18 June 2013

The case for base-twelve, Part 1

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This is going to be another of my pet rants (like this one)—the kind that people who know me in real life may have heard five or six times now. I'm going to go into waaaaay more detail than I ever have in person, though. So maybe getting it all out of my system on the internet will mean they won't have to hear it anymore? (HAH!)

This topic's a favorite of mine because it challenges some of our most basic assumptions, and because the solution I advocate for is at once sensible yet terribly impractical. Basically my point is that instead of ten, we should be counting to twelve.

I'm by no means the first person to say as much but, even so, I don't think it occurs to most people that there's even an option to count to anything besides ten. It's just not the sort of thing you'll encounter unless you're involved in computer science (nope), are really into mathematics/number theory (nope), or are just a huge dork with too much time on your hands (ding-ding-ding!). In fact, I don't want to alarm you, but the ideas in this series of posts may very well BLOW YOUR MIND. :O (They had that effect on me when I was first introduced to them, anyway.)

To start, we need to understand that the symbol "10," regardless of how many things it actually represents, is very important. As the first number with more than one digit it basically says, "Okay, at this point we've finished one 'set' of things, and now we're starting over with a new 'set.'" So a number like "27" basically means, "two complete 'sets,' plus seven."

The big question I'm asking here is, Why is this many things: (o o o o o o o o o o) considered a full set? In other words, Why is ten the first two-digit number?

The truth is that there's no real reason—perhaps other than the fact that we happen to have ten fingers to count on. But you may notice that that's not a very good reason. If human beings were like Homer Simpson, then eight might have been considered a full set and thus represented by "10;" all-in-all, it's troublingly arbitrary.

And so while the way we count seems incredibly natural to us, it's actually just one of many (infinite, really) possible systems. The one we use is called base-ten, or decimal. You could hypothetically have a system based on any value (base-ten, base-seven, base-five-hundred, whatever)—it just means you start two-digit numbers when you've reached the amount named after "base-". They wouldn't all be equally convenient, however. And as you'll see, that's one of my main points in discussing all this: some systems are more useful than others and in my opinion the one we use, base-ten, is not the best. Base-twelve (duodecimal, or dozenal) is far superior.

 "What's so bloody great about twelve?" you may be asking yourself. Well, I'm happy to explain...

In your day-to-day life, when you're separating things into groups or sections, how do you usually do it? My guess is that you very often find yourself cutting things in half, or in quarters, or in thirds. The trouble with that is that ten is divided evenly in only one of those cases. For quarters and thirds, you inevitably wind up with fractions. Not the worst thing in the world, admittedly, but we could have it so much better. Twelve is evenly divisible by two, three, four, and six. Ten can say the same for only two and five. And really, how often do you divide things into fifths? (If we didn't happen to use base-ten then you'd probably do it even less.) Quarters and thirds on the other hand are incredibly useful, and in base-twelve they'd come out as a whole number—no fractions or decimals. Basically, practical math would be so much easier if we used base-twelve.
A sure sign that you're looking at a Sophisticated Math Diagram is that it makes you hungry for Skittles.

Even in societies that use the base-ten system you will see twelve used prominently, and I think that's a testament to its usefulness. There are twelve inches in a foot, two sets of twelve hours in a day, and just consider all the things you buy that are packaged by the dozen. It's just a terribly useful number of things. Some ancient societies, like the Egyptians, did indeed use a base-twelve system. And, in fact, the reason we have a twenty-four-hour day is because it was inherited from the ancient Egyptians.

Of course, base-twelve as a long-standing societal norm and the notion of suddenly switching to it from base-ten are two very different things. While math would be easier, math would have changed. That's simply not something we're mentally well-equipped to deal with. And aside from the psychological, there's also the practical: we don't have established methods for properly expressing a base-twelve system in speech or writing. In the next part we're going to delve deeper into base-twelve by imagining what it might look like in practice. It'll involve understanding just what we mean by "number," and perhaps we'll invent a couple numbers of our own to get things working.

Continue to Part 2 to see what it looks like.

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