The Rudolf Steiner Archive

24. Truths of Spiritual Science — A Few Thoughts on “Calculating Horses”

Question and Answer

[ 1 ] The question has been raised as to what lies behind the now-famous calculating horses of Elberfeld and the horses that display other forms of wisdom. Let me note from the outset: I am not familiar with the events surrounding the calculating and otherwise performing horses of Elberfeld, since I was not there; however, I did become acquainted with Mr. von Osten’s very similar horse, “Clever Hans,” who caused such a sensation in Berlin for a long time. One might actually be a little surprised that, while at the time virtually all of Berlin was interested in this “Clever Hans,” this interest was able to fade so quickly, when you really think about it. The fleeting nature of interest today is particularly evident here. There were all sorts of other interesting things to experience there as well. At first, anyone hearing about it for the first time was quite skeptical; until they decided to take a closer look at the facts, because there were indeed quite credible reports that “Clever Hans” was performing feats that were only surpassed in degree. He had already performed complex calculations, extracted roots, and so on; he also found the correct card in a card game and so on. It can be said that, little by little, it became impossible to deny that something extraordinary was going on. The owner turned to outsiders, called in experts, animal trainers, and so on. A commission of philosophical scholars was invited.

[ 2 ] And finally, a treatise has been published, written by a certain Dr. [Pfungst]. It is quite an interesting piece. After rejecting everything the people present had said, the philologist arrived at the following conclusion: Of course, “clever Hans” cannot actually do the math, but he is influenced by Mr. von Osten or others who present him with the task. And these influences now had to be explained in as materialistic a way as possible.

[ 3 ] The idea that something could truly have had a soul-to-soul effect was no longer acceptable to the professors of our time; for today’s philologists have already completely forgotten about the soul. Well, these philologists did assume influences existed—specifically, influences of the most materialistic nature possible. They assumed that people make very subtle gestures, and that these are then transmitted to the animal. For example, one instructs the animal to find the square root of 16. One makes subtle gestures that express what one has in mind—that is, what the root of 16 is; the horse perceives these gestures and, by tapping its hoof, indicates the root of 16. This has been described in quite realistic terms.

[ 4 ] So they turned to true animal experts for help. Yet even these experts, who were well versed in the subtleties of gestures, could not identify any subtleties that might influence the animal. The people who truly understood how the animal follows the gaze could find no evidence of such gestures. So one must conclude: A person can perceive these gestures only if they have worked for years in a physiological or philological laboratory. The ingenious explanation was offered that only a private lecturer who has worked for years in a laboratory can perceive what the horses perceive. But materialism was saved. It is truly a masterstroke that one denies any psychological influence, yet now claims that a horse can already know what one can only discover through years of work in a physiological laboratory.

[ 5 ] We need to take this matter more seriously. I would like to try to present to you what has become clear to me; but I must emphatically point out that what I am about to say—precisely because it is so extraordinarily complicated—can be described as nothing other than a hypothesis; a hypothesis, however, which I believe further occult research will confirm. When one considers the matter in this way, it becomes clear that it is indeed extraordinarily complicated, that we are truly dealing with phenomena of a highly peculiar nature, and that I actually dare only to formulate a kind of hypothesis, an occult hypothesis about the matter—one that I can form from the observations I was able to make when I saw how Mr. von Osten interacted with the horse. I am certain it will later be confirmed by occult research.

[ 6 ] For it became clear to me that mathematical thinking—the entire process of mathematical imagination—is something far more objective than people generally suppose; that the entire process of mathematical imagination is actually something that functions like a kind of automaton, and in the following way: The reasons for this mathematical conception are that the entire mathematical conception lies in the constitution of the Earth itself. For the Earth is not that undifferentiated entity that people theoretically imagine it to be. It is extraordinarily finely structured and acts from within upon the beings that inhabit it.

[ 7 ] In humans, mathematical aptitude depends primarily on the three canals in the middle ear that are involved in balance, and there is a kind of connection in humans between this organ in the ear and the entire nervous system comprising the spinal cord. For when a person makes mathematical judgments, we can see that he is, much more than is commonly believed, an observer. Rather, the mathematical judgments form themselves, and in the field of mathematics in particular, a person is more of a kind of automaton.

[ 8 ] That is why one of the peculiarities of mathematics is that one truly feels the urge to turn the entire field of mathematics into a kind of automaton. In our number system, one counts only to ten, then counts the tens, and so on. This internally automates the entire process of calculation. There really is an inner regularity in numbers that is bound to the Earth in a kind of mathematical automatism. In human beings, this automatism does not have such a strong effect, because human beings are set apart from this automatism, and the power of judgment does intervene and holds back the entire mathematical automatism.

[ 9 ] Now it is remarkable how the entire spiritual atmosphere of the horse in the case of “Clever Hans” works in such a way that, simply by touching anything on this horse, the entire sphere of the Earth is, as it were, set in motion … and due to the different position of its spinal cord compared to that of humans, this horse participates in the life of the Earth. And what is actually thinking here is, in essence, the Earth; it thinks through the horse’s entire system. So that one really has the impression: On the one hand, one is dealing with the Master from the East, who does not need to work out the individual arithmetic problems, but who merely touches upon something mathematical; thereby he integrates himself into the Earth’s mathematical automaton; which transfers itself to the horse’s spinal cord, and the horse can now express it entirely on its own, entirely through its soul, but the Earth is the mediator of the soul. Never has the mediating role of the mathematical automaton come so strongly to my consciousness as in this case of “Clever Hans.”

[ 10 ] This is how the interaction between the spiritual essence of the Lord of the East and the spiritual essence of the entire Earth manifests itself. I couldn’t help but think: If, in a telegraph apparatus, one connects the wire all the way to the Earth, then one needs only a single wire to the other apparatus. The Earth as a whole participates in this process. All one needs to do is pull the connecting wire: then the Earth itself becomes the cooperating apparatus. In the mechanical realm, it works such that when one enters the relevant signal on the keys of one apparatus, the signal reappears on the other apparatus. But when one is dealing with that which fills the earth—the mathematical automaton—a connection forms that can truly be called subterranean, a kind of conduit between the earth and the one who is in contact with the horse. The animal must allow itself to be integrated into the entire apparatus of the earth.

[ 11 ] For comparison, let me refer to what I observed regarding this many years ago. I got to know several young boys—one after another, not all at once. One of them was a rather dim-witted fellow in every respect. But when given a problem—a math example, for instance, finding the square root of a six- or seven-digit number—he was able to solve it. He could multiply long sequences of numbers together. A distinguished mathematics professor gave him a problem: to square a four-digit number. The professor had prepared the problem. The boy answered quickly, extracting roots from ten- to twelve-digit numbers. Suddenly he became restless; it wasn’t working, he grew frantic; he felt so strangely trapped inside this mathematical automaton: the professor had squared the wrong number.

[ 12 ] It must indeed be taken into account that the Earth plays a decisive role in this mental activity. And if we succeed in establishing contact through special psychological connections that exist between the trainer and the horse—which is attached to the human with a certain affection—then no conscious thought is necessary to solve the given task. Then a math problem can be presented that the horse does not have in its head. If the horse has been taught only the program: That is sufficient, because all of mathematics forms a unified whole, and therefore all roots are interconnected. Since everything in mathematics is interconnected, once the animal has been trained to this point, all one needs to do to express something is to give a signal, and the result will be exactly what was signaled. This is based on the connection between the human and the animal soul; the earth acts as the mediator. On a conscious level, the animal is preoccupied with the candies one offers it; while in its conscious life it lives only for the candy, in its subconscious it produces the most curious things. All these processes take place entirely in the subconscious realms. The horse, in its conscious mind, knows nothing of any of this. Nor does it have time, in the delight that the candy brings it as it constantly nibbles on it, to observe anything else.