Complexity; a science at 30

The scope of Complexity Long after the discovery of atoms and molecules it was still customary in science to think about a collection ofmany similar objects in terms ofsome "representative individual" endowed with the sum, or average of their individual properties. With the exception ofparticles physics and condensed matter theorywhere renormalisation group effects were fully recognised, scientists in various disciplines continued their research within the "mean field" framework. In fact, one may argue that this "mean field" / continuum / linear way of thinking is what conserved the classical sciences as independent sub-cultures. Indeed, the great conceptual jumps separating the various sciences and the accompanying paradoxes connected to the nature of life, intelligence, culture arise exactly from the failure of these assumptions. When "More Is Different" life emerges from chemistry, chemistry from physics, conscience from life, social conscience/ organisation from individual conscience etc. (The title of the present article associates the beginnings ofcomplexitywith the article"More Is Different"published 30 years ago by Phi! Anderson [1]). This study of the emergence ofnew collective properties qualitatively different from the properties of the "elementary" components of the system breaks the traditional boundaries between sciences: the "elementary" objects belong to one science-say chemistry-while the collective emergent objects to another one-say biology. As for the methods, they fall "in between": in the"interdisciplinaryspace". The ambitious challenge ofthe Complexity research (its "manifest destiny") is prospecting, mapping, colonising and developing this "interdisciplinary" territory [2]. For a visual impression ofthe fields and subjects involved in the synthesis that complexity tries to achieve see Fig. 1.