Let’s Get Dozenal

Around the time of the French Revolution, there was a global (or at least European) push to use the metric system for everything. Why would a rational society continue to use an antiquated, inefficient, incohesive system of measurement? Rather, we ought to build our measurements out of our system of numbers. Gone are the days of remembering how many teaspoons are in a tablespoon, how many yards are in a mile, or the boiling point of water. Everything will be easy powers of 10.

Like much of the social engineering born of the Enlightenment, this was actually a terrible idea.

While the metric system does have certain benefits in conversion (1 km = 1000 m; 1 m = 100 cm) it ties us to the decimal system.

We all use the base 10, or decimal, system. In other words, we use ten symbols to count: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The first symbol (0) signifies nothing (though it certainly is full of rage and fury.) Each after increments by 1. One we’ve used all of the symbols, we trade our ten ones for one “ten.” Then we can count with our ten symbols again. We can count our “tens” with those symbols, too. Ultimately, our numbers are structured like this:

an * 10n+ an-1 * 10n-1+. . .+ a2 * 102+a1 * 101+ a0 * 100

The number will be

anan-1 . . .a2a1a0.

In another way,

9,999,999 = 9* 106+ 9 * 105+9* 104+ 9 * 103+9* 102+ 9 * 101+9* 100; we have 9,000,000 + 900,000 + . . .

So, what’s the problem? This system is ingenious! Indeed it is, but it also gives us absolutely no reason to use ten symbols rather than three or eighteen. Think back to your multiplication tables for a moment. What are the three easiest numbers to multiply? Personally, I would say 2, 5, and 10. They have very nice patterns. They always end in 0; or 5 or 0; or 2, 4, 6, 8, or 0. Remember that the factors of 10 are 2, 5, and 10. They fit evenly into that unit. Why not choose a number with a ton of factors?

360 has a very long list of factors. But then we’d need 360 different symbols, and we’d have to remember and distinguish them. I’m a middle school math teacher. I can hardly tell the difference between 1, 4, and 9 sometimes.

So we want a balance, the virtuous mean between the number of symbols (which we want very low) and the number of factors (which we want very high.) 10 isn’t the right choice. It’s 12.

We’ll need 2 more symbols. Let’s use X (“dec”) for one more than 9, and E (“el”) for one more than dec. Then counting would go, “One, two, three, four, five, six, seven, eight, nine, dec, el, do” (pronounced like the thing you bake; it’s short for “dozen.”) Then we start over: “do-one, do-two, do-three, do-four, do-five,” and so on up to “do-nine, do-dec, do-el, two-do.” Once we have do dos, we have a “gro” (for gross; think of Bilbo’s Birthday Party.)

You’re laughing at me. I can tell. Or just giving me a “what are you on, Jack” type of look.

But look at this comparison:

It wouldn’t let me rotate it; sorry…

In base 10, multiples of 2, 5, 10, and (kinda) 3 have nice patterns. In base 12, it’s multiples of 2, 3, 4, 6, 12, and (kinda) 11. Fractions are better, too. In dozenal, 1/2, 1/3, 1/4, 1/6, and 1/12 are all simple non-repeating decimals (dozenals?): 1/2 = 0.6, 1/3 = 0.4, 1/4 = 0.3, 1/6 = 0.2, and 1/12 = 0.1. 1/5 isn’t pretty anymore (0.2497 repeating) but the only reason we cared about 1/5 was because it was pretty in base 10.

You can even still count on your fingers- the original reason behind the base-10 system. Each of your 4 non-thumb fingers has 3 segments. The Babylonians and Mayans used base-12 or base 12/base 5 hybrids to chart the heavens, measure time, and calculate angles. From thence cometh 12 hours, 60 minutes, and 360 degrees.

And what about 12 inches?

So cast off the decimal shackles of our forebears and join the Dozenal Revolution! Or not. The humble decimal system has served us well and won a place in our hearts.

Just keep off of my inches.

4 thoughts on “Let’s Get Dozenal

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