8 ms·

I really wish we'd just call them "rotation numbers" or something. "Imaginary" was always a ridiculous name.

kzrdude 4y ago
Yes, I hope the consensus eventually moves away completely from "imaginary". Complex numbers is already ok, so it doesn't need to change, only the terminology for that i axis. So what can we contribute, do you know any authors that have already found some new and better terminology and promoted it?
- jonsen 4y ago
  Electrical engineers don't use i, because i is used for current. They use j instead. I've heard them called jolly numbers.
HPsquared 4y ago
Negative numbers are imaginary enough already, really.
- deleted 4y ago
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alanbernstein 4y ago
I kind of like "geometric numbers".
tut-urut-utut 4y ago
- alangibson 4y ago
  Pointlessly obnoxious comment of the day right there
- macksd 4y ago
  Pretty sure by saying this about a set of numbers that exist and that are distinct from the Real set, you're actually making a point opposite from the one you think you are making.
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pvg 4y ago
It's no more or less ridiculous than 'negative', 'real' or 'odd'.
Chinjut 4y ago
"That this subject [imaginary numbers] has hitherto been surrounded by mysterious obscurity, is to be attributed largely to an ill adapted notation. If, for example, +1, -1, and the square root of -1 had been called direct, inverse and lateral units, instead of positive, negative and imaginary (or even impossible), such an obscurity would have been out of the question." — Gauss
- FredPret 4y ago
  Direct, inverse, and lateral are so much more productive than the labels we usually use. Can't believe I only ran into it now.
tasty_freeze 4y ago
How about "Cartesian numbers"? But my hunch is that somewhere someone has already taken that name for something else.
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idoubtit 4y ago
You should know the basics of the subject before stating that everyone is wrong and that the current standard is "ridiculous". You apparently confused "complex number" and "imaginary part". The latter made sense in the historical context, which was finding real solutions of quadratic equations (with real coefficients, of course). And please keep in mind that complex numbers are not rotations, and they do not map well to them. For instance, which rotations would be represented by the complex numbers "3", "4", "1-2i" and "8i"? You can map {plane rotations} to { r, |r| = 1 } using z ↦ r*z, but that's a circle, not a 2D space. To summarize, complex numbers can be thought of plane vectors, with an obvious geometric way to add them, and a non-obvious way to multiply them. The set of "rotations" is too vague and loosely related to complex numbers, e.g. 3D rotations are often represented by quaternions, which are more "complex" than complex numbers.
- jacobolus 4y ago
  > keep in mind that complex numbers are not rotations Complex numbers are (isomorphic to) "amplitwists": similarity transformations between plane vectors. If you want a pure rotation, you need a unit-magnitude complex number. The complex number 3 represents scaling by 3. The complex number 4 represents scaling by 4. The complex number 1 – 2i represents a scaling by √5 combined with a rotation clockwise by arctan(2). The complex number 8i represents a scaling by 8 combined with a quarter-turn anticlockwise rotation. > complex numbers can be thought of plane vectors No, (physics-style displacement) vectors and complex numbers are distinct structures and should not be conflated. Complex numbers are best thought of as ratios of planar vectors. A complex number z = v/u is a quantity which turns the vector u into the vector v, or written out, zu = (v / u)u = v(u \ u) = v. (Concatenation here represents the geometric product, a.k.a. Clifford product.) Mixing up vectors with ratios of vectors is a recipe for confusion. > non-obvious way to multiply them Multiplication of complex numbers is perfectly “obvious” once you understand that complex numbers scale and rotate planar vectors and i is a unit-magnitude bivector. > 3D rotations are often represented by quaternions, which are more "complex" than complex numbers. Analogous to complex numbers, quaternions are the even sub-algebra of the geometric algebra of 3-dimensional Euclidean space. Used to represent rotations, they are objects R which you can sandwich-multiply by a Euclidean vector v = RuR* to get another Euclidean vector, where * here means the geometric algebra “reverse” operation. Those of unit magnitude are elements of the spin group Spin(3). For more, see http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf
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otabdeveloper4 4y ago
I'm pretty sure they're always called "complex numbers" when you start using them. "Imaginary numbers" is something from a highschool curriculum.

Yes, I hope the consensus eventually moves away completely from "imaginary". Complex numbers is already ok, so it doesn't need to change, only the terminology for that i axis. So what can we contribute, do you know any authors that have already found some new and better terminology and promoted it?

jonsen 4y ago
Electrical engineers don't use i, because i is used for current. They use j instead. I've heard them called jolly numbers.

HPsquared 4y ago

Negative numbers are imaginary enough already, really.

deleted 4y ago
[deleted]

alanbernstein 4y ago

I kind of like "geometric numbers".

tut-urut-utut 4y ago

alangibson 4y ago
Pointlessly obnoxious comment of the day right there
macksd 4y ago
Pretty sure by saying this about a set of numbers that exist and that are distinct from the Real set, you're actually making a point opposite from the one you think you are making.

deleted 4y ago

[deleted]

pvg 4y ago

It's no more or less ridiculous than 'negative', 'real' or 'odd'.

Chinjut 4y ago

"That this subject [imaginary numbers] has hitherto been surrounded by mysterious obscurity, is to be attributed largely to an ill adapted notation. If, for example, +1, -1, and the square root of -1 had been called direct, inverse and lateral units, instead of positive, negative and imaginary (or even impossible), such an obscurity would have been out of the question." — Gauss

FredPret 4y ago
Direct, inverse, and lateral are so much more productive than the labels we usually use. Can't believe I only ran into it now.

tasty_freeze 4y ago

How about "Cartesian numbers"? But my hunch is that somewhere someone has already taken that name for something else.

deleted 4y ago
[deleted]

idoubtit 4y ago

You should know the basics of the subject before stating that everyone is wrong and that the current standard is "ridiculous". You apparently confused "complex number" and "imaginary part". The latter made sense in the historical context, which was finding real solutions of quadratic equations (with real coefficients, of course). And please keep in mind that complex numbers are not rotations, and they do not map well to them. For instance, which rotations would be represented by the complex numbers "3", "4", "1-2i" and "8i"? You can map {plane rotations} to { r, |r| = 1 } using z ↦ r*z, but that's a circle, not a 2D space. To summarize, complex numbers can be thought of plane vectors, with an obvious geometric way to add them, and a non-obvious way to multiply them. The set of "rotations" is too vague and loosely related to complex numbers, e.g. 3D rotations are often represented by quaternions, which are more "complex" than complex numbers.

jacobolus 4y ago
> keep in mind that complex numbers are not rotations Complex numbers are (isomorphic to) "amplitwists": similarity transformations between plane vectors. If you want a pure rotation, you need a unit-magnitude complex number. The complex number 3 represents scaling by 3. The complex number 4 represents scaling by 4. The complex number 1 – 2i represents a scaling by √5 combined with a rotation clockwise by arctan(2). The complex number 8i represents a scaling by 8 combined with a quarter-turn anticlockwise rotation. > complex numbers can be thought of plane vectors No, (physics-style displacement) vectors and complex numbers are distinct structures and should not be conflated. Complex numbers are best thought of as ratios of planar vectors. A complex number z = v/u is a quantity which turns the vector u into the vector v, or written out, zu = (v / u)u = v(u \ u) = v. (Concatenation here represents the geometric product, a.k.a. Clifford product.) Mixing up vectors with ratios of vectors is a recipe for confusion. > non-obvious way to multiply them Multiplication of complex numbers is perfectly “obvious” once you understand that complex numbers scale and rotate planar vectors and i is a unit-magnitude bivector. > 3D rotations are often represented by quaternions, which are more "complex" than complex numbers. Analogous to complex numbers, quaternions are the even sub-algebra of the geometric algebra of 3-dimensional Euclidean space. Used to represent rotations, they are objects R which you can sandwich-multiply by a Euclidean vector v = RuR* to get another Euclidean vector, where * here means the geometric algebra “reverse” operation. Those of unit magnitude are elements of the spin group Spin(3). For more, see http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf

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otabdeveloper4 4y ago

I'm pretty sure they're always called "complex numbers" when you start using them. "Imaginary numbers" is something from a highschool curriculum.