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# highly-complex system diagrams

# 0.1 Highly-complex systems

# 0.1.1 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.

# 0.2 Diagrams of simple and highly-complex systems

###### 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’:

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

# 0.3 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.

## Mathematics Subject Classification

37B25*no label found*93D15

*no label found*18A05

*no label found*93D21

*no label found*37B10

*no label found*

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