Scientific Disciplines and Anthroposophy

GA 73a — 31 March 1920, Dornach

7. Questions following a lecture by E.A.K. Stockmeyer on “Anthroposophy and Physics”

Preliminary note: In his lecture, E.A.K. Stockmeyer had spoken, among other things, of warmth corresponding to will, light to imagination, chemistry to feeling, which feels the external within. The lecture was not written down; the stenographer merely recorded the following scheme written on the blackboard: “Life forces / chemical forces / light / warmth / gases / fluids / solids”.

Question: Conventional mathematics encompasses solids, liquids and gases in terms of shape, surface and direction of force. How do you imagine a mathematics of the thermal, chemical and life spheres?

Rudolf Steiner: Well, the first thing to do is to extend the field of mathematics in a way that is appropriate to the subject if we want to encompass higher fields, or I should say, even if we only want to encompass them in an analogous mathematical way.

If we consider that in the 19th century there arose the need to extend mathematics itself – I will mention only what has already been mentioned on other occasions, I believe only yesterday, that there arose the need to add to Euclidean non-Euclidean geometry, — when one considers that at that time the need arose to carry out calculations for higher manifolds than we usually do, then we already have a hint at extensions of mathematics. And we may say: When we consider ordinary ponderable matter, we do not come to use any appropriate application of other manifolds than that of the ordinary three-dimensional manifold.

But today there is still so little inclination to enter into an appropriate view of the fields of heat, chemical and life elements that the continuation of mathematical thinking into these fields is still very problematic today.

For example, there is absolutely no contradiction between the failure to recognize the essence of mass, as propagated by physicists, and the failure to consider the essence of the image of light as presented by Goethe. A reasonable physicist will of course reject the idea of considering the essence of things. However, this immediately leads to the dilemma: the physicist may refuse to go into the essence of things; but anyone who then, from the conventional physical, physical point of view, brews up a philosophy no longer just refuses to do so, but declares: one cannot penetrate into the essence of things at all.

And so we have [today a very one-sided view of the] earth, since in physics we are never concerned with mere geology, but with what results as a conclusion from such a single field for overall knowledge. Thus we are already dealing with harmful consequences of what has gradually emerged over time for physics, not mathematically, but as a mechanistic world view.

What Goethe means when he says that one should not actually speak of the essence of light, but should try to get to know the facts, the deeds and sufferings of light - for these, after all, give a complete description of the essence of light - is not at all identical with the rejection of the question as to the nature of the light, but precisely the indication that a correct, a real phenomenology - which is arranged in the sense that it was discussed here yesterday - ultimately gives a picture of the essence that is being considered. Insofar as it is and wants to be phenomenology and is correct phenomenology, insofar as it concerns the mechanistic field, it gives us a picture of the essence, namely of the essence of the phenomena.

And so one can indeed say: when it is not a matter of mechanical phenomena or of that which is merely mechanical in physical phenomena, when it is a matter of other areas than the mechanical, then the mechanistic view of these other areas of phenomena hinders any advance towards an actual essence of things that can be recognized by the human being. And in this respect it is necessary to emphasize the radical difference between such a phenomenology, as Goethe means and as it can be cultivated in Goetheanism, and what basically wants to dispense with delving into the essence of things.

This has nothing to do with any supposed advantage of the mechanistic method for the drive to dominate over nature. For, ladies and gentlemen, it is self-evident that in the very field in which there have been great triumphs in recent centuries, namely in the technical-mechanical field, the mechanistic part of knowledge of nature could provide a certain satisfaction of the urge to dominate nature. But just ask to what extent this urge to dominate nature has been left behind in other areas precisely because it has been rejected to penetrate to an equally profound level of knowledge as has been striven for in the mechanistic field.

The difference between the mechanistic field and those fields that start with the physical and then go up through the chemical to the organic and so on is not that in these higher fields one is dealing only with qualitative properties or the like, but the difference lies in the fact that what relates to the mechanistic field, to mechanistic physics, is simple, it can be observed, it is the most elementary. Therefore, we have also achieved a certain satisfaction of the instinct to dominate nature in this most elementary field.

But then the question arises: how do we satisfy this urge to dominate when we move into the higher realms that no longer follow mechanistic [laws]? And here we must certainly expect that there will also come times when our domination of nature extends a little beyond the merely mechanistic realm.

In the mechanistic field it is extremely easy, through lack of control, lack of control in the cognitive sense, to bring about, I would say, revenge of nature, revenge of reality. If someone builds a bridge for the railroad without proper knowledge of the mechanistic laws, then at some appropriate opportunity the bridge will collapse and the train will rush down the embankment. In this case, the reaction will immediately manifest itself in the form of an improper control of the cognitive drive. If the control has to relate to somewhat more complicated areas, which, however, must be taken not from the quantitative or the mechanistic, but must be taken precisely from the procedure of actually working out a phenomenology, then this proof is perhaps not always so easy. It can be said with a fair degree of certainty that a bridge built with a deficient cognitive drive will collapse after the third train has crossed it. But today it is not easy for a doctor to immediately recognize the connection between the cognitive drive and the domination of nature when a patient dies. It is less said that the doctor has cured someone to death than that someone has built a bad bridge.

In short, one should be a little more sparing with this emphasis on the urge to dominate nature, purely on the basis of the well-known fact that it is only in the field of mechanistic technology that such a satisfaction of the urge to dominate has become possible through the mechanistic view of nature. Other views of nature will be able to give a completely different satisfaction of the urge to dominate. For example, I will just point out – I already pointed this out from a different point of view yesterday – that one can never build a bridge from the mechanistic world view to the human being, but that the bridge is immediately built when a correct phenomenology is applied.

In Goethe's Theory of Colors, you not only have the presentation of physiological phenomena, the presentation of physical phenomena, but you have the whole field transferred to the sensual-moral effect of colors, where the phenomenon, the whole field, is immediately brought to the human being. And from this area, to which Goethe is still pointing – the sensual-moral effect of colors – one comes, if one continues to work spiritually, to the complete area of human knowledge and thus again to the complete area of knowledge of nature.

And in a way it would perhaps be good if attention were drawn to the fact that a large part of what humanity experiences today as decadent phenomena within European culture is connected with the fact that we have only brought it to a satisfaction of the urge to dominate on one side, on the mechanistic side. We have indeed come a long way in this respect; not only have we built railways and created telegraphs and telephones, until we came to wireless telegraphy, but we have even gone so far in satisfying the urge to dominate that we have destroyed large parts of Europe by concreting them over. We have taken it as far as destruction by thoroughly satisfying the urge to dominate.

It is now as follows: this satisfaction of the urge to dominate nature, which has led to destruction, was basically a straightforward continuation of the purely technical urge to dominate; it lay in the straightforward continuation. These things also belong to those which must now be thoroughly eradicated if the unhealthy expansion of the mechanistic view to encompass all physical phenomena is to be replaced by something that does not simply eliminate the truly specific nature of physical , but when one actually moves away from the mechanization of ideas, which, in their field, give a very good physics, to that which is specific to physical phenomena.

And here it must be pointed out that precisely this approach, which of course cannot be taken to its ultimate conclusions in one hour, that this approach will lead to an expansion of the mathematical field itself, out of the corresponding reality. We must realize that it is precisely out of the mechanistic confusion that such things have become possible, that over the last thirty, forty, fifty years all sorts of views have been put forward about the so-called ether. It was Planck, the physicist mentioned earlier in relation to another field, who finally came to the conclusion: If one wants to talk about the ether in physics at all, then one must not ascribe any material properties to it. One must not think of it materially. So physics has been pushed to the point of not ascribing any material properties to the ether.

What, then, are the actual errors in the ether ideas, in the ether concepts? Well, my dear audience, they did not consist at all in the fact that too little mathematics were done or something like that, but in the fact that one - because one was only inspired by the tendency to extend the mathematical over the specific extended to the specific physical, that one used wrong mathematics in formulas in which the effects of the ether also played a part, that one used the quantities in the same way as one uses them for ponderable matter. The moment we realize that the possibility of inserting ordinary quantities into mathematical formulas ceases when we enter the etheric realm, the impulse will arise to seek a real extension of mathematics itself. You see, one only needs to point out the twofold aspect. The physicist Planck says: If one wants to talk about the ether at all in physics, then in any case one must not ascribe any material properties to it. And in Einstein's theory of relativity, or in relativity theory in general, one found it necessary to eliminate the ether altogether.

Now, the ether cannot be canceled! This is something that I can only hint at now. Rather, the point is that the moment we move from the ether to our physical formulas, that is, to the mathematical formulas that are applied to physics, we are forced to insert negative quantities into the formulas.

We have to insert these quantities negatively - just as we also move from positive to negative quantities in formal physics - simply because, by advancing from positive matters to zero, we have in the ether neither a nothing - what Einstein means - nor a pure negative that must be thought of as a something - as Planck says - but because the ether must be thought of as something that is endowed with properties that are as opposed to the properties of matter as negative numbers are to positive ones. And here, even before we come to realize the character of the negative itself, the pure extension of the mathematical [into the negative] – one may now dispute what a negative quantity is – gains a certain significance for reality, even before we come to realize the character of the negative itself, the extension of the numerical line into the negative gains a certain significance for reality.

Of course, I am well aware that in the 19th century there was a significant dispute in the field of mathematics between those who saw something qualitative in the positive and negative signs, while others saw only a subtrahend in the negative signs, for whom the negative minuend is missing. But that is not the point. The point is that we may indeed be obliged to follow the same path in physics itself that we follow in formal mathematics from the positive to the negative, by moving from ponderable effects to ethereal effects. Then we have to see what will come out of the formulas if we decide to treat the quantities in this way.

And then it will come about, despite the fact that much solid work has been and can be done in formal mathematics, that we are simply obliged to use imaginary quantities in physics as well, for the positive and negative quantities. But in this way we come to a mediation with the quantities in nature.

I am well aware that this has only been very briefly outlined, summarized in just a few words. But I must nevertheless draw attention to the fact that in progressing from ponderable matter up to where one comes to the life forces, one is compelled everywhere to insert negative quantities into the formulas, precisely for the reversal of the material quantitative in general, and that then, as soon as one goes beyond life, one is compelled to move from mere negative quantities to imaginary quantities. But then you don't just have formal quantities, but quantities that now have the property that they no longer refer to the [positive or negative] material, but to the substantial, which thus qualitatively-internally relates to both the ethereal as well as to the ponderable, just as the imaginary number line relates to the positive and negative numbers, to the real number line - so that one can indeed connect what one has in formal mathematics with certain areas of reality.

It would be very unfortunate if attempts to approximate human ideas to reality, to bring human ideas to submerge into reality, were to fail because of the trivial notion that what truly rational physics has to offer would satisfy human instinct for domination of nature to a lesser extent. It would satisfy him more than the so glorified application of the mechanistic world view to mechanistic technology. This mechanistic technology has certainly brought great things to humanity in the development of culture. But those who are always talking about how calculating physics – that is, physics calculated in the way that physics has calculated up to now – how physics has brought glorious progress in the field of natural science and in the technical field, they should consider that other fields may have suffered greatly from this mere focusing of attention on the purely technical field. And to escape from the plight, from the decadence into which mere technical control and its foundations, mere mechanistic knowledge, has brought us, to escape from this plight, from this decadence, we would be in great need of a leaning towards a physics that really cannot speak in the same way of a rejection of the knowledge of the essence, as it must indeed apply to the mechanical field, which is accessible to mechanistic knowledge.

Yes, you see, it is so easy for the mechanical field to dispense with essence because this essence, I would say, is so obvious, because it is spread out in space. And it is somewhat more difficult to achieve the same in the field of physics as in the field of the mechanistic. Hence all the talk of not getting into the essence. It is easy for the physicist to simply refuse to recognize the essential if he only wants to think in mechanistic terms. Because behind what today's formulas, as they are used today to express this [mechanistic] mathematically, there is no essence. The essence only begins where one no longer just applies these formulas, but where one penetrates into the mathematical essence itself.

That was just to answer the question of how one might think of the mathematical in an extended way beyond the imponderable.