On Certain Number Theoretical Aspects of TGD

Abstract

Recently a considerable progress has occurred in the understanding of number theoretic aspects of quantum TGD. In this article  the details of the adelicization boiling to p-adicization for various p-adic number fields, in particular those assignable to ramified primes, are discussed.  p-Adic fractals and holograms emerge very naturally and  the  iterations of (f₁; f₂) to Go(f₁; f₂) = (g1(f₁; f₂); g2(f₁; f₂)  define hierarchical fractal structures analogs to Mandelbrot and Julia fractals and p-adically  mean exponential explosion of the complexity and information content of cognition. The possible relationship to biological and cognitive evolution  is highly interesting. Both p-adicization and hyperfinite finite factors of type II₁, which both allow a description of finite measurement resolution. The relationship between these two building bricks of TGD is discussed.