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Archetypes and the infinite

We can gain insight into the archetypes through the finite and infinite in mathematics. There is no finite way to encompass mathematical truth even when that truth is constrained to statements about the future states of a computer following the precise deterministic steps of a program. This is important not only for questions that refer to an indefinite future. Exact mechanistic predictions are rare for complex real world problems. We need to come up with general principles that help us predict the consequences of our actions when we are not able to model precisely what those consequences will be. This can involve the same mathematical principles that allow us to decide that some programs will never halt without being able to observe their behavior for an infinite time.

The unknowable creative aspect of the properties of numbers and the unknowable creative aspect of matter are the same thing. It is this creativity that has expressed itself in our world as it is today and that continually unfolds in ways that we can never predict or control. The archetypal images of the human psyche are formed from this creative process and point toward it.

The mathematics of creativity as described in Chapter 6 allow us to know with mathematical precision some of the properties and constraints of creativity. It allows us to make connections between some human instincts and general mathematical properties. It opens the Jungian notion of archetype to mathematical analysis. This does not lessen the divine mystical nature of archetype. On the contrary it shows the divine mystical nature of mathematics.


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Next: The necessity of archetypes Up: Applying mathematics to consciousness Previous: Number and Archetype   Contents


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