Mandala is a Tybetan concept of a diagram for meditation. It is a map of reality. It is believed that if you look at a mandala long enough, the inner meaning of everything should emmerge.
Here are six diagrams that are sort of mathematical mandalas. Each is to capture the core and essence of one of the formalisms of Lagrangian/Hamiltonian description of motion. The cube contains also Thermodynamics interpreted in terms of symplectic structure. (and electrodynamics added as bonus).
These diagrams tell how bodies move, how light propagates, and what connects the two.
This is a seed page for Math 531, Fall 2009.