Livin' la Vida Dozenal!

A mathematician, a physicist, and an engineer find themselves in an anecdote. After some observations and rough calculations, the engineer realizes the situation and starts laughing. A few minutes later, the physicist understands as well, and chuckles happily to himself, as he now has enough experimental evidence to publish a paper. This leaves the mathematician somewhat perplexed, as he had noticed right away that he was the subject of an anecdote. He had deduced quite rapidly the presence of humor from similar anecdotes, but he considers this anecdote to be too trivial a corollary to be significant, let alone funny.

I don't know when I will run out of anecdotes, but I'll try to keep them coming.

I wanted to share something that has made my everyday life easier. I think it could be a huge benefit to anyone who wants to try. Basically, we are all using a system that makes our lives more difficult. That system is... Base 10. The decimal numbering system is sapping energy out of your life everyday. Here's why.

The number 10 is divisible by 2 and 5. That means if you divide 10 by 2 or 5, you get a nice answer, 5 or 2. If you divide by anything else, the answer is messy. Like the unfortunate repeating  decimal when you divide by three: 3.333333333333... on to infinity. Divide by four and you get 2.5. Not as nice as the 2 or 5. The problem is divisibility. The number 10 simply doesn't have very many divisors, although at least it isn't prime.

That makes 12 a much better candidate. It is divisible by 2,3,4, and 6. A system based on 12 would make more sense. It turns out there already is such a system, called duodecimal or dozenal. I like the name "dozenal" better because it emphasizes the everyday utility of the system: it is based on a dozen things instead of 10. The reason we have "dozens" in the first place is because it is so much more natural. And not just for eggs. Because 12 is divisible by 2,3,4, and 6, you can easily take half a dozen, a third of a dozen, a fourth of a dozen, and a sixth of a dozen without breaking eggs. That is convenient. 

You might wonder why we use decimal, then. We have 10 fingers. That is the only reason. Counting naturally comes in 10's because of our hands. How could a base 12 system be easy if we can't count on our hands? Well, we can easily count to 12 on the pads of the fingers on one hand. Three pads times four fingers is 12. (Counting like that, and then counting up the twelves on the other hand is why the Babylonians used a base 60 system.) So, counting is easy, but what about math? For math, we need symbols.  

The base of a numbering system is how many units it takes before you have to reset and use another digit. With base 10, there is not a single symbol for 10, we just combine the ten symbols we already have: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. So we need two more symbols to make dozenal work. There are several different suggestions for the new symbols. I like Χ and Ɛ, called dec and el. So the numbering goes ...8, 9, Χ, Ɛ, 10, 11,... and sounds like ...eight, nine, dec, el, do, do-one... 

That seems hard, but it is not bad when you get used to it. But now the fun begins. In decimal, the patterns of multiplication can be difficult. Think of the multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33... So the pattern of last digits is 3, 6, 9, 2, 5, 8, 1, 4, 7, 0. In dozenal, the pattern is 3, 6, 9, 0 (do). Multiplying by 4 gives: 4, 8, 0. Those patterns are much easier to teach children than the decimal patterns. Division is nicer too: 10/2 = .6, 10/3 = .4, 10/4 = .3, 10/6 = .2. So many more divisions come out cleanly, and they are useful ones. In everyday life, we use halves, thirds, and fourths constantly. Having them come out so nicely would be really convenient for cooking, buying things, splitting treats between kids, or whatever else people do. 

And then there's dozenal time. It still uses the same hours we do, but the hours are split up into 12 units, each of five normal minutes. So reading a dozenal clock doesn't involve multiplying the number for the hour by 5 to get the minutes. If both hands point at the 3, we say 3:15, whereas dozenalists say 3:3.  

It doesn't stop at telling time. They have divided up the five minute chunks into smaller groups of a dozen, until they arrived at a base unit of time, the tim, that is about 1/6 of a second. Then they defined a length unit based on that time and the acceleration of gravity on earth. That unit is the grafut, and is near to our foot. One square grafut is a surf, one cubic foot is a volm, and it goes on. They have redefined all units to measure anything in terms of dozenal numbers and everyday utility. For you scientists and engineers, the mass unit, the maz, and the force unit, the mag, are equivalent under earth gravity, because they were defined that way. No need to use a conversion factor. Three cheers for dozenal!

That is why I'm glad I converted. Everyday math is easier to do, and dozenal time is more straightforward. The dozenal system of units is simpler for everyday use, and I probably use my dozenal ruler everyday. I am also glad I found it relatively early in my kids lives, so they can grow up using a more intuitive system. My wife is having a hard time converting, but I think that is because her heart isn't in it.

If you want to simplify your life, convert to dozenal. If you can get enough people around you to convert, you can live in an "island of dozenalism" where you only have limited interactions with the barbaric decimal world. And then life will be great.     

For more on dozenal:
Numberphile: http://www.youtube.com/watch?v=U6xJfP7-HCc&noredirect=1
Dozenal Society of America: http://www.dozenal.org/drupal/
Dozenal measurements: http://www.dozenal.org/drupal/sites/default/files/tgm.pdf
A great article: http://www.guardian.co.uk/science/alexs-adventures-in-numberland/2012/dec/12/dozenalists-world-unite-tyranny-ten

For more on numbering systems:
Numberphile on base 60: http://www.youtube.com/watch?v=R9m2jck1f90
Numberphile on hexadecimal: http://www.youtube.com/watch?v=9xbJ3enqLnA
Wikipedia:
http://en.wikipedia.org/wiki/Binary_number
http://en.wikipedia.org/wiki/Octal
http://en.wikipedia.org/wiki/Duodecimal
http://en.wikipedia.org/wiki/Hexadecimal
http://en.wikipedia.org/wiki/List_of_numeral_systems