The Emergence of Complexity

In the previous page we addressed how “entropy” is driven by the Law of Large Numbers (LLN) and “emergent symmetry-breaking” is driven by the Reverse Law of Large Numbers (RLLN).

In this post we will address how the “Collaborative Interplay” of these 2 “mathematical forces” brings about The Emergence of Complexity…

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LLN and The Emergence of Diversity

At its extreme the RLLN can be an outright choice between alternatives, but Mother-Nature more usually restricts the RLLN to the emergence of local and regional imbalance – rather than a full system-wide symmetry-break.

When individual agents adapt to, or influence their neighbors localized symmetry-breaking clusters begin to emerge.  But within the wider system the LLN ensures (the emergence of) diversity, because different areas/localities/regions will randomly veer off in many different directions from the “Most Probable Distribution”.

To put this another way!  Any system devoid of any adaptive behavior is akin to a thermal-like system.  In such thermal-like systems there is no diversity because no element makes any decision to be one thing or another; each element is always in “superposition”; each is, in itself, a little bit of everything.  In a system where the elements adapt to each other however, local regions will randomly make different local decisions, and consequent different parts of the system will move in different directions; which ensures the system-wide “Emergence of Diversity”!   

Co-Emergence & “Integration for Free”

The emergence of diversity means that what comes into existence must be in some way complementary, or at least be accommodative to the presence of co-emergent entities.  Over time this mutual accommodation fine-tunes the integration of these co-emergent entities.  This is self-organized integration for free.  This process of the self-organizing integration of co-emergent diversity leads to the “Emergence of Integrated Diversity”! 

The Mystery of Spontaneous Complexity

From the outset, the science of complexity has wrestled with the obvious contradiction of the emergence of complexity in a universe dominated by the SLOT.  Consequently, complexity has long tried to address the question “what is the source of spontaneous order?”  As it turns out however, Spontaneous Order does not arise in defiance of the SLOT but with the help of it.

All fluid-like adaptive systems are capable of both spontaneous viscosity and spontaneous mixing.  It is the collaborative interplay of symmetry-breaking positive reinforcement, and the integrating force of the SLOT that molds formless uniformity into complex structures of integrated co-emergent diversity, which have effectively self-organized themselves into existence!

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In Summary

Complexity occurs when internal interactions become too coarse for a system to simply synchronize and stabilize to a single fine-tuned equilibrium.  Complexity is simple a form of “Coarse Damping” to uniformity – a form of coarse symmetry.  It is

The emergence of symmetry-breaking resistance to the gravitational pull of a finely-tuned and symmetric, but fundamentally bland and featureless thermal equilibrium.

So ultimately complexity is in reality actually a coarse version of the SLOT, it is the SLOT in disguise – “Complexity is Coarse Entropy”  driven by “Incompressible Mathematics”.