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ultra-complex systems
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(Topic)
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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.
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 Rosetta 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.
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.
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"ultra-complex systems" is owned by bci1.
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Cross-references: complex, simple, commutative, transformations, morphisms, dynamic system, representation, object, non-commutative, simple algebra, dimensions, higher dimensional algebras, characteristic, diagrams, categorical, square, levels, theory, categorical ontology, represents
There are 10 references to this entry.
This is version 16 of ultra-complex systems, born on 2008-07-12, modified 2008-10-18.
Object id is 10771, canonical name is UltraComplexSystems.
Accessed 1431 times total.
Classification:
| AMS MSC: | 37B10 (Dynamical systems and ergodic theory :: Topological dynamics :: Symbolic dynamics) | | | 93D21 (Systems theory; control :: Stability :: Adaptive or robust stabilization) | | | 18A05 (Category theory; homological algebra :: General theory of categories and functors :: Definitions, generalizations) | | | 93D15 (Systems theory; control :: Stability :: Stabilization of systems by feedback) | | | 37B25 (Dynamical systems and ergodic theory :: Topological dynamics :: Lyapunov functions and stability; attractors, repellers) | | | 18A40 (Category theory; homological algebra :: General theory of categories and functors :: Adjoint functors ) | | | 00A30 (General :: General and miscellaneous specific topics :: Philosophy of mathematics) |
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Pending Errata and Addenda
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![$\displaystyle \xymatrix@C=5pc{[SUPER-COMPLEX] \ar [r] ^{(\textbf{Higher Dim})} ... ...-COMPLEX) \ar [d]^{onto}\\ COMPLEX& \ar [l] ^{(\textbf{Generic Map})}[SIMPLE]} $](http://images.planetmath.org:8080/cache/objects/10771/js/img1.png "$\displaystyle \xymatrix@C=5pc{[SUPER-COMPLEX] \ar [r] ^{(\textbf{Higher Dim})} ... ...-COMPLEX) \ar [d]^{onto}\\ COMPLEX& \ar [l] ^{(\textbf{Generic Map})}[SIMPLE]} $")