# ultra-complex systems

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## 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