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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)

@varx now I want to release a text that comes not in volumes but in quaternions

@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 🤷

@max @aparrish I actually don't know enough about quaternions to even know if I want an answer.

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? 😕

@aparrish good post 🤘🏼

EdenDestroyer@edendestroyer@mastodon.social@aparrish I absolutely love any discussion around the word "volume"