COMPLEXITY


Capra79
The Importance of Pattern
Living Systems
The recent advances in our understanding of living systems are based on twodevelopments that originated in the late 1970s. 
One was the discovery of the new mathematics of complexity
The other was the emergence of a powerful novel concept, that of self-organisation.
 
 Wright243
energetic interplay between zero-sum and non-zero-sum forces -organic evolution, given long enough, was very likely to produce creatures so complex, and so intelligent, as to be capable of sponsoring cultural evolution - a cultural evolution that would then naturally extend evolution's general drift toward deeper and vaster complexity. - the second law of thermodynamics - organisms preserve distinctions - growth of an organism creates new order and structure

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COMPLEXITY-THEORY

complexity theory

George Johnson
Fire in the Mind
Viking 1996
pg 110

COMPLEXITY, ENTROPY, AND THE PHYSICS OF INFORMATION
Wojciech H. Zurek

Mark Buchanan
NEXUS
Small Worlds and the Groundbreaking Science of Networks
W.W.Norton 2002
pg 12" The purpose of science is to find meaningful simplicity in the midst of disorderly complexity". Herbert Simon

pg 48

SMALL WORLDS - SYNCHRONY

How can a bunch of cells or crickets or anything else managed to synchronise their activity without the aid of any external guidance all orchestration?

This is a question not just of biology but of mathematics, for it seems to reach beyond the details of crickets, heart cells, or what have you, and to point towards some general organising tendency in nature. Indeed, in the past two decades, neuro-scientists have discovered that the synchronised firing of millions of neurons in the human brain appears to be essential to some of the most basic functions of perception. Something quite similar even takes place among the several hundred members of an enthusiastic audience, whose clapping sometimes falls into rhythmic perfection.

Computation: Watts and Strogatz found that the insects were able to manage the synchronisation almost as readily as if everyone were talking to everyone else. By itself, the small world architecture of the reduction in the required number of links by a factor of thousands. There is a profound message lurking here - the message not about biology but about computation.
From an abstract point of view, the group of fireflies trying to synchronise themselves is making an effort in computation. As a whole, the group attempts to process and manage myriads signals, counter-signals and counter-countersignals travelling between individual fireflies, all in an effort to maintain the global order. This computational task is every bit as real as those taking place in a desktop computer or in the neural network of the human brain. Whatever the setting, computation requires information to be moved between different places. And since the number of degrees of separation reflects the typical time needed to shuttle information from place to place, the small world architecture makes for computational power and speed.
Of course, no one knows how fireflies are really connect within a swarm. Indeed, only a few species manage the synchronisation trick.Watts and Strogatz had not answered all the questions about fireflies, and many remain unanswered still.
Nevertheless, they had learned that in terms of computational design, small world architecture is especially important "good trick". When it comes to computation, though, nothing is so wondrous as the human brain. And so it was natural to wonder, might the brain also exploit the small world trick?....Does it point to some deeper design principle of nature? In their three-page paper in the June 4,1998, issue of "Nature", Duncan Watts and Steve Strogatz unleashed all these findings on an unsuspecting scientific community. Their paper touched off a storm of further work across many fields of science. As we will see an upcoming chapters, a version of their small world geometry appears to lie behind the structure of crucial proteins in our bodies, the food webs of our ecosystem, and even the grammar and structure of language we use. It is the architectural secret of the Internet and despite its apparent simplicity it is in always a new geometrical and architectural idea of immense importance.

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