My last novel, SPIN CONTROL, was about complexity theory - a subject so enthralling that even three years of research and writing couldn't dull my enthusiasm.

A nonfictional presentation of my thoughts on complexity theory would probably be about as exciting as an exhibition of my fingernail clippings. However, other people have said extremely interesting things about it. I've quoted some of them below in the hopes of sparking your interest in an emerging and controversial field of science.

Most of these quotes are from published material; others are based on interviews or email exchanges with people I spoke to while writing SPIN CONTROL. I've linked to the authors' books or websites wherever possible. These links are a good place to start getting a grasp on this slippery and fascinating subject.

Scientists have long been baffled by the existence of spontaneous order in the universe. The laws of thermodynamics seen to dictate the opposite, that nature should inexorably degenerate toward a state of greater disorder, greater entropy. Yet all around us we see magnificent structures -- galaxies, cells, ecosystems, human beings -- that have somehow managed to assemble themselves. This enigma bedevils all of science today.' Steven Strogatz

Every decade or so, a grandiose theory comes along, bearing an ominous-sounding C-name. In the 1960s it was cybernetics. In the '70s it was catastrophe theory. Then came chaos theory in the '80s, and complexity theory in the '90s. In each case, the skeptics at the time grumbled that these theories were being oversold and that the results were either wrong or obvious. Then everyone had a good laugh and went back to the lab bench for some more grinding, reductionist science, walled off from their colleagues in adjoining disciplines, who were themselves grinding away on their own tiny corners of the universe . . . . What's different now is a feeling in the air. Even the most hard-boiled mainstream scientists are beginning to acknowledge that reductionism may not be powerful enough to solve all the great mysteries we're facing: cancer, consciouness, the origin of life, the resilience of the ecosystem, AIDS, global warming, the functioning of a cell, the ebb and flow of the economy . . . . What makes all these unsolved problems so vexing is their decentralized, dynamic character, in which enormous numbers of components keep changing their state from moment to moment, looping back on one another in ways that can't be studied by examining any one part in isolation. In such cases the whole is surely not equal to the sum of the parts. These phenomena, like others in the universe, are fundamentally nonlinear. Steven Strogatz

GENERAL COMPLEXITY LINKS

Santa Fe Institute
Complex Adaptive Systems Research Page
Cornell Interdisciplinary Graduate Training in Nonlinear Systems
University of Michigan Center for the Study of Complex Systems
Yale Haskins Lab Complex Systems Page

'Chaos caught many people's imaginations in the 1980s: simple rules could produce arbitrarily complex patterns which appear quite random. As the millenium draws to a close, more and more of these phenomena seem like different aspects of an underlying paradigm: complexity. Not just a new scientific theory or body of data, it challenges fundamental attitudes to the way we do science. Although it might be intuitively apparent that a system is complex, defining complexity has proved difficult to pin down with numerous definitions on record. As yet there is no agreed theory of complexity. Much of the mathematics is intractable and computer simulation plays a major part.' Terry R. J. Bossomeyer, David G. Green

'[C]haos is an important source of novelty and variety in living systems ... critical phase changes in the bahaviour and structure of complex systems may provide mechanisms by which nature exploits chaos ... Kauffman (1992) and Langton (1990, 1992) have suggested that the 'edge of chaos' - the phase change between ordered and chaotic behavious for automata -- plays a central role in evolution. They suggest that because systems near the edge have the richest, most complex behaviour, such systems can adapt better and therefore have a selective advantage over other systems. They therefore suggest that living systems have evolved to lie close to the edge of chaos.' Terry R. J. Bossomeyer, David G. Green

CHAOS LINKS (mostly pretty pictures)

Chaos On-Line Journal
Chaos Hypertext Book
Chaos Theory and Fractals
Strange Attractors (No, not the comic book . . . )
more strange attractors . . .
. . . And some more strange attractors

'What makes social systems most appealing intellectually is the existence of hierarchies. When organization of this kind occurs, there is often more to a whole society than the sum of its parts. Yet even the most emergent properties of the society's behavior remain strictly ordered by the devices of communication and regulation operating at the level of the organism. This perception is not a mere truism. There is no way to predict which devices have evolved in particular species, even though general principles can be adduced that affect all of the species together.' E. O. Wilson and Bert Hoddobler

The dynamics of ant colony life has some features in common with many other complex systems: Fairly simple units generate complicated global behavior. If we knew about how an ant colony works, we might understand more about how all such systsems work, from brains to ecosystems. Because we don't yet comprehend any natural complex system, I think it is premature to dsay how general a theory we may eventually achieve. The intriguing question about task allocation is how might an ant react to local events, in a simple way, that in the aggregate produces colony behavior? The same kinds of questions come up over and over, throughout biology. How do neurons respond to each other in a way that produces thoughts? How do cells respond to each other in a way that produces the distinct tissues of a grwoing embryo? How do spedcies interact to produce predictable changes, over time, in ecological communities? These are the big, general questions of biology, and many of us dream that when we have the answers, from different fields of biology, it will be possible to see similar processes at work from cells to ecosystems. . . . Deborah M. Gordon (Ants at Work, 1999)

BIOCOMPLEXITY LINKS

Princeton Center for Biocomplexity
Gordon Lab (Stanford University)
Tom Seeley's work on distributed decision-making in honeybees
Stephen Pratt's work on distributed decision-making in ants
Biocomplexity Thesaurus
Center for the Study of Institutions, Population, and Environmental Change
Cornell Biogeochemisty and Environmental Complexity Program
Chris Adami's Biocomplexity and Evolutionary Biology Page (CalTech)

'The animal realm exhibits several cases of social systems having poor individual capabilities when compared to their complex collective behaviors. This is observed at different evolutionary stages, from bacteria, to ants, caterpillars, mollsucs and larvae. Moreover, the same causal processes that originate these behaviors are largely conserved in higher level species, like fishes, birds, and mammals . . . . This suggests that the underlying mechanisms have proven evolutionarily extremely effective and are therefore worth of being analyzed when trying to achieve the similar goal of performing complex tasks by distributing activities over massively parallel systems composed of computationally simple elements.' Alberto Colorni, Marco Dorigo, Vittorio Maniezzo

‘The structure and thinking power of the human brain has been the same for tens of thousands, if not hundreds of thousands, of years ... People who have studied ‘primitive’ gatherer-hunter societies that used stone tools have found that they are not so primitive. The amount of knowledge crammed into the brain of a hiunter is as extenseive as it is subtle. Researchers who have accompanied aboriginal hunters on their rounds have been bewildered by how they find, identify and track prey they may not visually encounter for hours on end. The ability tyo find hidden plant foods is equally remarkable. It is probable that the capacity of the average individual mind is fully taxed in a gatherer-hunter tribe. As the knowledge contained in increasingly large and technologically advanced societies has risen dramatically , the capacity of individual human minds has not expanded to accommmodate the new knowledge. We have been forced to spread out chunks of the new knowledge among a multitude of minds taught over extended periods of education. Humans have also been forced to invent written tablets, books, computers, and the like to store and transmit a knowledge base to large to story even in billions of brains.’ -Gregory S. Paul, Earl Cox. (Beyond Humanity: Cyberevolution and Future Minds, 1996)

COMPUTER SCIENCES AND COMPLEXITY

Complex Systems and Parallel Computers
Swarm Intelligence Resources
Eric Bonabeau Interview
Marco Dorigo's Publications
Amorphous Computing (MIT)
University of Waterloo Theoretical Computer Science
Chicago Journal of Theoretical Computer Science