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I can certainly see the mathematical appeal but as an end user I'm still not convinced. If you're still dealing with rotations, points lines etc as subtypes, do

I can certainly see the mathematical appeal but as an end user I'm still not convinced. If you're still dealing with rotations, points lines etc as subtypes, do you care whether they're all implemented internally the same way or as they are now with vectors quaternions matrices etc? Is geometric algebra even more efficient than these or is it purely aesthetic? What I'm saying is, if my code is strongly typed and deals with these various geometric objects, what benefit do I get if they're internally implemented with geometric algebra as opposed to how they are now?

Nevermark 3y ago
If you have the general form, and subtyping, then you have everything in a simpler interface. And you get all the subtype to subtype operations for free, bug free, since they are all just subtype operations themselves. If you haven’t played around with geometric algebra, you should try it. It is consistent across any. N dimensions. And when you are using it in an application, it’s easier to see why things are related the way they are. You have fewer equations.
- chpatrick 3y ago
  OK but I already have the subtype to subtype operations available bug-free today. Why do I care if they're implemented in geometric algebra or not, especially if it's less efficient?
  - Nevermark 3y ago
    If you have what you need, then you have what you need. If you were starting greenfield, geometric algebra probably simplifies more than you would guess, and represents more. When anything gets simpler, more consistent, and more powerful, most of us start having ideas that would never have occurred to us before. Same story as any other significant language and/or notation improvements. It is a mystery to me why it has taken so long to catch on and replace disparate less capable notations. Inertia I guess. Hard to change geometry across education all at once, but piecemeal would be very messy. I don’t know any reason it would be less efficient.

Nevermark 3y ago

If you have the general form, and subtyping, then you have everything in a simpler interface. And you get all the subtype to subtype operations for free, bug free, since they are all just subtype operations themselves. If you haven’t played around with geometric algebra, you should try it. It is consistent across any. N dimensions. And when you are using it in an application, it’s easier to see why things are related the way they are. You have fewer equations.

chpatrick 3y ago
OK but I already have the subtype to subtype operations available bug-free today. Why do I care if they're implemented in geometric algebra or not, especially if it's less efficient?
- Nevermark 3y ago
  If you have what you need, then you have what you need. If you were starting greenfield, geometric algebra probably simplifies more than you would guess, and represents more. When anything gets simpler, more consistent, and more powerful, most of us start having ideas that would never have occurred to us before. Same story as any other significant language and/or notation improvements. It is a mystery to me why it has taken so long to catch on and replace disparate less capable notations. Inertia I guess. Hard to change geometry across education all at once, but piecemeal would be very messy. I don’t know any reason it would be less efficient.