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Symmetry Breaking ... what it means ...
There are several crucial issues involved with symmetry breaking, the decoding, encoding and general transduction of confluencial topology. One is the production of loci which statistically compound the amount of perceived information.
Another concern is, if my thesis is correct, that entropy of factors at one level of organization induces automatically negentropy in the next frame of assembly, then how does the "negative" quality arise? ... other than simply observing occurances and accepting its verity. ... like the confinement of two jugglers to staying close in order to increase the general distribution of juggled objects? One enlargement of distribution forcing a reduced distribution of the next level of organization.
Typically, we apply Abelian commutative relations to the Apollonian "excluded middle", and so treat all values as "positive". But, consider this diagram where s and t are the Apollonian Cb and Ca respectively. If any k (along the line C) is the reference locus defining the two values of Ca,b, then in measuring from one diameter end point of C to the other, k is being approached in one case and retreated from in the other. 'Approach' is a diminishing value (-) and 'retreat' is an increasing value (+) relative to k as locus-0.
In other words, 'breaking symmetry' not only adds exponential dimensionality, it incorporates a non-Abelian quantitative change in content, and, the inclusion of a "negative" measure component.
Symmetry breaking combines all the original commutative factors and compounds it with non-commutative relations as well. Simply put, there are no 'pure' Abelian or non-Abelian systems. Confluencial topological changes in which exponential values change, automatically include new relationships and variances in commutivity ... with all that implies for "information content" of systems. Abelian relations are sub-sets of non-Abelian relations. They co-exist, with the only mathematical difference being the what we choose to focus on and examine in more depth.