[See link at bottom of post to read the entire book and view the Figures referred to within this post.]

On Divination and Synchronicity : The Psychology of Meaningful Chance Studies in Jungian Psychology by Marie Louise Von Franz.

Lecture 1

You may perhaps know of the amusing fact that originally divination was always practiced in churches. The old Jews, for instance, had a divination oracle in their sanctuaries in Jerusalem and on certain occasions when the priest wanted to consult Yahweh he tried through such oracles to discover the will of God. In all primitive civilizations divination techniques have been used to find out what God, or the gods, want, but in time this has been discontinued and outgrown; it has become a dark, magical, and despised practice, but today this lecture is being given in the (parish church), a nice little synchronicity.

The view of the world which Jung tried to bring back into focus, and on which divination basically rests, is that of synchronicity; therefore before we go into details about the problems of divination we have to remember what Jung said about synchronicity. In his Foreword to the English edition of Richard Wilhelm’s translation of The I Ching or Book of Changes, he gives a very good summary of the difference between causal and synchronistic thinking. Causal thinking is, so to speak, lineal. There is a sequence of events A, B, C, D, and you think backwards and wonder why D appears because of C, why C appears because of B, and why B because of A, like some kind of inner or outer event. One tries to trace back in one’s mind why these coordinate effects have worked.

We know that through the investigations of modern physicists it has now been proved that on the microphysical level this principle is no longer completely valid; we can no longer think of causality as absolute law, but only as a tendency or prevailing probability. So causality is shown to be a way of thinking which satisfies our mental grasp of a cluster of physical events, but does not complete ly get at the core of natural laws, it only delineates general trends or possibilities. Synchronistic thinking, on the other hand, one could call field thinking, the center of which is time.

Time also comes into causality since we normally think that the cause comes before the effect. In modern physics it sometimes looks as if the effect came before the cause, and therefore they try to turn it round and say that you could still call that causal; but I think Jung is right in saying that that is enlarging and twisting the idea of causality ad absurdum so far that it loses its meaning. Normally, cause always comes before effect, so there also is a lineal idea of time, before and after, with the effect always after the before.

Synchronistic thinking, the classic way of thinking in China, is thinking in fields, so to speak. In Chinese philosophy such thinking has been developed and differentiated much more than in any other civilization; there the question is not why has this come about, or what factor caused this effect, but what likes to happen together in a meaningful way in the same moment? The Chinese always ask: “What tends to happen together in time?” So the center of their field concept would be a time moment on which are clustered the events A, B, C, D, and so on (Figure 1).

Figure 1.: Field of time (time-bound ensemble of events).

Richard Wilhelm puts it very well in his Introduction to the I Ching where he speaks of the complex of events which occur at a certain time moment.

In our causal thinking we have made a big separation between psychic events and physical events, and we only watch to see how physical events produce, or have a causal effect upon, each other and on psychological events. Right up to the 19th century the idea still persisted in the sciences (and it still does in those less developed) that only physical causes have physical effects and psychic causes psychological effects; for instance, Freud’s way of thinking: “This woman is neurotic and has an idiosyncrasy as the result of a childhood trauma.” That would be the same kind of thinking but transposed onto the psychological level.

The question now being asked is whether there are interactions between those two lines. Is there something like a psychic cause for physical events and vice versa? That is a problem of psychosomatic medicine. Interactions between those two chains of causality can be proved: you may read a letter saying that somebody you loved very much has died, and get physiological effects; you may even faint, a reaction caused not by the ink and the paper, but by the psychic content of the communication. There is a causal interaction between those two lines which one is only now beginning to investigate.

The synchronistic, i.e., the Chinese way of thinking, however, is completely different. It is a differentiation of primitive thinking in which no difference has ever been made between psychological and physical facts. In their question as to what likes to occur together, one can bring in both inner and outer facts. For the synchronistic way of thinking it is even essential to watch both areas of reality, the physical and the psychic, and to notice that at the moment when one had these and these thoughts or these and these dreams which would be psychological events such and such outer physical events happened; i.e., there was a complex of physical and psychological events. Though causal thinking also poses the problem of time in some form because of the before and after, the problem of time is much more central in the synchronistic way of thinking because there it is the key moment a certain moment in time which is the uniting fact, the focal point for the observation of this complex of events.

In modern Western science, algebraic means are used to describe the probabilities of the sequence of events algebraic matrices of different forms and algebraic functions and curves. The Chinese also use mathematics for the description of their laws of synchronicity. They use something like mathematical matrices but not algebraic abstractions; they use the individual natural integers (1, 2, 3, 4, 5, 6, 7), so one could say that the mathematics of this Chinese way of thinking would be the different qualifications one can draw from the series of natural integers, the common laws which one can abstract from them. One uses the 3, 4, and 5 to grasp a cluster of events in a mathematical form.

The basis of the science of mathematics, or the scientific mathematics of synchronistic thinking, is therefore the series of natural integers, and one finds that in all techniques of divination. The simplest form of divination is the binary: hit or miss. One throws a coin and gets heads or tails and accordingly decides whether one will go or not to the Rigi, or whichever direction you are undetermined about. Hit or miss is the basic idea of all divination but in different civilizations there are differentiated techniques by which to read the situation better at a certain time moment.

The Western way of thinking is an extraverted orientation, namely first to look at the events and then to abstract a mathematical model. The Eastern, or Chinese way, is to use an intuitive mental model to read the event, namely natural integers. They turn first to the event of throwing heads or tails, that is a psychic and a psycho-physical event. The question of the diviner is psychic, while the event is that the coin falls either heads or tails, from which the further outer and inner events can be read. So it is an outlook completely complementary to ours.

What is important in China, as Jung also pointed out in his essay called ”Synchronicity: An Acausal Connecting Principle,” is that the Chinese did not get stuck, like many other primitive civilizations do, into using divination methods only to predict the future whether for instance one should marry or not. One asks the priest and he says: “No, you won’t” or you will “get her.” That is something practised all over the world, not only officially but by many people quite silently in their rooms

when they lay Tarot cards, etc., or they have little rituals: “If today the sun shines, then I’ll do such and such a thing.” Man constantly thinks that way and even scientists have these little superstitions, telling themselves that because the sun shone into their room when they got up they knew that today this and this would come off right. Even if one discards it in one’s conscious Weltanschauung, the primitive man in us constantly uses this kind of prognostication of the future with the left hand, so to speak, and then shamefacedly denies it to his rationalistic brother, though he is much relieved to discover that the other does that too! In this stage divination cannot evolve and become differentiated; it remains a kind of primitive guessing technique, trying to guess the future by some technical means.

That is practiced, as I say, by us and more openly in all primitive civilizations. If one wants to travel in Africa one goes to a medicine man who throws a few chicken bones, and according to the way they fall, whether more into the red or the white section he has drawn on the ground, and in what constellation, he will say whether the journey will be successful or not, and whether to go or not. Before any big enterprise, such as hunting or making a long dangerous journey to Johannesburg, or whatever it is, one first always consults such an oracle and then acts accordingly. We do the same thing more secretly but in both cases I’ll mention some exceptions later it is not built into the Weltanschauung and therefore remains a kind of undeveloped primitive practice, a ritual game, so to speak, which we tend not to integrate into our conscious view of reality.

The Chinese, like all primitive civilizations, still had this primitive technique until it was forbidden. In the market place of every Chinese town there were a few I Ching priests who would throw coins for you or take the yarrow stalks, and get answers to your questions, but then it was forbidden. In 1960 Mao thought of slightly releasing the rationalistic political pressure on the masses and found out that there were two possibilities: either to give more rice, or to allow the use of the I Ching, and all those whom he consulted told him that the people were more eager to use the I Ching again than to get more food. Spiritual food, and the I Ching was their spiritual food, was more important to them, so it was allowed for I think one or two years and then he strangled it again. It is very typical for the Chinese that even a bowl of rice and they are very hungry was less important than again to have their beloved Book of Changes and its spiritual orientation.

The great merit of the I Ching is due to two remarkable geniuses, namely the legendary King Wên and the Duke of Chou, who developed what was originally a primitive oracle system into a complete philosophic Weltanschauung. They treated the oracle and its ethical consequences philosophically; they thought about its psychological consequences and presuppositions and through that it has in China become the basis of a very deep and very broad Weltanschauung. Jung writes in his paper on synchronicity that this has happened only in China, but I chanced to discover that it has also happened in Western Nigeria. There were certain medicine men there who by their oracle technique geomancy in their case developed a whole religious philosophy, naturally slightly more primitive than the Chinese one, but also a complete religious and philosophical viewpoint about the oracle, not using it just as a prognostication technique.

Those are the two instances of which I know. There is probably a third, but I have not been able to get hold of the material; as far as I can find out only one paper has been written on it, but I cannot get hold of it anywhere. The old Mayan civilization which, as has become more and more evident, is dependent on central Asia and therefore linked up with the Chinese civilization, also had an I Ching type of oracle technique, and I would guess from the quality of their civilization that they also had a philosophical outlook and viewpoint about it and that it was not just a left hand prognostication technique. One man, Schultze-Jena, published a small paper on it, but though I have been chasing that for two years I cannot find it anywhere in Switzerland, and as far as I know the author only writes of the techniques of the Mayan oracle and not of its philosophical background.

We can, however, do some guessing about this because in Mayan philosophy all the gods were time and number gods. All the main figures of the Mayan myths have a specific number which is even expressed in their names. The greatest hero, for instance, is Hunabku the name comes from Hun, meaning one and then there is the great hero Seven Hunter; every great god is both a number and a time moment in the calender year. So there is a union of an archetypal figure with a certain time moment and a certain natural integer. This gives a hint that probably the Mayan oracle was philosophically linked with that kind of view, but as I say I have not yet found any details on it.

Let us therefore stay for the moment with the Chinese way of thinking. There is an excellent book on this by the sociologist Marcel Granet, La Pensée Chinoise, who says that the Chinese never thought in quantities but always in terms of qualitative emblems. Jung would have said “symbols,” and I will use that term so as to make it simpler for us. According to the Chinese, numbers describe regular relationships of events and things, exactly as they do for us. We try with mathematical algebraic formulae to describe regular relationships. As a category, causality is the idea for discovering such relationships, and for the Chinese too, numbers express the regular relationship of things not in their quantitative way, but in their qualitative hierarchy they qualify the concrete orderedness of things. We could not disagree with that for it is more or less the same as with us, except that their accent is on the quality level.

But it goes further in China, where they believe that the universe probably has an ultimate basic numerical rhythm. The same question arises with us now, for in modern physics it is thought that one might possibly find one basic rhythm of the universe which would explain all the different phenomena, but for us that is at present just a kind of speculative idea held by some modern physicists. The Chinese simply assumed that this rhythm of all reality existed, that it was a number pattern, and that all relationships of things with each other in all areas of outer and inner life therefore mirror this same basic number pattern in a form conceived as a rhythm.

Until the end of the 19th century, the Chinese also had a much more energetic and dynamic outlook on the world than we had, believing that everything was energy in flux. Actually we now think the same but we arrived at the idea much later and by scientific means. Their primary assumption from all time was that everything is outwardly and inwardly a flux of energy, which follows certain basic and recurring numerical rhythms. In all areas of events one would always finally arrive at this mirror image, the basic rhythm a matrix of the cosmos. For those who are not so mathematically minded, a matrix is any regular array of numbers in several columns; there may be any number of rows and columns, but always in a rectangular arrangement.

For the Chinese one of the basic matrices, or arrangements of the universe, was a quadrangular matrix a magic square called the Lo Shou (Figure 2), which sets the basic rhythm. It is a so-called magic square because whichever way you add up the figures the result is always 15, and it is also the only magic square which has only three elements in each row or column. So it is really a mathematically unique thing.

There are many magic squares with more rows and more possibilities of addition, but the simplest is this one and it has only eight solutions. I would say it is one of the most highly symmetrical number matrices to be found in arithmetic. The Chinese discovered it intuitively and for them it represented a basic mirror or rhythmic image of the universe seen in its time aspect. I will return to that later.

The Chinese had two ideas or aspects of time: namely timeless time or eternity, unchanging eternity, with superimposed on it cyclic time. We live normally, with our consciousness, in cyclic time, according to Chinese ideas, but there is an eternal time une durée créatrice, to use an expression of Bergson’s underneath, which sometimes interferes with the other. Ordinary Chinese time is cyclical and follows this pattern.

They arranged the innermost chambers of their imperial palace on such a pattern; also all musical instruments were tuned according to it, all dances and all protocol, as well as what a Mandarin and what a commoner had to do at the funeral of his father. In every detail this number pattern always played a role, because it was thought to be the basic rhythm of reality; therefore in different variations in music, in protocol, in architecture, everywhere this same pattern was always put in the center.

The underlying numerical order of eternity is called the Ho-tou (Figure 3), a mandala and also a cross. There is again 5 in the middle. One counts 1, 2, 3, 4, and then moves to the middle 5, then 6, 7, 8, 9, and then back to 10 10 would really be in the middle. One must always cross and come back to the middle. Actually it is the movement of a musical dance because it always emanates into four and contracts into the middle it has a systole and diastole movement. The Lo Shou is the world of time in which we live, and underneath is always the eternity rhythm, the Ho-tou. That idea underlay the whole cultural and scientific application of mathematics in China. Let us compare it with our viewpoint.

I want to read you in detail what the well-known mathematician, Hermann Weyl, says about it in his book Philosophy of Mathematics and Natural Science. You know that until about 1930 the great and passionate occupation of most mathematicians was the discussion of the fundamentals. They hoped, as has been the fashion nowadays, to rediscuss the fundamentals of all science. But the famous German mathematician, David Hilbert, created a new construction of the whole building of mathematics, so to speak, and hoped that this would contain no internal contradictions.

There would be a few basic axioms on which one could build up all branches of mathematics: topology, geometry, algebra, and so on; it was to be a big building with solid foundations in a few axioms. That was in 1926, and Hilbert was even bold enough to say: “I think that with my theory the discussion of fundamentals has been forever removed from mathematics.”

Then in 1931 came another very famous mathematician, Kurt Goedel, who took a few of those basic axioms and showed that one could reach complete contradictions with them: starting from the same axioms, one could prove something and its complete opposite. In other words, he showed that the basic axioms contain an irrational factor which could not be eliminated. Nowadays in mathematics one must not say that obviously this is so-and-so, and that therefore that and that is also so, but: “I assume that it is so-and-so, and if so then that and that follows.” The axioms must be presented as assumptions, or must be postulated, after which a logical deduction can be made, but one cannot infer that what has been assumed or postulated could not be contradicted or doubted as an absolute truth.

In order to make such assumptions, mathematics are generally formulated in such terms as: “It is self-evident,” or “It is reasonable to think” that is how mathematicians posit an axiom nowadays, and from there they build up. From then on there is no contradiction, only one conclusion is possible, but in ”it is reasonable to assume,” that is where the dog lies buried, as we say. Goedel showed that, and thus threw over the whole thing. Strangely enough that did not reopen the discussion of fundamentals. From then on, as Weyl says, nobody touched that problem, they just felt awkward and scratched behind their ears and said, “Don’t let’s discuss fundamentals, there’s nothing doing: it is reasonable to assume, we cannot go beyond that,” and there the situation rests today.

Weyl, however, went through a very interesting development. At first he was very much attracted by the physicist, Werner Heisenberg. He was very much of a Pythagorean and was attracted by the numinosity and irrationality of natural integers. Then he became fascinated by David Hilbert, and in the middle of his life had a period during which he became more and more attracted by Hilbertian logic and dropped the problem of numbers, treating them, erroneously as I think, as simply posited quantities.

He says, for instance, that natural integers are just as though one took a stick and made a row of marks, which one then named conventionally; there was nothing more behind them, they were simply posited by the human mind and there was nothing mysterious about them; it was “reasonable and self-evident” that one could do that. But at the end of his life he added (only to the German edition of his book on the philosophy of mathematics, and shortly before his death) this passage:

The beautiful hope we had of freeing the world of the discussion of fundamentals was destroyed by Kurt Goedel in 1931 and the ultimate basis and real meaning of mathematics are still an open problem. Perhaps one makes mathematics as one does music and it is just one of man’s creative activities, and though the idea of an existing completely transcendental world is the basic principle of all formalism, each mathematical formalism has at every step the characteristics of being incomplete [which means that every mathematical theory is consistent in itself but is incomplete, at the borders are questions which are not self-evident, are not clear, and are incomplete] in so far as there are always problems, even of a simple arithmetical nature, which can be formulated in the frame of a formalism, but which cannot be decided by deduction within the formalism itself.

That is put in a mathematician’s complicated way; put simply, it means that I daresay it is self-evident, by which I posit something irrational, because it is not self-evident. Now one could make an uroboros movement and say: “But from my deduction I can reprove my beginning.” You cannot! You cannot from the deductive formalism afterwards deduce a proof,except by a tautology, which naturally is not allowed, even in mathematics.

We are therefore not surprised that in an isolated phenomenal existence a piece of nature surprises us by its irrationality and that one cannot analyse it completely. As we have seen, physics therefore projects everything which exists onto the background of possibility or probability.

That is important because it sums up in one word what modern science does. In other words, any fragment of phenomenal existence, let us say these spectacles, contains something irrational which one cannot exhaust in physical analysis. Why the electrons of these millions and millions of atoms of which my spectacles consist are in this place and not in another, I cannot explain; therefore through physics, when it comes to a single event in nature, there is no completely valid explanation.

The single event is always irrational, but in physics one proceeds by projecting this onto the background of a possible, i.e., one makes a matrix. For instance, in these spectacles there are so many atoms and so many particles of them, and so on, and out of a whole group one can make a mathematical formula in which one could even count the particles not 1, 2, 3, 4, 5, but by projecting onto the background of what is possible. That is why these matrices are nowadays used in engineering and so on, because one can cope with the uncountable; they provide an instrument with which to cope with the things which cannot be counted singly. Weyl says:

It is not surprising that any bit of nature we may choose [these spectacles or anything] has an ultimate irrational factor which we cannot and never will explain and that we can only describe it, as in physics, by projecting it onto the background of the possible.

But then he continues:

But it is very surprising that something which the human mind has created itself, namely the series of whole natural integers [I told you that he has this erroneous idea that the human mind created 1, 2, 3, 4, 5, by making dots], and which is so absolutely simple and transparent to the constructive spirit, also contains an aspect of something abysmal which we cannot grasp.

That is the confession of one of the most remarkable because one of the most philosophically oriented modern mathematicians, Hermann Weyl. We can naturally say that we do not believe what he believed, namely that the natural integers simply represent the naming of posited dots, therefore to us it is not surprising that natural integers are abysmal and beyond our grasp. He believed that, and that is why he could not understand. It is incredible that it should be so, but it is so; in other words, because the natural integers have something irrational (he called it abysmal) the fundamentals of mathematics are not solid, because the whole of mathematics is ultimately based on the givenness of the series of natural integers.

Now precisely because numbers are irrational and abysmal to quote Weyl they are a good instrument with which to grasp something irrational. If one uses numbers to grasp the irrational, one uses irrational means to get hold of something irrational, and that is the basis of divination. They took those irrational, abysmal numbers which nobody has so far understood, and tried to guess reality, or their connection with reality but into the divination problem there also enters the problem of time.

Divination has to do with synchronicity, and Jung has in so many words called the synchronistic phenomena para-psychological phenomena. I want you to keep that in mind because, as you know, in modern science physicists and psychologists are now trying to find the union of physics and psychology in the area of para-psychological phenomena. They have a hunch, or guess, that para-psychological phenomena might give us a clue to the union of physis and psyche. Now in divination, and I am here referring specifically to number divination, one would therefore also have to deal with the para-psychological phenomenon, which at the same time is linked up with the number. Jung has called number the most primitive expression of the spirit and so we have now to go into what we understand, from the psychological standpoint, by the word spirit.

Jung, in trying to specify how he uses the word spirit, first quotes a lot of colloquial terms in which spirit is used as something like a non-material substance, or as the opposite of matter.* We also generally use the word spirit to indicate something that is a cosmic principle, but we use the same word when we speak of certain of man’s psychological psychic capacities or activities like the intellect, or the capacity to think, or reason. For instance, one could say: “He has a spiritual outlook,” or “This idea comes from a distorted spirit,” or something like that. Again we use the word as a collective phenomenon such as in the word Zeitgeist which is now generally not even translated into English it is a German term to express the irrational fact that each period of time has a certain spirit.

For instance, the Renaissance had a certain spirit as illustrated in its art, its technology, mathematics, and religious outlook everywhere. All these phenomena which characterize the 16th century could be summed up as the spirit of the Renaissance. In that sense the word is simply used as a collective phenomenon, the sum of ideas common to many people. One could also speak of the spirit of Marxism or of National Socialism, when it would be the common collective ideas of a whole group. There is therefore, Jung continues, a certain opposition between a spirit, which has a kind of extra-human existence outside man the cosmic spirit as opposed to the matter of the cosmos and something which we experience as an activity of the human ego.

If we say of somebody that he has a distorted spirit, that means his ego complex is working intellectually in a wrong way. Jung therefore continues: If something psychic, or psychological (i.e., a psychological event) happens in the individual and he has the feeling that it belongs to him, then he calls it his spirit for instance which, by the way, would be quite wrong, but which many people do. If I suddenly had the idea of giving you a good example, then I would feel that it was my good idea, my spirit produced it. If something psychological happens which seems strange to the individual, then it is called a spirit, in the sense of something like a ghost, and then one experiences it as possession.

Let us assume that suddenly I felt impelled to keep saying, “the geraniums are blue,” “the geraniums are blue,” “the geraniums are blue.” Then, because that would be crazy, and seem to me quite strange compared with what I am now doing here, I would say: “My God, what devil, or ghost, put such a crazy idea into my head, it is possessing me and making me talk nonsense!”

If it were a good idea then I’d follow it right through! Now primitives are more honest: everything which comes to them unexpectedly from within they call spirit; not only that which is bad and which possesses one, but anything of which they would say: ”My ego did not make it, it suddenly came to me” that is spirit. In the latter case, when the spirit is still outside, when I get possessed by having to say or do something which seems not to belong to my ego, then it is a projected aspect of my unconscious; it is a part of my unconscious psyche which is projected and then experienced as a para-psychological phenomenon.

That happens when you get into a state in which you are not yourself, or into an emotional upset where you lose control of yourself, but afterwards wake up completely sober and look at the stupid things you did during your possessed state and wonder what got into you: something got hold of you, you weren’t yourself, though while you were behaving like that you thought you were it was just as if an evil spirit or the devil had got into you.

These things one must not just take in a kind of colloquial amusing way, but quite literally, for a devil or we would say, more neutrally, an autonomous complex temporarily replaces the ego complex; it feels like the ego at the time, but it isn’t, for afterwards, when dissociated from it, one cannot understand how one came to do or think such things.

One of the main ways in which we use the word spirit is in speaking of the inspiring, vivifying aspect of the unconscious. Now we know that for the ego complex to get in touch with the unconscious has a vivifying and inspiring effect, and that is really the basis of all our therapeutic efforts. Sometimes neurotic people, who have become closed up in their neurotic vicious circle, as soon as they go into analysis and have dreams, get excited and interested in the dreams and then the water of life flows again; they once more have an interest and therefore are suddenly more alive and more efficient. Then somebody may say: “What has happened to you? You have come alive again” but that only happens if the individual succeeds in making contact with the unconscious, or one could say “with the dynamism of the unconscious,” and especially with its vivifying, inspiring aspect.

Jung therefore defines spirit, from the psychological angle, as the dynamic aspect of the unconscious. One can think of the unconscious as being like still water, a lake which is passive. The things one forgets fall into that lake; if one remembers them one fishes them up but it itself does not move. The unconscious has that matrix, womb aspect, but it also has the aspect of containing dynamism and movement, it acts on its own accord for instance, it composes dreams. One could say that composing dreams while one sleeps is an aspect of the spirit; some master spirit or mind composes a most ingenious series of pictures which, if one can decipher them, seem to convey a highly intelligent message.

That is a dynamic manifestation of the unconscious, where the unconscious energetically does something on its own, it moves and creates on its own, and that is what Jung defines as spirit. There is naturally an unclear borderline between the subjective and the objective; but in practice if one feels that it belongs to one then it is one’s own spirit, and if one does not feel it belongs to one, then one calls it the spirit, or a spirit. That depends on whether one feels akin or not akin to it, close to it or not close to it.

Jung sums up by saying that spirit contains a spontaneous psychic principle of movement and activity; secondly, that it has the quality of freely creating images beyond our sense perception (in a dream one has no sense perception the spirit or the unconscious creates images from within, while the sense perceptions are asleep); and thirdly, there is an autonomous and sovereign manipulation of those images.

Those are the three characteristics of what Jung calls the spirit, or the dynamism of the unconscious. It is spontaneously active, it freely creates images beyond sensual perceptions, and it autonomously and in a sovereign manner manipulates those images. If one looks at one’s dreams, one sees that they are composed of impressions from the day before. For instance, one read something in a paper, or experienced something in the street, or talked to Mrs. So-and-So, and so on. The dream takes these fragments and makes a completely new and meaningful potpourri out of that.

There one sees the sovereign manipulation of the pictures: they are put into another order and manipulated into a completely different sequence with a completely different meaning, though one still recognizes that the single elements have been taken from, for instance, memory remnants of the day before. That is why many people think that is the whole explanation of the dream: “Oh, I read about a fire yesterday in the paper, that is why I dreamt about a fire,” and then one has to begin, as always, by saying: “Yes, but look at the connections in which the fire has been put, very different from what you read.” That would be the spirit, that unknown thing in the unconscious which rearranges and manipulates inner images.

This factor which produces and manipulates inner images is completely autonomous in primitive man, but through the differentiation of consciousness it slowly comes closer to consciousness, and therefore in contrast to primitives we say we do it in part. For instance, we often say that we have a good idea or we invent something new. A primitive man would never say that a bow and arrow, for instance, were his invention he would say that the way to construct a bow and arrow was revealed to him by the bow and arrow god, and then tell an origin myth, of how to a certain hunter his divinity appeared in a dream or vision and revealed to him how to make a bow and arrow.

So the larger our consciousness is, and the more it develops, the more we get hold of certain aspects of the spirit of the unconscious, draw it into our subjective sphere, and then call it our own psychic activity or our own spirit. But, as Jung points out, a great part of the original phenomenon remains naturally autonomous and therefore still is experienced as a para-psychological phenomenon. In other words, we must not assume that at our present stage of consciousness, where we have assimilated more than a certain amount of the spirit of the unconscious and made it our own i.e., made it the possession of the ego complex so that the ego complex can manipulate it that we have the whole thing. There is still an enormous area of that spirit which manifests as it did originally, completely autonomously, and therefore as a para-psychological phenomenon, as it does among primitive people.

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 Pythagorean s 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.”

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 in-deterministic 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-thirty-second.

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.

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.

Not being a mathematician and physicist I had generally to rely on rather popularized material and there the physicist, when he wants to explain probability, always uses the example either of dice or cards. Just keep that in mind. If he explains the theorem of Bernoulli he begins by saying, “Well you see if you have so and so many cards,” and so on. The same way is always used to explain probability to a lay person. But why just that example? That is amusing! But to go now to the fact, it means that all mathematics, and their use in modern physics, are based on the principle of admitting an inability to make single predictions of single events, but aiming at being able to do so when it comes into thousands and billions of events which then gain a great amount of accuracy.

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.

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.

http://www.tuks.nl/pdf/Reference_Material/Aetherforce_Libary/Other/%5BMarie-Louise_von_Franz%5D_On_Divination_and_Synchronicity.pdf : The Psychology of Meaningful Chance Studies in Jungian Psychology by Marie Louise Von Franz.

Lecture 1

You may perhaps know of the amusing fact that originally divination was always practiced in churches. The old Jews, for instance, had a divination oracle in their sanctuaries in Jerusalem and on certain occasions when the priest wanted to consult Yahweh he tried through such oracles to discover the will of God. In all primitive civilizations divination techniques have been used to find out what God, or the gods, want, but in time this has been discontinued and outgrown; it has become a dark, magical, and despised practice, but today this lecture is being given in the (parish church), a nice little synchronicity.

The view of the world which Jung tried to bring back into focus, and on which divination basically rests, is that of synchronicity; therefore before we go into details about the problems of divination we have to remember what Jung said about synchronicity. In his Foreword to the English edition of Richard Wilhelm’s translation of The I Ching or Book of Changes, he gives a very good summary of the difference between causal and synchronistic thinking. Causal thinking is, so to speak, lineal. There is a sequence of events A, B, C, D, and you think backwards and wonder why D appears because of C, why C appears because of B, and why B because of A, like some kind of inner or outer event. One tries to trace back in one’s mind why these coordinate effects have worked.

We know that through the investigations of modern physicists it has now been proved that on the microphysical level this principle is no longer completely valid; we can no longer think of causality as absolute law, but only as a tendency or prevailing probability. So causality is shown to be a way of thinking which satisfies our mental grasp of a cluster of physical events, but does not complete ly get at the core of natural laws, it only delineates general trends or possibilities. Synchronistic thinking, on the other hand, one could call field thinking, the center of which is time.

Time also comes into causality since we normally think that the cause comes before the effect. In modern physics it sometimes looks as if the effect came before the cause, and therefore they try to turn it round and say that you could still call that causal; but I think Jung is right in saying that that is enlarging and twisting the idea of causality ad absurdum so far that it loses its meaning. Normally, cause always comes before effect, so there also is a lineal idea of time, before and after, with the effect always after the before.

Synchronistic thinking, the classic way of thinking in China, is thinking in fields, so to speak. In Chinese philosophy such thinking has been developed and differentiated much more than in any other civilization; there the question is not why has this come about, or what factor caused this effect, but what likes to happen together in a meaningful way in the same moment? The Chinese always ask: “What tends to happen together in time?” So the center of their field concept would be a time moment on which are clustered the events A, B, C, D, and so on (Figure 1).

Figure 1.: Field of time (time-bound ensemble of events).

Richard Wilhelm puts it very well in his Introduction to the I Ching where he speaks of the complex of events which occur at a certain time moment.

In our causal thinking we have made a big separation between psychic events and physical events, and we only watch to see how physical events produce, or have a causal effect upon, each other and on psychological events. Right up to the 19th century the idea still persisted in the sciences (and it still does in those less developed) that only physical causes have physical effects and psychic causes psychological effects; for instance, Freud’s way of thinking: “This woman is neurotic and has an idiosyncrasy as the result of a childhood trauma.” That would be the same kind of thinking but transposed onto the psychological level.

The question now being asked is whether there are interactions between those two lines. Is there something like a psychic cause for physical events and vice versa? That is a problem of psychosomatic medicine. Interactions between those two chains of causality can be proved: you may read a letter saying that somebody you loved very much has died, and get physiological effects; you may even faint, a reaction caused not by the ink and the paper, but by the psychic content of the communication. There is a causal interaction between those two lines which one is only now beginning to investigate.

The synchronistic, i.e., the Chinese way of thinking, however, is completely different. It is a differentiation of primitive thinking in which no difference has ever been made between psychological and physical facts. In their question as to what likes to occur together, one can bring in both inner and outer facts. For the synchronistic way of thinking it is even essential to watch both areas of reality, the physical and the psychic, and to notice that at the moment when one had these and these thoughts or these and these dreams which would be psychological events such and such outer physical events happened; i.e., there was a complex of physical and psychological events. Though causal thinking also poses the problem of time in some form because of the before and after, the problem of time is much more central in the synchronistic way of thinking because there it is the key moment a certain moment in time which is the uniting fact, the focal point for the observation of this complex of events.

In modern Western science, algebraic means are used to describe the probabilities of the sequence of events algebraic matrices of different forms and algebraic functions and curves. The Chinese also use mathematics for the description of their laws of synchronicity. They use something like mathematical matrices but not algebraic abstractions; they use the individual natural integers (1, 2, 3, 4, 5, 6, 7), so one could say that the mathematics of this Chinese way of thinking would be the different qualifications one can draw from the series of natural integers, the common laws which one can abstract from them. One uses the 3, 4, and 5 to grasp a cluster of events in a mathematical form.

The basis of the science of mathematics, or the scientific mathematics of synchronistic thinking, is therefore the series of natural integers, and one finds that in all techniques of divination. The simplest form of divination is the binary: hit or miss. One throws a coin and gets heads or tails and accordingly decides whether one will go or not to the Rigi, or whichever direction you are undetermined about. Hit or miss is the basic idea of all divination but in different civilizations there are differentiated techniques by which to read the situation better at a certain time moment.

The Western way of thinking is an extraverted orientation, namely first to look at the events and then to abstract a mathematical model. The Eastern, or Chinese way, is to use an intuitive mental model to read the event, namely natural integers. They turn first to the event of throwing heads or tails, that is a psychic and a psycho-physical event. The question of the diviner is psychic, while the event is that the coin falls either heads or tails, from which the further outer and inner events can be read. So it is an outlook completely complementary to ours.

What is important in China, as Jung also pointed out in his essay called ”Synchronicity: An Acausal Connecting Principle,” is that the Chinese did not get stuck, like many other primitive civilizations do, into using divination methods only to predict the future whether for instance one should marry or not. One asks the priest and he says: “No, you won’t” or you will “get her.” That is something practised all over the world, not only officially but by many people quite silently in their rooms

when they lay Tarot cards, etc., or they have little rituals: “If today the sun shines, then I’ll do such and such a thing.” Man constantly thinks that way and even scientists have these little superstitions, telling themselves that because the sun shone into their room when they got up they knew that today this and this would come off right. Even if one discards it in one’s conscious Weltanschauung, the primitive man in us constantly uses this kind of prognostication of the future with the left hand, so to speak, and then shamefacedly denies it to his rationalistic brother, though he is much relieved to discover that the other does that too! In this stage divination cannot evolve and become differentiated; it remains a kind of primitive guessing technique, trying to guess the future by some technical means.

That is practiced, as I say, by us and more openly in all primitive civilizations. If one wants to travel in Africa one goes to a medicine man who throws a few chicken bones, and according to the way they fall, whether more into the red or the white section he has drawn on the ground, and in what constellation, he will say whether the journey will be successful or not, and whether to go or not. Before any big enterprise, such as hunting or making a long dangerous journey to Johannesburg, or whatever it is, one first always consults such an oracle and then acts accordingly. We do the same thing more secretly but in both cases I’ll mention some exceptions later it is not built into the Weltanschauung and therefore remains a kind of undeveloped primitive practice, a ritual game, so to speak, which we tend not to integrate into our conscious view of reality.

The Chinese, like all primitive civilizations, still had this primitive technique until it was forbidden. In the market place of every Chinese town there were a few I Ching priests who would throw coins for you or take the yarrow stalks, and get answers to your questions, but then it was forbidden. In 1960 Mao thought of slightly releasing the rationalistic political pressure on the masses and found out that there were two possibilities: either to give more rice, or to allow the use of the I Ching, and all those whom he consulted told him that the people were more eager to use the I Ching again than to get more food. Spiritual food, and the I Ching was their spiritual food, was more important to them, so it was allowed for I think one or two years and then he strangled it again. It is very typical for the Chinese that even a bowl of rice and they are very hungry was less important than again to have their beloved Book of Changes and its spiritual orientation.

The great merit of the I Ching is due to two remarkable geniuses, namely the legendary King Wên and the Duke of Chou, who developed what was originally a primitive oracle system into a complete philosophic Weltanschauung. They treated the oracle and its ethical consequences philosophically; they thought about its psychological consequences and presuppositions and through that it has in China become the basis of a very deep and very broad Weltanschauung. Jung writes in his paper on synchronicity that this has happened only in China, but I chanced to discover that it has also happened in Western Nigeria. There were certain medicine men there who by their oracle technique geomancy in their case developed a whole religious philosophy, naturally slightly more primitive than the Chinese one, but also a complete religious and philosophical viewpoint about the oracle, not using it just as a prognostication technique.

Those are the two instances of which I know. There is probably a third, but I have not been able to get hold of the material; as far as I can find out only one paper has been written on it, but I cannot get hold of it anywhere. The old Mayan civilization which, as has become more and more evident, is dependent on central Asia and therefore linked up with the Chinese civilization, also had an I Ching type of oracle technique, and I would guess from the quality of their civilization that they also had a philosophical outlook and viewpoint about it and that it was not just a left hand prognostication technique. One man, Schultze-Jena, published a small paper on it, but though I have been chasing that for two years I cannot find it anywhere in Switzerland, and as far as I know the author only writes of the techniques of the Mayan oracle and not of its philosophical background.

We can, however, do some guessing about this because in Mayan philosophy all the gods were time and number gods. All the main figures of the Mayan myths have a specific number which is even expressed in their names. The greatest hero, for instance, is Hunabku the name comes from Hun, meaning one and then there is the great hero Seven Hunter; every great god is both a number and a time moment in the calender year. So there is a union of an archetypal figure with a certain time moment and a certain natural integer. This gives a hint that probably the Mayan oracle was philosophically linked with that kind of view, but as I say I have not yet found any details on it.

Let us therefore stay for the moment with the Chinese way of thinking. There is an excellent book on this by the sociologist Marcel Granet, La Pensée Chinoise, who says that the Chinese never thought in quantities but always in terms of qualitative emblems. Jung would have said “symbols,” and I will use that term so as to make it simpler for us. According to the Chinese, numbers describe regular relationships of events and things, exactly as they do for us. We try with mathematical algebraic formulae to describe regular relationships. As a category, causality is the idea for discovering such relationships, and for the Chinese too, numbers express the regular relationship of things not in their quantitative way, but in their qualitative hierarchy they qualify the concrete orderedness of things. We could not disagree with that for it is more or less the same as with us, except that their accent is on the quality level.

But it goes further in China, where they believe that the universe probably has an ultimate basic numerical rhythm. The same question arises with us now, for in modern physics it is thought that one might possibly find one basic rhythm of the universe which would explain all the different phenomena, but for us that is at present just a kind of speculative idea held by some modern physicists. The Chinese simply assumed that this rhythm of all reality existed, that it was a number pattern, and that all relationships of things with each other in all areas of outer and inner life therefore mirror this same basic number pattern in a form conceived as a rhythm.

Until the end of the 19th century, the Chinese also had a much more energetic and dynamic outlook on the world than we had, believing that everything was energy in flux. Actually we now think the same but we arrived at the idea much later and by scientific means. Their primary assumption from all time was that everything is outwardly and inwardly a flux of energy, which follows certain basic and recurring numerical rhythms. In all areas of events one would always finally arrive at this mirror image, the basic rhythm a matrix of the cosmos. For those who are not so mathematically minded, a matrix is any regular array of numbers in several columns; there may be any number of rows and columns, but always in a rectangular arrangement.

For the Chinese one of the basic matrices, or arrangements of the universe, was a quadrangular matrix a magic square called the Lo Shou (Figure 2), which sets the basic rhythm. It is a so-called magic square because whichever way you add up the figures the result is always 15, and it is also the only magic square which has only three elements in each row or column. So it is really a mathematically unique thing.

There are many magic squares with more rows and more possibilities of addition, but the simplest is this one and it has only eight solutions. I would say it is one of the most highly symmetrical number matrices to be found in arithmetic. The Chinese discovered it intuitively and for them it represented a basic mirror or rhythmic image of the universe seen in its time aspect. I will return to that later.

The Chinese had two ideas or aspects of time: namely timeless time or eternity, unchanging eternity, with superimposed on it cyclic time. We live normally, with our consciousness, in cyclic time, according to Chinese ideas, but there is an eternal time une durée créatrice, to use an expression of Bergson’s underneath, which sometimes interferes with the other. Ordinary Chinese time is cyclical and follows this pattern.

They arranged the innermost chambers of their imperial palace on such a pattern; also all musical instruments were tuned according to it, all dances and all protocol, as well as what a Mandarin and what a commoner had to do at the funeral of his father. In every detail this number pattern always played a role, because it was thought to be the basic rhythm of reality; therefore in different variations in music, in protocol, in architecture, everywhere this same pattern was always put in the center.

The underlying numerical order of eternity is called the Ho-tou (Figure 3), a mandala and also a cross. There is again 5 in the middle. One counts 1, 2, 3, 4, and then moves to the middle 5, then 6, 7, 8, 9, and then back to 10 10 would really be in the middle. One must always cross and come back to the middle. Actually it is the movement of a musical dance because it always emanates into four and contracts into the middle it has a systole and diastole movement. The Lo Shou is the world of time in which we live, and underneath is always the eternity rhythm, the Ho-tou. That idea underlay the whole cultural and scientific application of mathematics in China. Let us compare it with our viewpoint.

I want to read you in detail what the well-known mathematician, Hermann Weyl, says about it in his book Philosophy of Mathematics and Natural Science. You know that until about 1930 the great and passionate occupation of most mathematicians was the discussion of the fundamentals. They hoped, as has been the fashion nowadays, to rediscuss the fundamentals of all science. But the famous German mathematician, David Hilbert, created a new construction of the whole building of mathematics, so to speak, and hoped that this would contain no internal contradictions.

There would be a few basic axioms on which one could build up all branches of mathematics: topology, geometry, algebra, and so on; it was to be a big building with solid foundations in a few axioms. That was in 1926, and Hilbert was even bold enough to say: “I think that with my theory the discussion of fundamentals has been forever removed from mathematics.”

Then in 1931 came another very famous mathematician, Kurt Goedel, who took a few of those basic axioms and showed that one could reach complete contradictions with them: starting from the same axioms, one could prove something and its complete opposite. In other words, he showed that the basic axioms contain an irrational factor which could not be eliminated. Nowadays in mathematics one must not say that obviously this is so-and-so, and that therefore that and that is also so, but: “I assume that it is so-and-so, and if so then that and that follows.” The axioms must be presented as assumptions, or must be postulated, after which a logical deduction can be made, but one cannot infer that what has been assumed or postulated could not be contradicted or doubted as an absolute truth.

In order to make such assumptions, mathematics are generally formulated in such terms as: “It is self-evident,” or “It is reasonable to think” that is how mathematicians posit an axiom nowadays, and from there they build up. From then on there is no contradiction, only one conclusion is possible, but in ”it is reasonable to assume,” that is where the dog lies buried, as we say. Goedel showed that, and thus threw over the whole thing. Strangely enough that did not reopen the discussion of fundamentals. From then on, as Weyl says, nobody touched that problem, they just felt awkward and scratched behind their ears and said, “Don’t let’s discuss fundamentals, there’s nothing doing: it is reasonable to assume, we cannot go beyond that,” and there the situation rests today.

Weyl, however, went through a very interesting development. At first he was very much attracted by the physicist, Werner Heisenberg. He was very much of a Pythagorean and was attracted by the numinosity and irrationality of natural integers. Then he became fascinated by David Hilbert, and in the middle of his life had a period during which he became more and more attracted by Hilbertian logic and dropped the problem of numbers, treating them, erroneously as I think, as simply posited quantities.

He says, for instance, that natural integers are just as though one took a stick and made a row of marks, which one then named conventionally; there was nothing more behind them, they were simply posited by the human mind and there was nothing mysterious about them; it was “reasonable and self-evident” that one could do that. But at the end of his life he added (only to the German edition of his book on the philosophy of mathematics, and shortly before his death) this passage:

The beautiful hope we had of freeing the world of the discussion of fundamentals was destroyed by Kurt Goedel in 1931 and the ultimate basis and real meaning of mathematics are still an open problem. Perhaps one makes mathematics as one does music and it is just one of man’s creative activities, and though the idea of an existing completely transcendental world is the basic principle of all formalism, each mathematical formalism has at every step the characteristics of being incomplete [which means that every mathematical theory is consistent in itself but is incomplete, at the borders are questions which are not self-evident, are not clear, and are incomplete] in so far as there are always problems, even of a simple arithmetical nature, which can be formulated in the frame of a formalism, but which cannot be decided by deduction within the formalism itself.

That is put in a mathematician’s complicated way; put simply, it means that I daresay it is self-evident, by which I posit something irrational, because it is not self-evident. Now one could make an uroboros movement and say: “But from my deduction I can reprove my beginning.” You cannot! You cannot from the deductive formalism afterwards deduce a proof,except by a tautology, which naturally is not allowed, even in mathematics.

We are therefore not surprised that in an isolated phenomenal existence a piece of nature surprises us by its irrationality and that one cannot analyse it completely. As we have seen, physics therefore projects everything which exists onto the background of possibility or probability.

That is important because it sums up in one word what modern science does. In other words, any fragment of phenomenal existence, let us say these spectacles, contains something irrational which one cannot exhaust in physical analysis. Why the electrons of these millions and millions of atoms of which my spectacles consist are in this place and not in another, I cannot explain; therefore through physics, when it comes to a single event in nature, there is no completely valid explanation.

The single event is always irrational, but in physics one proceeds by projecting this onto the background of a possible, i.e., one makes a matrix. For instance, in these spectacles there are so many atoms and so many particles of them, and so on, and out of a whole group one can make a mathematical formula in which one could even count the particles not 1, 2, 3, 4, 5, but by projecting onto the background of what is possible. That is why these matrices are nowadays used in engineering and so on, because one can cope with the uncountable; they provide an instrument with which to cope with the things which cannot be counted singly. Weyl says:

It is not surprising that any bit of nature we may choose [these spectacles or anything] has an ultimate irrational factor which we cannot and never will explain and that we can only describe it, as in physics, by projecting it onto the background of the possible.

But then he continues:

But it is very surprising that something which the human mind has created itself, namely the series of whole natural integers [I told you that he has this erroneous idea that the human mind created 1, 2, 3, 4, 5, by making dots], and which is so absolutely simple and transparent to the constructive spirit, also contains an aspect of something abysmal which we cannot grasp.

That is the confession of one of the most remarkable because one of the most philosophically oriented modern mathematicians, Hermann Weyl. We can naturally say that we do not believe what he believed, namely that the natural integers simply represent the naming of posited dots, therefore to us it is not surprising that natural integers are abysmal and beyond our grasp. He believed that, and that is why he could not understand. It is incredible that it should be so, but it is so; in other words, because the natural integers have something irrational (he called it abysmal) the fundamentals of mathematics are not solid, because the whole of mathematics is ultimately based on the givenness of the series of natural integers.

Now precisely because numbers are irrational and abysmal to quote Weyl they are a good instrument with which to grasp something irrational. If one uses numbers to grasp the irrational, one uses irrational means to get hold of something irrational, and that is the basis of divination. They took those irrational, abysmal numbers which nobody has so far understood, and tried to guess reality, or their connection with reality but into the divination problem there also enters the problem of time.

Divination has to do with synchronicity, and Jung has in so many words called the synchronistic phenomena para-psychological phenomena. I want you to keep that in mind because, as you know, in modern science physicists and psychologists are now trying to find the union of physics and psychology in the area of para-psychological phenomena. They have a hunch, or guess, that para-psychological phenomena might give us a clue to the union of physis and psyche. Now in divination, and I am here referring specifically to number divination, one would therefore also have to deal with the para-psychological phenomenon, which at the same time is linked up with the number. Jung has called number the most primitive expression of the spirit and so we have now to go into what we understand, from the psychological standpoint, by the word spirit.

Jung, in trying to specify how he uses the word spirit, first quotes a lot of colloquial terms in which spirit is used as something like a non-material substance, or as the opposite of matter.* We also generally use the word spirit to indicate something that is a cosmic principle, but we use the same word when we speak of certain of man’s psychological psychic capacities or activities like the intellect, or the capacity to think, or reason. For instance, one could say: “He has a spiritual outlook,” or “This idea comes from a distorted spirit,” or something like that. Again we use the word as a collective phenomenon such as in the word Zeitgeist which is now generally not even translated into English it is a German term to express the irrational fact that each period of time has a certain spirit.

For instance, the Renaissance had a certain spirit as illustrated in its art, its technology, mathematics, and religious outlook everywhere. All these phenomena which characterize the 16th century could be summed up as the spirit of the Renaissance. In that sense the word is simply used as a collective phenomenon, the sum of ideas common to many people. One could also speak of the spirit of Marxism or of National Socialism, when it would be the common collective ideas of a whole group. There is therefore, Jung continues, a certain opposition between a spirit, which has a kind of extra-human existence outside man the cosmic spirit as opposed to the matter of the cosmos and something which we experience as an activity of the human ego.

If we say of somebody that he has a distorted spirit, that means his ego complex is working intellectually in a wrong way. Jung therefore continues: If something psychic, or psychological (i.e., a psychological event) happens in the individual and he has the feeling that it belongs to him, then he calls it his spirit for instance which, by the way, would be quite wrong, but which many people do. If I suddenly had the idea of giving you a good example, then I would feel that it was my good idea, my spirit produced it. If something psychological happens which seems strange to the individual, then it is called a spirit, in the sense of something like a ghost, and then one experiences it as possession.

Let us assume that suddenly I felt impelled to keep saying, “the geraniums are blue,” “the geraniums are blue,” “the geraniums are blue.” Then, because that would be crazy, and seem to me quite strange compared with what I am now doing here, I would say: “My God, what devil, or ghost, put such a crazy idea into my head, it is possessing me and making me talk nonsense!”

If it were a good idea then I’d follow it right through! Now primitives are more honest: everything which comes to them unexpectedly from within they call spirit; not only that which is bad and which possesses one, but anything of which they would say: ”My ego did not make it, it suddenly came to me” that is spirit. In the latter case, when the spirit is still outside, when I get possessed by having to say or do something which seems not to belong to my ego, then it is a projected aspect of my unconscious; it is a part of my unconscious psyche which is projected and then experienced as a para-psychological phenomenon.

That happens when you get into a state in which you are not yourself, or into an emotional upset where you lose control of yourself, but afterwards wake up completely sober and look at the stupid things you did during your possessed state and wonder what got into you: something got hold of you, you weren’t yourself, though while you were behaving like that you thought you were it was just as if an evil spirit or the devil had got into you.

These things one must not just take in a kind of colloquial amusing way, but quite literally, for a devil or we would say, more neutrally, an autonomous complex temporarily replaces the ego complex; it feels like the ego at the time, but it isn’t, for afterwards, when dissociated from it, one cannot understand how one came to do or think such things.

One of the main ways in which we use the word spirit is in speaking of the inspiring, vivifying aspect of the unconscious. Now we know that for the ego complex to get in touch with the unconscious has a vivifying and inspiring effect, and that is really the basis of all our therapeutic efforts. Sometimes neurotic people, who have become closed up in their neurotic vicious circle, as soon as they go into analysis and have dreams, get excited and interested in the dreams and then the water of life flows again; they once more have an interest and therefore are suddenly more alive and more efficient. Then somebody may say: “What has happened to you? You have come alive again” but that only happens if the individual succeeds in making contact with the unconscious, or one could say “with the dynamism of the unconscious,” and especially with its vivifying, inspiring aspect.

Jung therefore defines spirit, from the psychological angle, as the dynamic aspect of the unconscious. One can think of the unconscious as being like still water, a lake which is passive. The things one forgets fall into that lake; if one remembers them one fishes them up but it itself does not move. The unconscious has that matrix, womb aspect, but it also has the aspect of containing dynamism and movement, it acts on its own accord for instance, it composes dreams. One could say that composing dreams while one sleeps is an aspect of the spirit; some master spirit or mind composes a most ingenious series of pictures which, if one can decipher them, seem to convey a highly intelligent message.

That is a dynamic manifestation of the unconscious, where the unconscious energetically does something on its own, it moves and creates on its own, and that is what Jung defines as spirit. There is naturally an unclear borderline between the subjective and the objective; but in practice if one feels that it belongs to one then it is one’s own spirit, and if one does not feel it belongs to one, then one calls it the spirit, or a spirit. That depends on whether one feels akin or not akin to it, close to it or not close to it.

Jung sums up by saying that spirit contains a spontaneous psychic principle of movement and activity; secondly, that it has the quality of freely creating images beyond our sense perception (in a dream one has no sense perception the spirit or the unconscious creates images from within, while the sense perceptions are asleep); and thirdly, there is an autonomous and sovereign manipulation of those images.

Those are the three characteristics of what Jung calls the spirit, or the dynamism of the unconscious. It is spontaneously active, it freely creates images beyond sensual perceptions, and it autonomously and in a sovereign manner manipulates those images. If one looks at one’s dreams, one sees that they are composed of impressions from the day before. For instance, one read something in a paper, or experienced something in the street, or talked to Mrs. So-and-So, and so on. The dream takes these fragments and makes a completely new and meaningful potpourri out of that.

There one sees the sovereign manipulation of the pictures: they are put into another order and manipulated into a completely different sequence with a completely different meaning, though one still recognizes that the single elements have been taken from, for instance, memory remnants of the day before. That is why many people think that is the whole explanation of the dream: “Oh, I read about a fire yesterday in the paper, that is why I dreamt about a fire,” and then one has to begin, as always, by saying: “Yes, but look at the connections in which the fire has been put, very different from what you read.” That would be the spirit, that unknown thing in the unconscious which rearranges and manipulates inner images.

This factor which produces and manipulates inner images is completely autonomous in primitive man, but through the differentiation of consciousness it slowly comes closer to consciousness, and therefore in contrast to primitives we say we do it in part. For instance, we often say that we have a good idea or we invent something new. A primitive man would never say that a bow and arrow, for instance, were his invention he would say that the way to construct a bow and arrow was revealed to him by the bow and arrow god, and then tell an origin myth, of how to a certain hunter his divinity appeared in a dream or vision and revealed to him how to make a bow and arrow.

So the larger our consciousness is, and the more it develops, the more we get hold of certain aspects of the spirit of the unconscious, draw it into our subjective sphere, and then call it our own psychic activity or our own spirit. But, as Jung points out, a great part of the original phenomenon remains naturally autonomous and therefore still is experienced as a para-psychological phenomenon. In other words, we must not assume that at our present stage of consciousness, where we have assimilated more than a certain amount of the spirit of the unconscious and made it our own i.e., made it the possession of the ego complex so that the ego complex can manipulate it that we have the whole thing. There is still an enormous area of that spirit which manifests as it did originally, completely autonomously, and therefore as a para-psychological phenomenon, as it does among primitive people.

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 Pythagorean s 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.”

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 in-deterministic 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-thirty-second.

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.

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.

Not being a mathematician and physicist I had generally to rely on rather popularized material and there the physicist, when he wants to explain probability, always uses the example either of dice or cards. Just keep that in mind. If he explains the theorem of Bernoulli he begins by saying, “Well you see if you have so and so many cards,” and so on. The same way is always used to explain probability to a lay person. But why just that example? That is amusing! But to go now to the fact, it means that all mathematics, and their use in modern physics, are based on the principle of admitting an inability to make single predictions of single events, but aiming at being able to do so when it comes into thousands and billions of events which then gain a great amount of accuracy.

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.

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.