highly-complex system diagrams

0.1 Highly-complex systems

0.1.1 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 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-complex dynamics from the super-complex dynamics of human organisms coupled via social interactions in 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, $U_{CS}$ is defined as an object representation in the following non-commutative diagram of systems and dynamic system morphisms or ‘dynamic transformations’:

\xymatrix@C=5pc{[SUPER-COMPLEX]\ar[r]^{(\textbf{Higher Dim})}\ar[d]_{\Lambda}&~{}~{}~{}(U_{CS}=ULTRA-COMPLEX)\ar[d]^{onto}\\ COMPLEX&\ar[l]^{(\textbf{Generic Map})}[SIMPLE]}

0.3 Remarks

Note that the above 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 categorical ontology theory of levels as the highest level of complexity that emerged through biological and social coevolution over the last $2.2$ million years on Earth.

Title	highly-complex system diagrams
Canonical name	HighlycomplexSystemDiagrams
Date of creation	2013-03-22 18:30:13
Last modified on	2013-03-22 18:30:13
Owner	bci1 (20947)
Last modified by	bci1 (20947)
Numerical id	7
Author	bci1 (20947)
Entry type	Topic
Classification	msc 37B25
Classification	msc 93D15
Classification	msc 18A05
Classification	msc 93D21
Classification	msc 37B10
Related topic	RosettaGroupoids
Related topic	StrongAIThesis
Related topic	CategoricalDynamics