As I mentioned in the thread on history, and confused Elizabeth about (sorry Elizabeth ), when you see a number, mentioned in a story or even in an article or explanation, there is a 50% chance that it isn't the number you think it is. * sighs * The reason for this is that the dominant number system in Ccwiicc is not base ten, like ours, but base twelve.

Unlike our world, all the people on the world do not use the same numbering system. The different groups, tribes, and nations all have a different way of doing it. The most efficient and therefore most used and widespread of these systems is the Ssexanê system – which just happens to be in base twelve. Why not just skip the confusion and just translate all the numbers into the more familiar base as you come across them? The calendar is base twelve, common colloquialisms refer to base twelve, all the dates and historical periods and so forth are in base twelve, the most used directions (like North, South, and so on) are in base twelve, the musical scale is in base twelve, the measuring system is in base twelve – in short, it would be almost impossible to remove from the picture. So I don't even try.

Not only are most things in base twelve, also, but the ones that aren't are in some other even worse base, like base four or base eight – and the differences between the mathematical systems of the different peoples is an unignorable part of their culture and dealings with each other.

So I'm stuck with it.

Now, I try to at least translate the numbers into the familiar base for y'all, when I remember and have the time – but that might just be more confusing, 'cause then you never know whether I did do it or I didn't. * winces * I'll do my best to keep it as little confusing as I can, but I can't promise much. If in doubt, ask questions. And remember – half the time you see a number, it will not be what you think it is.


Just for the mathematically minded (or for those who suffer from sleep deprivation), I will give a quick explanation of what a base is, and a link to how to change a number between bases.

When you count, you do it like this:

1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 9 –

Just a sec. What comes next? Two numbers.

10.

And then you do it again.

11 – 12 – 13 – 14 – 15 – 16 – 17 – 18 – 19....

That is base ten. When you get to ten, you don't just add on another weird doodle to represent it – you stack up the old ones. That way you don't have to make up an infinite number of weird doodles and then memorize them all.

So what if you didn't stop making up doodles at ten?...

1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 9 – <another weird doodle> – <and another weird doodle> –

And then 10.

That makes it base twelve, instead of base ten.

And of course, any other base works just the same...base eight, base four, base forty-four. It just depends on how many symbols it takes before you start stacking them.

Since my keyboard doesn't support alternate weird doodles from the ones that normal people use, when I am using base twelve I refer to ten as X, and to eleven as Y. So counting would go like this:

1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 9 – X – Y – 10 – 11 – 12 – 13 – 14 – 15 – 16 – 17 – 18 – 19 – 1X – 1Y – 20 – 21 – 22 – 23 – 24 – 25 – 26 – 27 – 28 – 29 – 2X – 2Y – 30 – 31– 32 – 33 – 34 – 35 – 36 – 37 – 38 – 39 – 3X – 3Y – 40 – 41 – 42 – 43 –

* rubs eyes and jerks head up from bowing over the keyboard – literally * That always makes me sleepy...typing numbers. * gives head a vigorous shake * Anyway – * smile * – that's how it goes.


And that is why a number can be something other than what you think it is. If you count in base ten on the number line I made there, you will notice how that goes – 29 in base twelve counts up to 33 in base ten, and so on. This is how you can switch between bases – linkie.

Two tangential comments:

Counting in bases larger than ten (or at least in base 16) is a fairly common situation in computer science (which was my field in college); normally letters are borrowed from the beginning of the alphabet until you don't need anymore, so that in hexadecimal (base 16) we count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, etc.

A language that I've done some development work on counts in base 7.

(Do you have counting-words to represent your base-12 culture's numerals?)

I didn't actually know that. Quite interesting. Why do they need higher bases for computer science?

:cool:

Yes, and a lot of other rules and set ups for their system. I should do a post on that sometime... But anyway, the Ssex numerals are Viis, Sunn, Hhea, Shye, Xehh, Jeje, Nmug, Rêet, Diiv, Suunj, Nnun, and Nmemu.

Computers "speak" base 2, but numbers in base 2 get really long really quickly and the arithmetic is highly unwieldy for human beings, so they get "abbreviated" to the equivalent octal (base 8) or hexadecimal when we need to deal with data at that level. Hexadecimal is the only one that gets used often in "the real world," but other obscure bases come up fairly often in the CS-related math classes where this is taught, to make sure that we understand the concepts and principles involved rather than just having memorized a trick for converting from base 16 to 10 and vice versa or something like that.