What is a concrete example of a distributed self-organizing physical system?
Let us examine the dynamical system of atoms in a gas as modeled by hard spheres (meaning that the atoms contain no internal structure and only interact on contact). On an atomic scale, the atoms are in constant motion (item 4 above) and over any small time interval interact with atoms nearby but not atoms at any distance (item 6). In the determination of their dynamics, there is no global control (item 2), only local interactions. All necessary information to characterize completely the system is contained in the atoms: their position and velocity (1). Their velocities and local number density will not be single valued, but a distribution (3) that varies with specific atoms and the location in the domain. On a macroscopic scale, the hard sphere gas exhibits global properties (item a). But if we look at a single atom, we cannot determine its global properties, e.g., viscosity. It is only through the collective dynamics that the property of viscosity is measurable and defined. Hence, vi
