PlanetPhysics/Highly Complex Systems

Highly-complex systems

Introduction

Modeling the emergence of the ultra-complex system of the human mind--based on the super-complex human organism-- one needs to consider an associated progression towards [[../InfinityGroupoid/|higher dimensional algebras]] from the lower dimensions of human neural network [[../MathematicalFoundationsOfQuantumTheories/|dynamics]] and the simple algebra of physical dynamics, as shown in the following, essentially [[../AbelianCategory3/|non-commutative]] [[../CategoricalDiagramsDefinedByFunctors/|categorical diagram]]. One can represent by [[../PiecewiseLinear/|square]] categorical diagrams the emergence of ultra-complex dynamics from the super-complex dynamics of human organisms coupled via social interactions in characteristic patterns represented by Rosetta biogroupoids, together with the complex--albeit inanimate--systems with `chaos' as discussed next.

Diagrams of simple and highly-complex systems

An ultra-complex system, $U_{CS}$ is defined as an [[../TrivialGroupoid/|object]] [[../CategoricalGroupRepresentation/|representation]] in the following [[../NonCommutativeDynamicModelingDiagrams/|non-commutative diagram]] of [[../SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence/|systems]] and [[../GenericityInOpenSystems/|dynamic system]] [[../TrivialGroupoid/|morphisms]] or `dynamic transformations':

Failed to parse (unknown function "\xymatrix"): {\displaystyle \xymatrix@C=5pc{[SUPER-COMPLEX] \ar [r] ^{(\textbf{Higher Dim})} \ar[d] _{\Lambda}& [[User:MaintenanceBot|MaintenanceBot]] ([[User talk:MaintenanceBot|discuss]] • [[Special:Contributions/MaintenanceBot|contribs]])(U_{CS}= ULTRA-COMPLEX) \ar [d]^{onto}\\ COMPLEX& \ar [l] ^{('''Generic Map''' )}[SIMPLE]} }

Remarks

Note that the above [[../TrivialGroupoid/|diagram]] is indeed not `natural' (i.e. it is not commutative) for reasons related to the emergence of the higher dimensions of the super--complex (biological/organismic) and/or ultra--complex (psychological/neural network dynamic) levels in comparison with the low dimensions of either simple (physical/classical) or complex (chaotic) dynamic systems.

An ultra-complex system represents the human mind and consciousness from the standpoint of a [[../CategoricalOntology/|categorical ontology]] theory of levels as the highest level of [[../Complexity/|complexity]] that emerged through biological and social coevolution over the last $2.2$ million years on Earth.