I found Hermann Weyl's 'Symmetry' in the library, sought out via a circuitous route by way of Stafford Beer's 'radar' reading list and a fascinating discussion yesterday. It's beautiful. What's interesting is the two uses of the word 'symmetry' - one for proportion, the other for mathematical bilateral symmetry, and the way the two forms of usage relate.
Symmetry and pattern are related. Musical forms have symmetry: typically A-B-A forms, but the second A is often not the same as the first. It happens at a different moment. I wonder if physical symmetry is also like this - happening at a different 'moment'; the moment when the pattern is first cognised, and the moment when it is re-cognised. What does symmetry tell us about ourselves? What does it tell us about the flow of our experience as we are geared to respond to it? But that the symmetry which has the most powerful effect on us is often imperfect. What are the regulating moments of playful experience that go on as we look at a sphere or a cube?