Life at the Edge of Chaos

By the late 1970s some scientists truly believed that the `end of science' was at hand. After all the major conceptual foundations had been laid earlier in the century: quantum mechanics and relativity in physics, Darwinism in biology. Particle physics was putting the finishing touches on the `standard theory' which explained the structure of matter in terms of strange things called `quarks'. Yes, the grand `Theory of Everything' was close to completion, many believed, as they stood back admiring the classical beauty of their construction. Unfortunately, unbeknownst to the assembled, the structure had more than a few warps, cracks and sealing problems. And whilst the admirers were `ooh-ahhing' over the symmetry of this line and that, others of a more practical persuasion were puzzling over these imperfections. Why, they kept asking, didn't many of the theories attempt to address some of the really thorny problems in science, such as how the simple molecules of the primordial soup managed to produce the first cell? How have ancient ecosystems remained stable for millions of years only to disappear in an instant?

So the dissenters began tinkering. Mathematician Mandelbrot with his weird “fractal geometry” revealed strange structures buried deep within simple equations. Biologist May found odd population fluctuations in simple ecologies. Physicists Farmer and Crutchfield discovered extremely strange behaviour in simple pendulums. Their emerging discipline is now familiar to most with a passing interest in science as chaos theory.

However, chaos theory is a smaller part of a larger edifice: the new sciences of complexity . To begin to understand what complexity is and what it means for science and society, let's start with a simple game...

The “Game of Life” is a simple yet ingenious construction for understanding the concepts of complexity. Consider a TV divided into a grid of cells, each of which can be in one of two states: dead or alive. Each of these cells is then given a simple, local rule specifying the conditions under which a cell will be dead or alive.

The whole grid is then “seeded” with some random distribution of dead and alive cells and the rule is applied to the grid, resulting in new grid of cells. The rule is then applied again for each cell, and so on, so that the viewer can watch as checkerboard patterns of dead and alive cells shuffle on screen. Contrary to expectation: random patterns of grid cells rearranging on screen with no order or coherence, the “Game of Life” produces definite lifelike structures which evolve, move, merge, coalesce and fragment on screen.

Enter Christopher Langton, part-time bluegrass guitarist, part-time programmer, part-time college dropout. Langton spent most of the 1970s on the fringe of the college scene around Cambridge and Boston following the conceptual scent of vague ideas about adaptation and self-organisation through browsing through bookshops and taking the odd course. The scent eventually led Langton to invest in an Apple II and begin experimenting himself. Fascinated by the spidery, life-likeness of these “cellular automata” structures (the “Game of Life” is a special case), Langton discovered the work of Stephen Wolfram. Wolfram had found that there were four possible types of cellular automata rules.

Class I were “doomsday rules”: no matter what initial seed, all the cells would die within one or two time steps. Class II rules were marginally more interesting: any initial seed would quickly form into a set of static, pulsating blobs. Class III were the other extreme completely: the patterns they produced were so frenetic, there appeared to be no order or predictability. Class IV rules were the most unusual and strange: these rules did not produce static structures, or chaotic patterns. What was they produced were complicated structures that split, grew and mutated: “Game of Life” falls neatly into this category.

At this time chaos theory was just beginning to hit the scientific mainstream. Chaos said that by varying a certain parameter, you can effectively “dial” the desired behaviour from a system. For an example, consider the drips of water from a tap. If the flow rate of water is set less than a certain critical value, the drops will fall regularly with a predictable period, order. Turn up the flow past the value and the drops will come hither and thither at completely unpredictable times: chaos . But, exactly at the critical value of flow rate, the system is balanced right at the “edge” of order and chaos. A slight nudge left and the drops come regularly, slight nudge right and the system plunges into chaos: drops are unpredictable.

This “edge” of chaos notion was so tantalisingly close to what he saw by varying the laws in cellular automata, that Langton wondered whether there could be a connection. Working late into the nights on his Apple II, Langton found that the phenomenon were exactly the same! In fact it reminded him of something from his undergraduate physics days: it was very similar to watching a transition from a solid to a fluid: a phase transition. Treating the critical parameter as a sort of `temperature' for both cellular automata and chaotic systems, he produced graphs that would say to a physicist: phase transition !

The connection was stunning, analogies were appearing everywhere and it seemed that information, computation and dynamics were emerging to be connected in a very fundamental way. Langton now had the following analogies:

The patterns produced in the Game of Life; adaptive life-like structures evolving and mutating like cells under a microscope, seemed to suggest more. Could there be yet another analogy? Could the very process of life itself be connected with varying some sort of parameter? Could life have something to do with this “edge of order and chaos”?

By 1982 Chris Langton had finally convinced the University of Michigan to allow him to do a Ph.D. on the new subject, which he began calling “Artificial Life”. “Artificial Life studies man-made systems which exhibit behaviours characteristic of natural living systems”, wrote Langton, in the introduction to Artificial Life in 1987. Langton firmly believed that these patterns and processes of life, could somehow be “abstracted” from a `real' biological system. Using a computer analogy: “life” is the “software”: the processes, the instructions that use whatever “hardware” is available: the mitochondria, cells or DNA. During this time Langton had discovered that others had smelt that crazy, elusive scent and their numbers were growing.

The Santa Fe Institute in New Mexico was such a place. Founded in 1984 by the nearby Los Alamos' Center for Nonlinear Studies, the Institute was fast becoming a mecca for people frustrated with the straight-laced conventionalism of mainstream academia. Langton fitted in immediately. Gone were the days of late night hacking on his Apple II, denial of grant applications, polite letters of refusal for postdoc positions. He suddenly found himself surrounded by people who knew what he was talking about. Langton: “At the meeting we almost embraced each other. There was this real camaraderie, this sense of `I may be crazy - but so are all these other people'”. Here Langton had finally found his niche.

Here were physicists, mathematicians, biologists, economists, archeologists and engineers, all sharing common interests in the new concepts of complexity: adaptation, learning, chaos and emergence. There was heady atmosphere here that recalled the counterculture of the 1960s. Scientists talked of experiencing “a new way of seeing the world twice a day”.

The ideas of complexity theory seemed to many of these scientists to hold the promise of uniting two previously disparate trends in science: reductionism (the descendant of Newtonianism) and vitalism. Reductionism holds that a complete description of any science can be found by understanding the “bits” that make it up. Vitalism maintains that there is some “unanalysable” `elan vital' or `life force' which is responsible for the wonderful organisation in life.

In complexity theory, neither is completely correct, there is both a reductionistic and vitalistic flavour: both a `bottom-up' and `top-down' component. Reductionism appears in the form that no predetermined outcome is built into any of the model of complex behaviour, whether they be Artificial Life or cellular automata. Complex behaviour emerges as a result of the models. But there is vitalism in the sense that the `emergent' properties of these models; such as the adaptive behaviour in Game of Life, are observable and have an identity independent of the rules that underlie them. Do these properties somehow then affect the underlying rules, thus completing the circle? Nobody knows yet. This is the stuff that could provide the paychecks for scientists and philosophers for years, however the ideas of complexity at least seem to be making some of the issues a little more transparent.

And as for Dr. Christopher Langton (his Ph.D. was finally awarded in May 1991), his work and others at the Institute is continuing, the final answers are not in yet. Perhaps Langton's final notion of “life at the edge of chaos” is more than just analogy. Perhaps the conditions for life are best between the `static': the stagnant and sterile and the `noisy': where seething, roiling biological forces destroy the delicate conditions necessary for life. Perhaps the final suggestive metaphor is one that relates to life itself.:

Life and Intelligence Too static <-> “Life” <-> Too noisy

The trend of increasing specialisation, hermetically sealed corporate and military-oriented research, runs completely contrary to the spirit of the new sciences of complexity. The discoveries cut such great swathes across traditional disciplines that it also makes a mockery of “turf-protection” in the academic world. By marrying computer science with economics, archeology with theoretical physics, ecology with anthropology, years of tradition is being challenged.

Professor Murray Gell Mann, Nobel Prize winner and Chairman of the Santa Fe Institute: “It will be a slow and difficult process for each university to change from its old message, `Learn a traditional subject and stick to it', to the new message, `It is all right to learn how to make connections among different subjects'... The message that it all right to think about the relations among different approaches to the world, may then spread more readily to the world at large...”

The new discoveries also point to fundamental flaws in the perception of science. The traditional image of a scientist patiently gathering data, designing experiments, and writing papers in a kind of “conveyor-belt” way, completely ignores the role of a myriad nonscientific factors. The role of metaphor, analogy and intuition are nowhere more obvious than in the new connections being forged by complexity. Roger Jones in his 1982 book, Physics as Metaphor writes: “Physical science is a metaphor with which the scientist, like the poet, creates and extends meaning and value in the quest for understanding meaning and purpose...The humanities are concerned with questions of existence, meaning, value and beauty - matters which all of us feel to be essential, integral, human. It is ironic and tragic that we have come to feel that physics is not deeply motivated by those same human issues.”

Dr. George Cowan, Director of the Santa Fe Institute suggests that such a reconciliation is becoming possible: “[Complexity theory] represents, to me, a reintegration of a scientific enterprise that has become almost totally fragmented over the past few centuries - a recombining of the analysis and rigour of the physical sciences with the vision of the social scientists and the humanists.”

There is also an personal dimension to scientific discovery that has often been ignored. Dr. Brian Arthur, an economist with the Santa Fe Institute describes it this way: “It's people who like process and pattern, as opposed to people who are comfortable with stasis and order. I know that every time in my life that I've run across simple rules giving rise to complex emergent messiness, I've just said, 'Ah isn't it lovely!'. And I think that when other people run across it, they recoil.”

© 1993 Alex Lancaster