There is no over-arching theory of complexity that allows us to ignore the contingent aspects of complex systems. If something really is complex, it cannot by adequately described by means of a simple theory. Engaging with complexity entails engaging with specific complex systems. Despite this we can, at a very basic level, make general remarks concerning the conditions for complex behaviour and the dynamics of complex systems. Furthermore, I suggest that complex systems can be modelled.
Paul CilliersRelated topics
basic complex complexity contingent dynamics general model simple something specific meansRelated quotes
In the Autumn semester, 1955, I taught Principles of Economics, and found it a challenge to convey basic microeconomic theory to students. Why/how could any market approximate a competitive equilibrium? I resolved that on the first day of class the following semester, I would try running a market experiment that would give the students an opportunity to experience an actual market, and me the opportunity to observe one in which I knew, but they did not know what were the alleged driving conditions of supply and demand in that market.
Vernon L. Smith
The emergence of computer technology in World War II and its rapidly growing power in the second half of this century made it possible to deal with increasingly complex problems, some of which began to resemble the notion of organized complexity. Initially, it was the common belief of many scientists that the level of complexity we can handle is basically a matter of the level of computational power at our disposal. Later, in the early 1960s, this naive belief was replaced with a more realistic outlook.
George Klir
In 1925 Heisenberg made a new attempt, on entirely novel lines, to obtain an explanation of atomic spectra. Working in collaboration with Bohr, he had come to the conclusion that the imperfections of Bohr's theory had been a consequence of assuming too simple a model for the atom. For Bohr had not only assumed that the atom consisted of particles moving through space and time, but also that the particles inside atoms were of the same kind as the electrons outside atoms.
James Jeans
Cellular automata are discrete dynamical systems with simple construction but complex self-organizing behaviour. Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes. Characterizations of the structures generated in these classes are discussed. Three classes exhibit behaviour analogous to limit points, limit cycles and chaotic attractors. The fourth class is probably capable of universal computation, so that properties of its infinite time behaviour are undecidable.
Stephen Wolfram
Concerning the Gods, there are who deny the very existence of the Godhead; others say that it exists, but neither bestirs nor concerns itself nor has forethought for anything. A third party attribute to it existence and forethought, but only for great and heavenly matters, not for anything that is on earth. A fourth party admit things on earth as well as in heaven, but only in general, and not with respect to each individual. A fifth, of whom were Ulysses and Socrates, are those that cry:- I move not without Thy knowledge!
Epictetus