Monday, March 31, 2014

Math and Sciences Monday: Cheaper by the Dozen (Also it's better mathematically)

As many of my friends know, I have long been (at least a year) an advocate for changing our number system to base twelve, or dozenal, as it is known by it's fans, and it's technical name being the duodecimal system, which is how it is addressed by smart people with degrees. The supporters for this cause are far and few between, and I know this for two reasons:
  • Everyone I told about it either met me with a blank stare, or said it will never happen. 
  • When I typed the word "dozenal" just now, spell check insisted it wasn't a word. 
So I have decided to compile a list of advantages of this new system, in addition to a (short) list of disadvantages.
First, you might need to know what base twelve is! We use the the decimal system, though it's often referred to as base ten. That means we count like this:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
The fact that it is base ten means that on the tenth number we add a zero, and so forth for every multiple of ten. We have ten digits in the system, (1-9 & 0) and to multiply by the base only requires adding a zero at the end. In base twelve, you count like this:
1, 2, 3, 4, 5, 6, 7, 8, 9, ᘔ*(dek), Ɛ*(el), 10(doh)
Dek is equal to ten, el is equal to eleven, and doh is equal to twelve. So in base twelve, instead of multiplying by ten to add a zero, you multiply by doh, which is the mathematical decimal equivalent of twelve. For further reading on base twelve, I suggest you read the wikipedia article on it, or if you prefer to read something that doesn't sound or look like you need several degrees in mathematics to understand, there are plenty of articles and books that cover the basics and/or advanced ideas behind dozenal. If you're looking for the basics, watch Schoolhouse Rock's "Hey there little twelve-toes" or read the section on base twelve in Here's Looking at Euclid, by Alex Bellos[1]. If you prefer something a bit more complicated, or took my advice and did these things and want to continue, I suggest you read through Dozenal Society of America's (DSA) paper on basic mathematics using base twelve.
Now for the reasons to switch! But first off, because I believe in a fair fight, I will list every single reason that I could find to not switch to base twelve:
  1. We have ten fingers (some argue this is ten reasons)
  2. It will be too hard to transition
Tell me if I missed any, (I didn't) but these two reasons are really small hurdles to jump for the greater good of mathematics. I have now compiled a list of great reasons to switch to base twelve:
  1. It works better mathematically, especially pertaining to divisors. Our current system, base 10, the base has two whole number divisors other than one and itself: 2 & 5. And what are the four easiest numbers to count by? Ones and tens, obviously. And then fives and twos, due to the fact they are divisors and ten, and more familiar and cohesive. Meanwhile, 12 has four divisors other than one and itself. So theoretically, if we switched to base twelve, anyone who learned basic mathematics could count by ones, twos, threes, fours, sixes, and twelves, as easily as people can count by fives using base ten.
  2. It will make (a little) sense of why we don't use the metric system. I thought about making a table showing why, but it would probably just be better to make an entirely new measurement system when/if we switch bases.
  3. Our current rite of passages pertaining to ages will be better divisible, and subsequently be easier to remember/make more sense. If you think about it, there are a few ages to consider that will be changing to better numbers. Thirteen, the age where you become a young adult, would be printed as 11, and is one higher than doh. This makes sense, considering the transition to young adult is now takes place at the same time as the transition to "the numbers beyond 10" (in this case "10" being "doh"), which is generally the number a young child would first learn to count to, their first milestone. Eighteen, the age in which someone becomes an adult, would now be printed as 16, and would be equal to a doh and a half. 
  4. It pertains to our divisions of time. The number twelve being our base would improve our calender because of it's divisibility. I am now going to list our units of time, with it's base twelve equivalent in parentheses after each unit. There are 12(10) months in a year, with 30/31(26/27) days in each month most of the time. There are 7(7) days in a week. 24(20) hours in a day (which makes 12(10). 60(50) minutes in an hour. 60(50) seconds in a minute. Note how all things either become a cleaner rounder number (days in a month, hours in a day, minutes in an hour, seconds in a minute), or don't really change that much (days in a month, days in a week).
I hope to come up with more reasons later, (hopefully expand to a list of twelve) but that's all for now.


  1. FYI, you might be interested in the dozenal proposal that was submitted to Unicode: it was accepted for encoding in the future: - this means you'll have a real digit character rather than the Canadian language "ᘔ" and Latin letter E "Ɛ" you used in this blog post. You can watch the progress of these characters at by searching for "218A". Regards, Steven.

  2. anyways, it's an interesting proposal on the math. We do have ten digits - meaning fingers. I'm more used to base 2, 8 and 16 math myself. Anyways, this is a great blog, I should get my own blog back up someday. But it's down for good reason (fatherhood)

  3. Thanks for sharing the Unicode link! While base 2, 8, and 16, have some very good uses in specific circumstances, (binary being used for computer code, for example) base 12 is simply the most practical in normal everyday mathematics.