On Boolean Algebras, Stone Spaces & TGD

Abstract

The Discussion with Stephen King on social media about Stone spaces led to a highly interesting development of ideas concerning Boolean, algebras, Stone spaces, and p-adic physics.  I have discussed these ideas already earlier but the improved understanding of the notion of Stone space helped to  make the ideas more concrete. The basic ideas are briefly summarized. p-adic integers/numbers correspond to the Stone space assignable to Boolean algebra of natural numbers/rationals with p = 2 assignable to Boolean logic.   Boolean logic generalizes for n valued logics with prime values of $n$ in special role. The decomposition of set to n subsets defined by an element of n Boolean algebra  is obtained by  iterating Boolean decomposition n -2 times. n - valued logics could be interpreted in terms of error correction allowing only bit sequences, which correspond to n<p<2^k in k-bit Boolean algebra.  Adelic physics would correspond to the  inclusion of all p-valued logics in single adelic logic. The Stone spaces of p-adics, reals, etc.. have huge size and a possible identification (in absence of any other!) is in terms of concept of real number assigning to  real/p-adic/etc... number a fiber space consisting of all units obtained as ratios of infinite primes. As real numbers they are just units but has complex number theoretic anatomy and would give rise to what I have assigned the terms  algebraic holography and number theoretic Brahman = Atman.