thinking: the concept of matter. And an ignorabimus in the face of the concept of matter is essentially the confession: I have achieved clarity; I have struggled through to an awakening of full consciousness, but thereby I have lost the essence of man in my thinking, in my explanations, in my comprehension.

And now we turn to look within. We turn away from matter to consider the inner realm of consciousness. We see how within this inner realm of consciousness representations pass in review, feelings come and go, impulses of will flash through us. We observe all this and notice that when we attempt to bring the inner realm into the same kind of focus that we achieved with regard to the external world, it is impossible. We seem to swim in an element that we cannot bring into sharp contours, that continually fades in and out of focus. The clarity for which we strive with regard to outer nature simply cannot be achieved within. In the most recent attempts to understand this inner realm, in the Anglo-American psychology of association, we see how, following the example of Hume, Mill, James, and others, the attempt was made to impose the clarity attained in observation of external nature upon inner sensations and feelings. One attempts to impose clarity upon sensation, and this is impossible. It is as though one wanted to apply the laws of flight to swimming. One does not come to terms at all with the element within which one has to move. The psychology of association never achieves sharpness of contour or clarity regarding the phenomenon of consciousness. And even if one attempts with a certain sobriety, as Herbart has done, to apply mathematical computation to human mental activity [das Vorstellen], to the human soul, one finds it possible, but the computations hover in the air. There is no place to gain a foothold, because the mathematical formulae simply cannot comprehend what is actually occurring within the soul. While one loses man in coming to clarity regarding the external world, one finds man, to be sure—it goes without saying that one finds man when one delves into consciousness—but there is no hope of achieving clarity, for one swims about, borne hither and thither in an insubstantial realm. One finds man, but one cannot find a valid image of man.

It was this that du Bois-Reymond felt very clearly but was able to express only much less clearly—only as a kind of vague feeling about scientific research on the whole—when in August 1872 he spoke his ignorabimus. What this ignorabimus wants to say in essence is that on the one hand, we have in the historical evolution of humanity arrived at clarity regarding nature and have constructed the concept of matter. In this view of nature we have lost man—that is, ourselves. On the other hand we look down into consciousness. To this realm we want to apply that which has been most important in arriving at the contemporary explanation of nature. Consciousness rejects this lucidity. This mathematical clarity is entirely out of place. To be sure, we find man in a sense, but our consciousness is not yet strong enough, not yet intensive enough to comprehend man fully.

Again, one is tempted to answer with an ignorabimus, but that cannot be, for we need something more than an ignorabimus in order to meet the social demands of the modern world. The limit that du Bois-Reymond had come up against when he spoke [about] his ignorabimus on August 14, 1872 lies not within the human condition as such but only within its present stage of historical human evolution. How are we to transcend this ignorabimus? That is the burning question.

• 1. “... that social renewal must begin with the renewal of our thinking.” The original German (“... dass die soziale Erneuerung vom Geiste ausgehen musse”) might be translated alternately “that social renewal must proceed from the spirit.” The German word “Geist”—bane of all who would translate German into English—embraces two meanings that remain in English quite distinct “mind” and “spirit.” The translator must choose one, even though the German always implies both. If he chooses the former, he runs the risk of seriously distorting the author's intentions (as did the man who translated Hegel's Phanomenologie des Geistes as The Phenomenology of Mind). If he chooses the latter, he flies in the face of the dubious connotations that “spirit” and “spiritual” convey—no doubt as a result of the basically empirical cast of English thought. Although “Geist” as Steiner uses it should almost invariably be translated “spirit” (which of course comprehends “wind”), here the context has led us to choose the more restricted meaning.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

We have seen that one arrives at two limits when one seeks either to penetrate more deeply into natural phenomena or, proceeding from the state of normal consciousness, to penetrate more deeply into one's own being in order to uncover the essential nature of consciousness. Yesterday we showed already what happens at the one limit to knowledge. We have seen that man awakes to full consciousness in coming into contact with an external, physical world of sense. Man would remain a more-or-less drowsy being, a being with a sleepy soul, if he could not awake in confronting external nature. And what has happened in the spiritual evolution of humanity, in man's gradual acquisition of knowledge about external nature, is actually nothing other than what happens every morning when we awake out of sleep or dream-consciousness by confronting an external world. This latter is a kind of moment of awakening, and in the course of the evolution of humanity we have to do with a gradual awakening, a kind of long, drawn-out moment of awakening.

Now, we have seen that at this frontier a certain inertia on the part of the soul very easily comes into play, so that when we come up against the extended world of phenomena we do not proceed in the manner of Goethean phenomenology by halting at this frontier and ordering the phenomena according to the representations, concepts, and ideas we have already gained, describing them in a systematic, rational manner, and so forth. Instead, we roll on a bit farther beyond the phenomena with our concepts and ideas and thereby create a world, for example a world of metaphysical atoms, molecules, and so forth. This world, when it is so constituted, is merely a fabrication of the mind, a world into which there enters a creeping doubt, so that we have to unravel again the theoretical web we have spun. And we have seen that it is possible to guard against such a violation of this frontier of our knowledge through phenomenalism, through working purely with the phenomena themselves. We have also had to show that at this point in our striving for knowledge something emerges that commends itself to our use as an immediate necessity: mathematics and that part of mechanics that can be comprehended without any empirical observation, i.e., the entire compass of so-called analytical mechanics.

If we call to mind everything comprehended by mathematics and analytical mechanics, we have before us the system of concepts that allows us to enter into phenomena with the utmost certainty. And yet, as I began to indicate yesterday, one should not deceive oneself, for the whole manner in which we call forth the notions of mathematics and analytical mechanics, this process within our souls, is entirely different from that employed when we experiment with or observe sensory data and then seek to comprehend them, when we try to gather knowledge from sensory experience. In order to arrive at the fullest clarity regarding these matters one must bring all one's mental energy to bear, for in this realm full clarity can be attained only with the greatest mental exertion.

What is the difference between accumulating knowledge from sensory experience in a Baconian manner and the more inward mode of apprehension we find in mathematics and analytical mechanics? One can sharply differentiate the latter from those modes of apprehension that are not inward in this way by formulating clearly the concepts of the parallelogram of motion and the parallelogram of forces. One theorem of analytical mechanics states that two angular vectors proceeding from one point result in a third vector. To say, however, that a vector of a specific force here [see diagram: a] and a vector of a specific force here [b] result in a third force, which can also be determined according to the parallelogram—that is another notion altogether.

The parallelogram of motion lies strictly within the province of analytical mechanics, for it is internally consistent and demands no external proof. In this it is like the Rule of Pythagoras or any other geometrical axiom, but the existence of the parallelogram of forces can be determined only by experience, by experimentation. In this case, we bring something into that which we work through inwardly: the force that can be given only empirically from without. Here we no longer have a pure, analytical mechanics but an “empirical mechanics.” One can thus differentiate sharply between that which is still actually mathematical—as we still conceive mathematics today—and that which leads over into conventional empiricism.

Now one stands before this phenomenon of mathematics as such. We comprehend mathematical truths. We proceed from mathematical phenomena to certain axioms. We weave the fabric of mathematics out of these axioms and then stand before an architectonic whole apprehended by the mind's eye [im inneren Anschauen]. If we are able by means of energetic thinking to differentiate sharply this inner apprehension from anything that can be experienced outwardly, we must see in this fabric of mathematics something that arises through an activity of soul entirely different from that which underlies our experience of the outer objects of sensation. Whether or not we arrive at a satisfactory comprehension of the world depends to a tremendous extent on our being able to make this clear distinction out of inner experience. We thus must ask: where does mathematics originate? Nowadays this question is still not pursued rigorously enough. One does not ask: how is this inner activity of the soul that we need in mathematics, in the wonderful architecture of mathematics—how is this inner activity of the soul different from that whereby we grasp external nature through the senses? One does not pose this question and seek an answer with sufficient rigor, because it is the tragedy of the materialistic world view that, while on the one hand it presses for sensory experience, on the other hand it is driven unawares into an abstract intellectualism, into a realm of abstraction where one is isolated from any true comprehension of the phenomena of the material world.

What kind of capacity is it, then, that we acquire when we engage in mathematics? We want to address ourselves to this question. In order to answer this question we must, I believe, have reached a complete understanding of one thing in particular: we must take fully seriously the concept of becoming as it applies to human life as well. We must begin by acquiring the discipline that modern science can teach us. We must school ourselves in this way and then, taking the strict methodology, the scientific discipline we have learned from modern natural science, transcend it, so that we use the same exacting approach to rise into higher regions, thereby extending this methodology to the investigation of entirely different realms as well. For this reason I believe—and I want this to be expressly stated—that nobody can attain true knowledge of the spirit who has not acquired scientific discipline, who has not learned to investigate and think in the laboratories according to the modern scientific method. Those who pursue spiritual science [Geisteswissenschaft] have less cause to undervalue modern science than anyone. On the contrary, they know how to value it at its full worth. And many people—if I may here insert a personal remark—were extremely upset with me when, before publishing anything pertaining to spiritual science as such, I wrote a great deal about the problems of natural science in a way that appeared necessary to me. So you see it is necessary on the one hand for us to cultivate a scientific habit of mind, so that this can accompany us when we cross the frontiers of natural science. In addition, it is the quality of this scientific method and its results that we must take very seriously indeed.

You see, if we consider the simple phenomenon of warmth that appears when we rub two bodies together, it would be utterly unscientific to say, regarding this isolated phenomenon, that the warmth had been created ex nihilo or simply existed. Rather, we seek the conditions under which this warmth was previously latent and now appears by means of the bodies. We proceed from the one phenomenon to the other and thus take seriously this process of becoming [das Werden]. We must do the same with the concepts that we consider in spiritual science. So we must first of all ask: is that which manifests itself as the ability to perform mathematics present in man throughout his entire existence between birth and death? No, it is not always present. It awakes at a certain point in time. To be sure, we can, while still remaining empirical regarding the outer world, observe with great precision how there gradually arise out of the dark recesses of human consciousness faculties that manifest themselves as the ability to perform mathematics and something like mathematics that we have yet to discuss. If one can observe this emergence in time precisely and soberly, just as scientific research treats the phenomena of the melting or boiling point, one sees that this new faculty emerges at approximately that time of life when the child changes teeth. One must treat such a point in the development of human life with the same attitude with which physics, for example, teaches one to treat the melting or boiling point. One must acquire the ability to carry over into the complicated realm of human life the same strict inner discipline that one can acquire by observing simple physical phenomena according to the methods of modern science. If one does this, one sees that in the course of human development from birth, or rather from conception, up to the change of teeth, the soul faculties enabling one to perform mathematics manifest themselves gradually within the organism but that they are not yet fully present. Now we say that the warmth that manifests itself in a body under certain conditions was latent in that body beforehand, that it was at work within the inner structure of that body. In the same way we must be entirely clear that the capacity to perform mathematics, which becomes most evident at the change of teeth and reveals itself gradually in another sense, was also at work beforehand within the human organization. We thus arrive at an important and valuable insight into the nature of mathematics—mathematics taken, of course, in the very broadest sense. We begin to understand how that which is at our disposal after the change of teeth as a soul faculty worked previously within to organize us. Yes, within the child until approximately its seventh year there works an inner mathematics, an inner mathematics not abstract like our external one but full of active energy, a mathematics which, if I may use Plato's expression, not only can be inwardly envisioned [angeschaut] but is full of active life. Up to this point in time there exists within us something that “mathematicizes” us through and through.

When we ask at first entirely superficially what can be seen by looking empirically at this “latent mathematics” in the body of the young child, we are led to three things resembling inner senses. In the course of these lectures we shall come to see that one can indeed speak of senses within as well. Today I want only to indicate that we are led to something that develops an inward faculty of perception similar to the outward perception developed by the eyes and ears, except that the former remains unconscious within us during these first years. And if we look within, look into our own inner organization not like nebulous mystics but with all our powers of apprehension, we can find within three functions similar to those of the outward senses. We find inner senses that exercise a certain activity, a certain inner mathematics, just in those first several years. One encounters first of all what I would like to call the sense of life. This sense of life manifests itself in later years as a perception of our inner state as a whole. In a certain way we feel either well or unwell. We feel comfortable or uncomfortable: just as we have a faculty for perceiving outwardly with the eyes, so also do we have a faculty for perceiving inwardly. This faculty is directed toward the whole organism and is for that reason dark and dull; yet it is there all the same. We shall have more to say about this later. For the moment I want to anticipate this later discussion only by remarking that this sense of life is—if I may use a tautology—especially active in the vitality of the child up until the change of teeth.

Another inner sense that we must consider when we look within in this way is that which I would like to call the sense of movement. We must form a clear conception of this sense of movement. When we move our limbs, we are aware of this not only by viewing ourselves externally but also by means of an internal perception. Also when we walk: we are conscious that we are walking not only in that we see objects pass and our view of the external world changes but also in that we have an internal perception of the movements of the limbs, of changes within ourselves as we move. Normally we remain unaware of the inner experiences and perception that run parallel to the outer because of the strength of the external impressions, much as a dim light is “extinguished” by a bright one.

And a third inward-looking faculty is the sense of balance. The sense of balance is what enables us to locate ourselves within the world, to avoid falling, to perceive in a certain way how we can bring ourselves into harmony with the forces in our environment. We perceive this process of bringing ourselves into harmony with our environment inwardly. We thus can truly say that we bear within ourselves these three inner senses: the sense of life, the sense of movement, and the sense of balance. They are especially active in childhood up to the change of teeth. Around this time of the change of teeth their activity begins to wane, but observe to take but one example, the sense of balance—observe how at birth the child has as yet nothing enabling it to attain the position of balance it needs in later life. Consider how the child gradually gains control of itself, how it learns at first to crawl on all fours, how it gradually achieves through its sense of balance the ability to stand and to walk, how it finally is able to maintain its own balance.

If one considers the entire process of development from conception to the change of teeth, one sees therein the powerful activity of these three inner senses. And if one can attain a certain insight into what is happening there, one sees that there is at work in the sense of balance and the sense of movement nothing other than a living “mathematicizing” [ein lebendiges Mathematisieren]. In order for it to come to life, the sense of life is there to vitalize it. We thus see a kind of latent realm of mathematics active within man. This activity does not entirely cease at the change of teeth, but it does become at that time considerably less pronounced for the remainder of life. That which is inwardly active in the sense of balance, the sense of movement, and the sense of life becomes free. This latent mathematics becomes free, just as latent heat can become liberated heat. And we see how that which initially was woven through the organism as an element of soul becomes free. We see how this mathematics emerges as abstraction from a condition in which it was originally a concrete force shaping the human organism. And because as human beings we are suspended in the web of existence according to temporal and spatial relationships, we take this mathematics that has become free out into the world and seek to comprehend the external world by means of something that worked within us up until the change of teeth. You see, it is not a denial but rather an extension of natural science that results when one considers rightly what ought to live within spiritual science as attitude and will.
We thus carry what originates within ourselves beyond the frontier of sense perception. We observe man within a process of becoming. We do not simply observe mathematics on the one hand and sensory experience on the other but rather the emergence of mathematics within the developing human being. And now we come to that which truly leads over into spiritual science itself. You see, that which we call forth out of our own inner life, this “mathematicizing,” becomes in the end an abstraction. Yet our experience of it need not remain an abstraction. In our time there is, to be sure, little opportunity for us to experience mathematics in a true light. Yet at a certain point in the development of Western civilization there does come to light something of this sense of a special spirit in mathematics. This comes to light at the point where Novalis, the poet Novalis, who underwent a good mathematical training in his studies, writes about mathematics in his Fragments. He calls mathematics a grand poem, a wonderful, grand poem.

One really must have experienced at some time what it is that leads from an abstract understanding of the geometrical forms to a sense of wonder at the harmony that underlies this inner “mathematicizing.” One really must have had the opportunity to get beyond the cold, sober performance of mathematics, which many people even hate. One must have struggled through as Novalis had in order to stand in awe of the inner harmony and—if I may use an expression you have heard often in a completely different context—the “melody” [Melos] of mathematics.

Then something new enters into one's experience of mathematics. There enters into mathematics, which otherwise remains purely intellectual and, metaphorically speaking, interests only the head, something that engages the entire man. This something manifests itself in such youthful Spirits as Novalis in the feeling: that which you behold as mathematical harmony, that which you weave through all the phenomena of the universe, is actually the same loom that wove you during the first years of growth as a child here an earth. This is to feel concretely man's connection with the cosmos. And when one works one's way through to such an inner experience, which many hold to be mere fantasy because they have not actually attained it themselves, one has some idea what the spiritual scientist [Geistesforscher] experiences when he rises to a more extensive grasp of this “mathematicizing” by undergoing an inner development of which I have yet to speak and which you will find fully depicted in my book, Knowledge of the Higher Worlds and Its Attainment.² For then the capacity of soul manifesting itself as this inner mathematics passes over into something far more comprehensive. It becomes something that remains just as exact as mathematical thought yet does not proceed solely from the intellect but from the whole man.

On this path of constant inner work—an inner work far more demanding than that performed in the laboratory or observatory or any other scientific institution—one comes to know what it is that underlies mathematics, that underlies this simple faculty of the human soul which can be expanded into something far more comprehensive. In this higher experience of mathematics one comes to know Inspiration. One comes to understand the differences between what lives in us as mathematics and what lives in us as outer-directed empiricism. In this outer-directed empiricism we have sense impressions that give content to our empty concepts. In Inspiration we have something inwardly spiritual, the activity of which manifests itself already in mathematics, if we know how to grasp mathematics properly—something spiritual which in our early years lives and weaves within us. This activity continues. In doing mathematics we experience this in part. We come to realize that the faculty for performing mathematics rests upon Inspiration, and we can come to experience Inspiration itself by evolving into spiritual scientists. Our representations and concepts then receive their content in a way other than through external experience. We can inspire ourselves with the spiritual force that works within us during childhood. For what works within us during our childhood is spirit. The spirit, however, resides in the human body and must be perceived there through the body, within man. It can be viewed in its pure, free form if one acquires through the faculty of Inspiration the capacity not only to think in mathematical concepts but to view that which exists as a real force in that it organizes us through and through up until the seventh year. And that which manifests itself partially in mathematics and reveals itself as a much more expansive realm through Inspiration can be inwardly viewed, if one employs certain spiritual scientific methods about which—as I have said—I plan yet to speak. One thereby gains not merely new results to add to those acquired through the old powers of cognition but rather an entirely new mode of apprehension. One acquires a new “Inspirative” cognition.

The course of human evolution has been such that these powers of Inspirative cognition have receded with the passage of time, after having been present earlier to a very high degree. One must come to understand how Inspiration arises within the inner being of man—that same Inspiration that survives in the West only in the diluted, intellectual experience of mathematics. The experience can be expanded, however, if only one comprehends fully the inner nature of that realm; only then does one begin to understand what lived in that earlier consciousness transmitted to us actually only from the East, from the Vedanta and the other Eastern philosophies that remain so cryptic to the Western mind. For what was it that actually lived within these Eastern philosophies? lt was something that arose through soul faculties of a mathematical nature. It was an Inspiration. It was not merely mathematics but rather something attained within the soul in a way similar to that in which one performs mathematics. Thus I would say that the mathematical atmosphere emanating from the Vedanta and similar ancient world views is something that can be understood from the perspective one attains in rising again to enter the realm of Inspiration. If one can raise to vivid inner life that which works unconsciously in mathematics and the mathematical sciences and can carry it over into another realm, one discovers the same mathematical element that Goethe viewed. Goethe modestly confessed that he did not have proficiency in mathematics in any conventional sense. Goethe has written on his relationship to mathematics in a very interesting series of essays, which you can find in his scientific writings under the heading “Relationship to Mathematics.” Extraordinarily interesting! For despite Goethe's modest confession that he had not acquired a proficiency in the handling of actual mathematical concepts and theories, he does require one thing: he calls for a phenomenalism such as he employed in his own scientific studies. He demands that within the secondary phenomena confronting us in the phenomenal world we seek the archetypal phenomenon [Urphänomen]. But just what kind of activity is this? He demands that we trace external phenomena back to the archetypal phenomenon, in just the same way that the mathematician traces the outward apprehension [äusseres Anschauen] of complex structures back to the axiom. Goethe's archetypal phenomena are empirical axioms, axioms that can be experienced.

Goethe thus demands, in a truly mathematical spirit, that one inwardly permeate phenomena with mathematics. He writes that we must see the archetypal phenomena in such a way that we are able at all times to justify our procedures according to the rigorous requirements of the mathematician. Thus what Goethe seeks is a modified, transformed mathematics, one that suffuses phenomena. He demands this as a scientific activity.

Goethe was able, therefore, to suffuse with light the one pole that otherwise remains so dark if we postulate only the concept of matter. We shall see how Goethe approached this pole; we modern must, however, approach the other, the pole of consciousness. We must investigate in the Same way how soul faculties manifest their activity in the human being, how they proceed from man's inner nature to manifest their activity externally. We shall have to investigate this. It shall become clear that we must complement the method of investigating the external world offered by Goethean phenomenology with a method of comprehending the realm of human consciousness. It must be a mode of comprehension justifiable in the sense in which Goethe's can be justified to the mathematician—a method such as I tried to employ in a modest way in my book, Philosophy of Freedom.³

At the pole of matter we thus encounter the results yielded by Goethean phenomenology and at the pole of consciousness those attained by pursuing the method that I sought to establish in a modest way in my Philosophy of Freedom.

Tomorrow we will want to pursue this further.

• 2. Wie erlangt man Erkenntnisse der hoheren Welten?, Berlin, 1909 (Knowledge of the Higher Worlds and Its Attainment. Anthroposophie Press, Spring Valley, N.Y., reprinted 1983).
• 3. Die Philosophie der Freiheit, Berlin, 1894 (The Philosophy of Freedom, Anthroposophic Press, Spring Valley, N.Y., 1964). Earlier translations of this book (1922, 1938, and 1963) bore the title The Philosophy of Spiritual Activity, following a suggestion given by Steiner himself. The English word “freedom” connotes a passive state; the German “Freiheit” (as is clean from the following lecture), an objective basis for moral action achieved through intense inner activity.