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As described above the discrete character of the components (i.e. the multi-agent character) is crucial for the macroscopic behavior of the complex systems. In fact, in conditions in which the (partial differential) continuum approach would predict a uniform static world, the slightest microscopic granularity insures the emergence of macroscopic space-time localized collective objects with adaptive properties which allow their survival and development [5].

The exact mechanism by which this happens depends crucially of another unifying concept appearing ubiquitously in complex systems: auto-catalyticity. The dynamics of a quantity is said auto-catalytic if the time variations of that quantity are proportional (via stochastic factors) to its current value. It turns out that as a rule, the 'simple' objects (or groups of simple objects) responsible for the emergence of most of the complex collective objects have auto-catalytic properties. In the simplest example, the size of each 'simple' object jumps at every time instant by a (random) quantity proportional to its current size.

Autocatalyticity insures that the behavior of the entire system is dominated by the elements with the highest auto-catalytic growth rate rather than by the typical or average element [6].

This explains the conceptual gap between sciences: in conditions in which only a few exceptional individuals dominate, it is impossible to explain the behavior of the collective by plausible arguments about the typical or 'most probable' individual. In fact, in the emergence of nuclei from nucleons, molecules from atoms, DNA from simple molecules, humans from apes, there are always the un-typical cases (with accidentally exceptional advantageous properties) that carry the day. This effect seems to embrace the emergence of complex collective objects in a very wide range of disciplines from bacteria to economic enterprises, from emergence of life and Darwinism to globalization and sustainability. Its research using field theory, microscopic simulation and cluster methods is only at its beginning.

Next: The Birth of Macroscopic Objects from Microscopic 'Noise'
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Previous: Multi-Agent Modeling of Reaction-Diffusion Systems