In How Many Limbs Should Humans Have? I described my Limb Law, an empirical law I discovered which relates how long an animal’s limbs are to how many limbs it has. This law is explained by virtue of animals having evolved a limb design that minimizes the amount of needed materials to reach out into the world (see links to my academic work in the previous piece).

To see the Limb Law in action, go to my web site where you can play with an animal’s limb length and watch how the optimal number of limbs changes. Roughly speaking, the animal designs you can create in this program are the ones we find on Earth (…among radially-directed-limbed animals).

The Limb Law applies to more than just animal legs. By “limbs” I refer to any appendages that reach out, *and so the hypothesis applies to hands as well*, but where a hand’s “limbs” are its digits.

The only thing we must keep in mind in order to apply the Limb Law to hands is that hands are not free-range animals, but are, rather, connected to an animal. Hands have digits pointing away from the arm that connects to the hand, and so have only about half of the digits one would expect if the hand were roaming the world on its own.

In light of this fingers-are-the-hand’s-limbs observation, in this piece I’d like to ask…

*Why do we have ten fingers?*

In addition to being fundamentally interesting, this question also has deep implications for why we use a base-10 number system (rather than a base-2 or base-8 system, each which would arguably be better).

How can the Limb Law tell us how many fingers we should have, given that it only tells us the relationship between limb length and number of limbs?

Because hands like ours have plausible constraints on how long their fingers should be. Hands must close, i.e., their fingers must be able to reach back over the palm and cover it up. And that simple requirement is enough to enable us to predict roughly how many fingers we should have.

Recall that the Limb Law was that the number of limbs, N≈2π/k, where k was the “limb ratio,” k = L/(L+R), where L is limb length and R the radius of the body.

The demand that finger length be approximately the diameter of the palm means that the finger length should be about twice the palm’s “radius”. So, L≈2R. It follows that k ≈L/[L + (L/2)] = 2/3. And, plugging in k=2/3 into the equation for the number of limbs, N, we have N≈2π/ (2/3) = 3*π ≈ 9.42.

That is, given that fingers must be roughly as long as the diameter of one’s palm, then there should be about 9.42 fingers poking out from the circumference of the palm.

But remember that palms aren’t animals living freely on their own, but are attached to arms, and thus we expect palms to have digits on only about one half of their circumference. So, 9.42 is twice what we should expect for the number of fingers. Divide 9.42 by 2 and we have 4.78 fingers per hand. Or, about five.

Could it be that your run-of-the-mill alien would also have ten fingers, and thus get saddled with base-10?

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There was a healthy discussion when this was posted at Science20.com, and it is worth repeating one exchange here. Here is the comment, followed by my reply…

We have a maximum of 5 digits per limb, because ancient ancestors of all subsequent quadrupeds settled on 5 digits per limb, after initially starting out with a higher number (7 or 8 digits per limb – see for example, http://www.dinosaurjungle.com/prehistoric_animals_acanthostega.php ).

My reply…

The fact that number of digits has tended to

onlyfall among tetrapods (from polydactylous to pentadactylous and lower in many cases) could mean there is some kind of (genetic or developmental) difficulty in adding digits, as you suggest. But abnormal polydactyly is fairly common in vertebrates (including humans), and often has a hereditary component. On this basis it would seem that adding a digit is possible. And, evolution can take more creative approaches as well, like the Giant Panda extra pseudo-digit you mentioned.Rather than supposing that there is some kind of difficulty in adding digits, or some kind of upper limit of five, an alternative hypothesis is that the original polydactylous tetrapod had simply “too many” digits for most hand designs relevant for terrestrial environments, and that tetrapods ever since have been disproportionately losing digits to fill in vacant spots in design space, with only the occasional added digit. That is, the tendency for digit loss over time may be due to adaptive selection pressures, not a no-adding-digits constraint.

So, I’m not convinced that developmental / genetic constraints force a five digit maximum.

Also, I’m of course not suggesting that prior “evolutionary stages are planning ahead for the number of fingers humans would need in millions of years time.”

And, at any rate, all this is beside the point. Let’s suppose that some kind of historical accident were to

force exactly five digitson all progeny of an animal, and that some of those progeny became primates with our hand design. Is it true that it is a historical accident that we have five fingers, in this thought experiment? Not quite. Being stuck with five digits would have constrained the kinds of hand (and body) designs possible for this animal’s progeny. Some hand designs, and animal designs, would then be out of reach to this lineage. The hand designswithinreach for such a lineage would be ones which work really well with five digits. …and one such hand design is the “grasper” one where the digit length is of similar length to the palm diameter, very roughly our hand. The question is whether our hand/digit design is optimal in some hypothesized sense. My suggestion is that our 5 digits and our digit-length-to-palm ratio are “designed for one another” (because that relationship is consistent with cheap reaching-out wiring costs). My suggestion is an engineering hypothesis, not a historical hypothesis. If five-ness was historically fixed, then what historically evolved was the length of the digits to become a proper grasping hand. To put it another way, if our long ago ancestors had, say, three fingers, and could not add new ones, then primates would probably not have evolved in the first place, because the hand would have led the lineage down new design paths.

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*This first appeared on May 17, 2010, as a feature at Science 2.0*

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*Mark Changizi is Professor of Human Cognition at 2AI, and the author of The Vision Revolution (Benbella Books) and the upcoming book Harnessed (Benbella Books).*

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