He takes reals to be "stretch" and imaginaries to be "rotate". As in, real space, not an abstraction like "complex plane".
Then the imaginary unit becomes, not just rotation by pi/2 but a "basis vector" for rotation.
Putting on my physicst/engineer hat. this identifies rotations with the axis of rotation, which points outside the plane. (Disclaimer: this is not exactly how the author thinks about it.)
(In contrast. The basis vector of "stretches", btw which include 180-degree rotations, stay in the plane:)
The math is not novel but the perspective is.
Now this can be generalized to 3D rotations, whence you think of (the unit) quaternions as 3 independent axes of rotations.
(Euler angle and Euler formula become muddled :)
There's also the "rotational derivative" (angular velocity) bit which is THE THING worth mulling over. I think is the really novel bit (again. perspective, not math-- but I have not worked out his [degree] arithmetic )
(He calls it the fundamental equation in the video)
The physicist gets reminded of Legendre transforms (think <p,q> (- H)), where p here means angular momentum :)
It will be most cool if he can use this style to explain the "Feynman belt trick" without symbols or animation :)
Then the imaginary unit becomes, not just rotation by pi/2 but a "basis vector" for rotation.
Putting on my physicst/engineer hat. this identifies rotations with the axis of rotation, which points outside the plane. (Disclaimer: this is not exactly how the author thinks about it.)
(In contrast. The basis vector of "stretches", btw which include 180-degree rotations, stay in the plane:)
The math is not novel but the perspective is.
Now this can be generalized to 3D rotations, whence you think of (the unit) quaternions as 3 independent axes of rotations.
(Euler angle and Euler formula become muddled :)
There's also the "rotational derivative" (angular velocity) bit which is THE THING worth mulling over. I think is the really novel bit (again. perspective, not math-- but I have not worked out his [degree] arithmetic )
(He calls it the fundamental equation in the video)
The physicist gets reminded of Legendre transforms (think <p,q> (- H)), where p here means angular momentum :)
It will be most cool if he can use this style to explain the "Feynman belt trick" without symbols or animation :)
https://en.wikipedia.org/wiki/Tangloids
https://en.wikipedia.org/wiki/Plate_trick#The_belt_trick