I was born in 1938, which is a long time ago
and it was about seven or eight, just towards the end of the war, when I got into maths.
Totally accidentally, 'cause I met a fella in a pub. In those days
they had children's rooms because people worked round the clock and and took - all went out, with the kids, to the pub to relax.
Chap came up to me, I lived in Bristol. So he said, '"ere. How's your maths then?"
Mate of me dad's, I said, all right?
He said, how's your multiplication? I said, it's all right. He said, shall I show you how the Russians do multiplication?
I said if you like? He said come 'ere, come 'ere. He says, say you want to multiply 9 times 13
He said, you write 'em sideways like that; and what they do, they halves and doubles everything.
So what we're gonna do is half nine. So give me a half a nine:
I said that's four and a half. He said four and a half. Oh, hang on, he said. The Russians have purges, things
they don't like and one thing they don't like, is fractions. They hates em' so we'll scrub that out
call it 4. Half a 9 is 4. Half of 4 is 2, half of 2 is 1. Now, that's one side.
Now what you do then, he said, is you double the other side. So two 13s, I'll do it,
you tell me if it's right. 26, 2 of those is 52 and 2 of those 104. And
now we've got four each side. Now. there's another purge the Russians had:
one thing they really couldn't stand, worse than fractions, they couldn't stand
even numbers on the left-hand side, they couldn't abide 'em. Well let's have a look.
Well, that's odd but that's even so out goes the whole row - gone. That's even - out goes the whole row. That's odd.
So what you got left you adds up. 13 'n' 4 is 17, plus a hundred and would you believe 9 times
13 equals
117. And that works with any numbers,
every single time. (Brady: I want to see it again Johnny, I want to see another example)
- so - (Brady: can we do another one?)
I'll give you - we'll do it the other way around, it doesn't matter what numbers you use. We'll do 13 times 9.
Half of 13, 6 and a half
Forget that, half of 6? 3. Half of 3? 1 and a half, forget the half. Two 9s? 18 - two 18s?
36 - two 36s?
72, and we got four each side.
But there's an even one here on the left-hand side. So that line goes out, and now when you add them up:
117, and 13 times 9 is also under 17. - (Brady: Triple figure? Quadruple? - Any figures you like
I tried to trace this back, and I found it's very difficult because people in rural areas - before schools - in
Victorian times, and long before that used to use this. In Elizabethan times we know they used it, this system of doubling and halving.
But I traced it back even further. I traced it back to about four and a half thousand years ago,
in Egypt. And they did it a slightly different way.
So let's say you want to multiply 9 times 13 again,
all right?
What they would do is write the 13 down, and here they'd write a 1 - double it, 2.
double it, 4, double it, 8,
double it, 16, stop. We don't need 16, we're only multiplying by 9. So we've got enough.
Two 13s? 26. Two of those, 52, two of those 104, okay.
They were told there's only one way to make 9, from these numbers on the left hand side, and sure enough,
it's 8 and 1 makes 9 so out goes that one, and out goes that one, and
13 and 4 is 17.
A hundred, and you got the same answer, 9 times 13 equals 117. That was the Egyptian method. Now,
can we link this very old mathematics to the present day?
Yes, we can, Let's do this one. Let's score the ones we use with the 1 and the ones we didn't use with a 0,
reading up. And what you would get is 1001. And, 1001 is the binary
number for 9. Why is it the binary number?
'Cause it's made up of an 8, and a 1. Binary numbers worked like this; 1, 2,
4, 8. 1, is there. 2?
It's one of those, and none of those. 3 is one of each. 4 is one of those and none of those.
5 is one of those, and one of those - a 4 and a 1, and so on.
And here, 8 and 1 is 9, and that's the binary number for 9. The binary number for 10 would be 1 0 1 0, okay?
And that would give you 8 and 2 is 10. And sure enough, 10 times 13 is 26, and 104, is 130.
So all this ancient maths, is linked to the very maths that makes our computers work,
our televisions work, our satellites, and everything else. Digital information.
It's what makes the world go round, today.
[Brady:] This episode was supported by Brilliant.
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But to get your teeth into more binary have a look at Brilliant's beautifully prepared courses.
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Brilliant.org/numberphile, there's even a link down in the video description if you don't want to type it in
It's quite amazing, you take - you want the binary number for any number. Give me a number to find the binary number
Twenty....? (Brady: 9) - 29, right 29. Are you ready, the binary number. Half of that is
14 and a half
forget the half.
Half of 14 is 7, half of 7 is 3 and a half - forget the half,
half of 3 is 1 and a half, forget the half, right? And the binary number the 29 is 1
1 1
Not that one, because it's even. 1.
1 1 1 0 1 - so if you want to find the binary number of *any* number you write it down,
reduce it by halves, forgetting the fractions,
score the numbers 1 or 0 going up and that will be the binary number, for any number you choose.
It's so simple