PatrickPowers wrote:gonegahgah wrote:I was thinking about our 4D people and it is most like they would have a tripod side-by-side stance.
I say two legs in 4D. Not stable in 4D, but two legs are not stable here in 3D either and it doesn't stop us.
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The question isn't so much stable or not stable; the question is
how (un)stable. Two legs are not stable in 3D, but they are at least stable in the horizontal plane, leaving only a single axis in which the standing creature may fall. Even on a windy day it's not hard to keep your balance against the gust of the wind by pushing against the direction you would fall.
In 4D, however, two legs would mean there are
two dimensions along which you may fall, i.e., there's now a 360° circle of directions in which you may fall. That's much harder to control, and would be similar to standing on one leg in 3D. It isn't impossible, but quite hard, and likely requires frequent hopping to restabilize yourself.
Having said that, however, there
is a way to be have a semi-stable stance on two legs in 4D: if your feet are perpendicular to each other, and you stand such that they fall on two opposite edges of a tetrahedron on the 3D surface of a 4D planet, say. This configuration is quite stable, and you can walk by lifting one foot (edge of tetrahedron) and putting it down on the opposite side of the other foot (forming a second tetrahedron sharing an edge -- the first foot -- with the first tetrahedron). For maximum stability your feet would have to extend in both directions from your leg, forming an inverted T shape (instead of the L shape we have in 3D).
An equivalent configuration to this is if you have 4 legs at the corners of a tetrahedron, and walk by lifting two legs at a time and planting them on the other side of the other two legs. One could surmise that 4-legged creatures would have such a configuration of legs for upright walking. But I'd expect non-upright creatures to have more limbs than 4; perhaps 6 or 8, in triangular prismic or cubic configuration, say. Or possible in octahedron formation (as triangular antiprism: 3 limbs in the front, 3 limbs in the back in dual orientation).
In dimensions higher than 4D, the number of limbs would probably increase quite quickly in order to maximize stability. Even for upright-walkers, the number of limbs would have to be quite high in order to compensate for the dramatic increase in the number of directions one could fall.