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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.

# 11.11.11 - 數字愛好者

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VoiceTube 發佈於 2012 年 12 月 13 日    Doris 翻譯    Evangeline 審核

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