5 ms·

Absolutely agree. What's your preferred terminology? I like "Forward" and "Reverse" for positive and negative number and "Lateral" for the imaginary unit, sinc

Absolutely agree. What's your preferred terminology? I like "Forward" and "Reverse" for positive and negative number and "Lateral" for the imaginary unit, since it is just perpendicular to the Forward and Reverse numbers.

klmadfejno 6y ago
Good and evil.
- deleted 6y ago
  [deleted]
_jal 6y ago
Spooky and strange?
- andrewprock 6y ago
  Human and Werewolf.
  - kortex 6y ago
    Spooky Werewolf Algebras on the Monster group. Coming to arxiv this October.
Robotbeat 6y ago
I just think of them as different axes on a 2D Cartesian plane. That’s basically how they work. EDIT: similarly, quaternions as a number in 4D, with that extra dimension being handy for avoiding the instability problems when you get near “gimbal lock” in 3D rotations.
- phkahler 6y ago
  But the quaternions sort of make the real component special dont they?
  - kortex 6y ago
    That it more an effect of how we use them in computer geometry. Unit quaternions with ijk plus real map to an xyz tilt plus a rotor. But I believe you could pick any such mapping. On the other hand, dual quaternions do care which is the dual component, since multiplying by complex numbers looks like true rotation, while multiplying by a dual looks like rotation around a point at infinity, aka translation. So in that case maybe there is something special about the real component.
injb 6y ago
That's pretty close to what Gauss said they should be called: "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" (https://shitohichiumaya.blogspot.com/2016/10/gausss-quote-for-positive-negative-and.html https://shitohichiumaya.blogspot.com/2016/10/gausss-quote-fo...)
yccs27 6y ago
I also like the name "lateral unit", maybe call the field "planar numbers"?

klmadfejno 6y ago

Good and evil.

deleted 6y ago
[deleted]

_jal 6y ago

Spooky and strange?

andrewprock 6y ago
Human and Werewolf.
- kortex 6y ago
  Spooky Werewolf Algebras on the Monster group. Coming to arxiv this October.

Robotbeat 6y ago

I just think of them as different axes on a 2D Cartesian plane. That’s basically how they work. EDIT: similarly, quaternions as a number in 4D, with that extra dimension being handy for avoiding the instability problems when you get near “gimbal lock” in 3D rotations.

phkahler 6y ago
But the quaternions sort of make the real component special dont they?
- kortex 6y ago
  That it more an effect of how we use them in computer geometry. Unit quaternions with ijk plus real map to an xyz tilt plus a rotor. But I believe you could pick any such mapping. On the other hand, dual quaternions do care which is the dual component, since multiplying by complex numbers looks like true rotation, while multiplying by a dual looks like rotation around a point at infinity, aka translation. So in that case maybe there is something special about the real component.

injb 6y ago

That's pretty close to what Gauss said they should be called: "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" (https://shitohichiumaya.blogspot.com/2016/10/gausss-quote-for-positive-negative-and.html https://shitohichiumaya.blogspot.com/2016/10/gausss-quote-fo...)

yccs27 6y ago

I also like the name "lateral unit", maybe call the field "planar numbers"?