## Biology Question #80

A.E., a 20 year old male from the Internet asks on October 12, 1999,

Why do we have five fingers? My idea is that one of nature's themes is "having enough." It's like a log function. It increases rapidly to a point then increases very slowly. That's when changes stop. Probably we will not gain much by having 6 or more fingers so nature wouldn't go through the problem of changing the structure of the hand to fit in a 6th finger. What do you think?

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### Mark Changizi, psychologist, Caltech answered on October 5, 2004

Here is the back-of-the-envelope calculation for the number of fingers. Look at your hand, and you'll see that your finger lengths are very roughly the same as your palm diameter. Who knows why; that is for someone else to explain (or me sometime in the future). But given this, it means that the body (palm) radius is half the limb (i.e., digit) length.

Let B be the body (palm) radius, and L the limb length. The above empirical observation that the palm *diameter* is roughly the same as finger length means that

L = 2B.

The limb ratio, k, is defined as L/(L+B).

We have, then, k = 2B/(2B+B) = 2B/3B = 2/3.

Recall that my hypothesis predicts that the number of limbs, N, is approximately equal to 2*pi/k, when limbs are 360 degrees around a body. We have, then

N = 2*pi/k = 2*pi/(2/3) = (3/2)*2*pi = 3*pi = 9.425

But recall that for hands, only half the perimeter has been selected to have digits (unlike a free-floating starfish where limbs are needed 360 degrees around). So, the prediction for hands is only 1/2 of the prediction above, which is 3*pi/2 = 9.425/2 = 4.7, or approximately 5. Yes indeed, we have 3*pi/2 fingers! Fingers and pi have more in common than cherry stains! For more on this, visit Changizi's website.

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