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Mathematics and consciousness

Mathematics is the study of all possible structures. Conscious experience has a structure and that structure is subject to mathematical analysis. Mathematics can teach us about possible transformations of structure and thus consciousness. Through mathematics we can extrapolate from the experience that is the essence of the human mind to what life and conscious experience may evolve into.

The capacity for subtle self reflection is a defining characteristic of human consciousness. This capacity characterizes a level of conscious experience. In mathematics it is common to measure the power of a mathematical system by the level of self reflection or iteration that is definable within the system. Mathematics shows that there is no finite limit to the levels of subtle self reflection in finite systems. No existing system nor any finite structure can ever capture all the possibilities.

Expanding the level of self reflection of a being seems to expand the nature of conscious experience as has happened in the evolutionary hierarchy culminating in human experience. Evolution creates such structures because they have survival value. They allow better prediction of future events. Mathematics shows that unbounded evolution is possible only if diversity expands without limit.

Evolution operates on itself. Competition and cooperation between branches on the tree of life provide the rich ecosystem from which a structure as sophisticated as the human mind has evolved. Through man the evolutionary process has become conscious of itself and is able to use mathematics to understand aspects of its structure. Through mathematics we can understand the boundary conditions that will allow us to take conscious control of evolution without stifling creativity.


Completed second draft of this book

PDF version of this book
next up previous contents
Next: Logically determined unsolvable problems Up: Mathematical structure Previous: Mathematical structure   Contents


Mountain Math Software
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