# 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 (http://planetmath.org/RosettaGroupoids), 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, ${U}_{C\mathit{}S}$* is defined as an object representation in the following non-commutative
diagram of systems and dynamic system morphisms^{} or ‘dynamic transformations^{}’:

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

## 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.

Title | highly-complex system diagrams |

Canonical name | HighlycomplexSystemDiagrams |

Date of creation | 2013-03-22 18:30:13 |

Last modified on | 2013-03-22 18:30:13 |

Owner | bci1 (20947) |

Last modified by | bci1 (20947) |

Numerical id | 7 |

Author | bci1 (20947) |

Entry type | Topic |

Classification | msc 37B25 |

Classification | msc 93D15 |

Classification | msc 18A05 |

Classification | msc 93D21 |

Classification | msc 37B10 |

Related topic | RosettaGroupoids |

Related topic | StrongAIThesis |

Related topic | CategoricalDynamics |