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See also: Research.BottPeriodicity
Bott periodicity
I am learning about this and will be writing about it.
This is an important mathematical phenomenon which I think models the eight-cycle of divisions of everything. Which is to say, it models our states of mind (the ways that our mind's global workspace can be carved up into perspectives) and the ways that we can shift from one state of mind to another by various degrees of self-reflection, that is, by adding one, two or three perspectives. The crucial point is that carving up the mental space into eight perspectives is basically the same as not carving it up into any perspectives at all.