Sumerian base sixty, and how it haunts us.

I like that everyone in the comments yesterday gets the significance of base sixty. Or at least, has the same reaction to it that I do, which is, "WHY IN...??!!??" The reason I know what little I know about number theory and history is due entirely to the Sumerians. I first heard about the base sixty thing in College Part One, and have been digging around through history and tech books ever since, trying to figure out why exactly they did it. No one really knows. There are half a dozen theories, but I've got my own. (Big shock.)

But first, a word or ten about the Sumerians themselves. 'Cause, see, they were really weird.

The biggest deal, when it comes to the Sumerians, is that nobody knows who they were. That is to say, they just popped up in the Middle East one day seven-ish thousand years ago. Culturally, linguistically, they're different than the people who lived around them. It's thought they came from central Asia, somewhere near modern Kazakhstan, but nobody really knows for sure. This is useful to know, because it plays a part in some of these number theories. Plus I like historic mysteries, so I almost HAVE to mention it.

Sumerians, and most other middle-eastern civs of the day, ran on clay. They were in a double river valley (Tigris and Euphrates, cradle of civilization, blah blah, don't you remember this from sixth grade?) and so they had all the clay they could use, and they did use it. For everything. Building, storage, cooking, decorating, and most importantly for us, record keeping. They didn't write on paper. They wrote on lumps of clay. If those lumps of clay were then fired (either on purpose, or by accident in the equivalent of house fires), they literally lasted forever unless someone ground them to dust.

Politically, the Sumerians used a theocratic city-state system. Which means each city-state was run by a PRIEST, and the cities were centered around a temple, not a palace. Each city was dedicated to a different god, and it's thought the pantheon's doings in later years reflect the political jockeying of the city-states in the very early years. Because this civilization lasted three thousand years, in different forms.

And depending on how you look at it, it survives today, right here on your computer, in the lower right corner if you're running Windows.

So, why did the Sumerians use base sixty? Well. There are theories. Lots of theories. In short:

-It has been suggested (since the fourth century, no less) that base sixty was chosen because it has a huge number of divisors (numbers it can be divided by), and therefore was 'easiest to use'. I've had modern mathematicians offer this as a theory, also, when I've discussed it with them. The problem with this theory is, civilizations 'choose' which base number system to use when they're counting goats on their fingers; they have no concept of what a divisor IS at the time the base system is established.

-The system is based on the days of the year. 365.24something days, rounded down to 360, and from there sixty becomes a 'natural' unit. This has the same problem as the first theory: when they were establishing the base system for their civilization they couldn't have known how many days there were in the year. They needed the advanced math to figure out the days in the year, BEFORE they could choose base sixty. There are related theories of base sixty established by 'natural' reckoning, like the hours of the day, the visible diameter of the sun, or number of planets (that they could observe with the naked eye). You still need advanced math to figure this stuff out BEFORE you decide to use base sixty.

-It is based on their system of weights and measures. Which totally screws up cause and effect, like the earlier ideas.

-It arose when the Sumerians moved into the area, and combined with another civilization that was already in the area, and somehow base ten plus base six (and why in hell would they be using base six? It just triggers more questions) equals base sixty. Sure, you can get base sixty easily from that doing the MATH, but culturally it makes no real sense. Usually one civilization snuffs out the other - at least culturally, if not literally - and moves on from there.

-It's really base twelve (duodecimal), which isn't totally unheard of in other parts of the world, like Western Europe (a dozen donuts, anyone?)

-Mystical reasons. The mathematicians were also priests and used numerology all the time. Different gods were represented by different numbers, and the upper god of Heaven (An/Anu) was sixty. Again there's a big question of cause and effect going on.

What do I think? As usual, I think it's a combination of all these reasons. Or most of them.

Going from what I know of the Sumerian numbering system (and you're gonna have to take my word for it, or read the article, 'cause I don't wanna be here all day), I think they were running equally on base ten and base twelve, and the sixty came up just as an easy factor for both those systems. (5x12=60, 6x10=60, that's the lowest number where the two systems 'meet' neatly.) It would make sense then, that their most 'good' god, the highest, most celestial, would be assigned the number they would see as wholeness, the one that is the neatest factor of both numerical systems they were using.

Base ten was probably the original system, the holdover from goat-counting on their fingers, and was, for the most part, used for practical purposes.

Base twelve was probably created by the priest/ruler class. I bet it was used, originally, for 'holy' purposes, for all those reasons listed above. 360 days in the year, six visible planets, etc. It looked to the priests like the natural world ran on sixes and twelves, so that's what they used. Note that the stuff we still use base twelve for is the stuff they would have considered holy - time, planets, astronomy, geometry.

As for everything else, like their accounting (boy howdy, do we have piles of their accounting tablets)? It's a jumble of the two systems. There are symbols in their writing system for 1, 10, 60, 600 (10x6), 3,600 (60x60 or 36x10). And so on. All other numbers were written as multiples of these symbols. What's that look like to YOU? To me that looks like base six/twelve and base ten jumbled together.

Now. This probably sounds insane, like a really dumbass way to run a civilization. But you know what? We're still dealing with vestiges of this dumbass system every day. And not just when you buy a dozen donuts instead of ten. The Sumerian system evolved over three thousand years, and was picked up by other civilizations (notably the Phonecians), and from there the Greeks, then the Romans, and here we are today, seven thousand-odd years later, still looking at dozens (see that? A special word for groupings of twelve, in an allegedly base ten civilization) of holdovers from those crazyass Sumerian priests/math geeks.

Look at your clock. Twenty-four hours in a day? Sorta. It's even more base twelve than that. Twelve hours of sunlight, and twelve hours of darkness. That's how it was originally figured. The clock - such as it was, usually a sundial - was 'reset' every sunrise and sunset. In older texts, even Roman ones, there are references to 'summer hours' and 'winter hours'. Because the days, regardless of length, were divided into twelve equal parts, and since the days are longer in summer, so are the hours. It doesn't stop there. Sixty minutes in an hour, sixty seconds in a minute. When we hit sixty, we start over at one. No one ever stops to think "why don't we go to a hundred before we start over?" or at least not very often.

Not only are there 360 degrees in a circle, it has carried over in the modern world to latitude and longitude, which is measured in minutes and seconds, all on base sixty just like time minutes and seconds on a clock. Yes. Modern GPS systems ultimately run on base twelve, like the ancient Sumerians.

Twelve months in a year. An arbitrary division, but twelve was seen as the 'neat' number to divide it into. Thirty days in a month; half of sixty. (We've since tinkered with the calendar, adding days and moving them around here and there, but the basic organization of it remains the same.)

And for Americans, the Imperial measurement system is a jumble of base ten and twelve. Twelve inches in a foot. 36 inches in a yard (3x12).

I imagine for the ancient Sumerians it was just as simple to switch back and forth, and they did it just as easily as modern humans, with just as little thought to it.

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If we're still having fun with this, and everyone's interested, tomorrow I can do zero, and how it's not really the big deal it's made out to be - sort of.

For anyone finding this SUPER fascinating, I suggest "The Universal History of Numbers", by Georges Ifrah. (Oh, look! He has a new book out!) Unfortunately it is a translation, and therefore a bit dry, but it's still a really amazing book.