PlanetPhysics/Highly Complex Systems

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, together with the complex--albeit inanimate--systems with `chaos' as discussed next.

Diagrams of simple and highly-complex systems
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':

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

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.