Quaternions seem to be the optimal solution for representing rotational operators in 3space.
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Replying to @RitaJKing
If you want to efficiently rotate an object in 3space (which our brains clearly do), quaternions are your best bet, so yes, I guess they exist as parameters to learned cortical neural circuits that rotate object geometries.
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Replying to @RitaJKing
You could also learn operators that "smush" the rotations together in fewer, the same or more dimensions, but you'd see artifacts when you use them: some sequences of rotations will consistently have worse results than others. The brain should correct that towards the optimum.
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Replying to @Plinz
I picture bees experimenting with honeycomb in a different shape.
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Replying to @RitaJKing
Interesting thought. The honeycomb itself is probably generated via fixed angles and edge length. If the bee can build from all angles, it must be rotation invariant. But if the bee only ever builds from a small set of angles, geometric rotation won't be necessary.
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Replying to @Plinz
It might be true that they only ever build from a small set of angles, but how are the angles and edge length fixed? Inherently because of the bee itself, or is this just what the bees learn from other bees/honeycomb to do? https://askdruniverse.wsu.edu/2015/11/02/why-do-bees-make-hexagons/ …
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Replying to @RitaJKing
The comb generation algorithm is probably genetically fixed, because the optimum size of the cell is given by the larva size of the species, not the environment, so why waste time and error on learning?
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Hexagons are as close as you can get to a circle if the circles share as much wall as possible.
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