(Another spiffy ref courtesy of Making Light)
Counting in Babylon
Be sure to read all the way down to the number systems stuff. While you're at it, read the rest of the lecture series info pages (here). If you're afraid of math or science, it'll do you good. Builds character.
Back to my point. Apparently, Babylonians used base sixty instead of base ten. This is hard to describe, because unless you work with computers on daily basis, you have no need to think about different 'bases'. Western civ is built on base ten, baby, but computers run on binary* (base two). We've so completely internalized base 10 that it's hard to even think about thinking about another base system.
Base 10 means you count on your fingers from one to 10.
Now you've used up all your fingers, what do you do? Assuming you're wearing shoes, you put a rubber band on your pinky. Or hold your left hand behind your back. Or turn your hands towards your face instead of away. Anything to indicate that although you are using the exact same fingers that you just counted 1 through 10 on, you are now counting 11 to 20.
Now, suppose you're a little kid during summer. You won't run out of digits to count on until you get all the way to twenty, because,
1. you took your shoes off the second summer vacation started;
2. you're flexible enough to touch your toes to begin with.
So, now you can count all the way up to 20 before you need to 'mark' that you've overlapped your digits and when you get to your thumb this time it means 5+20, not just 5.
That's base 20.
How do we write this down? Well if I write it down, (20), I'm writing in base ten, not 20, and I'm screwed up already. Can I say the alphabet instead, on my fingers and toes?
Sure. Why not. A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T -- there, that's my 20 symbols, A-J for my fingers and K-T for my toes.
So, what happens when I need to count forty bottlecaps by the side of the road? (Hey, I'm a kid on summer vacation.)
I can get up to 20, or T, with my fingers and toes, and then I'm back to that starting left-side pinky. Right-side, maybe, depending on which hand I write with. What do I do?
Maybe I draw a line underneath the T bottlecap, and then count up another T (or twenty) bottlecaps and mark underneath it. I then skip past my row and say " there are 2 lines, so that's 2 sets of T (twenty), which means a grand whopping total of forty bottlecaps. I'm rich!"
But then a car drives past, splashes muddy water all over me and the bottle caps, erases all my careful marks, and even gets specks on my glasses.
Well, maybe, I scoop up all the bottlecaps I can grab in the mud and run home, because it's lunchtime already, and I got Important Kid Stuff to do.
Maybe, just maybe, after lunch, I grab a crayon and the back of mom's phone bill and haul out the mess of bottlecaps and start counting them all over again from the beginning.
This time, though, I count J (ten) bottlecaps using my fingers, and write with the crayon:
J
On the back of mom's phone bill. That's my mark for ten. J bottlecaps.
I count more bottlecaps, using my toes, and get all the way up to T bottlecaps (twenty). So I cross out the J and write:
T
Well, once again, I'm at point where I need to re-use fingers and toes in order to count past T. What to do, what to do?
I could do this. Make two columns on the paper, one for individual fingers and toes, and one for the second time around on those same fingers and toes.
How would I write T+A (twenty+one) bottlecaps, then?
AA
Reading from left to right, that's one full set of fingers and toes (the 'A' on the left) and one pinky finger.
The leftmost column is the number of twenties I've counted (just one), and the rightmost column is the number of individual fingers-n-toes I've counted. Which in this case, is also one.
I count another bottlecap:
AB
One twenty plus two fingers.
I count three more bottlecaps. I've just used up one hand and embarked on the other, I'm at:
AE
I count more bottlecaps, using up all my fingers:
AJ
That's one twenty, plus ten fingers. If I was counting out loud I would have said "twenty-one, twenty-two, twenty-three, twenty-four, twenty-five, twenty-six, twenty-seven, twenty-eight, twenty-nine, thirty!" by now.
So, I embark on the toes and use them up, going from
AK to AL to AM to AN to AO to AP to AQ to AR to AS to
two whole sets of twenty
And how to write that? Not AT, but B0, where 0 is just a placeholder for "nuthin in the onesies column yet". Because the B in that left-column location tells us "two 'sets' of twenty".
So,
BA
would be what, then? Two sets of twenty plus one, or A. Forty-one. BA. All just different ways of saying the same thing. Why I could add another left column if I had gobs and gobs more bottlecaps and I had to count more than twenty sets of twenty.
SS = nineteen sets of twenty plus nineteen fingers-n-toes. I count one more bottlecap, and....
ping
A00
One 'batch' of "twenty sets of twenty" (ain't that a mouthful), plus zero 'sets' of twenty, plus zero 'onesies'. Phew. Time for some cookies and milk in another minute.
Now, we've just talked about base 20 counting (hey, look at that 20, that's a number in base ten isn't it? The 0 is a placeholder, right? And the 2 in that left column means "two sets of ten", doesn't it? Doesn't it? Hot dog!).
But the Babylonians apparently used base 60.
In base sixty BA wouldn't mean "two sets of twenty plus one", and 21 wouldn't mean "two sets of 10 plus one", but two sets of sixty plus one. How's that for a lot? How's that for different bases? Why A00 would be a batch of sixty sixties, or 3600 bottlecaps, which would blanket the floor of my bedroom up to my ankles and have plenty left over to taunt my friends with.
Base 60. Wow. I'd be richest!
* Why are computers binary, you ask? Ah, because computers are very primitive devices, compared to human beings. They can 'conceptualize' only "on" or "off". If on=1, and off=0, computers can only think in ones and zeroes. Think of it as if they only have thumbs and no fingers or toes. So, they wrap around back to the first hand when counting, very very quickly, poor things. No flexibility at all.