diff --git a/Elements-and-observables.md b/Elements-and-observables.md new file mode 100644 index 0000000..3d46ab3 --- /dev/null +++ b/Elements-and-observables.md @@ -0,0 +1,24 @@ +## Separation + +Elements don't interact directly with each other, and constraints don't interact directly with each other either. In other words, the graph of direct interactions among elements and constraints is bipartite. + +### Contrasts + +Elements | Observables +---|--- +Naturally seen as geometric objects | Naturally seen as quantities +No notion of valence; can interact with any number of constraints | Many important observables have fixed valence +An assembly consisting entirely of elements seems meaningful and potentially useful | An assembly consisting entirely of observables seems hard to interpret + +***To do:** Expand and clarify list of contrasts.* + +## Unification + +Can we realize constraints as geometric objects? For example: + +* A real angle constraint might be seen as a pair of infinitesimal ribbons crossing at a fixed angle along a circle +* An imaginary angle constraint might be seen as a circle that passes perpendicularly through a pair of spheres, with a fixed cross ratio. + +Maybe being subject to a constraint can then be seen as a kind of incidence. + +***To do:** Explore ideas for unifying elements and observables in spite of the contrasts described above.* \ No newline at end of file