Hey folks 😁 here's an update on my geometric algebra programming environment project

"Oh, by the way, I can at any point rotate all the variables around." 🤯

Nice! I was wondering a bit what this could be used for, but the obvious first use case is as a learning tool for geometric algebra. Which is probably the most underappreciated corner of mathematics today.

😅 That is indeed the main part of the goal! It's propaganda

Some retro sci-fi aesthetic choices there, some subconsciously similarity to some Amiga UI? As for "backsolving," constraint satisfaction is a good way to approach that kind of question. Read

line = plane1 ^ plane2

as establishing a constraint. The semantics of how to fix

line

,

plane1

, and

plane2

depends on an objective function and other constraints. When read as a definition, you have the implicit constraint that

plane1

and

plane2

are already been fixed. In some contexts, a satisfying way to satisfy constraints is to make them kind of springy.