21:03
Hm, I'd need to think about both of those points. I'd argue, that yes, bilateral symmetry has an advantage even if you're limbless and crawling or swimming, since then you move straight when you wiggle side to side. The real question is, does that also happen in 4D?
In 3D, a sea-worm-like creature can wiggle in the plane perpendicular to its body to move forward, but it prefers to pick an axis in that plane, since that involves less movement. In 4D, I'm tempted to say that it still picks an axis, but it's not as clear. Infinite lines can move around each other in 4D without changing direction, unlike in 3D, so that might allow the worm movement options that involve what from our perspective looks like it's moving its body through itself.
For instance, if you picture the worm turning itself inside out, moving its insides forward and pushing backward with its outside skin, that's a mode of movement that's available in 4D (in this case the 'insides' aren't the actual 4D interior of the worm, but rather just a 3D cross-section). Like in the animation from the Wikipedia page on hypercubes: en.wikipedia.org/wiki/Hypercube#Related_families_of_polytopes
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Jun22
Jun '1923
Jul8
Discussion on question by Logan R. Ke…
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