Regularities and Randomness: Evolving Schemata in Science and the Arts

Abstract

This chapter deals with the study of regularities and randomness. The name for this subject is plectics, derived from the Greek word plektos for “twisted” or “braided,” cognate with plexus in Latin complexus originally “braided together,” from which the English word complexity is derived. The word plektos is also related, more distantly, to plex in Latin simplex, originally “once folded,” that gave rise to the English word simplicity. The name plectics thus reflects the fact that we are dealing with both simplicity and complexity. There is one exception to this context dependence, encountered, for example in the mathematical theory of computational complexity, when a sequence of similar systems of larger and larger size is considered and only their behavior is looked at as the size approaches infinity. An entity is described at a given level of detail, in a given language, assuming a given knowledge and understanding of the world and the description is reduced by coding in some standard manner to a string of bits (zeroes and ones). All programs that cause a standard universal computer to print out that string of bits and then stop computing. The length of the shortest such program is called the algorithmic information content.