thinking about how the word "volume" both contradicts the assumed low-dimensionality of text (text isn't just lines, and it's not just page surfaces—it takes up space!) but also affirms the abstractness of text (it's a "volume" but not a volume of any mass or material in particular)
@aparrish I've just looked up the etymology and wow, apparently "volume" comes from "volvere", to turn or revolve -- because books used to be scrolls. And that seems to be the root of the other meanings somehow?
@aparrish Hmm... quaternions are weird, though. They represent a rotation in 3-space using 4 coordinates. Can they represent 4-space?
@varx @aparrish I don’t know if you are actually looking for an answer, but I believe it is: No. You just want matrices for rotation after 3-space. (But a quaternion has the shape of a 4-space vector.)
My recollection is that quaternions take a shortcut through matrix math via the complex plane somehow I don’t recall, but there’s imaginary numbers involved, spooky. Imaginary numbers like to reproduce like rabbits and apparently a 4-space quaternion equiv. is almost as long as a 4x4 matrix 🤷
The more I think about this the less I understand what it would mean to have text come in quaternions.
Quaternions represent rotations in 3-space, although *non-uniquely*. Limit it to the unique solution (pick one of the two equivalent unit quaternions, right?) and you have three rotations. A scroll is just one rotation. (Or is two, since you wrap around from right to left again?) Would a quaternion text roll up three ways? 🙂
Or maybe it's about this: A volume is Cartesian; you read left to right, top to bottom, front to back. But text in a quaternion would be read, uh... in weird circular sweeps? 😕
@varx @aparrish Imaginary numbers result from square roots (primarily), which likely means the Pythagorean theorem is deeply involved somehow (a^2 = b^2 + c^2), which means trying to read a quaternion probably involves a lot of triangles and it is easiest if you are vegetarian and have a small, weird math commune/cult.
@varx @aparrish Yeah, I think that mostly is just people find imaginary numbers too spooky or complex (pun intended). I had Calculus professors that tried to impart that imaginary numbers/complex numbers get a bad reputation from name alone. They need a new PR firm. The square roots of negative numbers are still very useful numbers, we just have a hard time historically picturing them visually and gave them some of the dumbest names. Even negative numbers have a bad rep in general, though.
@aparrish perhaps language is a soil https://ask.metafilter.com/319149/Why-point-out-that-soil-must-occupy-space
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