Dek, El, Do - The Dozenal System
The Decimal System dominates Western Society. A lot of people aren't aware that they're conditioned to think of numbers in a way that relates to ten. It is common to audibly hear expressions of our dissatisfaction at something like the price of a £1.99 double cheeseburger because it's not a tidy £2, and perhaps more so because it means we're lumped with an increasing amount of coppers, but how useful is the decimal number system? Would the dozenal system be an improvement?
I mean not to totally debunk the decimal system, nor list all of it's disadvantages, however there seems to be no Mathematical significance to the use of the decimal system, perhaps there's some Anatomical significance since (most) humans have ten digits on their hands and and ten on their feet. I'd just like to take a glance into looking at numbers in a different light, if not only for entertaining a different perspective, then for looking at a transdecimal system that may have a greater practical use.
12 Is a better base for a number system because 2, 3, 4, and 6 can go into it and thus make it more versatile than 10, in which only it can only be divided by 2 and 5. The fact that 12 has more factors than 10 makes it easier for children and adults alike to learn the dozenal times tables. Think of the multiplication tables that were most easiest for you to learn. . . 2 and 5, right? That's because 2 and 5 are multiples of 10. 12 has 2,3,4 and 6 as multiples, so this means that more of the times tables are significantly easier for a base 12 number system. This divisibility also gives the imperial measure of a foot its use, because it is made of 12 inches.
Let's get acquainted with the dozenal system. There are 3 extra numerals to learn: Dek, El and Do. Dek represents a decimal equivalent of 10, El represents a decimal equivalent of 11, & Do(Short for Dozen) represents a decimal equivalent of 12. So the first 'Do' numerals appear as so: 1, 2, 3, 4, 5, 6, 7, 8, 9, X, E, 10.
- X - Dek
- E - El
- 10 - Do
To demonstrate how easy the 2, 3, 4 & 6 times tables would be, here they are:
(Note: The two times table is still all even numbers, the 3 times table all ends in 0, 3, 6, 9, the 4 times table all ends in 0, 4, 8 and the 6 times table all ends in 6 or 0.)
The dozenal system also tidies up fractions and percentages. A decimal third, or 33.3 recurring becomes 40%, 1/6 becomes 20% instead of 16.6 recurring, 1/8 becomes 16% instead of 12.5, 1/9 becomes 14% instead of 11.11 recurring. 1/12 obviously becomes 10% instead of 8.3%.
If your curiosity has been piqued and you wish to look further into the use of the dozenal system, there are many societies that advocate the use of base 12, the main one being The DSA(Dozenal Society Of America). J.R.R. Tolkeins Elvish languages even use a hybrid of the dozenal system.
For me, the dozenal system is tempting because of it's potential practicality, I enjoy numbers and challenging my ways of thinking.
For a great chapter on alternative number systems and indeed a great book on the history of Mathematics, check out Alex's Adventures In Numberland by Alex Bellos.