in https://yorkporc.wordpress.com/2014/01/22/modeling-turings-quantum-machine-in-terms-of-the-quantum-harmonic-oscillator/ we refereed to rotating the geometry itself.
We recall the 1 dimensional argument and its relationship to rotating from https://yorkporc.wordpress.com/2013/12/28/rotations-and-one-dimensional-representations/
im not sure one really needs the couplets idea. Don’t we recall drawing a wheel wiring for both I and j?
If we think back to ECM mark II, it would make sense for this kind of Turing wheel-generating wheels cage to be used in the ECM’s middle cage, remembering these wheels don’t rotate. Since the effect is a bijection, of course it requires a random output from the first wheel cage – all of which is consistent with how ECM worked. Of course, the resulting probability density of bits on 5 streams, as steckered by the middle wheel cage for each sensitibity level, would then control whether the associated 5 polyalphabetic wheels were individually held back from stepping on, as each character was processed.