# ultra-complex systems

\xyoptioncurve

## 0.1 Ultra-complex systems

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.

### 0.1.1 Preliminary Data:

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 http://planetmath.org/RosettaGroupoidsRosetta 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.

###### 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’:

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

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.

Title | ultra-complex systems |

Canonical name | UltracomplexSystems |

Date of creation | 2013-03-22 18:11:40 |

Last modified on | 2013-03-22 18:11:40 |

Owner | bci1 (20947) |

Last modified by | bci1 (20947) |

Numerical id | 19 |

Author | bci1 (20947) |

Entry type | Topic |

Classification | msc 00A30 |

Classification | msc 18A40 |

Classification | msc 37B25 |

Classification | msc 93D15 |

Classification | msc 18A05 |

Classification | msc 93D21 |

Classification | msc 37B10 |

Synonym | extremely complex systems |

Synonym | the mind |

Related topic | CategoricalOntology |

Related topic | RosettaGroupoids |

Related topic | StrongAIThesis |