Turings model as path counting


http://www.stanford.edu/class/ee363/lectures/pf.pdf

Each power of the kth generator is indeed a rotation of the associated cycle (a fractional path). But, in a path world of length k, from i to j, its also the length i+power to j. Thus we want the total powers to sum to zero so we are, overall, localizing on a zero-length point, which is orthogonal to _every_ vector (in the n dimensional space).

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