ultra-complex systems

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0.1 Ultra-complex systems

An ultra-complex system represents the human mind from the standpointof a generalized Categorical Ontology Theory of Levels as the highest level of complexity thatemerged through biological and social coevolution over the last $2.2$ million years on Earth.

0.1.1 Preliminary Data:

One can represent in square categorical diagrams the emergence of ultra-complexdynamics from the super-complex dynamics of human organisms coupled via social interactionsin characteristic patterns represented by http://planetmath.org/RosettaGroupoidsRosetta biogroupoids, together with the complex–albeit inanimate–systems with ‘chaos’. With the emergence of the ultra-complex system of the human mind– based on the super-complex human organism– there is always an associatedprogression towards higher dimensional algebras from the lowerdimensions of human neural network dynamics and the simple algebraof physical dynamics, as shown in the following, essentially non-commutative categorical diagram.

Definition 0.1.

An ultra-complex system, $U_{C\mathit{}S}$ is defined as an object representation in the following non-commutativediagram of systems and dynamic system morphisms or ‘dynamic transformations’:

Note that the above diagram is indeed not ‘natural’ (i.e. it is not commutative) for reasonsrelated to the emergence of the higher dimensions of the super–complex(biological/organismic) and/or ultra–complex (psychological/neural network dynamic) levels in comparison withthe low dimensions of either simple (physical/classical) or complex (chaotic) dynamic systems.