Rosetta biogroupoids

Rosetta biogroupoids

Background

It seems that the awareness of the self of other individuals developed at first, and then,
through–and as

as an

extension

of the others

– to oneself,

self awareness

emerged in a final step. Such pre–historic, societal/social interactions that are based on consensus, are also called ‘mutual’.
These considerations lead to a natural

representation

of one’s ‘self’ emergence in terms of the following mathematical concept.

Definition 0.1

.

A

Rosetta biogroupoid

,

𝖱

𝖦

, is a representation of

characteristic

, star-connected
patterns of two–way social (cooperative) interactions:

⟺

, or

⇕

, that are defined as

topological groupoids

𝖦

S

with star– (

*

), or rose– like, internal

symmetries

. From a strictly topological
viewpoint, a

Rosetta biogroupoid

is a particular type of highly

connected

network

, or oriented multi–graph, consisting of

central

nodes (vertices) connected through bi-directional edges representing the mutual interactions
between individuals in a population or society; thus, it can also be regarded as a particular type of low-dimensional

CW complex

with a (CW) cellular structure (

http://planetmath.org/CWComplexDefinitionRelatedToSpinNetworksAndSpinFoams

) determined by the organisms, such as humans, and their mutual interactions.

Example

An especially interesting case of Rosetta

groupoids

is that of

freely generated

structures over a graph

, or

network

, of social interactions with different degrees/orders or levels of connectivities; a good example is that of the Erdös ‘connectivity’ number, defined by the length of the chain connecting an Erdös co-author of a published mathematical paper with Erdös to another co-author of the first one, and so on.

A

‘Rosetta biogroupoid’

structure can be depicted as in the following

diagram

, but possibly with as many as twenty five branches from the center, reference individual:

\xymatrix

⁢

&

⁢

Neighbour’s Self

\ar

⁢

[

d

]

⁢

&

⁢

Neighbour’s Self

\ar

⁢

[

r

]

⁢

&

⁢

Oneself

\ar

⁢

[

r

]

⁢

\ar

⁢

[

l

]

⁢

\ar

⁢

[

u

]

⁢

\ar

⁢

[

d

]

⁢

&

⁢

Neighbour’s Self

\ar

⁢

[

l

]

⁢

&

⁢

Neighbour’s Self

\ar

⁢

[

u

]

⁢

&

(0.1)

Diagram 1

:

A Rosetta biogroupoid

of
consensual, societal interactions leading to self-awareness, one’s
self and full consciousness; there could be as few as five, or as
many as twenty five, individuals in a pre-historic society of
humans; here only four are represented as branches.

Remark:

such cooperative interactions caused- through social and biological coevolution- the emergence of human (and/or ‘humanoid’) structured languages with both syntax and semantics; the latter in their turn facilitated the development of self-awareness and the emergence of the human mind as an

ultra-complex system

, and consciousness as an ultra-complex (meta-process) of processes.

Title

Rosetta biogroupoids

Canonical name

RosettaBiogroupoids

Date of creation

2013-03-22 18:11:57

Last modified on

2013-03-22 18:11:57

Owner

bci1 (20947)

Last modified by

bci1 (20947)

Numerical id

48

Author

bci1 (20947)

Entry type

Topic

Classification

msc 92C30

Classification

msc 92B99

Classification

msc 92B20

Classification

msc 92B05

Synonym

coevolution groupoids

Synonym

social interaction group patterns

Related topic

UltraComplexSystems

Related topic

CategoricalOntology

Related topic

ErdHosNumber

Related topic

ComplexSystemsBiology

Related topic

SupercategoriesOfComplexSystems

Related topic

Biogroupoids

Related topic

AbstractRelationalBiology

Related topic

CWComplexDefinitionRelatedToSpinNetworksAndSpinFoams

Related topic

HighlyComplexSystems

Defines

topology of social interactions

Defines

social networking

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