Why We Should Forget Our Numbering System and Switch to Dozenal

June 16, 2016 | Joanne Kennell

Clock about to strike 12
Photo credit: public domain

You can still count on your fingers!

It is pretty easy to count in chunks of 10. In fact, it is the foundation of our universally-adopted, completely arbitrary numbering system, known as the decimal system. But there are groups out there, one of them being The Dozenal Society of America, who think we should also be learning to count in twelves.

The base-10 number system emerged for one simple reason — we have five fingers on each hand. However, base-10 is not used in all cultures — numbering systems can range from base-1, in some regions of Papua New Guinea, all the way up to base-400 in the Niger-Congo.

Admittedly, counting in 10s is a little easier than counting in groups of 12, but as mathematicians point out, base-10 is not without its problems. In fact, some argue that base-12 is really the way to go.

Here’s why we should have adopted a base-12, or duodecimal, counting system — and how it may still be possible to do so.

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12 is a highly composite number. In fact, it is the smallest number with exactly four divisors: 2, 3, 4, and 6 (six if you count 1 and 12). On the other hand, 10 only has two divisors: 5 and 2 — both of which are prime numbers (a natural number with exactly two whole, positive divisors: itself and 1).

It is easier to divide weights and measurements into 12 parts, such as halves, thirds, and quarters, and it would also be easier to tell time. Five minutes is a 12th of an hour, so instead of saying “five past one”, we could say “one and a twelfth” hours. However, this would require a new clock (which you will see below).

Counting Fingers

Critics of the dozenal system argue that we would lose the benefits of finger counting. However, as “dozenalists” point out, each of our fingers consists of three parts. Starting with your index finger, and using your thumb as a pointer, you can count the first three digits (working from the bottom to the top of the finger). Then using your middle finger, you can denote 4, 5, 6, and so on.

Photo credit: Рыцарь поля/wikipedia (CC0)

And we can use our second hand to display the number of completed base twelves — all the way up to 144 (12 x 12).

What we would have to get used to is how our numbering would change. For a base-12 system to work, we need to add two new symbols for 10, and 11, and 12 would now be represented as 10. Why? These numbers were derived from having one complete set of 10 plus an additional number represented in the second column.

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To fix this problem, ten is a rotated 2 (or X) and 11 is a reversed 3 (or E). Our counting would look like 1, 2, 3, 4, 5, 6, 7, 8, 9, X, E, 10. These last three numbers are pronounced “dek,” “el,” and “doh.” For example, if we wanted to pronounce 15 in duodecimal, we would say “doh-five.” Doh-five is 17 in the base-10 system because doh is twelve and we are adding 5.

Photo credit: Watchduck/Wikipedia (CC0)

This can be extended to larger numbers as well. Duodecimal 64 would be pronounced as six-doh-four. And if we needed to surpass the number EE (el-doh-el), or 143, we need a new word for the digit in the third column.

The word for 144 decimal, or 100 dozenal, is called “gros” (the “s” is silent). A three-digit dozenal number, such as 25X, would be pronounced “two-gros-five-doh-dek.” In decimal, this number is 358.

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How did they get this number? It’s pretty simple:
Two-gros = 2 x 144 = 288
Five-doh = 5 x 12 = 60
Dek = 10

Add these all up and it equals 358.

And a “mo”, or 1000 dozenal, is 1,728 in decimal (12 x 12 x 12). If we wanted to write the year 2016 in base-12, it would be 1,200, or “mo-two-gros.”

Could we ever switch over? At this point, it would be extremely difficult and expensive, but not impossible. Converting currency would be the first and most crucial step, followed by an education campaign and a rewrite of school textbooks as a start. However, this change is unlikely.

So what do you think? Once you got used to the new symbols and how to count, would you prefer to use the base-12 system?

h/t: Gizmodo

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