Biologic

In this paper we explore the boundary between biology and the study of formal systems (logic). In the end, we arrive at a summary formalism, a chapter in "boundary mathematics" where there are not only containers but also extainers ><, entities open to interaction and distinguishing the space that they are not. The boundary algebra of containers and extainers is to biologic what boolean algebra is to classical logic. We show how this formalism encompasses significant parts of the logic of DNA replication, the Dirac formalism for quantum mechanics, formalisms for protein folding and the basic structure of the Temperley Lieb algebra at the foundations of topological invariants of knots and links.Comment: 36 pages, 9 figures, LaTeX documen

Following Knots Down Their Energy Gradients

This paper details a series of experiments in searching for minimal energy configurations for knots and links using the computer program KnotPlot. The most interesting phenomena found in these experiments is the dependence of the trajectories of energy descent upon the initial geometric conditions of the knotted embedding.Comment: 18 pages, 13 figures, MsWord documen