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.
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.
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?
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
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
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