Self-organized criticality resulting from minimization of perpetual disequilibration

A bootstrapping system is proposed in order to describe nonlogical properties of living systems, in which the velocity of observation propagation is finite. A cellular automaton (CA) model of the system combines two logics which are the a priori non-Boolean logic and the a posteriori Boolean logic. Because of inconsistency between the two logics, the system evolves perpetually generating disequilibrium and perpetually equilibrating the generated disequilibrium. The system tends to self-organize to the border between order and disorder, and shows critical behaviours as class IV CA. Although the critical behaviors of the two systems are similar, the bootstrapping system has twice stronger undecidability than class IV CA or edge of chaos dynamics. It is stressed that real living systems are not computable and should be described by strongly undecidable systems.