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Number and Archetype

After C. G. Jung had completed his work on synchronicity in ``Synchronicity: An Acausal Connecting Principle,'' he hazarded the conjecture, already briefly suggested in his paper, that it might be possible to take a further step into the realization of the unity of psyche and matter through research into the archetypes of the natural numbers. He even began to note down some of the mathematical characteristics of the first five integers on a slip of paper. But, about two years before his death, he handed the slip over to me with the words: ``I am too old to be able to write this now, so I hand it over to you.'' -- Marie-Louise von Franz, from the preface of Number and Time[49].

The mathematical properties of numbers are discovered, absolute and creative. At some point in time each of them may be discovered, but at any point in time only an infinitesimal fragment of them can be known. These seemingly paradoxical properties come from mathematics' concern with the potentially infinite in a universe in which everything that exists is a particular finite experience.

The archetypes have been built from an unfathomable history of experience. The details of those experiences are different, but there are structural similarities that are universal enough to find their way into our genes. The generality that makes these experiences important enough to incorporate in our genetics makes it problematic to apply the experience to specific situations. To a large degree life is a process of refining archetypal material into ideas, intuitions, art and behavior that have value in our life and times. Jung saw medieval alchemy as providing both a metaphor for this process and as an intuitive and intellectual study of the process[28,27,30].

Archetypal material related to sex, birth and family is among the most basic and direct. The refinement of this archetypal material to deal with contemporary reality is extremely difficult as the immense problems we are having today in family structure confirm. The difficulty is rooted in the contradictory and competitive nature of the archetypes.

The problem is not just to refine archetype images individually to golden nuggets of practical value. Their deepest values can only be realized through a union of contradictory claims[30]. For example the competition between career and family that creates so many problems is a real one. It does not have a solution. The problem is a creative force that can lead us to a deeper development of self or to destruction.


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