Explore the intersection of computation and dynamics in this comprehensive lecture. Delve into topics such as Hamiltonian paths, the nature of computation, reductions, and various computational models including Turing machines and cellular automata. Examine partial differential equations, continuous computation, and physical computation through differential analyzers. Investigate scientific computation, partial recursive functions, and discontinuities. Discover the fascinating world of symbolic dynamics, clever manifolds, and the three-strand braid. Analyze the Principle of Least Action and its relation to the Braid Group. Gain insights into a common dichotomy in the field, bridging the gap between computational theory and dynamic systems.