On Divination and Synchronicity, some Views by Von Franz

History of Mathematics

If one looks at the history of mathematics one can see very clearly how the spirit becomes subjective. For instance, the natural integers or numbers, as you probably all know, were for the Pythagoreans cosmic divine principles which constituted the basic structure of the universe. They were gods, divinities, and at the same time the basic structural principle of all existence. Even Leopold Kronecker still said that the natural numbers were the invention of the Godhead and that everything else was Man's handiwork.

Nowadays, in this time of so-called enlightenment where everything irrational and the word God anyhow is thrown out of human science, a real attempt has been made in formalistic mathematics to define number in a form which would exclude all irrational elements, with the definition of numbers as a series of marks (1, 2, 3, 4, 5) and a creation of the human mind. Now the spirit is seemingly owned by the ego complex, the mathematician's ego owns and created numbers! That is what Weyl believed, and that is why he said: I cannot understand that something completely simple which the human mind has created suddenly contains something abysmal. He should only have asked whether the human mind had really created them. He feels as if he were now manipulating the phenomenon completely, but that is not true.

Primitives, if they have twenty horses, cannot count the horses themselves but they use twenty sticks and then they say, one stick, one horse, two sticks, two horses, three sticks, three horses, and then they count the sticks and with them they can count the number of horses. That is a very, very widespread way in which man learned to count. We still do it on our fingers if somebody enumerates things, we point to our fingers, using them as a helping quantity. All counting began with the helping quantity. When man first could count something and then had to count more, he used his fingers; or in many, many primitive civilizations they use dots or counting sticks and then when something has to be counted sticks are put down and counted and that is the helping quantity.

Thus if we do what Hermann Weyl did we simply go back to that primitive way, we count the helping quantity; but that is only an action of the human mind, not the numbers themselves. To make such helping sticks or dots is an activity of ego consciousness by which one can count; it is a construction of the human mind but the number itself is not, and there is the great error.

So we have to turn back and say, Yes, numbers have an aspect in which they are entities which the human mind can posit and manipulate. We can assume a certain amount of numbers, an arithmetical law, a situation, and that can be manipulated completely freely and arbitrarily, according to our ego wishes, but we manipulate only the derivative; the original thing which inspired one to make counting sticks and so arrive at the number of horses, for instance, that idea one has not got hold of, it is still autonomous, it still belongs to the creative spirit of the unconscious, so to speak.

At the time of Weyl, therefore, one simply discarded the study of single numbers because one always stumbled over something completely simple and queer: one had just posited four dots, and then suddenly those four dots developed qualities which one had not posited. In order to get away from that awkward situation and keep up the illusion that numbers were something one had posited and could manipulate with one's conscious mind, Weyl says: "The single numbers are not emphasized in mathematics but one projects them by a specific procedure onto the background of infinite possibilities and then copes with them that way."

That is what most modern mathematicians do. They simply take the theory of natural integers, from one to N, and cope with it as a whole; they say simply that is the series of natural integers which has certain qualities for instance every number has a predecessor, a successor, a position, and a ratio. One knows that as a whole, and then one can construct other mathematics with complex and irrational numbers, etc. One then derives much higher forms, always of types (one could say of numbers), and one deals with that simply as what the mathematician calls a class, ignoring the seven, the fifteen and the 335 in it.

Therefore one deals with an algebraic idea and only with those qualities which are common to all natural integers. With those one can build a lot, but more or less, as Weyl says, "ignore the single integer." Mathematicians are very honest people; they never deny that the single number has irrational, individual qualities, they are simply not interested. Poincare, for instance, is even more honest, he says that all natural integers are irrational individuals, but that is exactly why one cannot make many general theories in number theory about them, and why they are not very prolific for mathematics. They are not very useful, because there are too many single cases and not enough generalities from which one can make a theorem. That was Poincare's viewpoint, he did not say it was not interesting, but that we do not like it so much because one cannot make theorems out of it. We would have to pay attention to the single case and that we do not like as mathematicians, because temperamentally we prefer to make general theories which are generally valid.

Therefore in the history of mathematics one can very clearly see what Jung characterized as the general development of the human mind: that anything which we now call our subjective spirit, including our mental activities in science, was once the objective spirit that means the inspiring movement of the unconscious psyche but with the development of consciousness, we have got hold of a part that we now manipulate and call our own, behaving as if it were something which we completely possess. That has happened in the whole development of mathematics: from numbers being gods, they have been desecrated into being something which is arbitrarily posited by a mathematician's ego. But the mathematicians are honest enough to say: No, that is not the whole of it, strangely enough there are things which I wanted and have had which still slip and do things which they ought not to do, they have not become the slaves of our consciousness completely.

History of Physics

A parallel development has happened in the history of physics where now, more and more, the concept of probability is used and one tries to ignore as much as possible the single case. Wolfgang Pauli therefore said: Because of the indeterministic character of natural law, physical observation acquires the character of an irrational unique actuality and a result you cannot predict; against it stands the rational aspect of an abstract order of possibility which one posits with the help of the mathematical concept of probability and the psi function.

In other words, physics is now confronted with a great split, namely all the pre-calculations are based on the concept of probability and are calculated in matrix and other algebraic forms, but with them one can only state a general probability. Then one makes an actual observation which is a unique actual event. Now these actual unique observations, even if they cost ten million dollars, for instance, and they do nowadays, in the realm of microphysics one cannot repeat infinitely so as also to get a certain practical probability. There is therefore an immense gap, and that is why Pauli says the actual experiment (let's say with a particle in a cyclotron) is an irrational just-so story which generally does not quite fit the calculated probability. That is why nowadays one fudges all those equations in physics; in fact one just cheats a bit to bind them to each other, and one cannot make actual accurate predictions any more.

Naturally, physicists have thought about that! How does that happen? Why can one not make an actual prediction which should really give actual numerical results, not only a statistical probability? Pauli very clearly states that it comes from the presuppositions, because the experiment is an actual single event and the means of calculation in mathematics are based on the principle of probability, which excludes, and does not apply to, the unique event.

Therefore we now have to go deeper into the problem of probability and say: How does that happen? The simplest way of explaining probabilities, and the way I am going to use because it is apparently the archetypal pattern, is with cards. One has a set of 32 cards and may pick one card. The probability that out of the 32 cards one gets, say, the Ace of Hearts, is one-thirtysecond. One has just that much chance and no more. If I say you may pick ten times, then naturally the probability of getting the Ace of Hearts is much better, and if you may pick a thousand times then the chance becomes still better, and so on.

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In other words repetition is the secret of probability: the more one repeats the situation, the more accurately the probability can be formulated, till finally, and that is the statistical formulation, one gets to a limit value where one can say that when one has N (that means an infinite number of draws) then a limit can be made pretty accurately. That, in popularized, simplified form, is what underlies calculable probability.

Now, as a wicked psychologist, and not believing in this, or rather seeing this as a very one-sided operation of the human mind, one has to ask two questions: first, naturally, one sees oneself that it is a very questionable or a very one-sided grasp of reality which modern science gets by applying these techniques, and therefore one is justified in asking if there are not other possibilities with other means. For the moment, however, I want to ask the other question: Why on earth did millions of highly intelligent scientists in Western Europe and America and the Western world believe in the law of great numbers as if it were God? Because, actually, if one discusses these problems with modern natural scientists they just believe this is it, that it is our way of getting at reality and describing it scientifically and accurately. There is the implication that this is where one gets at the truth of inner and outer factors and everything else; it must be statistically proved and it must cover itself with this concept of probability.

That is my great criticism of Rhine of Duke University. Even he was foolish enough to believe that if he wanted to sell parapsychological phenomena to the scientific world then he must prove them statistically or with the concept of probability and-- what a fool!-- he ended up by that in enemy territory. He should have stayed on his own territory. He tries to prove with the very means which eliminates the single case, something which is only valid in the single case. That is why I do not believe in that whole investigation. I do not believe in what they do in Duke University. They became seduced by the Zeitgeist of America, and because they wanted to prove to other scientists that their parapsychology is real science they used a tool which is absolutely inept and inadequate for the purpose. That is my personal view.

Under an Archetipe

Let us now first ask why that mania of believing in the law of great numbers has possessed the Western mind? After all, those who believe in it are, in the main, the most developed and intelligent people in our civilization. They are not fools. Now why do they believe in it? If somebody believes, as a kind of holy conviction, something which after one has woken up about it proves to be a very partial and partly an erroneous viewpoint, then the psychological suspicion always exists that these people are under the secret influence of an archetype. That is what makes people believe things which are not true.

If one looks at the history of science one sees that all the errors in science, or what we now call errors, have been due to the fact that people in the past were fascinated by an archetypal idea which prevented them from observing facts further. That archetypal concept satisfied them, it gave them a subjective feeling of this is it and therefore they gave up looking for further explanations. Only when a scientist came along and said, Now I am not so sure of that, and brought new facts did they wake up and ask: Why on earth did we believe that other story before, it appears now to be erroneous! Generally one sees that one was under the spell, the emotional, fascinating spell of an archetypal idea.

We have therefore to ask what archetypal idea is behind the spell which now grips the minds of modern scientists? Who is the lord of great numbers, seen from a mythological standpoint? If one studies the history of religion and comparative mythology the only beings who ever were able to manipulate great numbers were gods, or the godhead. God, even in the Old Testament, counted the hairs of our head. We cannot do that, but He can. Moreover, the Jews refused to be counted because only God was allowed to know the number of His people and to count the population was sacrilege. Only the Divinity could count.

Most primitive societies that still live in the aboriginal state of the collector and hunter type, for instance the Australian aborigines, all have a binary system. They count to two and then they count on in couples. They have no word beyond two, they count one, two; two, one, two; two, two, one, one, two, and so on. In most primitive civilizations they can either count to two, or to three, or to four. There are different types and beyond a certain number they say many, and where many begins there begins the irrational, the godhead.

There one sees how man, in learning to count, took away a little bit of territory from that all-counting god, just a little bit, the one and the two; that is what he can manage, the rest still belongs to the all-counting god. In counting to three and then four and then five, he slowly gains territory, but there always comes the moment when he says many, and there he gives up counting; there the other counts, namely the unconscious (or the archetype, or the godhead), which can count infinitely, and can out-count every computer.

That is the fascination and I will go on from there next time.