Subject: Mathematics and
physics of the decision and perception (recognition) process; conclusions
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
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 introduced in the detailed information . 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).
Since 2015 the approach was extended and the connection of "information" with geometry addressed in wgeoapp1.pdf.
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 of life on earth.