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Very exciting ! Reminds me of the time when I learned how imaginary numbers were related to rotations...

by BlueTemplar 6y ago

andi999 6y ago
Be prepared to get excited again when reading about quarternions.
- nimish 6y ago
  Clifford or geometric algebra generalizes this to spinors in any dimension and signature, so you also get the dirac equation for free in a sense
  - BlueTemplar 6y ago
    Yeah, quaternions didn't seem that exceptional, "just" the generalization to rotations in 3D, but Geometric Algebra did get me excited because I finally managed to understand what was the whole deal with those weird "pseudo-vectors"... https://www.av8n.com/physics/clifford-intro.htm https://www.av8n.com/physics/clifford-intro.htm
    - andi999 6y ago
      Your link does not explain rotation with Clifford algebra (except 90 degree rotations)
      - BlueTemplar 6y ago
        Yeah there's a whole dedicated webpage about that : https://www.av8n.com/physics/rotations.htm https://www.av8n.com/physics/rotations.htm > In this document, we discuss rotations, including simple rotations in the plane but also including compound rotations around multiple axes in three or more dimensions. We briefly survey four ways of pictorially representing rotations: two vectors in the plane of rotation, triad before and after rotation, axis plus amount of rotation, and yaw/pitch/roll. These can (respectively) be formalized in terms of (respectively) Clifford algebra i.e. quaternions, matrices, Rodrigues vectors, and Euler angles.
DigiDigiorno 6y ago
"If +1, -1, and √-1 had been called direct, inverse and lateral units, instead of positive, negative, and imaginary (or impossible) units, such an obscurity would have been out of the question." - Gauss (translated), a couple hundred years ago. Of all the things to rename, this may be at the top of my list. I think some kids get lost in the abstraction specifically because the name "imaginary" isnt helpful in understanding the underlying concept.
- gumby 6y ago
  > Of all the things to rename, this may be at the top of my list. I think more confounding is that the electron carries a negative charge. This mistake goes back to Franklin but we can’t blame him; from the data he had he had a 50/50 chance of getting it right.
  - BlueTemplar 6y ago
    Having separate terms for "entropy" and "(lack of) information" is IMHO way worse : https://news.ycombinator.com/item?id=27095212 https://news.ycombinator.com/item?id=27095212

Very exciting ! Reminds me of the time when I learned how imaginary numbers were related to rotations...

andi999 6y ago

Be prepared to get excited again when reading about quarternions.

nimish 6y ago
Clifford or geometric algebra generalizes this to spinors in any dimension and signature, so you also get the dirac equation for free in a sense
- BlueTemplar 6y ago
  Yeah, quaternions didn't seem that exceptional, "just" the generalization to rotations in 3D, but Geometric Algebra did get me excited because I finally managed to understand what was the whole deal with those weird "pseudo-vectors"... https://www.av8n.com/physics/clifford-intro.htm https://www.av8n.com/physics/clifford-intro.htm
  - andi999 6y ago
    Your link does not explain rotation with Clifford algebra (except 90 degree rotations)
    - BlueTemplar 6y ago
      Yeah there's a whole dedicated webpage about that : https://www.av8n.com/physics/rotations.htm https://www.av8n.com/physics/rotations.htm > In this document, we discuss rotations, including simple rotations in the plane but also including compound rotations around multiple axes in three or more dimensions. We briefly survey four ways of pictorially representing rotations: two vectors in the plane of rotation, triad before and after rotation, axis plus amount of rotation, and yaw/pitch/roll. These can (respectively) be formalized in terms of (respectively) Clifford algebra i.e. quaternions, matrices, Rodrigues vectors, and Euler angles.

DigiDigiorno 6y ago

"If +1, -1, and √-1 had been called direct, inverse and lateral units, instead of positive, negative, and imaginary (or impossible) units, such an obscurity would have been out of the question." - Gauss (translated), a couple hundred years ago. Of all the things to rename, this may be at the top of my list. I think some kids get lost in the abstraction specifically because the name "imaginary" isnt helpful in understanding the underlying concept.

gumby 6y ago
> Of all the things to rename, this may be at the top of my list. I think more confounding is that the electron carries a negative charge. This mistake goes back to Franklin but we can’t blame him; from the data he had he had a 50/50 chance of getting it right.
- BlueTemplar 6y ago
  Having separate terms for "entropy" and "(lack of) information" is IMHO way worse : https://news.ycombinator.com/item?id=27095212 https://news.ycombinator.com/item?id=27095212