ultra-complex systems

\xyoption

curve

0.1 Ultra-complex systems

An ultra-complex system represents the human mind from the standpoint of a generalized 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.

0.1.1 Preliminary Data:

One can represent in 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 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 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.

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]}

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.

Title	ultra-complex systems
Canonical name	UltracomplexSystems
Date of creation	2013-03-22 18:11:40
Last modified on	2013-03-22 18:11:40
Owner	bci1 (20947)
Last modified by	bci1 (20947)
Numerical id	19
Author	bci1 (20947)
Entry type	Topic
Classification	msc 00A30
Classification	msc 18A40
Classification	msc 37B25
Classification	msc 93D15
Classification	msc 18A05
Classification	msc 93D21
Classification	msc 37B10
Synonym	extremely complex systems
Synonym	the mind
Related topic	CategoricalOntology
Related topic	RosettaGroupoids
Related topic	StrongAIThesis