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> i, j, and k are ... bivector rotation operators Well, that’s like calling the imaginary unit “a rotation operator.” (I mean, sure, you can do things like tha
by Koshkin 6y ago
> i, j, and k are ... bivector rotation operators
Well, that’s like calling the imaginary unit “a rotation operator.” (I mean, sure, you can do things like that with abstract algebraic constructs, marvel for a few moments, but then you move on, searching for the true meaning - which never happens to lie with any particular representation or an application.)
- ajkjk 6y agoyes, i would call `i` a rotation operator. Something like millions of person-years have been based on the pedagogical nightmare of complex numbers as normally treated.
- madhadron 6y ago> you move on, searching for the true meaning Which turns out to show up when you go beyond three dimensions. In two and three dimensions, numerical coincidence let you identify different grades of operation. In 3D space, i, j, and k are unit vectors...and unit bivectors. As soon as you hit 4D you have to separate that out, and things get a lot clearer. This is why people keep harping about geometric algebra.