60 - Numberphile


Uploaded by numberphile on 18.05.2012

Transcript:

THOMAS WOOLLEY: So the number we're talking about now is 60.
Now, it's quite a big number, so you may not
meet it all the time.
But you do use it a lot when telling the time, which, of
course, there are 60 seconds in a minute, 60
minutes in an hour.
But why 60?
Why this random number 60?
Well, it all goes back to the Babylonians.
Thank you, Babylonians.
Because what they wanted back then was a very nice number
that divides quite easily.
So if you think about the number 60,
what divides it cleanly?
1, of course, 2, 3, 4, 5, and 6.
And in fact, it's the smallest number that's
divisible by all of these.
But why is this important?
Because you can take half of it.
You can take a quarter of it.
You can take a fifth of it.
You can take a third of it.
You can divide 60 up in a lot of ways.
So if you're cooking in this base, you can cook with lots
of fractions of that.
So if you don't want to cook a whole meal, you can cook half
a meal, or a third of a meal, or things like that.
Again, if you're telling time, you can have a
quarter of an hour.
You can have 20 minutes.
You can have half an hour.
You can have three-quarters of an hour.
It all divides 60 very nicely.
And when you don't have computers, you need a number
that you can divide nicely so you get nice, round numbers at
the end of it, because they're easier to work with.
So I mean, 60, if 60's so nice, why do we use 10?
BRADY HARAN: You just asked my next question.
Go on, tell me why.
THOMAS WOOLLEY: Well, the idea is that we use 10 because we
have 10 fingers.
so you can just count along.
As you're a child, you'd count 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Well, what's thought is that the Babylonians actually
counted to 60 on two hands.
They would use each knuckle on one hand to count to 12, and
then count the number of 12s on the other.
So you'd go 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
One set of 12.
And then you do it again.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
Two sets of 12.
And again and again, until you get five sets of
12, which is 60.
Highly divisible, and you can use it on your hands.
So when the Babylonians were working with this number 60,
they were also very good astronomers.
And what they found is that the year is
pretty much 360 days.
So that's the length of time it takes for the Earth to go a
full circle.
And that's why the circle is divided up into 360 degrees.
And further, each degree is then
divided up into 60 minutes.
You can have an arc minute, which is a 60th of a degree.
And that, further, is then 60 seconds, 60 arc seconds of
that 60 minutes.
BRADY HARAN: I wonder if we came close to living in a
world where 60 became our base?
THOMAS WOOLLEY: Like I say, it's very, very difficult.
I mean, you could write, well, there's 57.
We use it, two numbers.
For a Babylonian to write 57, they would have to write 1, 2,
3, 4, 5, 6.
1, 2, 3, 4, 5, 6, 7.
It's a lot easier to write like that than that.
So these are how they drew their numbers, because they
had a little stylus that they would into clay.
And the stylus had a triangular end.
So the stylus would look something like that.
And so when they were doing ones, they'd use the tip, and
go 1, 2, 3, 4, 5, 6, 7, all the way up to 10.
And the 10, they'd turn the stylus on the side and create
one of those shapes.
So each one of those is 10.
Each one of these is a 1.
And so there we have 57.
BRADY HARAN: That's their version of a Sharpie.
Exactly, yeah.
It's really good.
1, 2, 3, 4, 5, 6.
Ba-ba-ba-ba ba ba.
Ba-ba-ba-ba ba ba.