Also on the list of things that likely exist in brains and we might want to look for: quaternions
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Replying to @Plinz
We've been studying quaternions at Science House. Would love to hear more!
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Replying to @RitaJKing
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 is a form of correcting towards the optimum, since bees only make hexagons but theoretically could make triangles, for example.
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The hexagonal lattice is the optimal packing in 2D, but it would be wasteful to let every bee figure that out by herself.
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Replying to @Plinz
Everything is a process of optimization from stardust to whatever's ahead
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Replying to @RitaJKing
But for proper evolution you need the first cell, so it is restricted to very narrow conditions and a lot of initial luck. And ahead of us is the rising tide of entropy that will mercilessly drown the last survivors of super volcanos, meteors, ice ages, AI singularities and ennui
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