Computing with High-Dimensional Vectors

I will walk through an example of identifying languages based on the similarity of 10,000-dimensional vectors computed from text. The vectors are made from random 10,000-D vectors for letters with three operations: vector addition, coordinate wise multiplication, and shuffling of coordinates.  A fully general system of computing can be built on these operations.  It requires a memory with a circuit resembling the cerebellar cortex.  I will point out the underlying math and look forward to a discussion of what this kind of computing might be good for.