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Start sketching ideas about separation and unification

Vectornaut 2025-01-24 09:59:55 +00:00
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## 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.*