Over the last decade the study of complexity, chaos, and complex networks, have gained maturity and added, if not significant science and math, a philosophy of interconnectedness in the sciences.

Nearly 15 years ago a friend plunked down James Gleick's Chaos on the table, and with wide-eyed exuberance akin to some follower of a cult, began to tell me about chaos and complexity, and the underlying patterns and structure of not just a few things, but of just about everything. Back then I dismissed most of it as new fangled fad, in fact at the time just about everything past the year 0 seemed like rehash to me. Get off my porch with your 'new science', kids, we've seen it all before, the Greeks had seen the same patterns in nature and geometry thousands of years ago.

Since then I've known I was wrong to dismiss it so easily. Over the last decade the study of complexity, chaos, and complex networks, have gained maturity and added, if not significant science and math, a philosophy of interconnectedness in the sciences. While the jury is still out as to whether these new models reflect with complete accuracy the way the universe works, they seem tantalizingly close to doing this, and continue to hold up. And, hell, they certainly have added to the art of CG in movies and games if nothing else. One way in which the study of complexity proves not only interesting but also potentially useful, is in networks, the subject of Nexus.

Mark Buchanan discusses, specifically, what is being called 'small-worlds' theory, best exemplified by the familiar term 'six degrees of separation'. Buchanan explains the creation of this concept by social psychologist Stanley Milgram and subsequent researchers attempts to mathematically describe the bizarre fact of such a 'small world'* with so many members. Turns out many researchers, often independently, in different fields were coming to the exact same conclusions, same algorithms, same math, and same graphs when looking at things as diverse as:
-- Epidemics and social networks.
-- Ecosystems and the effects of the extinction of a species.
-- Crime rates, social waves and trends, language**, memes.
-- The web, internet, and computer networks in general.
-- Swarm behavior in insects, humans rioting.

All of these things seem to operate according to the same patterns. Buchanan clearly explains how elements within a enormous network of billions of members can generate the odd 'six degrees' phenomenon by linking to one another through random links, hubs, and 'weak ties'. The fact one can find the exact same consistent ratios in the web as an ecosystem or a worm's neurosystem allows Buchanan to touch on a wide range of topics. The first half of the book he concentrates on the general concepts of networks, complexity, and 'small-world' theory. The second half he explores the implications. He details the work done by scientists and mathematicians such as Watts and Strogatz, Mark Granovetter, Lev Landau, and Paul Erdos. While it may be true that people have noticed many of these recurring patterns for a very long time, it has only been until very recently that the actual underpinning dynamics can be described, and to some extent, predicted. Computer models have allowed the study of complexity and in this case complex networks, to advance rapidly. While the study of complexity was originally concerned with elements usually left to physicists, the study of complex networks very naturally now includes not only 'diffusion-limited aggregation' but also exactly why and how you are merely six degrees away from Kevin Bacon.

Nexus, Small Worlds and the Groundbreaking Theory of Networks
by Mark Buchanan
235 pages.
Norton 2002 (Paperback 2003)

* As in, 'gee, I can't believe we know the same person, gosh, what a small world.'
** Burroughs had famously stated 'Language is a virus'. Laurie Anderson turned that into an interesting song.

-------------------
related links:
--Seeds of Destruction (added 2004-01-16)
--Complexity Digest
--A bibliography on the subjects
--An early piece by Vinge on Singularity