To expect the primes to be uniform in distribution would seem a just so idealization i.e. atypical. Randomness is just an idealization. One could also consider the clustered primes in 3-dimensions, with still a non-uniform distribution, and compare it to non-uniform distribution of matter in early universe. Evenly distributed matter (DM and LM) for the early universe would seem like a special condition, since non-uniform distribution (voids, proto-voids, and non-void regions) for macro-scale would seem more typical. Thus physical models would seem to have to describe just evolution from such more typical early macro-stage, rather than assuming perfect uniformity (randomness) for such distribution. The latter being just an idealized assumption. One could compare to alternative scenarios (top-down, and bottom-up models – but not enough time). However perhaps one has to accept the early universe distribution of matter as like physical truth; not so unlike the clustered primes as mathematical truth? That is, was there no choice, as the the curtain rises at the end of Dark Age? TMM
November 29, 2012
Distribution of Primes versus that of matter (LM and DM) for early universe; both non-uniform – mathematical and physical truth?
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