Unknown’s phd dissertation
we were seeing early how the commutator group could be a generator; and in expander graphs (and quantum crypto equivalents) how the commutators and their components, generated at each evolution, were then used as generators of the next transition matrix. Of course, the trick was to “preserve” the family trait (going forward).
The quote address going backward. Having defined a operator that constructs the transition matrix at time t (and then applies it to the set observations (represented by an observation function), we learned how that matrix acts on the observer able to generate a new transition function (Tt) (still able to act on the next observable function in the time sequence). But, the quote also points out how there is also a limiting notion, when one forms a limit back at time=0, taking the observed differences at two time points.
The point is that this new operator (constructed by differentiating the sample space) is a “generator” of the process. One can imagine almost a refining process that continually readjusts the spectral analysis of the sugar, as it wander down the conveyor belt – able to reproduce the samples under an iterative evolution from its “stored information”.
Of course, this should feel JUST like figuring out a wheel’s setting- from tunny rectangles, using colossus wheel breaking. And of course in Tunny, folks differentiated (suitable) streams(delta’ed). And then they conducted a “refining” operation (convergence) that “purified the extract”.
we see how one anticipates considering the delta’ing of characters (by xor’ing), and the delta’ing of that stream too (to create the second differentials of all pairs).