ISRZ

(What was the date on the following? Your laptop may have some info if you search...)

"You could also now go back and quickly assess the "prime evolution" idea in terms of your newfound dynamical systmes knowledge.

OK - you have the choice - is this going to be an (1) iterative thing (where you apply a 'diffeomorphism' of some sort to the space of Beurling configurations) or (2) a continuous thing, i.e. a flow on that space, whatever that space is. Note that (1) is THE SAME PROCESS EVERY TIME, not something dependent on the configuration. I was envisioning something vaguely like a Hamiltonian flow on some infinite dimensional phase space, where some external force or field was being applied.

You could make a simplified model with a finite number of points interacting, attractively or repulsively in a way determined by some 'physical laws' dependent on their arithmetic configuration at any given point. We may not be able to model this, but we could define a phase space, and be sure that it provided a flow. You are arguing that th eprimes constitute a fixed point, probably even an asymptotic fixed point. This means that left alone, a g-prime configuration would evolve, but if it got within a particular neighbourhood of the classical configuarion, it would then have to approach it in limit. In this way, there's the possibility that there could be configurations which never got anywhere near the classical one. So this would correspond to your long-distant imaginings about stability - you could kick the classical primes and within some limits, they would return to their original state. If it's possible to define such a phase space (well, it could be seen as some subset of some function space, I suppose, but there's then the problem of defining differentiability, etc.) then there might exist any number of such flows. You have in mind the possibility that there might be one "very special" one, the specifics o fits dynamics filling in some major theoretical holes somewhere. There may be dynamcial systems theory which would apply here, but it's a difficult problem. Worth bearing in mind though, the idea of a flow on the space of Beurling configurations. Could you look at Poincare section maps? Actually this isn't an unreasonable idea. Beurling thought of g-primes. I don't know how to describe the space of all such configurations, but if we could think of it as a phase space and consider the possibilitites of flows on such a space, we might well find something of interest to analytic number theorists. Just a thought. Maybe I should leave it at that."

Something in ISRZ about use of noncommutative geometry to 'probe beneath planck scale' - this may well be relevant to your psizoom page.