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> Quaternions are not a "model of vectors. I dont think I agree. Yes they are not the Gibbsian vector but they are a pretty damn good model of what we want to

by srean 8y ago

> Quaternions are not a "model of vectors. I dont think I agree. Yes they are not the Gibbsian vector but they are a pretty damn good model of what we want to model as vectors. Its already a little closer to geometric algebra / calculus than Gibbsian vectors. Its a pity that Grassman and Clifford's work gained attention much later. Once javascript is out of the bag one cant do much about it. Thats how I feel about Gibbsian vector calculus and geometric algebra. Not that javascript or Gibbsian vectors are bad, quite the contrary, they are astonishing in their own right and scope, but one still feels they could have been so much better.

tntn 8y ago
I think geometric algebra is a very cool and elegant approach as well, but it has not yet proved useful or valuable to working engineers. If we want to compare to programming languages, perhaps Haskell vs. C. One is beautiful and elegant, the other is down to earth and conceptually simple for "normal" people. One is primarily used by academics and researchers, the other is used to build the world. Both are admirable.
- srean 8y ago
  > has not yet proved useful or valuable They would have, had they been the "first mover". Hence my Javascript analogy Had a better language been released at that time it would have been just as useful and valuable. In fact much more so. But as is usual, a "worse_is_better" first mover accrues so much head start in the mind share and in the tooling / literature that it becomes impractical to switch, especially when both can express the same set of things (just that one does it more concisely than the other). Another shallower example: imperial vs metric units. I dont think its like Haskel::C at all. Haskell is way more mathy and has a steeper learning curve than C. One who can master curl divergence and vector stoke's theorem can master geometric algebra with less effort
- jacobolus 8y ago
  > not yet proved useful or valuable to working engineers The people who value it are those who must deal concretely with the details of the model on a daily basis: computer programmers working in graphics, computer vision, robotics, physical simulation, ... It doesn’t do all that much for many pure mathematicians who are happy to hand-wave away the fine details content with the knowledge that the languages can be proven equivalent by someone else, just like it doesn’t do much for the type of engineers who just use someone else’s software for their work. Of course, the current mess is a major point of pain/confusion for the generations of undergraduates studying vector calculus. But they should go through the same hazing ritual the rest of us did, right? It’s only fair.

by srean 8y ago

tntn 8y ago

I think geometric algebra is a very cool and elegant approach as well, but it has not yet proved useful or valuable to working engineers. If we want to compare to programming languages, perhaps Haskell vs. C. One is beautiful and elegant, the other is down to earth and conceptually simple for "normal" people. One is primarily used by academics and researchers, the other is used to build the world. Both are admirable.

srean 8y ago
> has not yet proved useful or valuable They would have, had they been the "first mover". Hence my Javascript analogy Had a better language been released at that time it would have been just as useful and valuable. In fact much more so. But as is usual, a "worse_is_better" first mover accrues so much head start in the mind share and in the tooling / literature that it becomes impractical to switch, especially when both can express the same set of things (just that one does it more concisely than the other). Another shallower example: imperial vs metric units. I dont think its like Haskel::C at all. Haskell is way more mathy and has a steeper learning curve than C. One who can master curl divergence and vector stoke's theorem can master geometric algebra with less effort
jacobolus 8y ago
> not yet proved useful or valuable to working engineers The people who value it are those who must deal concretely with the details of the model on a daily basis: computer programmers working in graphics, computer vision, robotics, physical simulation, ... It doesn’t do all that much for many pure mathematicians who are happy to hand-wave away the fine details content with the knowledge that the languages can be proven equivalent by someone else, just like it doesn’t do much for the type of engineers who just use someone else’s software for their work. Of course, the current mess is a major point of pain/confusion for the generations of undergraduates studying vector calculus. But they should go through the same hazing ritual the rest of us did, right? It’s only fair.