Journeys in Non-Classical Computation I: A Grand Challenge for computing research

A gateway event is a change to a system that leads to the possibility of huge increases in kinds and levels of complexity. It opens up a whole new kind of phase space to the systemÕs dynamics. Gateway events during evolution of life on earth include the appearance of eukaryotes (organisms with a cell nucleus), an oxygen atmosphere, multi-cellular organisms and grass. Gateway events during the development of mathematics include each invention of a new class of numbers (negative, irrational, imaginary, ...), and dropping Euclid's parallel postulate. A gateway event produces a profound and fundamental change to the system: Once through the gateway, life is never the same again. We are currently poised on the threshold of a significant gateway event in computation: That of breaking free from many of our current Òclassical computationalÓ assumptions. Our Grand Challenge for computer science is to journey through the gateway event obtained by breaking our current classical computational assumptions, and thereby develop a mature science of Non-Classical Computation