'The Mystery of the Prime Numbers', Secrets of Creation vol. 1 by Matthew Watkins

Marie-Louise von Franz

The Jungian scholar Marie-Louise von Franz, writing about the significance of number, used an ancient Chinese story to illustrate a point. The essence of the story is as follows:

Two armies were engaged in a battle, which had reached a critical stage. One of the armies had eleven generals, and they held an emergency council in order to decide whether their army should attack or retreat. Each offered his opinion, three in favour of attacking and eight in favour of retreating. However, this was not a conventional vote in the 'democratic' sense we are familiar with. To the ancient Chinese, three is a number associated with unanimity. Therefore the eleven generals agreed that the faction in favour of attacking, despite their number being smaller, had a more favourable number, and that their opinion should be followed. The army attacked, and won the battle.

Whether this ever actually occurred is not that relevant here. The story illustrates an approach to number which is almost completely alien to the Western mind. As von Franz constantly reminds her readers, number has both qualitative and quantitative aspects.

Ancient Chinese culture structured much of its thought, art, religion, architecture, social organisation, etc. around 'qualitative resonances' between certain natural numbers and various types of situations, attitudes, structures, shapes, colours, animals, plants, character-types, bodily organs, etc. Viewed through the conceptual filters of the Western scientific mind this all looks very unfamiliar. There is no doubt that this way of thinking played a significant rôle in the development of Chinese civilisation. But from our point of view, these resonances do not refer to anything 'real', so they are generally dismissed as a sinological curiosity of little importance.

This tendency has not been confined to China. To quote von Franz directly:

"[There is a] tendency at play in number investigations [which] adheres faithfully to the Pythagorean-Platonic standpoint on number in spite of all the opposition of "pure" mathematicians. It consists chiefly of a collection of the mythological and symbolic assertions of mankind concerning numbers contained in various historical works, some of which are of the greatest value. In these collections, however, the part played by the unconscious is once again ignored, leading to the erroneous idea that symbolic statements, such as one for example which declares the number three to be "masculine," are absolute truth. The striking uniformity of mankind's assertions on number symbolism have repeatedly attracted the attention of number symbolists, although recently one of them, Werner Danckert, justly pointed out that the ideas of different cultures on this subject also display great variations." (from Number and Time, p.30-31).

At the other end of the spectrum, Western civilisation has built itself entirely around the quantitative approach. Undertakings are generally based around things being stronger, bigger, older, cheaper, more profitable, or some other quantitative scaling of a category. It is worth remembering that Western mathematics has its origins in numerology or number mysticism, much as astronomy has its roots in astrology and chemistry in alchemy. The divergence of mathematics from number mysticism appears to have begun with the Pythagorean cult, although the circumstances surrounding this process are still very unclear . In any case, despite these origins, academic mathematics now denies all connections with any kind of numerology. It is regarded as little more than superstitious nonsense, at best of minor historical interest.

All science, engineering, and technology is based on (quantitative) mathematics. Economics, possibly the aspect of peoples' lives where number is most important, could almost be described as 'hyper-quantitative' - operating mathematically in a quantitative way, yet throughout its development referring less and less to quantities of anything physically real. Rather worryingly, the current trend globally seems to be leading towards the supremacy of quantitative-economic thought (i.e. maximising profit, minimising cost, etc.) over all other forms of value-judgement. This tendency is discussed at great length in René Guénon's extraordinary book The Reign of Quantity and the Signs of the Times.

To quote von Franz from Number and Time once again:

"The gradual development of occidental scientific thinking proceeded by the sifting of a more rigorously defined idea of causality out of the "magical" ideas of the past, and at the same time the pursuit of a purely quantitative definition of number through the elimination of its qualitative aspect. This one sided development has reached its peak today. For this reason Jung suggested coining the term "synchronicity," so that certain aspects of reality which are not included in the causal description of nature can be interpreted as synchronistic events without the necessity of regressing into an archaic form of magical-causal thinking. Similarly it seems to me desirable to introduce a new qualitative concept of number to complement our hitherto prevailing quantitative number concept without falling back into magical-numerological speculations on this account."

The following is an excerpt from "Representation, Comprehension and Communication of Sets: the Role of Number" by A.J.N. Judge:

Marie-Louise von Franz (of the C J Jung Institute, Zurich) has conducted an extensively documented study into the significance of number for mathematicians, in philosophy, and as symbols of psychological significance, in a deliberate effort to bridge the gap between psychology and physics. As she puts it, her remarks "balance to some extent on the razor's edge between philosophical-mathematical and numerical-symbolical statements" (ref. (9), p.33-34). She deliberately bridges the gap between Western and other concepts of number, which is an aspect of a current debate into the wider interpretations of the concepts of science, space, and time, which have hitherto been supposed to conform conveniently to the Western versions (40) [33].

She notes that Niels Bohr has stressed that an important step had been taken toward realizing the ideal "of tracing the description of natural phenomena back to combinations of pure numbers, which far transcends the boldest dreams of the Pythagoreans" (9, p.16). She argues that if we accept Wolfgang Pauli's contention that "certain mathematical structures rest on an archetypal basis, then their isomorphism with certain outer-world phenomena is not so surprising" (9, p.19).

She sums up her argument as follows:

"To sum up: numbers appear to represent both an attribute of matter and the unconscious foundation of our mental processes. For this reason, number forms, according to Jung, that particular element that unites the realm of matter and psyche. It is "real" in a double sense, as an archetypal image and as a qualitative manifestation in the realm of outer-world experience. Number thereby throws a bridge across the gap between the physically knowable and the imaginary. In this manner it operates as a still largely unexplored mid-point between myth (the psychic) and reality (the physical), at the same time both quantitative and qualitative, representational and irrepresentational.

Consequently, it is not only the parallelism of concepts (to which Bohr and Pauli have both drawn attention) which nowadays draws physics and psychology together, but more significantly the psychic dynamics of the concept of number as an archetypal actuality appearing in its "transgressive" aspect in the realm of matter. It preconsciously orders both psychic thought processes and the manifestations of material reality. As the active ordering factor, it represents the essence of what we generally term 'mind'." (9, p.52-53)

She concludes that: "Most probably the archetypes of natural integers form the simplest structural patterns in . . . (the common unknown confronting both physicist and psychologist) ... that manifest themselves on the threshold of perception." (9, p.56) In order to explore further, it is therefore necessary to return "to the individual numbers themselves, and gather together the sum total of thought, both technical and mythological assertions, which they have called forth from humanity. Numbers, furthermore as archetypal structural constants of the collective unconscious, possess a dynamic, active aspect which is especially important to keep in mind. It is not what we can do with numbers but what they do to our consciousness that is essential." (9, p.33)

Von Franz outlines the recommended programme as follows:

"When we take into account the individual characteristics of natural numbers, we can actually demonstrate that they produce the same ordering effects in the physical and psychic realms; they therefore appear to constitute the most basic constants of nature expressing unitary psycho-physical reality." (9. p.303)

C.R. Card and V.V. Morariu, "In Remembrance of Marie-Louise von Franz"

T.J. McFarlane, "Quantum Physics, Depth Psychology, and Beyond"


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