22C:096
Computation, Information, and Description

Course Outline

This outline is provisional and subject to change. I may change it if I find that the order doesn't work as I hoped. You may propose changes to focus on topics that especially interest you.

• Models of computation: powerful behavior from trivial rules
• Descartes' program for achieving certain knowledge: powerful conclusions from trivial postulates
• Computation as a process designed for maximum certainty
• Formal systems: the computational foundations of mathematics
• Hilbert's program for achieving security in mathematics
• Structural properties of all computing systems
• Uncomputable functions, unprovable truths (Gödel's theorem), the impossibility of Hilbert's program
• Definition of information; meaning in mathematical logic
• Interpreting a priori knowledge through information theory
• Computer programs as descriptions (Kolmogorov/Chaitin complexity)
• Interpreting probability through description theory
• The genetic code as a programming language
• Artificial life: what sorts of programming systems allow interesting evolution?
• Quantum computation