Tripping on Tripedalism

Importance: 3
Confidence level: 6
Length: 1400 words

The Idirans are a powerful race from Consider Phlebas, the first book of Iain Banks’ “Culture” series. Each is very strong, several times larger than a human, and is tripedal. A creative choice, but three legs is the very worst number.

In the most basic sense, to make a free-standing structure stable requires at least 3 points of contact on the ground (if you try to balance a V upside down on its two points, it would just fall down to the side; this is why humans put cameras on tripods). But to move, an organism needs to be able to lift up at least one of its legs. Then four legs should be the minimum for most land-dwelling species.

Like a typical physicist, I’ve elided over several of the messier engineering aspects here. Some animals do not use four legs: humans and pangolins, the two most awesome species on the planet, both walk on two legs. They do this by actually putting their heelbone on the ground, in contrast to most mammals that walk on their toes (hooves are toes, etc). Doing this essentially provides them four points of contact for stability. Other animals use four or more legs to walk but move at speed on two, like kangaroos, lizards, and cockroaches, both in real life and in your nightmares from now on. Birds use two legs but frequently have toes pointing backwards, and also suck at walking [citation needed]. In all these cases, having less than four legs either comes at a disadvantage or is somehow worked around.

However, you should now grow suspicious. Why is there all this talk of twos and fours, without 3? How would we build a 3-legged animal if we were to go about it ourselves, being the intelligent creator that evolution never could be? First we might want to look at the nearest neighbors.

Kangaroos use their tail as a figurative third leg in some circumstances, like when boxing, the closest we get to the Idiran morphology. The tripod fish rests on three spines, two from pelvic fins and one from a caudal fin, and does not move like this for the stability reasons stated above. But both of these examples use a tail as a fake third leg, which we don’t want. Why not build an actual third leg into the organism if this structure is good for fitness? Why do 0 animals have this?

The unfinished answer is that it seems very difficult to create organisms at scale without symmetry. DNA is currently the most information-dense object in the universe, and is as such being used by the superhero George Church to make far more compact hard drives, but even with that title is far too underpowered to specify the placement and type and content of every cell of the body. Scientists are delving into epigenetic processes and how large-scale structure can emerge at the moment, but I have to be pretty hand-wavy here. And yet we can see empirically that every animal more complex than a sponge exhibits either radial or bilateral symmetry (organisms do break symmetry at times, but only for important things like the heart or human brain). Radial symmetry is better compression information-theoretically, because you can form 16 parts of an organism for the price of one, and works well underwater where all directions are functionally the same. However, bilateral symmetry dominates on land, possibly due to considerations of being confined to a plane. Given its dominance on the earth, there is probably some other reason though. I might conjecture that mitosis plays a part, because a cell splits into two, but all we can really do is note that this is entirely dominant. Further, evolution briefly tried a mix of the two called biradial symmetry and immediately cast it aside as an underperformer (octopodes, despite their seeming eight radial legs and two bilateral eyes, are entirely bilateral).

Given these symmetry considerations, to build a three-legged organism, we would have a few options. We could replace mitosis with something like tritosis, but this is unlikely to work because unzipping DNA falls into two halves. We could replace DNA so that it fell into thirds, but this seems really hard for structural reasons (any biochemists out there who want to postulate a mechanism are free to do so). Since the information pipeline is the main issue, we could add some compression algorithm much stronger than the current savings through symmetry and epigenetics that scientists haven’t yet fleshed out. This also seems hard, given the huge savings already in place, but could be possible. We could also replace DNA with a more compressed info source. Unfortunately, given that DNA stores one bit for every roughly 80 atoms and is in a very tight structure already, we could only get a further factor of a few from this through using a different chemical with fewer atoms per bit or better folding properties. This is probably not enough to be able to fully replace symmetry’s compression, but perhaps doable if we naively assume bilateral symmetry to have only a factor of two compression rate and search through all the organic compounds possible.

And yet, even after we figure out how to build one, would it ever be worth it? If we look a little further into the kinematics from the beginning, we can say probably not. A four-legged beast can pick up a leg as long as its center of gravity is within the triangle created by their other three points of contact. They naturally have their center of gravity either touching all four possible triangles or very close to it (think about it for yourself). This requires only a miniscule movement to free any leg for stepping. Similarly, humans evolved wider hips so that they could rotate their legs toward the center of their body, keeping both legs under them and requiring only a tiny bit of a shift to move from one to the other, as you have undoubtedly noticed during dull cocktail parties. A three-legged being can either adopt the humans’ method of keeping their legs under them or spread them wider. If the legs are spread wide, the Idiran would have two options: shift all of its weight from the center of the triangle the edge that the two planted legs are on, so it would not begin to topple immediately, or else take a rapid step that then had to decelerate the falling body. This step of catching a fall is very energy-intensive, and shifting its weight to one triangle-edge would be quite bad as well (which is worse is a question for the engineers). And no cop-outs saying that maybe it had enough energy to spare: evolving three legs is difficult, so if four legs were better, it should evolve these instead. If it opted instead to keep its legs under it like humans, it would quickly notice that it was walking and standing in a linear motion just like humans, and losing most of the stability benefit accorded by the third leg. At this point, the third leg has become almost more of a burden than a benefit: imagine yourself with a third leg. How would you coordinate the steps so that you stayed on balance, and didn’t get any legs in front of another? It is difficult. Perhaps possible, when stretching for creativity, but very difficult.

To me, it seems fairly unlikely that a large three-legged organism would evolve. The books imply it has biradial symmetry with radial legs and bilateral torso, so at the very least this should probably be replaced with a fully radial body: three arms, three eyes, etc. I would bet a small amount of money at 5:1 odds that less than 5% of animals we find on other planets are tripedal, or 40:1 that the first dominant species we find is not tripedal (or something, I’m trying to make this possible to actually evaluate at some time in the future), and 2:1 that fewer than 10% of species that are tripedal are also biradial. If anyone wants to take these bets or propose an alternative, let me know.

I don’t wish to be the small-minded person whose boxes the sci-fi writers are actively trying to think outside of. Overconfidence is truly one of our biggest curses. My concern is only that this is one of the situations where our constant overconfidence has been replaced by an almost mythic demand for underconfidence, and that has real ramifications on humanity’s forecasting ability. Whether a reader or an author, taking a few moments to consider whether there are underlying constraints that make something implausible is a very helpful background process to run. We know a lot more about astroeconomics and astrobiology than some people would have you think.

I also want to say that small centaurs should be dominant everywhere. What’s up with that, evolution?

Appendix: legs in more than 3 dimensions





3 thoughts on “Tripping on Tripedalism

  1. anon2 says:

    Centaurs aren’t a good idea:

    Tiny centaurs would be more viable than large centaurs, at least, but there’s still no reason for them to have two rib cages, or hands that they use to not climb trees with. If they need to reach up to grab something, better to make them into tiny giraffes by extending their neck than to give them two new limbs, I think.


  2. Fascinating that we have a whole stackexchange for worldbuilding, thank you for the pointer!

    I was using centaurs figuratively, though; it seems that an animal with two hands for tools and four legs for running would be very well-adapted. Instead of actually having two ribcages, I was thinking more like a horse with dexterous arms from its neck, or the 6 legs of an insect. However, the points about the difficulties of oxygen exchange are well-made, and in general go about halfway to convincing me we should have 2 legs instead of 4.


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