It's Kind of Weird That We Use Base 10

Originally published February 27, 2015

Ten digits per human, so it makes sense that we use base ten for our number system, right? No, actually if we insisted on using all the fingers on both hands, we could have settled on base 11 or base 12, and base 11 makes the most sense.

Each hand has six possible states of information, the one with no digits out and the five with a different number of digit out each. Actually there are a lot more possible ones, involving ups and downs and whizbangs. You could even invent a whole language out of them. But for now let's assume there are six.

The fist, or alternatively the imitation of a tube, represents zero. Remember that the first digit of a number system is 0, not 1. That's why base 10 stops at 9.

The reason base 12 doesn't make sense is that since fist represents zero, the second hand displaying that state adds no information. Adding zero does nothing. It's like adding nothing, it looks like it's adding something, but is actually not contributing any information at all. Get it?

One potential solution to that is to have the fist mean something else when it's accompanying a full five-fingered hand. But then it would be ambiguous, which aside from being inelegant would also create practical difficulties and not just in edge cases.

So it makes the most sense to use base 11, in which we have a zero and then ten more digits for each finger. I don't really understand why we don't, unless each culture failed to take zero into account in the finger-counting system or they all had a preference for an even-numbered (or at least non-prime?) base.

This isn't really related, but I've been idly pondering lately how it might have affected fairness intuitions if, supposing we ended up as a 7- or 11-digited creature, simple division notions like "half" or "even" were less immediately physically salient in the structure of each creature's own body. In a nine-fingered culture, you'd have almost as easy a time inventing the indifference distribution by supposing scenarios where three people each get three parts of the prize. But with a prime number the only available distribution is one part per person, rather than, say, a compelling five-for-one when there are ten parts divided to two people.

Would fairness intuitions even arise in such a society? Or would some non-egalitarian concept, perhaps one of "Bread to the wise, riches to men of understanding, favour to men of skill" supersede it entirely? I don't know.

This is just a blog post. It doesn't mean anything. I don't know what I'm talking about and it doesn't matter