The "Science" of Complex Systems

Since the mid-1980s, there has been explosive development in a broad area variously called by such epithets as "Complexity Studies", "Complex Adaptive Systems", or "Non-Linear Dynamics". It is no coincidence that this arose just as powerful computers were becoming widely available, since although some of the relevant phenomena had been discovered by Poincaré in 1890, it was only their demonstration in computer models that raised them to widespread attention. Edward Lorenz's seminal (re-)discovery of the "butterfly effect" in 1961/2 came through re-running weather simulations on an early computer, when he found that the model showed "sensitive dependence on initial conditions". Such sensitivity came to be understood as the defining characteristic of "chaos", as popularised in a famous 1987 book by James Gleick: Chaos: Making a New Science.

Tractability, Availability, and the Limits of Imagination

Sensitive dependence on initial conditions can very easily be demonstrated, even with simple linear equations, by including a discontinuity at an appropriate point. Thus for example if x is a value between 0 and 1, iterative mapping of x to the fractional part of 10x will map 0.14159... to 0.4159..., then 0.159..., then 0.59... (so the path of 0.14178... will separate at the fourth stage, corresponding to the decimal place where it differs, mapping to 0.78... rather than 0.59...). Such sensitive dependence becomes ubiquitous in many systems of non-linear equations, as Poincaré had discovered in his work on the "three body problem". These points make it all the more striking how little theoretical attention was paid to "chaotic" phenomena prior to the computer age. One plausible explanation for this is simply the sheer intractability of such phenomena without computational assistance: it made more sense for scientists to devote their careers to phenomena governed by linear equations, which are far more manageable and crucially tend to be decomposable (because combinations of linearly governed effects are themselves linear).

The realistic prospect of progress acts as a powerful focus of scientific attention. But also, in turn, if a particular focus is shared by the scientific community as a whole, then it becomes hard even to imagine possibilities outside that paradigm. Thus the predominant focus on linear, decomposable systems naturally gave rise to a paradigmatic view of science as proceeding by "reductionist" decomposition of apparently complex phenonema into relatively simple components. It was only the development of widely available computers (and, especially, their accompaniment with graphical displays) that forced non-reducible, non-linear, and more holistically complex phenomena into the limelight, making them impossible to ignore while simultaneously providing a new tool for their investigation. The consequent explosive growth of "Complexity Studies", with its spawning of numerous high-powered research groups around the world, thus provides both a fascinating case-study for the sociologist of science, and a rare opportunity for the philosopher of science to witness – and even to participate in – the breaking and forging of new paradigms.

A Sceptical Note

All this does not imply any wholehearted joining of the "Complexity Science" bandwagon, with its suggestion that we have here a new science in the making. On the contrary, if it is true that scientific attention has hitherto been paid to a relatively narrow range of phenomena, this makes it a priori rather unlikely that everything remaining outside that range will fit comfortably into a single "science". (Perhaps in a few generations the study of "non-linear systems" will seem as quaint as "non-integer mathematics" or "non-air gases"!) The sceptical voices (such as Giorgio Israel, 2005) might prove to be right in questioning the prospects for satisfying unification of what currently passes under the name of "Complexity Studies". But such controversies should obviously attract, rather than repel, philosophers of science. Whether unification can be achieved or not, very important developments are going on here, with real prospects of permanently changing the scientific landscape over a wide range of disciplines. And the computer is the key tool that has made this possible.

Illustration of the Mandelbrot Set

Illustration of the Mandelbrot Set, a famous example of "chaos"