ABSTRACT
The notion that dissipation begets self-organization has remained informal, and not susceptible to rigorous proof or refutation, largely through lack of an adequate mathematical definition of organization. The chapter explores alternative definitions, proposes that organization be defined as "logical depth," a notion based on algorithmic information and computational time complexity. Two rather different kinds of computing resources have been considered in the theory of computational complexity: static or definitional resources such as program size, and dynamic resources such as time and memory. Algorithmic information theory allows a static complexity or information content to be defined both for finite and for infinite objects, as the size in bits of the smallest program to computer the object on a standard universal computer. Finite strings, such as minimal programs, which are incompressible or nearly so are called algorithmically random.
