chapter  1
15 Pages

Basic notions in the science of complex systems and nonlinear dynamics

ByROBERT HRISTOVSKI, NATÀLIA BALAGUÉ SERRE AND WOLFGANG SCHÖLLHORN

The historical roots of the complexity sciences can be traced back to ancient philosophers such as Aristotle (384-322 BC), whose famous saying, ‘The whole is more than the sum of its parts’, indicated the duality of holism versus reductionism in science. The beginning of modern Western science is mostly associated with the development of a mechanistic world view, originating in contributions from Galileo, Kepler and Newton in the seventeenth century. The mathematicoexperimental method became trend setting and in the same period Newton created the mathematical basis of dynamical systems theory. By showing explicitly that, celestial mechanics, Earthly tides and falling bodies were governed by the same law of universal gravity, he actually paved the way to what later became a foundation of general systems theory and particularly synergetics: the search for the same principles acting at different levels in the organization of matter. This world view may be conceived as a special kind of holism where general principles manifest themselves through different contexts, i.e. levels of organization. The whole manifests itself through different partial phenomena, owing to different contexts in which these phenomena are embedded.