From 413e6244d4e2e2615e9612605060d3b848c36555 Mon Sep 17 00:00:00 2001 From: Vectornaut Date: Tue, 25 Feb 2025 21:06:53 +0000 Subject: [PATCH] Answer question about scalars as elements --- Elements-and-observables.md | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/Elements-and-observables.md b/Elements-and-observables.md index 4b9869f..a78c0af 100644 --- a/Elements-and-observables.md +++ b/Elements-and-observables.md @@ -38,4 +38,10 @@ Maybe being subject to a constraint can then be seen as a kind of incidence. * 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.* + * *It's hard to imagine showing them in the 3D display view.* + * *Geometric algebra suggests some potential similarities.* + * *Since Clifford algebras are unital, they do each contain a field of scalars.* + * *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.