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  • Welcome to our first official video on our new channel called Numberphile,

  • all about different numbers.

  • We've decided to make out first video on a very special date,

  • that's the 11th of November 2011.

  • That's 11/11/11.

  • Or if you're American, that's 11/11/11, right?

  • So we've come to Nottingham Forest Football Stadium, which Brady insisted on.

  • 11 football players in a team.

  • Personally, I more think of 11 Doctor Who's, but never mind.

  • And we've just come in through Entrance 11.

  • If we walk this way up here to row 11, and I'm going to sit

  • right here in seat number 11, so 11, 11, 11.

  • So guess what we're going to talk about today?

  • BRADY HARAN: What?

  • JAMES GRIME: 11.

  • Yes, so recently we've had a lot of dates with ones and zeroes in them.

  • They're called binary days.

  • They're like binary numbers.

  • And this is the last binary day until next century.

  • When Brady first asked me to talk about the number 11,

  • especially for this date, I was worried.

  • I thought, well, it's a prime number, but I don't know what else I could talk about.

  • And then I realized there's a way that we use the number 11 every day, all the time.

  • We're going to use a book.

  • Now, you can do this yourself.

  • If you've got a book nearby, grab it.

  • And here's my book, this is Johnny Ball's Second Thinks.

  • Never leave home without it.

  • On the back of the book, there's a bar code.

  • And next to the barcode, there is an ISBN.

  • That's an International Standard Book Number.

  • And that number is going to be 13 digits long, or it's going

  • to be 10 digits long.

  • Actually, I'm not interested in the 13-digit number.

  • I want the 10-digit number.

  • Does your book have a 10-digit number on the back?

  • Now, here's something you can do with that number.

  • Let's write down my number here on the back--

  • 0140318194.

  • That's the ISBN number for old Johnny Ball there.

  • Now, the first number here actually tells you which

  • country the book was published.

  • The next few numbers tell you the name of the publisher.

  • The few numbers after that is the book itself.

  • And the very last number is called a check digit.

  • Let me show you something you can do.

  • I'm going to take the first digit, multiply it by 10.

  • OK, so 0 times 10.

  • That's quite easy, that's a 0.

  • The second digit there I'm going to times by 9.

  • So 1 times 9.

  • Quite easy again, that's 9.

  • The third digit I multiply by 8.

  • That's going to be four times 8.

  • That's 32.

  • The next digit I times by 7, and that's another

  • easy one for me.

  • That's a 0.

  • And you can keep going.

  • And the very last digit you multiply by 1.

  • So that's going to be 4 times 1, that's the number 4.

  • Now, what you do is you add these together so you're going

  • to make a number.

  • It's going to be something like 100, 200, 300,

  • that sort of size.

  • If I add these numbers together-- and I've done this

  • already, I've done this in my head.

  • If you add these numbers together, you will get here

  • the number 121.

  • And this number is a multiple of 11.

  • And it always will be.

  • If you try this yourself, you will get a multiple of 11.

  • In this case, this was 11 squared, 11 times 11.

  • Whatever you get, it's going to be a multiple of 11.

  • And they do this on purpose so that they can detect if

  • there's been an error.

  • If you inputted the book code in wrongly, if you swapped two

  • digits over by mistake, it will be

  • able to detect a problem.

  • It's called an error detection code.

  • The very last digit is chosen so that this will work.

  • Now, the very last digit will be a number between 0 and 10.

  • So for the first 9 digits, that's not a problem.

  • 0, 1, 2, 3, 4, 5.

  • The very last digit, the number 10, well, we don't have

  • a single digit for a 10.

  • So instead, you may see the letter X, which is the Roman

  • numeral for 10.

  • That's used for 10 instead.

  • So this part, well, that could be anything that

  • they want it to be.

  • But this number is completely engineered to make this work,

  • to make a multiple of 11.

  • If you have one of the 13-digit book codes, they use

  • a slightly different operation.

  • It's actually based on the number 10 instead

  • of the number 11.

  • OK, so this is the view from 11, 11, 11.

  • The number 11 is used for these error correction codes.

  • But error correction code, that idea is used

  • all over the place.

  • It's used with computers.

  • It's used with mobile phones if you're

  • trying to send a message.

  • And, well, in transmission, you can

  • lose some of the message.

  • So you want to be able to reconstruct the message

  • without having to send it all over again.

  • And you can do this yourself.

  • Again, this is with a CD.

  • And if you burn a CD, if you hold it up to the light, you

  • can even see where the tracks are.

  • And if you use a black pen here, a black marker pen, I

  • could put a dot on this CD, and this would represent

  • something like dirt or a scratch.

  • And this will still play.

  • It can compensate for this missing information.

  • Well, in a book code, we might know there is a missing five.

  • There's something we can do.

  • In a CD, it uses a whole equation with all sorts of

  • numbers, and you can use that equation to work out which

  • number is missing and what it is.

  • So we've done this with my CD in my computer right now.

  • I'm going to play you a song, a song all about numbers.

  • I thought it would be an appropriate choice.

  • You can hear it does still play.

  • If I pull it out, slightly more dramatic than a black

  • marker pen.

  • We actually drilled a hole through the CD.

  • So the data is actually literally missing.

  • Not just a black mark, we actually took out the data.

  • Yet the CD player can reconstruct it and still play

  • the song because it will use this error detection

  • technology, this mathematics that reconstructs the missing

  • information.

  • In fact, this hole is about 2 millimeters.

  • You can go up to about 2.5.

  • If I go even further, I've got one here with 3 millimeters, a

  • 3-millimeter hole.

  • This hole is too big.

  • Let's try it out.

  • I'm going to try and play this as well.

  • You'll notice the difference.

  • [MUSIC SKIPPING]

  • It's trying.

  • It's trying its best.

  • It doesn't play.

  • Too much missing information.

  • So 11 was just our starting point into a world of

  • mathematics and error correction code, something

  • that is used everywhere that makes your CD work, that makes

  • your mobile phone work, and, of course, makes that number

  • on the back of a book work.

  • And Brady insists that I remind you that, yes, it is

  • the number of players in a football team.

Welcome to our first official video on our new channel called Numberphile,

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