# Advocating base 12 number system

I had a calculus professor who suggested we should be using base 12 number system. What are the advantages of using such a system?

• I've occasionally wondered what the proponents of this claim are its advantages, but I've never thought about it. Commented May 14, 2013 at 22:19
• I wonder if "number systems" rather than "numeral systems" is the right name for a tag suitable for questions like this. Commented May 14, 2013 at 22:20
• I found some interesting answers here. To me the most interesting was the point about the subitizing range, which connects the mathematics to the biology/psychology of the human brain. Commented May 14, 2013 at 22:36
• Commented May 14, 2013 at 22:42
• In ancient Babylonia base 60 was used which is even better... Commented May 14, 2013 at 23:31

## 3 Answers

As I see it, there are two advantages. First, it's not too different from base 10, so it comes fairly naturally. Second, 12 has many divisors, so $1/2, 1/3, 1/4, 1/6, 1/8, 1/9, 1/12,\ldots$ would all be terminating decimals.

• Actually, the base 12 number system seems to have been common in the past, exactly due to 12 having many divisors. We even have traces of it in many languages (eleven and twelve, not oneteen and twoteen)
– vsz
Commented May 15, 2013 at 6:23

More factors: 1/2, 1/3, 1/4, 1/6 (and sometimes 1/12) are common fractions, which would turn out "even" (not infinite). The Babylonians where on to something with their base-60 system...

• Babylonians. You beat me to the punch! Commented May 14, 2013 at 23:46
• Babylonian numerals really seem a lot more like a combination of unary, base-10 and base-60 than pure base-60. Seems like it'd get pretty confusing in complex calculations. Commented May 15, 2013 at 2:44

Well, in the base $10$ number system it is as easy to multiply by 5 as to divide by 2 (the answers differ by 0 at the end). And it is as easy to multiply by 2, 4, 8... as to divide by 5, 25, 125..., by the same reason. So in the base $12$ number system it is as hard to divide by 2,3,4,6,12,4,9,16... as to multiply by 6,4,3,2,1,36,16,9..., and, therefore, one can trade division to multiplication in more instances...