Do we only use a base 10 system because we have 10 fingers and 10 toes?

Question

If we had 8 fingers and 8 toes, would we be using a base 8 system? I ask because it seems to me that one system is as good as any other, and there's nothing particularly special about powers of 10.

Answer 1

Yes, you are correct. If we had a thumb and only 3 fingers on each hand we would have a base-8 number system.

However we have a 60-base number system for measuring angles (degree, minute, second) and time (hour, minute, second). So, whose got 29 fingers and a thumb on each hand?

Then there is hexadecimal; base-16.

Answer 2

Dear Mac,

Actually, the ten system was not the first sophisticated counting system invented.  The Mayans used a base 22.  Aristotelian Greeks used 8.  Computer scientists have been using base two for many years.

Base ten is easy and convenient because that's what we learned first.

Tiger Toy

Answer 3

Indeed, most of our math is based (sorry, no pun intended) on the number 10 because we have 5 fingers on each hand.

If you look at other cultures (both ancient and present) that isn't the only base used, however.  Many cultures have a form of base-5 (for a single hand).  The ancient Babylonians had a system based on 12 and 5 for a combined system of base 60.  That's why a lot of things like time (60 minutes, 60 seconds) and angles (6 x 60 degrees in a circle, etc.) use 60.  They also picked multiples of 60 because they were nicely divisible by 2, 3, 4, 5, 6, 10, etc.

Inherently there isn't a real reason to settle on base-10 as an ideal base.  In fact, in many cases isn't the best.  For example, try writing out 1/3 as a decimal... it's a repeating decimal.  But if you were to write that in base-12, for example, you wouldn't have a repeating form of the number.

And computers, work really well with two states of on-off which leads to related bases of octal (base-8) or hexadecimal (base-16).

It is a very fascinating subject to think about why we "count" and represent numbers the way we do.