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# Complexogenesis

## Contents

Complexogenesis is the emergence of complexity. In order to understand this phenomenon, we have to ask ourselves: What even is complexity?
Complexity is the multiple combinations of merely simple functions/principles.
But to understand which role complexogenesis plays in the creation of diversity and life itself, we have to take an important detour into chaos theory and define entropy as factor of complexity increase and emergence as factor of relative complexity decrease.

## What is chaos?

Chaos, to be more concrete,deterministic chaos shouldn't be confused with randomness; Whereas randomness is merely a primarily manmade thing, nature's laws always have a hidden underlying principle; Chaos is merely defined by probabilistic determinism, and is still deterministic in that sense, that it follows logical rules. The only difference between probabilistic determinism and strict probabilism, that is common for linear binary logic, probabilistic determinism adds a tolerance interval of deviation to the strict deterministic prediction.
Emergence can be observed in ever-repeating patterns, resulting in probabilistic determined systems turn into merely strict deterministic ones after uncountable renditions; The tolerance interval shrinks more and more, until the deviation is so minimal that its formerly non-binary nature vanishes entirely.

Hence, chaos can be regarded as a more complex form of order:
And this chaos/ order can be classified into complexity levels.

The complexity levels depend on three main factors:

• quantity of recursion levels (quantity of nestings in the fractal tree pattern of systems/ amount of levels in hierarchies; kind of synonymous to a medium)
• interaction coefficient (quantity of the process of self-interference, dependent on entropy and emergence, per time interval; kind of synonymous to frequency, amplitude and wavelength combination)
• meta-mathematical dimensionality (quantity of structural interrelations one point has towards other points; kind of synonymous to a medium)

The interaction coefficient is embedded in quantity of recursion levels and meta-mathematical dimensionality, the two "mediums"
The two mediums are synonymous to spacetime, which relate very intertwinedly to gravity, a curvation of the medium.
The interaction coefficient is synonymous to matter in this analogy, which can be regarded as a highly knotted and interwoven form of spacetime itself as we will discuss in following chapters The structure-process-complex and Cosmic weaving.

For all factors an increase of their value also means an increase in complexity.

## What is entropy?

Entropy, from an utterly minimalistic/reductionistic point of view, works like an intrinsic force leading to interaction;
Say, elements/entities don't want to "sit still", and therefor entropy can also be regarded as an intrinsic force to move or oscillate, which then leads inevitable to interactions.
Entropy thus produces an increase of complexity.

In some system there arises a principle called emergence, which means that a system develops patterns its entities don't have themselves.

## What is emergence?

Emergence is a result of entropy, which is a process of complexification. On the other hand, emergence is a form of self-simplification, produced by a given amount of complexity.
In the upshot, emergence is nothing more but the process of a system that becomes so complex that it simplifies itself.

## Entropy-emergence-ratio

As emergence works as a kind of reverse-complexifier, say, a form of simplifier, emergence is a kind of antagonist or inversion of entropy itself.
If the ratio is larger on the emergence side, the system's relative complexity decreases.
If the ratio is larger on the entropy side, the system's relative complexity increases

## Levels of complexity

Complexity can be grouped into 5 main categories; Level 0, 1, 2, 3 and 4: The higher the level the bigger the meta-mathematical dimensionality, say the "intertwinedness".

### Zero complexity / Level 0 complexity

A level 0 complexity is marked by having no combinations and mixtures of different entities, it is a strict separation of different elements/ entities. No diversity can be found. This is a rather unnatural state in nature because the law of entropy is a kind of intrinsic force for interaction.

### Additional complexity / Level 1 complexity

Whereas the simplest form of order (Level 0) is strict separation of different entities, level 1 complexity starts to combine the different entities in a linear way.
If you make a very simple mixture in form of a simple sequence its complexity increases in form of an additional complexity.

It has a fixed structure and is created by a fixed process.

### Multiplicated complexity/ Level 2 complexity

If you let a system with level 1 complexity interfere/ knot with itself, you get a level 2 complexity, which is like multiplicated complexity.
This level is marked by systems that are self-referent, but are not self-interfering, and thus don't change their processes. It is a rigid self-replicating process that doesn't change.
This is a main principle that can be found in the sequences of DNA.

It has a flexible structure and is created by a fixed process (like Fn = Fn-1 + Fn-2/ Fibonacci sequence)
Fixed process = repeating pattern of the process that changes the structure.

### Powered complexity/ Level 3 complexity

If you let a system with a level 2 complexity interfere/ knot with itself, you get a level 3 complexity; which is like powered complexity.
This level is marked by recycling-loops that interfere with its own processes, they "re-program/ rewrite themselves", say they get self-interfering, additional to self-referent. Hence it is an adaptable self-replicating process.
This is the main principle of deep learning mechanisms in AI.
Systems with level 3 complexity have a highly nested nature; Each entity interacts with all other entities, including parents/ superordinated branches, siblings/ parallel branches, and also children/ subordinated branches.

It has a flexible structure and is created by a flexible process (Both the equation/ rules of processes can change as well as its structures, but gradually, so no abrupt changes that have utterly no relation to the previous equations/ rules of processes)

### Level 4 complexity

Level 4 and above have complexity like level 3 complexity, but are nested even more.

There is an overview of the aspects and attributes of each complexity level:

Complexity level Zero 1 2 3 4
synony
-
mous number system
- ima
-
ginary
real complex hyper-complex
dimen
-
sions
0D 1D 1D/2D 2D/3D ≥3D
structure - fixed flexible flexible flexible
process - fixed fixed flexible flexible
synony
-
mous to operations
-
plica
-
tion
poten
-
tiation
poten
-
tiation of poten
-
tiation
self-referent no yes yes yes yes
rigid self-replication no yes yes yes yes
linear self-inter
-
ference
no no yes yes yes
-
cation
no no no yes yes
self-simplifi
-
cation/ multi-dimen
-
sional self-inter
-
ference
no no no no yes
Absolute complexity increase 0 1+ 2+ 4+ 8+
Relative complexity increase
complexity increase relative to the entropy-emergence-ratio
0 0 *x / +x ±0 :x / -x; (decrease through self-simpli
-
fication)
Entropy-emergence ratio
larger emergence leads to reduction in the entropic degree of complexity/ decreases relative complexity
0 0 Entropy > Emergence Entropy ≅ Emergence Entropy < Emergence
row in Pascal's triangle - - 1 for 1D 2 for 2D 3 for 4D
4 for 8D
5 for 16D