Bruce J. MacLennan Computer Science Department University of Tennessee, Knoxville MacLennan.CS.UTK.edu
Over many years I have searched for the point where myth and science join. It was clear to me for a long time that the origins of science had their deep roots in a particular myth, that of invariance.
-- Giorgio de Santillana
In this paper I'll address the emergence of the discrete from the continuous, first in mythology and psychology, then in cognitive science and artificial intelligence. This will provide a context for considering some continuous neural processes that can result in (approximately) discrete behavior.
Many traditional cosmologies begin with a separation of the primordial massa confusa into opposites. For example, Euripedes said,
And the tale is not mine but from my mother, how Ouranos (Sky) and Gaia (Earth) were one form; and when they had been separated apart from each other they bring forth all things, and gave them up into the light: trees, birds, beasts, the creatures nourished by the salt sea, and the race of mortals. (fr. 484, Melanippe the Wise)
This separation, which is often associated with the creation of recognizable things, corresponds to the emergence into the world of the faculty of discrete categorization. With definite properties come definite things, and conversely the definiteness of things seems to depend on definite oppositions. Early philosophers enumerated many oppositions (e.g., hot/cold, dry/wet, light/dark, straight/curved, odd/even), but in myth they are often equated to the opposition most salient to all people: male/female. Thus the primordial separation creates a god and a goddess, whose subsequent union creates the world of things (though they retain their separate identities). In an editor's forward  Alan Watts observes that this process is reflected in an ancient series of images: