Should We Replace The Decimal System?
I saw an interesting post on a friend’s Facebook wall today. It talked about how bad the system for time is. You have base 12, base 24, and base 60. Which when you first start learning seems like a cruel joke. But once you become familiar with number bases you can’t help but be impressed by the genius of the people that decided to use these number bases that are really only used in clocks and calendars. Warning a lot of math and geeking about numbers is to follow. You can skip that for the point and the more generalized conversation if you don’t want to marvel at number base systems. This post does follow Betteridge’s Law but that’s not what the point is.
For those not familiar with why these bases are so useful for keeping time. Math with fractions is hard and was probably not accessible to most of the people. But you still needed people to be able to handle simple ideas like spending half a day. A third of an hour etc. What makes the numbers 12, 24, and 60 interesting is that 12 is evenly divided by 1, 2, 3, 4, 6, and 12 itself. 24 is evenly divided by 1, 2, 3, 4, 6, 8, 12, and 24 itself. Similarly 60 is evenly divided by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60 itself. Each of these numbers makes it very easy to divide by small numbers e.g., a quarter hour is 15 minutes.
What I was thinking about today is 12 or rather twelve and if it would have made a better base than the decimal system. The biggest advantage of having ten digits is that, well most of us have ten digits on our hands. And so we have a number system based on what was anatomically easy for us to understand. But the problem with this is that the number ten is only divisible by the numbers 2 and 5. And having more factors leads to easier math in several ways.
So let’s say we used base twelve as our primary number system. We’d have twelve digits (twigit?) instead of the ten we usually see. Say 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, t (representing the number ten), e (representing the number eleven). For starters dividing by 2, 3, 4, or 6 or their multiples would never result in a recurring decimal (twecimal?) fraction. Since 3 is smaller than 5 not only would it cover more numbers but 0.33 and 0.67 is one of the fractions we see.
Similarly how we can easily tell if a number divides evenly by 2 and 5 in the decimal system. In a base 12 system we would be able to tell at a glance. All numbers ending with an even twigit (0, 2, 4, 6, 8, t) are even. All numbers ending with 0, 3, 6, and 9 are divisible by 3. And similarly for 4 and 6.
Similarly when doing mental math I find it easier to divide by 2 and put a zero in front rather than multiple by 5. Similarly instead of dividing by 5 you can multiply by 2 and take away a 0. We’d be able to do similar tricks except pairing 2 with 6, and 3 with 4.
A final bonus anatomical feature is that we have twelve phalanges on the fingers of each hand and it is quite easy to count up to twelve, except we could have had two two base twelve digits. Making it trivial to count up to 144 using our fingers.
Base sixty wouldn’t be a practical base because we would have to remember 60 symbols, 120 additions, and 3364 multiplications to be able to effectively do math problems. This is something we wouldn’t be able to handle. However, base twelve is very close to ten and quite manageable. Searching I see a lot of people suggesting that a base 12 number system would be easier for us to deal with.
So I’ve made a very strong case for if we used base twelve our lives would be significantly better. So why not use base twelve instead of ten? Well, I would say even the proposition is ridiculous. Nobody in our society natively uses base twelve to do math. All of the reference materials we have use base ten. Everyone would have to change the base system in which they do calculations in favor of base twelve. This includes a large portion of the population that isn’t familiar with the concept of number bases. All our communication of numbers would need to be changed and even if we do that peple would interpret the numbers in base ten or be confused on what base is being used.
Now forget about base. A little bit easier mental math is nice but really not relevant. But it does lead to the interesting question. Even if you prove something is wrong but if it is fundamental to the way we function how can you move people to the better alternatives? Where will you find people that can train others in a radically different approach when they themselves are not native to the new paradigm? What are the components that need to be met to change a paradigm?
What are people’s thoughts? What is your favorite paradigm shifting change? What do you think were the key elements that needed to be met to cause a change in paradigm?
