On Serendip

A Story of Emergence Emerging
As Told by Mark Buchanan in Nexus
(As heard and retold by Paul Grobstein, Emergence Working Group, 15 September 2003
"discovery as emergence?")

Is history predictable? Popper, The Poverty of Historicism, 1957 changes in knowledge affect history
changes in knowledge are unpredictable
therefore history is unpredictable

Buchanan (2001):

pp 12-13
"over the past five years, sociologists, physicists, biologists and other scientists have turned up numerous unexpected connections between the workings of the human world and the functioning of other seemingly unrelated things: from the living cell and the global ecosystem to the Internet and the human brain

This is not to say that we lack free will, or that Karl Popper was wrong and history can be predicted. But it does suggest that many of the inherent complexities of human society actually have little to do with the complex psychology of humans; indeed similar patterns turn up in many other settings where conscious beings play no role at all."

p 18
"The study of networks is part of the general area of science known as 'complexity theory' ... some of the depest truths of our world may turn out to be truths about organization, rather than about what kinds of things make up the world and how those things behave as individuals ... "

p 20
"many of the most important world networks - economies, political systems, ecosystems, and so on - are poised perpetually on the very edge of instability and tumultuous upheaval. As a consequence, it is something akin to a universal law of nature that the course of history must necessarily be punctuated - and quite frequently - by seemingly inexplicable upheavals."

Some of the players (Note the linear sequence is misleading)

Small World One (random networks)
From Erdos, graph theory, a simple solution of the small world problem - random links

6 billion people, each knowing fifty others
1 degree of separation -> 50
2 -> 2,500
3 -> 125,000
4 -> 6,250,000
5 -> 312,500,000
6 -> 15,625, 000,000

BUT normal clustering?

Granovetter - "strong" links less significant than "weak" links - "strong" forms clusters - "weak" forms bridges

Small World Two (egalitarian random plus networks)
Watts and Strogatz - clustering plus random links - a second "small world" network -egalitarian

for 6 billion and fifty near neighbors - 50 million steps to get from one place to farthest

add 0.02 percent random - 8 degrees of separation
add 0.3 random - 5 degrees of separation

brain, C rhabditis, transportation networksare highly clustered small world, facilitates synchronization?

Small World Three (aristocratic random plus networks)
Baran - distributed redundancy

Actual internet/web (better links exist) - third kind of small world net - nodal (shades of Granovetter) - aristocratic scale free-distribution, "fat curve"
true also of metabolic networks, enzymes in cell metabolism, research/research paper links, food webs, influential businessmen, word linkages, river drainage basins

Barbarasi et al ...

Origin/explanation of aristocratic small world networks - "rich get richer"
Of egalitarian networks - constraints on "rich get richer" - second stage process (air traffic?)

Aristocratic small world networks degrade gracefully, more resistant to random damage even than random networks
but are also susceptible to infectious outbursts (because of weak links)

Ecology, epidemiology, economics, politics, and ... ?

pp 297
"We are now witnessing a transition from the science of the past, so intimately linked to reductionism, to the study of complex adaptive matter ...
At the core of this new way of doing science is the perception that the world is in many ways simpler than it appears. Behind the distribution of wealth that stirs up such heated political debate lies not a mess of thousands of competing factors but a simple process of random growth. Mathematically ... this process is nearly identical to the way the internet grows ... it is also nearly identical to the process by which business firms and cities grow ..."

small world graphs, from Santa Fe

Watts and Strogatz

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