The Rudolf Steiner Archive

7. Question following E.A.K. Stockmeyer’s lecture on “Anthroposophy and Physics”

Preliminary Remark: In his lecture, E.A.K. Stockmeyer had spoken, among other things, about how heat corresponds to the will, light to the imagination, and chemistry to the feeling that internally mirrors the external world. The lecture was not transcribed; the stenographer merely recorded the following outline written on the blackboard: “Life forces / chemical forces / light / heat / gases / liquids / solids.”

Question: Conventional mathematics deals with solids, liquids, and gases in terms of shape, surface area, and the direction of forces. How do you envision a mathematics of the realm of heat, chemistry, and life?

[ 1 ] Rudolf Steiner: Well, the first issue here is certainly that the field of mathematics as such must be expanded in an appropriate manner if one wishes to encompass higher realms—I would say—even if only analogously through mathematics.

[ 2 ] When one considers that, in the 19th century, a need arose to expand mathematics itself—I just want to mention what has already been mentioned on other occasions, I believe just yesterday, that the need arose to supplement Euclidean geometry with non-Euclidean geometry—if one considers that at that time the need arose to perform calculations for higher-dimensional manifolds than we usually deal with, then we already have an indication of extensions of mathematics. And we may well say: When we consider ordinary ponderable matter, we do not find any appropriate application for manifolds other than the ordinary three-dimensional manifold.

[ 3 ] However, there is so little inclination today to adopt a proper understanding of the fields of heat, chemistry, and the elements of life that extending mathematical thinking into these fields remains, even today, a truly problematic endeavor.

[ 4 ] For example, there is certainly no contradiction between the failure to recognize the nature of mass, as propagated by physicists, and the failure to address, for instance, the nature or image of light as presented by Goethe. The physicist, if he is reasonable, will of course refuse to delve into the nature of things. However, this immediately gives rise to a dilemma: The physicist may refuse to delve into the essence of things; but the one who today concocts a philosophy out of the common physical, scientific worldview no longer merely refuses to do so—he declares: One simply cannot penetrate the essence of things at all.

[ 5 ] And so we [today have a very one-sided view of the] Earth, since in physics we can never deal merely with geology, but rather with the conclusions that arise from such an individual field for our overall understanding. Thus, we are already dealing with the harmful consequences of what has gradually emerged for physics over time—not mathematically, but as a mechanistic worldview.

[ 6 ] What Goethe means when he says that one should not really speak of the essence of light, but should instead try to understand the facts, the actions and sufferings of light—for these, after all, provide a complete description of the essence of light— this is by no means identical with a rejection of the question regarding the nature of light, but rather a pointed indication that a correct, a true phenomenology—organized in the sense discussed here yesterday—ultimately provides precisely a picture of the nature in question. After all, [mechanics]—insofar as it is and intends to be phenomenology, and is true phenomenology as far as the mechanistic realm is concerned—does indeed provide a picture of the essence, namely, of the essence of phenomena.

[ 7 ] And so one can already say: If we are not dealing with mechanical phenomena or with that which is merely mechanical even in physical phenomena—if we are dealing with realms other than the mechanical—then the mechanistic view of these other realms of phenomena becomes an obstacle to advancing toward a true essence of things that is recognizable to human beings. And in this respect, it is necessary to emphasize the radical difference between a phenomenology such as Goethe conceives of—and as it can be cultivated in Goetheanism—and that which, in principle, seeks to refrain from addressing the essence of things.

[ 8 ] This, in turn, has absolutely nothing to do with any supposed advantage of the mechanistic method—for example, in terms of the drive to dominate nature. For, ladies and gentlemen, it goes without saying that in the very field where the great triumphs of the past centuries have occurred—namely, the technical-mechanical field—the mechanistic aspect of the understanding of nature, as its foundation, could provide a certain satisfaction of the drive to dominate nature. But one need only ask to what extent this drive to dominate nature has lagged behind in other fields, precisely because we have refused to advance to the same level of understanding in those areas as we have strived for in the mechanistic realm.

[ 9 ] The difference between the mechanistic realm and those realms that begin with the physical and then proceed through the chemical to the organic and so on—the difference does not lie in the fact that, in these higher realms, one deals only with [qualitative] properties or the like, but rather that what pertains to the mechanistic realm—to mechanistic physics—is simple; it allows us to observe what is most elementary. Therefore, even in this most elementary realm, we have managed to satisfy the drive to master nature to a certain extent.

[ 10 ] But this raises the question: How can we satisfy this drive for domination as we move into higher realms that no longer follow mechanistic [laws]? And there we will certainly have to reckon with the fact that there will indeed be times when our mastery of nature extends somewhat beyond the purely mechanistic realm.

[ 11 ] In the realm of mechanics, it is extraordinarily easy to bring about—through a lack of mastery, a lack of epistemological mastery over nature—well, I would say, nature’s revenge, reality’s revenge. If someone builds a railway bridge without a proper understanding of the laws of mechanics, the bridge will collapse at the first opportunity, and the train will plunge down the embankment. This immediately triggers a reaction stemming from a misguided exercise of the drive for knowledge. When this exercise must apply to somewhat more complex fields—fields that must be approached not from a quantitative or mechanistic perspective, but rather through the process of truly developing a phenomenology—then this demonstration may not always be so straightforward. One can say with a fair degree of certainty that, under certain circumstances, a bridge will collapse after the third train crosses it if that bridge was built with a deficient drive for knowledge. But today, one would not readily decide, when someone dies under a doctor’s care, to immediately establish the connection between the drive for knowledge and the mastery of nature in the same way. It is less common to say that a doctor has “cured” someone to death than to say that someone built a bad bridge.

[ 12 ] In short, one should be a bit more cautious about emphasizing this drive to dominate nature, based solely on the well-known fact that it is only in the realm of mechanistic technology that such satisfaction of the drive to dominate has become possible through the mechanistic view of nature. Other views of nature will still be able to provide a completely different form of satisfaction for the drive to dominate. For example, I would just like to point out—as I already did yesterday from a different perspective—that one can never bridge the gap from the mechanistic worldview to the human being, but that the bridge is immediately established when a proper phenomenology is applied.

[ 13 ] In Goethe’s *Theory of Colors*, you find not only a description of physiological phenomena and physical phenomena, but you also see that the entire field has been extended to include the sensory-moral effects of colors, where the phenomenon—the entire field—is immediately brought into relation with the human being. And from this realm—the sensory-moral effects of colors—to which Goethe still alludes, one arrives, by continuing to work within the humanities, at the complete realm of human knowledge and, through that, once again at the complete realm of knowledge of nature.

[ 14 ] And in a certain sense, it might be good to point out today that a large part of what humanity currently experiences as signs of decadence within European culture is connected to the fact that we have managed to satisfy the drive for domination only on one side—the mechanistic side. We have indeed come quite far in this regard—not only in building railroads, installing telegraphs and telephones, and advancing to wireless telegraphy, but we have even taken this satisfaction of the drive for domination so far that we have encased large parts of Europe in concrete, that we have destroyed them. We have brought about destruction through the thorough satisfaction of the drive to dominate.

[ 15 ] The fact is this: this satisfaction of the drive to dominate nature—which has led to its destruction—was, after all, essentially a direct continuation of the purely technical drive to dominate; it lay in that direct continuation. These things also belong to those that must now be thoroughly eradicated if the unhealthy expansion of the mechanistic view of all physical phenomena is to be replaced by something that does not simply obliterate what is truly specific to physical phenomena by flooding everything with mechanistic concepts, but rather when one actually moves away from the mechanistic nature of these concepts—which, in their own field, do indeed yield quite good physics—toward that which is specific to physical phenomena.

[ 16 ] And it must be pointed out that this very approach—which, of course, cannot be carried through to its ultimate consequences in a single hour—will lead to an expansion of the field of mathematics itself, based on the corresponding reality. We must be clear that it is precisely out of this mechanistic confusion that such things have become possible—that, in essence, all manner of views regarding the so-called ether have been put forward over the course of the last thirty, forty, or fifty years. It was the physicist Planck—mentioned earlier in connection with another field—who finally brought himself to formulate the following: If one wishes to speak of the ether in physics at all, one must in any case not attribute material properties to it. — One must not conceive of it as material. Physics has thus been compelled to refrain from attributing material properties to the ether.

[ 17 ] What, then, are the actual errors in the ideas about the ether, in the concepts of the ether? Well, ladies and gentlemen, they did not consist in doing too little mathematics or anything of that sort, but rather in the fact that — because one was driven solely by the tendency to extend mathematics beyond the realm of specific physics — applied the wrong kind of mathematics, inserting into the formulas—in which etheric effects also played a role—the quantities used for ponderable matter. The moment one realizes that the possibility of substituting the usual quantities into mathematical formulas ceases when we enter the realm of the ether, at that very moment the impulse will arise to seek a genuine extension of mathematics itself. You see, one need only point out two things. The physicist Planck says: If one wants to speak of the ether in physics at all, one must in any case not attribute any material properties to it. — And in Einstein’s theory of relativity—or in the theory of relativity in general—one found it necessary to eliminate the ether entirely.

[ 18 ] Now, the ether must not be dismissed! This is something I can only hint at for now. Rather, the point is that the moment we turn to the ether in our physical formulas—that is, in the mathematical formulas applied to physics—we are compelled to insert negative values into the formulas.

[ 19 ] We must treat these quantities as negative—just as we also move from positive to negative quantities in formal physics—simply because, as we proceed from positive matter toward nothingness, we have neither a “nothing” in the ether—as Einstein means—nor a pure negative that must be conceived as “something”—as Planck says—but rather because the ether must be conceived as something endowed with properties that are as opposite to the properties of matter as negative numbers are to positive ones. And here the mere extension of mathematics [into the negative]—one may now debate what a negative quantity is—here, even before one gets to the point of being clear about the nature of the negative itself, the extension of the number line into the negative already acquires a certain significance for reality as well.

[ 20 ] I am, of course, well aware that in the field of mathematics there was a significant controversy in the 19th century between those who saw something qualitative in the positive and negative signs, while others, in turn, saw in the negative signs merely a subtrahend, for whom the negative minuend is missing. But that is not the point; rather, the point is that we may in fact be compelled to follow the same path in physics that we take in formal mathematics—from the positive to the negative—by moving from ponderable effects to ethereal effects. Let us then examine what results will emerge from the formulas if we decide to treat the quantities in this way.

[ 21 ] And then, even though a great deal of solid work has been done—and can still be done—in formal mathematics regarding the validity of formal [imaginary] quantities, we will be compelled to use imaginary quantities in physics as well for positive and negative quantities. This, however, brings us into a relationship with the quantities found in the natural world.

[ 22 ] I am well aware that this is only a very brief outline, summarized in just a few words. But I must nevertheless point out that, as one progresses from ponderable matter all the way up to the realm of vital forces, one is compelled everywhere to introduce negative quantities into the formulas—precisely to represent the reversal of material quantity in general—and that, as soon as one moves beyond life, one is compelled to transition from mere negative quantities to imaginary quantities. There, however, one has not merely formal quantities, but quantities that now have the property of no longer relating to the [positive or negative] material, but to the substantial, which thus relates qualitatively and internally—both to the ethereal and to the ponderable—in the same way that the imaginary number line relates to the positive and negative numbers, to the real number line—so that one can in fact already connect what one has in formal mathematics with certain realms of reality.

[ 23 ] It would be deeply regrettable if attempts—which suggest bringing human ideas closer to reality, leading them to immerse themselves in reality—were to fail because of the trivial notion that what a truly rational physics offers would be less satisfying to humanity’s drive to master nature. It would satisfy that drive more than the much-glorified application of the mechanistic worldview to mechanistic technology. This mechanistic technology has certainly brought about magnificent achievements for humanity in the development of culture, on the one hand. But those who constantly speak of how “calculative physics”—that is, physics as it has been practiced up to now—has brought about glorious advances in the field of natural science and in the technical realm should consider that, under certain circumstances, other fields may very well have suffered greatly precisely because of this narrow focus on the purely technical realm. And in order to escape the misery, the decadence, into which the purely technical mastery and its foundations—the purely mechanistic understanding—have led us; in order to escape this misery, this decadence, we would indeed be in great need of turning toward a physics that truly cannot speak in the same way of a rejection of the knowledge of essence as must in fact apply to the mechanical realm, which is accessible to mechanistic knowledge.

[ 24 ] Yes, you see, the field of mechanics has it so easy to dispense with essence precisely because this essence—I would say—is so obvious, since it extends throughout space. And it is somewhat more difficult to make as much progress in the field of physics as in the field of mechanics. Hence all the talk about not being able to penetrate to the essence. The physicist has an easy time, if he merely wants to think mechanistically, of rejecting any understanding of essence. For behind what today’s formulas—as they are used today to express the [mechanistic] mathematically—there is no essence. Essence begins only where one no longer merely applies these formulas, but where one penetrates into the mathematical essence itself.

[ 25 ] This is merely to answer the question of how one might conceive of the mathematical in an expanded sense beyond imponderability.