1) Sir Roger Penrose, in his renowned book “The Emperor’s New Mind”, formulated the hypothesis that the nature of mathematical insight is non-algorithmic. He proved it through a classical logical argument (Gödel’s “incompleteness theorem” and the technique of reductio ad absurdum). This can be extended to any kind of scientific insight, and raises problems as to intra- and inter-communi-cability of information in some perceptual levels of living systems
2) the concept of “choice” is a central topic in describing, and even characterizing, living systems (“living matter is matter that chooses”, the famous biologist Lynn Margulis says)
3) information theory, originally conceived for telecommunication problems, was then extended to physical systems (L. Brillouin; Leo Szilard) to tackle some problems in statistical physics. It was successively applied to understand living systems.
Recent nanobiological research, and successful fundamental physical research (1995 – 1998), are deeply changing the notion of physical information, of information processing in living systems and in computer science. We are heading for the quantum world, where we will learn new powerful algorithms, and the very stimulating and comprehensively explanatory concept that
“Information is deeper than reality”