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ultracomplex systems and categorical dynamics
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(Topic)
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A relatively recent area (1958- ) of category theory, higher dimensional algebra and mathematical physics developing applications of categories, functors, natural transformations, higher dimensional categories and supercategories to dynamics in classical, quantum, complex and
super-complex systems.
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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"ultracomplex systems and categorical dynamics" is owned by bci1.
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See Also: categorical physics
| Also defines: |
ultra-complex systems |
| Keywords: |
categorical dynamics, dynamics in categories, ultra-complex systems, natural transformations |
Cross-references: diagram, morphisms, dynamic system, non-commutative diagram, representation, object, non-commutative, categorical diagrams, square, systems, dynamics, supercategories, natural transformations, functors, categories, mathematical physics, higher dimensional algebra, category theory
There are 2 references to this object.
This is version 5 of ultracomplex systems and categorical dynamics, born on 2008-12-16, modified 2009-06-24.
Object id is 331, canonical name is CategoricalDynamics.
Accessed 969 times total.
Classification:
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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]} $](http://images.physicslibrary.org/cache/objects/331/l2h/img2.png "$\displaystyle \xymatrix@C=5pc{[SUPER-COMPLEX] \ar [r] ^{(\textbf{Higher Dim})} ... ...-COMPLEX) \ar [d]^{onto}\\ COMPLEX& \ar [l] ^{(\textbf{Generic Map})}[SIMPLE]} $")