Thursday, December 7, 2017

Our generators should have rate of change

In the world where transaction rates are about the same, then our generators can be compared in rate by their window size.

But our generators are queue stable, so window size is the sum of the generator paths (in one of two isonormal forms).   That is just the generator norm, a ratio of two generators is a ratio of window sizes and is elasticity (not necessarily coherence).

Sounds great? Maybe, remember we promise to carry and conserve round off error.

In the  generator form, being fed by some fixed precision random uniform integer (leading zeros ignored) we get the typicals batched up along the reals.   But, if we are canonical, we are 2^N-1, we get the widow size directly from rank. 

We could do arithmetic on the uniform integers, but the round off error does not translate through an inversion of the generator.  The round off is unstable, in the indices. We have limited ourselves in the count of algebra operators we can carry as we are not really symmetric (no reversible inverse that carries round off)

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