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Answer question about "second-order constraints"

Vectornaut 2025-02-25 21:19:14 +00:00
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Elements-and-observables.md

@ -36,7 +36,6 @@ Maybe being subject to a constraint can then be seen as a kind of incidence.
## Questions/Cautions
* What is the status of a "second-order" constraint, e.g "these two observables are equal"? Are they just additional Constraints, even though their slots are other Constraints? If we use the "filter Constraints by an Element" metaphor, and we select a plane P and it shows us the three angle Constraints it is involved in and one of those angle Constraints theta is further constrained to be equal to another angle rho that does not involve P, does that equality constraint show up? Does rho itself show up?
* Could a Scalar be an element? I.e., a "free-floating" real number?
* *Scalars differ from elements like spheres and points in fundamental ways.*
* *They don't correspond to sets of points.*
@ -46,4 +45,6 @@ Maybe being subject to a constraint can then be seen as a kind of incidence.
* *If we eventually have reason to do algebraic operations on elements like spheres and points, their algebraic structure trait could be shared with scalars.*
* What is/should be the mechanism for making numerous angles identical be (say)? By experience, using a bunch of equality constraints and relying on transitivity becomes cumbersome and a bit hard to "see what's going on". Those interfaces that allow one to have "named quantities" and then use those "named quantities" as the values of other parameters have felt more understandable, and easier to manipulate.
* *From a user's perspective, I like the idea of promoting regulator set points from real numbers to expressions that can include variables.*
* *If every set point is an affine-linear combination of variables, I think we can enforce the resulting relations between set points using basically the same mechanism that we currently use to freeze entries of representation vectors.*
* *If every set point is an affine-linear combination of variables, I think we can enforce the resulting relations between set points using basically the same mechanism that we currently use to freeze entries of representation vectors.*
* What is the status of a "second-order" constraint, e.g "these two observables are equal"? Are they just additional Constraints, even though their slots are other Constraints? If we use the "filter Constraints by an Element" metaphor, and we select a plane $P$ and it shows us the three angle Constraints it is involved in and one of those angle Constraints $\theta$ is further constrained to be equal to another angle $\rho$ that does not involve $P$, does that equality constraint show up? Does $\rho$ itself show up?
* *If we promote set points to expressions that can involve variables, then the variable $\rho$ will appear in the expression for the set point $\theta$.*