18 June 2013

Miscellaneous thoughts related to base-twelve

If you haven't already, read my previous posts, "The case for base-twelve" (Part 1 and Part 2)

FINALLY we can get this whole
counting thing sorted out...

So no, I don't think switching to base-twelve is a feasible idea. I do lament the fact that it's not what we're using right now, though. It strikes me as a more elegant system, and it's a shame that happenstance has pretty much dictated that it'll never be the system we use. Unless, maybe, all of civilization collapses and the society that rises from the rubble happens to use it... But wishful thinking will get me nowhere.

One way I console myself over the fact that a modern, real-world base-twelve system will never be is to imagine a fictional society that uses it. Helpfully, I already happen to have a fictional society on hand. I can't recall if I've alluded to it before, but basically my friend and I have an imaginary continent in the North Pacific, on which I have an imaginary country called Morsenia. The whole thing sounds silly—and it is—but it's basically a collaborative thought experiment that gives us a mental playground for all sorts of hypotheticals. It's constantly-evolving geopolitical fan-fiction, more-or-less. Most of the concepts explored are political and historical, but in developing our countries' stories there's plenty of room for mulling on all sorts of subjects, like language, religion, and biogeography. All-in-all it's a fun excuse to learn a bunch of new things in a variety of subjects as you go about the business of building a believable country and culture.

In the past Morsenia was much more of a Mary Sue; I'd basically take all the things I think are good or cool ideas, say my country did them, and things would inevitably work out pretty well (so they were a wealthy, high-tech nation with a huge standing army filled with tilt-rotor aircraft and digital camo; but also they were somehow isolationist and relatively peaceful). I've made a lot of progress griming it up and throwing wrenches into the works to make it a little more believable (now they're poor and use decades-old weapons and equipment), but I still definitely use it as an intellectual testing ground for ideas I think might work well in real life. Base-twelve is one of those.

Visit Morsenia: Scenic repository of ideas
that I'm bitter over society not using
At least, I want it to be. There are a few things that have held me back from deciding "the Morsenians use(d) a base-twelve system." The first is having to decide whether they still use it or if it's been supplanted by the ubiquitous base-ten by now. If it has been replaced, which seems likely, I'd have to decide when they switched and what the transition was like. And frankly, I have no idea what that would entail. I don't know of any society having to make a switch like that in modern times, so whatever I came up with would probably be pure conjecture, whereas I prefer things to be a little more reality-based. I'm not close to making a decision about his hurdle, but I'm hopeful that I'll either come across a similar real-world scenario or be able invent one that's sufficiently plausible.

Another thing that's held me back is consideration for whether base-twelve would be believable enough as the system that had established itself in the first place. I've known that other societies have used it in the past, but I don't want to have to rely on merely that fact to make the case for it existing in Morsenia. I want to be able to make a compelling argument for it, but it's only recently that I've begun to feel like I can. While I already had a decent idea why twelve could be viewed as a symbolic number (even outside its divisibility) because of course there are twelve Moons in a solar year (a fact that probably every human society has been aware of*), there were other sticking points.

It seems silly, but a big part of my concern on the practical side of things was not knowing how folks would count on their fingers in a base-twelve society. In base-ten societies we obviously use our ten fingers, but I was at a loss for what folks counting in base-twelve would do. Maybe they also counted their palms? Or their legs? I even considered (since a large portion of Morsenian society came quite recently from nomadic horsemen) that they might use their horse's ears for the extra two. I also pondered ways to do it that didn't involve the ten fingers at allmaybe they had a traditional garment or accessory that had twelve notches or bumps or something, which they could count on. But I just felt more and more like I was grasping at straws.

It apparently just didn't occur to me that "how they counted on their fingers in base-twelve societies" was the sort of thing you could readily find online. I assumed incorrectly, however, since I managed to come across that very information while I wasn't even looking for it. I had Stumbled on an article which was explaining why we have a twenty-four-hour day, and in doing so it mentioned that it came down from the Egyptians, who had a base-twelve system. And in either in the article itself or perhaps in the comments, I saw it mentioned that the Egyptians would finger count by using their thumb to point to the three bones of each finger. Three points per finger over four fingers; that gives you twelve. I was overjoyed to read that, and it makes such perfect sense that I was a little disappointed in myself for not figuring it out. It's a lovely method and one that seems especially useful for visualizing fractions. Each finger is a quarter, pair them together for halves, and if you go side-to-side you get thirds.

Spock offers to help you visualize base-twelve fractions.
That article I was reading also explained how the sixty seconds-to-a-minute and minutes-to-an-hour came to us from the Babylonians via the Greeks. The Babylonians actually used a base-sixty system; I had thought the base-twenty system of the Mayans was unwieldy, so I can't even imagine trying to use base-sixty. The author expressed some confusion as to how a base-sixty system could even come about, and I must admit that I shared in their perplexity. But then someone in comments revealed just how straightforward and intuitive the answer actually is. What they said was basically this: Imagine someone counting to twelve on their fingers like the Egyptians did. How would they keep track of each set of twelve? With the five digits on their other hand.

Numbers in pen not strictly necessary. (Image Source)
BAM. Base-sixty. (Also, it turns out that not only is this sorta thing on the internet, but if you know what you're looking for you can easily find pictures from fellow dorks who've taken pictures of their hands in the process. In related news, I am bad at internet.) The sheer sensibility of it kind of blew me away, in a way that I haven't been in a long time regarding matters such as these, so that was great. I still think base-sixty is silly, though.

Base-twelve is just fine for my Morsenians. And now that I have a nifty method of finger counting, I'm a little more comfortable with the notion of them having used it. (Before I Googled for pictures of it, I had actually assumed the counting was done with the palm inward and the thumb counting on the side of the fingertips and the first two joints, rather than palm up and counting on the bones as you can see in the picture above. I'm actually kind of partial to my version, so that's likely what the Morsenians will use if they do wind up with the base-twelve system.) Thanks to that transition business that I mentioned the matter isn't quite settled, but it's a little closer.

Thanks for sticking with me through all this rambling about base-twelve. I think I've more-or-less exhausted my thoughts on the subject, but this post has made me realize I have a lot I could say about Morsenia. No lie: I've got maps, flags, wildlife, paintings of soldiers, a religious philosophy, and the beginnings of a spoken language and writing system; aside from being great sex deterrents they could also make for some interesting blog posts, I think, so be on the lookout for that in the future. Cheers.

* You may have noticed that in Part 1 I didn't list the twelve months of the year along with twelve hours × 2 per day and twelve inches in a foot. That's of course because humans didn't decide how many lunar months there are; that's just how it is. It so happens that it takes the Moon a little under thirty days to orbit the Earth and it takes the Earth a little over twelve × thirty days to orbit the Sun. There's no reason for them to be so near in value, but they are—somewhat conveniently I suppose.

Similarly, it's only a coincidence that we can have total solar eclipses. It isn't an inevitability that the Sun and Moon are each the right size and distance so that one can just about cover the other completely; it's simply happenstance. And actually the Moon is drifting away from us gradually, so eventually it'll be impossible.

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