highly-complex system diagrams

0.1 Highly-complex systems

0.1.1 Introduction

Modeling the emergence of the ultra-complex system of thehuman mind–based on the super-complex human organism– one needs to consider an associatedprogression towards higher dimensional algebras from the lower dimensions of human neural network dynamics and the simple algebra of physical dynamics, as shown in the following, essentially non-commutative categorical diagram.One can represent by square categorical diagrams the emergence of ultra-complexdynamics from the super-complex dynamics of human organisms coupled via social interactionsin characteristic patterns represented by Rosetta biogroupoids (http://planetmath.org/RosettaGroupoids), together with the complex–albeit inanimate–systems with ‘chaos’ as discussed next.

0.2 Diagrams of simple and highly-complex systems

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’:

0.3 Remarks

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.

An ultra-complex system represents the human mind and consciousness from the standpointof a 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.