Grasping Complexity

The century of complexity has come. Many people write and speak about complexity. The statement of the great physicist Stephen Hawking, “I think the next century will be the century of complexity,” in his ‘millennium’ interview on January 23, 2000 (San Jose Mercury News) became a widely cited prophecy. The face of science has changed (see cartoon in Fig. 1). Surprisingly, when we start asking about the essence of these changes and then critically analyze the answers, the result are mostly discouraging. Why do we talk about complexity? Somebody might answer that now we have to study non-linear systems and therefore they are complex. The answer seems to be plausible, nonlinearity results in non-additivity of parts and in the emergence of new phenomena: “The whole is more than the sum of its parts.” But objection appears immediately: non-linearity has been in the focus of scientific research already for more than a century. Poincaré and Lyapunov have studied nonlinear systems more than a century ago. Boltzmann’s equation and Navier–Stokes equation, the great nonlinear equations are more than a century old. Many ideas have been created and many methods developed. The study of non-linearity is not a symptom of the change of era. More than a thousand years ago Aristotle had written that “the whole is something besides the parts” (Metaphysics, Book 8, Chapter 6) and the Western culture had accepted this idea from the very beginning. By the way, ‘besides’ in this translation of Aristotle sounds much more precise than the widely spread ‘more’.