The archetype theories as described by Carl Jung are kind of fascinating. Though not at all mathematical in their nature, they go about it in a more philosophical way in describing the idea that all human beings share a pool of inherited “memories” stored in the primitive parts of our brains. This would be certain imagery, sounds etcetera, basically sensory data, that we are not necessarily consciously aware of, but rather things that trigger our imagination when exposed to things that suddenly bring these stored impressions briefly to life. In short this means that we have some hardwired memories that originate from the prehistory of mankind rather than our own personal experience.
Jung claims, if I remember correctly, that these stored memories, or simply archetypes are a driving force behind most forms of artistic expression, mainly in visual arts, but also frequently in things like music and literature. The bottom line would be that the closer you manage to represent a somewhat impressionistic interpretation of some archetype, deliberately or by accident, the more interesting the particular work of art will appear to its audience (and the creator obviously).
I believe there is a lot of truth in this. It can’t be a coincidence that certain themes in art appears in so many different cultures from way back in time before there was any major interaction between various parts of the world. If one would compare the arts and religious beliefs of the ancient native americans to that of the australian aborigines, for instance, one should find similarities that can’t possibly come from any representatives of these cultures actually having met eachother and exchanged ideas - but must come from something else.
The thing I like most about the theory, is that it can constitute a very elegant starting point for explaining various religous mysteries and “supernatural phenomenon” in a more down-to-earth manner than usual.