would math be easier if we were born with 12 fingers and used base twelve mathmatics?
the reason I ask is that 12 has more numbers it can be divided by evenly
10 can be divided by 1/2/5
12 can be divded by 1/2/3/4/6
it seems like it would be nice to be able to find a third of something without ending up with .333333333333333333333 and being able to find a fourth of something with no ‘decimal’ wouldn’t be too shabby either.
is there any part of base 12 mathmatics that make it harder than base 10? (other than the fact that we use base 10 and it would be hard to ever change that)
Let’s assume that the digits for base 12 are 0-b (a == 10 decimal, b == 11 decimal). a/3 would still be 3.33333333333. Or are you suggesting that there would be 10 of fewer things in the world if we counted in base 12?
One can indeed make the argument that several things would be more convenient if we had a number base with more factors. A limiting factor being the size of multiplication table and number of symbols one would have to remember, 12 seems like an optimal choice (60 would introduce a factor of 5, but that’s getting awful big). And there probably WOULD be 10 of fewer things, because we would naturally “metricize” in 12’s. 1/3 is a more commonly used fraction in daily life than 1/5, and it is probably an equitable trade to have 1/5 turn into a repeating decimal to have 1/3 come out even at one place.
There is actually a group called the duodecimal society which has existed for years (apparently now called the dozenal society). If any of them seriously think they are going to get people to change the number base we use on a day to day basis, they are sadly deluded, of course. But it’s entertaining to contemplate on a “what if” basis.
As yabob points out, the multiplication table is larger in base 12, but it’s surprisingly so. In base 10 you have to memorize 910/2=45 different things before you know the entire multiplication table (that’s not counting things like 03=0, which is easy); in base 12 the number is 11*12/2=66, almost half again as many. I’ve never felt it’s worth it just to be able to divide by 3 easily.
Personally, I prefer octal, but I realize I’m in the minority there.
owlofcreamcheese, you are correct that fractions would be a little easier, because 1/3 comes up a little more often than 1/5. However, the big downside to base 12, as I see it, is that the multiplication table has 66 entries, as opposed to 45 for base 10. A similar thing is true for the addition table. This makes learning it 47% harder for young students, and a smaller payoff later on when you do fractions. I think a better solution is base 6, the multiplication table for which has a mere 15 entries.
And now I see that everything I said has been said by someone or other in the last 15 minutes.
6 begins to make a lot of everyday numbers have an awful lot of digits in them.
While we’re doing things like this, I want to make playing cards have 60 card decks - 4 suits of 15. That way, the deck could be dealt out evenly to 3, 4, 5 or 6 players, and the extra factorability would probably suggest all kinds of new card games.
Not an awful lot of numbers. 1/log(6) is only 1.285. So at worst, the numbers will only be 28.5% longer. 5 digits instead of 4 isn’t the end of the world. Plus, you can say them faster, because we don’t have to deal with that meddling, two-syllable digit 7.
I’m for base 16 here… Hexidecimal is an existing numbering system that already does this. It may not divide by as many numbers as 12, but you can halve it more times:
16, 8, 4, 2, 1
12, 6, 3
10, 5
The number of times 2.5 and 1.25 come up in maths with base 10 makes me feel more inclined to switch to base 16 than base 12. Plus, there is a technical bias.
“Awful lot” is subjective - a 45 man roster for an NFL team would require 3 digit jersey numbers, phone numbers would have evolved with an extra digit or two. There’s a certain amount of inconvenience that accumulates in having to use 3 digits instead of 2, 4 instead of 3, etc. I’ll grant that 6 is another good choice from the standpoint of factorability vs. number of symbols.
BUT, there’s a “duodecimal society” (or “dozenal” if you prefer), and I know of no “hexal society”, which sounds like a coven anyway.
At least we didn’t evolve with one 13-fingered hand.
