4 March 1920, Stuttgart
My dear friends,
You will perhaps have noticed that in our considerations here, we are striving for a certain particular goal. We are trying to place together a series of phenomena taken from the realm of heat in such a manner that the real nature of warmth may be obvious to us from these phenomena. We have become acquainted in a general way with certain relations that meet us from within the realm of heat, and we have in particular observed the relation of this realm of the expansionability of bodies. We have followed this with an attempt to picture to ourselves mentally the nature of form in solid bodies, fluids and gaseous bodies. I have also spoken of the relation of heat to the changes produced in bodies in going from the solid to the fluid and from the fluid to the gaseous or vaporous condition. Now I wish to bring before you certain relations which come up when we have to do with gases or vapors. We already know that these are so connected with heat that by means of this we bring about the gaseous condition, and again, by appropriate change of temperature that we can obtain a liquid from a gas. Now you know that when we have a solid body, we cannot by any means interpenetrate this solid with another. The observation of such simple elementary relations is of enormous importance if we really wish to force our way through to the nature of heat. The experiment I will carry out here will show that water vapor produced here in this vessel passes through into this second vessel. And now having filled the second vessel with water vapor, we will produce in the first vessel another vapor whose formation you can follow by reason of the fact that it is colored. (The experiment was carried out.) You see that in spite of our having filled the vessel with water vapor, the other vapor goes into the space filled with the water vapor. That is, a gas does not prevent another gas from penetrating the space it occupies. We may make this clear to ourselves by saying that gaseous or vaporous bodies may to a certain extent interpenetrate each other.
I will now show you another phenomenon which will illustrate one more relation of heat to certain facts. We have here in the left hand tube, air which is in equilibrium with the outer air with which we are always surrounded. I must remind you that this outer air surrounding us is always under a certain pressure, the usual atmospheric pressure, and it exerts this pressure on us. Thus, we can say that air inside the left hand tube is under the same pressure as the outer air itself, which fact is shown by the similar level of mercury in the right and left hand tubes. You can see that on both right and left hand sides the mercury column is at the same height, and that since here on the right the tube is open to the atmosphere the air in the closed tube is at atmospheric pressure. We will now alter the conditions by bringing pressure on the air in the left hand tube, (\(2\) × \(p\)). By doing this we have added to the usual atmospheric pressure, the pressure due to the higher mercury column. That is, we have simply added the weight of the mercury from here to here. (Fig. 1b from \(a\) to \(b\)). By thus increasing the pressure exerted on this air by the pressure corresponding to the weight of the mercury column, the volume of the air in the left hand tube is, as you can see, made smaller. We can therefore say when we increase the pressure on the gas its volume decreases. We must extend this and consider it a general phenomenon that the space occupied by a gas and the pressure exerted on it have an inverse ratio to each other. The greater the pressure the smaller the volume, and the greater the volume the smaller must be the pressure acting on the gas. We can express this in the form of an equation where the volume \(V_1\) divided by the volume \(V_2\) equals the pressure \(P_2\) divided by the pressure \(P_1\).$$V_1:V_2 = P_2:P_2$$
From which it follows:$$V_1 · P_1 = V_2 · P_2$$
This expresses a relatively general law (we have to say relative and will see why later.) This may be stated as follows: volume and pressure of gases are so related that the volume-pressure product is a constant at constant temperature. As we have said, such phenomena as these must be placed side by side if we are to approach the nature of heat. And now, since our considerations are to be thought of as a basis for pedagogy we must consider the matter from two aspects. On the one hand, we must build up a knowledge of the method of thinking of modern physics and on the other, we must become acquainted with what must happen if we are to throw aside certain obstacles that modern physics places in the path to a real understanding of the nature of heat.
Please picture vividly to ourselves that when we consider the nature of heat we are necessarily dealing at the same time with volume increases, that is with changes in space and with alterations of pressure. In other words, mechanical facts meet us in our consideration of heat. I have to speak repeatedly in detail of these things although it is not customary to do this. Space changes, pressure changes. Mechanical facts meet us.
Now for physics, these facts that meet us when we consider heat are purely and simply mechanical facts. These mechanical occurrences are, as it were, the milieu in which heat is observed. The being of heat is left, so to speak, in the realm of the unknown and attention is focused on the mechanical phenomena which play themselves out under its influence. Since the perception of heat is alleged to be purely a subjective thing, the expansion of mercury, say, accompanying change of heat condition and of sensation of heat, is considered as something belonging in the realm of the mechanical. The dependence of gas pressure, for instance, on the temperature, which we will consider further, is thought of as essentially mechanical and the being of heat is left out of consideration. We saw yesterday that there is a good reason for this. For we saw that when we attempt to calculate heat, difficulties arise in the usual calculations and that we cannot, for example, handle the third power of the temperature in the same way as the third power of an ordinary quantity in space. And since modern physics has not appreciated the importance of the higher powers of the temperature, it has simply stricken them out of the expansion formulae I mentioned to you in former lectures.
Now you need only consider the following. You need consider only that in the sphere of outer nature heat always appears in external mechanical phenomena, primarily in space phenomena. Space phenomena are there to begin with and in them the heat appears. This it is, my dear friends, that constrains us to think of heat as we do of lines in space and that leads us to proceed from the first power of extension in space to the second power of the extension.
When we observe the first power of the extension, the line, and we wish to go over to the second power, we have to go out of the line. That is, we must add a second dimension to the first. The standard of measurement of the second power has to be thought of as entirely different from that of the first power. We have to proceed in an entirely similar fashion when we consider a temperature condition. The first power is, so to speak, present in the expansion. Change of temperature and expansion are so related that they may be expressed by rectilinear coordination (Fig. 2). I am obliged, when I wish to make the graph representing change in expansion with change in temperature, to add the axis of abscissae to the axis of ordinates. But this makes it necessary to consider what is appearing as temperature not as a first power but as a second power, and the second power as a third. When we deal with the third power of the temperature, we can no longer stay in our ordinary space. A simple consideration, dealing it is true with rather subtle distinctions, will show you that in dealing with the heat manifesting itself as the third power, we cannot limit ourselves to the three directions of space. It will show you how, the moment we deal with the third power, we are obliged, so far as heat effects are concerned, to go out of space.
In order to explain the phenomena, modern physics sets itself the problem of doing so and remaining within the three dimensional space.
You see, here we have an important point where physical science has to cross a kind of Rubicon to a higher view of the world. And one is obliged to emphasize the fact that since so little attempt is made to attain clarity at this point, a corresponding lack enters into the comprehensive world view.
Imagine to yourselves that physicists would so present these matters to their students as to show that one must leave ordinary space in which mechanical phenomena play when heat phenomena are to be observed. In such a case, these teachers of physics would call forth in their students, who are intelligent people since they find themselves able to study the subject, the idea that a person cannot really know it without leaving the three dimensional space. Then it would be much easier to place a higher world-view before people. For people in general, even if they were not students of physics, would say, We cannot form a judgment on the matter, but those who have studied know that the human being must rise through the physics of space to other relations than the purely spatial relations. Therefore so much depends on our getting into this science such ideas as those put forth in our considerations here. Then what is investigated would have an effect on a spiritually founded world view among people in general quite different from what it has now. The physicist announces that he explains all phenomena by means of purely mechanical facts. This causes people to say, Well, there are only mechanical facts in space. Life must be a mechanical thing, soul phenomena must be mechanical and spiritual things must be mechanical. Exact sciences will not admit the possibility of a spiritual foundation for the world. And exact science works as an especially powerful authority because they are not familiar with it. What people know, they pass their own judgment on and do not permit it to exercise such an authority. What they do not know they accept on authority. If more were done to popularize the so-called rigidly exact science, the authority of some of those who sit entrenched in possession of this exact science would practically disappear.
During the course of the 19th century there was added to the facts that we have already observed, another one of which I have spoken briefly. This is that mechanical phenomena not only appear in connection with the phenomena of heat, but that heat can be transformed into mechanical phenomena. This process you see in the ordinary steam locomotive where heat is applied and forward motion results. Also mechanical processes, friction and the like, can be transformed back again into heat since the mechanical processes, as it is said, bring about the appearance of heat. Thus mechanical processes and heat processes may be mutually transformed into each other.
We will sketch the matter today in a preliminary fashion and go into the details pertaining to this realm in subsequent lectures.
Further, it has been found that not only heat but electrical and chemical processes may be changed into mechanical processes And from this has been developed what has been called during the 19th century the mechanical theory of heat.
This mechanical theory of heat has as its principal postulate that heat and mechanical effects are mutually convertible one into the other. Now suppose we consider this idea somewhat closely. I am unable to avoid for you the consideration of these elementary things of the realm of physics. If we pass by the elementary things in our basic consideration, we will have to give up attaining any clarity in this realm of heat. We must therefore ask the questions: what does it really mean then when I say: Heat as it is applied in the steam engine shows itself as motion, as mechanical work? What does it mean when I draw from this idea: through heat, mechanical work is produced in the external world? Let us distinguish clearly between what we can establish as fact and the ideas which we add to these facts. We can establish the fact that a process subsequently is revealed as mechanical work, or shows itself as a mechanical process. Then the conclusion is drawn that the heat process, the heat as such, has been changed into a mechanical thing, into work.
Well now, my dear friends, if I come into this room and find the temperature such that I am comfortable, I may think to myself, perhaps unconsciously without saying it in words: In this room it is comfortable. I sit down at the desk and write something. Then following the same course of reasoning as has given rise to the mechanical theory of heat, I would say: I came into the room, the heat condition worked on me and what I wrote down is a consequence of this heat condition. Speaking in a certain sense I might say that if I had found the place cold like a cellar, I would have hurried out and would not have done this work of writing. If now I add to the above the conclusion that the heat conducted to me has been changed into the work I did, then obviously something has been left out of my thinking. I have left out all that which can only take place through myself. If I am to comprehend the whole reality I must insert into my judgment of it this which I have left out. The question now arises: When the corresponding conclusion is drawn in the realm of heat, by assuming that the motion of the locomotive is simply the transformed heat from the boiler, have I not fallen into the error noted above? That is, have I not committed the same fallacy as when I speak of a transformation of heat into an effect which can only take place because I myself am part of the picture? It may appear to be trivial to direct attention to such a thing as this, but it is just these trivialities that have been completely forgotten in the entire mechanical theory of heat. What is more, enormously important things depend on this. Two things are bound together here. First, when we pass over from the mechanical realm into the realm where heat is active we really have to leave three dimensional space, and then we have to consider that when external nature is observed, we simply do not have that which is interpolated in the case, where heat is changed over into my writing. When heat is changed into my writing, I can note from observation of my external bodily nature that something has been interpolated in the process. Suppose however, that I simply consider the fact that I must leave three dimensional space in order to relate the transformation of heat into mechanical effects. Then I can say, perhaps the most important factor involved in this change plays its part outside of three dimensional space. In the example that concerned myself which I gave you, the manner in which I entered into the process took place outside of three dimensions. And when I speak of simple transformation of heat into work I am guilty of the same superficiality as when I consider transformation of heat into a piece of written work and leave myself out.
This, however, leads to a very weighty consequence. For it requires me to consider in external nature even lifeless inorganic nature, a being not manifested in three dimensional space. This being, as it were, rules behind the three dimensions. Now this is very fundamental in relation to our studies of heat itself.
Since we have outlined the fundamentals of our conception of the realm of heat, we may look back again on something we have already indicated, namely on man's own relation to heat. We may compare the perception of heat to perception in other realms. I have already called attention to the fact that, for instance, when we perceive light, we note this perception of light to be bound up with a special organ. This organ is simply inserted into our body and we cannot, therefore, speak of being related to color and light with our whole organism, but our relation to it concerns a part of us only. Likewise with acoustical or sound phenomena, we are related to them with a portion of our organism, namely the organ of hearing. To the being of heat we are related through our entire organism. This fact, however, conditions our relation to the being of heat. We are related to it with our entire organism. And when we look more closely, when we try, as it were, to express these facts in terms of human consciousness, we are obliged to say, We are really ourselves this heat being. In so far as we are men moving around in space, we are ourselves this heat being. Imagine the temperature were to be raised a couple of hundred degrees; at that moment we could no longer be identical with it, and the same thing applies if you imagine it lowered several hundred degrees. Thus the heat condition belongs to that in which we continually live, but do not take up into our consciousness. We experience it as independent beings, but we do not experience it consciously. Only when some variation from the normal condition occurs, does it take conscious form.
Now with this fact a more inclusive one may be connected. It is this. You may say to yourselves when you contact a warm object and perceive the heat condition by means of your organism, that you can do it with the tip of your tongue, with the tip of your finger, you can do it with other parts of your organism: with the lobes of your ears, let us say. In fact, you can perceive the heat condition with your entire organism. But there is something else you can perceive with your entire organism. You can perceive anything exerting pressure. And here again, you are not limited strictly as you are in the case of the eye and color perception to a certain member of your entire organism. If would be very convenient if our heads, at least, were an exception to this rule of pressure perception; we would not then be made so uncomfortable from a rap on the head.
We can say there is an inner kinship between the nature of our relationship to the outer world perceived as heat and perceived as pressure. We have today spoken of pressure volume relations. We come back now to our own organism and find an inner kinship between our relation to heat and to pressure. Such a fact must be considered as a groundwork for what will follow.
But there is something else that must be taken into account as a preliminary to further observations. You know that in the most popular text books of physiology, a good deal of emphasis is laid on the fact that we have certain organs within our bodies by means of which we perceive the usual sense qualities. We have the eye for color, the ear for sound, the organ of taste for certain chemical processes, etc. We have spread over our entire organism, as it were, the undifferentiated heat organ, and the undifferentiated pressure organ.
Now, usually, attention is drawn to the fact that there are certain other things of which we are aware but for which we have no organs. Magnetism and electricity are known to us only through their effects and stand, as it were, outside of us, not immediately perceived. It is said sometimes that if we imagine our eyes were electrically sensitive instead of light sensitive, then when we turned them towards a telegraph wire we would perceive the streaming electricity in it. Electricity would be known not merely by its effects, but like light and color, would be immediately perceived. We cannot do this. We must therefore say: electricity is an example of something for whose immediate perception we have no organ. There are aspects of nature, thus, for which we have organs and aspects of nature for which we do not have organs. So it is said.
The question is whether perhaps a more unbiased observer would not come to a different conclusion from those whose view is expressed above. You all know, my dear friends, that what we call our ordinary passive concepts through which we apprehend the world, are closely bound up with the impressions received through the eye, the ear and somewhat less so with taste and smell impressions. If you will simply consider language, you may draw from it the summation of your conceptual life, and you will become aware that the words themselves used to represent our ideas are residues of our sense impressions. Even when we speak the very abstract word Sein (being), the derivation is from Ich habe gesehen, (I have seen.) What I have seen I can speak of as possessing being. In being there is included what has been seen. Now without becoming completely materialistic (and we will see later why it is not necessary to become so), it may be said that our conceptual world is really a kind of residue of seeing and hearing and to a lesser extent of smelling and tasting. (Those last two enter less into our higher sense impressions.) Through the intimate connection between our consciousness and our sense impressions, this consciousness is enabled to take up the passive concept world.
But within the soul nature, from another side, comes the will, and you remember how I have often told you in these anthroposophical lectures that man is really asleep so far as his will is concerned. He is, properly considered, awake only in the passive conceptual realm. What you will, you apprehend, only through these ideas or concepts. You have the idea. I will raise this glass. Now, in so far as your mental act contains ideas, it is a residue of sense impressions. You place before yourself in thought something which belongs entirely in the realm of the seen, and when you think of it, you have an image of something seen. Such an immediately derived image you cannot create from a will process proper, from what happens when you stretch out your arm and actually grasp the glass with your hand and raise it. That act is entirely outside of your consciousness. You are not aware of what happens between your consciousness and the delicate processes in your arm. Our unconsciousness of it is as complete as our unconsciousness between falling asleep and waking up. But something really is there and takes place, and can its existence be denied simply because it does not enter our consciousness? Those processes must be intimately bound up with us as human beings, because after all, it is we who raise the glass. Thus we are led in considering our human nature from that which is immediately alive in consciousness to will processes taking place, as it were, outside of consciousness. (Fig. 3) Imagine to yourselves that everything above this line is in the realm of consciousness. What is underneath is in the realm of will and is outside of consciousness. Starting from this point we proceed to the outer phenomena of nature and find our eye intimately connected with color phenomena, something which we can consciously apprehend; we find our ear intimately connected with sound, as something we can consciously apprehend. Tasting and smelling are, however, apprehended in a more dreamlike way. We have here something which is in the realm of consciousness and yet is intimately bound up with the outer world.
If now, we go to magnetic and electrical phenomena, the entity which is active in these is withdrawn from us in contrast with those phenomena of nature which have immediate connection with us through certain organs. This entity escapes us. Therefore, say the physicists and physiologists: we have no organ for it; it is cut off from us. It lies outside us. (Fig. 3 above) We have realms that we approach when we draw near the outer world the realms of light and heat. How do electrical phenomena escape us? We can trace no connection between them and any of our organs. Within us we have the results of our working over of light and sound phenomena as residues in the form of ideas. When, however, we plunge down (Fig. 3 below), our own being disappears from us into will.
I will now tell you something a bit paradoxical, but think it over until tomorrow. Imagine we were not living men, but living rainbows, and that our consciousness dwelt in the green portion of the spectrum. On the one side we would trail off into unconsciousness in the yellow and red and this would escape us inwardly like our will. If we were rainbows, we would not perceive green, because that we are in our beings, we do not perceive immediately; we live it. We would touch the border of the real inner when we tried, as it were, to pass from the green to the yellow. We would say: I, as a rainbow, approach my red portion, but cannot take it up as a real inner experience; I approach my blue-violet, but it escapes me. If we were thinking rainbows, we would thus live in the green and have on the one side a blue-violet pole and on the other side a yellow-red pole. Similarly, we now as men are placed with our consciousness between what escapes us as external natural phenomena in the form of electricity and as inner phenomena in the form of will.