Body plan of a 4D human-analog?

I am attempting to design aliens that live in a universe with a 4+1 space-time--i.e., a universe with four orthogonal spatial dimensions, rather than three, in addition to a fifth time dimension. In this universe, gravity follows an inverse cube law rather than an inverse square law, but it still results in large blobs of solid matter being pulled into (hyper)spheroidal planet shapes. 4D planets, however, have 3D hyperplanar surfaces, not 2D planar surfaces like planets in our universe. While 4D space comes with an array of other interesting features as well (like having an extra Platonic solid, knots made out of sheets instead of strings, and two independent components of angular momentum), it is the 3D nature of planetary surfaces that is most relevant here, as that dictates the geometry of limbs designed to contact and move over them.

Now, to state the obvious as background: humans have two legs, and two arms, derived from creatures that have 4 legs. In 3D space, standing on two legs is unstable, but it is (obviously) feasible to maintain balance on the free axis with active neurological control. There are, however, no creatures which get around on only one leg (modulo the occasional bird that can lock its joints to stand on one leg, nothing actually locomotes with one).

4 legs is a good number for an ancestral creature in 3-space, because in 3-space you need 3 points of contact to maintain stability, and having 4 legs allows you to move one at a time while keeping three points of contact on the ground. Also, having an even number of legs permits bilateral symmetry. Also due to symmetry considerations, we don't see any 3-legged, one-armed animals; having three legs would result in greater stability than two, but Earthling tetrapods that re-purpose some of their limbs as not-legs invariably do so in pairs.

Moving up into 4-space, you need four points of contact on a hyperplanar ground for stability; standing on three legs is as unstable as standing on two legs in 3-space, and standing on two legs in 4-space is as unstable as balancing on one leg in 3-space. Thus, it would seem unlikely for a 4D sophont to have only two legs (and definitely not just one!).

However, while we can reasonably exclude reasonably exclude one-legged and two-legged/two-armed body plans for the aforementioned stability reasons, it is not so obvious what limb arrangements would be reasonable, particularly since adding an extra dimension gives you more directions for limbs to stick out from a single body section (e.g., a shoulder girdle or hip girdle analog).

So: Does it make the most sense to attach only two bilaterally symmetric limbs to each body segment/shoulder girdle/hip girdle? Or, are there higher-order symmetries possible for limb arrangements?

posted almost 5 years ago

Logan R. Kearsley‭

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