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Subject:  Mathematics and physics of the decision and perception (recognition) process; conclusions
Some keywords:  temporary symmetry breaking, conservation law, discrete mathematics, finite past, finite calculus, discrete physics, quantum physics, relativity, proper time, decision, random walk, binomial distribution, pascal triangle, graph theory, recombination, measurement, recognition, perception, information theory, combinatorics 

The Recombination Principle:
Mathematics of decision and perception

The information paths from our decisions to our perceptions are finite, they branch finitely many times within the framework of a combinatorial law. Intention of this publication is to show concepts and also to propose mathematical approaches to this topic.

Strict argumentations can be found here. The information, which we perceive resp. measure from (past) physical reality, influences our decisions, and (our) decisions influence (future) physical reality. Every decision and every measurement implies the choice of one from several possibilities. This choice contains information which must be transferred. Therefore it isn't free of charge, it needs time and free energy. If this is ignored in mathematical physics, i.e. if the time independent axiom of choice and derived models (continuous number sets together with traditional differential and integral calculus) are used, there is a problem in the foundations - for these models cannot exist an equivalent in physical reality, and these models hide the connection between us (by presupposing infinite instead of finite branching depth between us) and these models don't show a fundamental information theoretical approach. This approach should (starting from symmetry breakings) incorporate the hierarchy of conservation laws - and derive these from a primary conservation law.

After illustration of the problem suggestions for consequent discrete mathematical approaches are made in the detailed information (which also contains the latest updates). The "probability of return" of separated conserved quantities plays a central role. Proper time proves to be proportional to the sum of probabilities for return to the starting point (symmetry center) of a Bernoulli random walk. The formulae indicate that the by us sent cumulative effect will be later perceived by us again in recombined form (summarily), and that the probability for this goes to 1 (in the course of proper time).

If you are interested: The combinatorics of real (discrete) physics can soon become so complicated that Software and computer emulations are necessary for us to get some insight.
If you have enough time: There are also a concise formulary and a formulary and some older texts  (in german language).
If you like: There is also some music.

A general conclusion:
- We should not overestimate the importance of the current (short term) partition of perceptible reality, and not underestimate the medium term relevance of increasing information exchange and conjoint history (and not underestimate the very long term relevance of conjoint contradiction free memory).
Remark (2015): Anthropogenic problems threaten future life on earth.