all about different numbers.

新推出的頻道是有關各種不同的數字

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

我們決定第一集要拍一個非常特別的日期

that's the 11th of November 2011.

也就是 2011 年 11 月 11日

That's 11/11/11.

在英國是 11/11/11 ( 註：日 / 月/ 年 )

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

如果你是美國人的話，則是 11/11/11 ( 註：月 / 日 / 年 )

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

我們來到英國諾汀漢森林隊的主場 ─ 城市足球場，Brady 堅持要來這個地方

11 football players in a team.

一個足球隊伍有 11 個 足球員

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

我個人是想到英國影集《異世奇人》11 位博士，不過這也無所謂

And we've just come in through Entrance 11.

我們剛從第 11 號入口進來會場

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

我們從這裡往上走到第 11 排，我就坐在

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

11 號位置，所以也是第 11 號入口的第 11 排 11 號座位

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

猜猜看我們今天的主題要談什麼呢？

BRADY HARAN: What?

Brady Haran：是什麼主題？

JAMES GRIME: 11.

James Grime：數字 11

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

我們近來許多日期含有數字 1 和 0

They're called binary days.

稱為二進制日

They're like binary numbers.

它們就好像二進位

And this is the last binary day until next century.

直到下個世紀前，這是最後的二進制日

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

當初 Brady 問我要先談談數字 11 的時候

especially for this date, I was worried.

尤其是 11 月 11 日，我當時蠻擔心的

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

我那時只想到 11 是質數，但我還真的不知道還有哪些內容可以談

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

但我後來發現我們每天無時無刻都會使用到 11 這個數字

We're going to use a book.

我們現在要用一本書來講解

Now, you can do this yourself.

你也可以自己做做看

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

如果你身邊正好有一本書，隨手拿著它

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

我手邊這本書，是強尼‧博爾撰寫的《思考的第二面向》

Never leave home without it.

出門時必帶的書籍

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

書的背後有條碼

And next to the barcode, there is an ISBN.

在條碼的旁邊有索書號

That's an International Standard Book Number.

這是國家標準書號

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

每個書號最多有 13 位數字，最少也有

to be 10 digits long.

10 位數字

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

事實上，我對於 13 位數字的書號沒興趣

I want the 10-digit number.

我要的是 10 位數字

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

你手上的書是 10 位數字的書號嗎？

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

你現在可以對那串數字做一件事

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

我先來寫下我這本書背後的索書號

0140318194.

0140318194

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

這是強尼‧博爾的書的索書號

Now, the first number here actually tells you which

索書號的第一個數字告訴你

country the book was published.

這本書是在哪個國家出版的

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

接下來的幾個數字告訴你出版商

The few numbers after that is the book itself.

再接下來的幾個數字代表書籍本身

And the very last number is called a check digit.

最後一位數字被稱為檢查數元

Let me show you something you can do.

讓我先來示範怎麼做

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

我現在將第一個數字乘以 10

OK, so 0 times 10.

0 乘以 10

That's quite easy, that's a 0.

答案是 0，這很簡單

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

第二位數字乘以 9

So 1 times 9.

1 乘以 9

Quite easy again, that's 9.

答案是 9，這也很簡單

The third digit I multiply by 8.

第三個數字乘以 8

That's going to be four times 8.

4 乘以 8

That's 32.

答案是 32

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

下一個數字乘以 7，這對我來說

easy one for me.

也是非常簡單的乘法

That's a 0.

答案是 0

And you can keep going.

你可以照著這樣的規則繼續計算

And the very last digit you multiply by 1.

最後一個數字乘以 1

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

4 乘以 1，答案是 4

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

現在你把加乘後的所有數字加總

to make a number.

得到一個數字

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

數字有可能是 100，200，或是 300 等等

that sort of size.

大約是這個範圍

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

我加總這些數字，我也已經算好了

already, I've done this in my head.

我剛才用心算方式計算

If you add these numbers together, you will get here

如果你加總這些數字，你會得到

the number 121.

121 這個答案

And this number is a multiple of 11.

121 便是 11 乘以 11

And it always will be.

不管是哪個數字排列，答案都是相同

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

如果你用自己的書去試算，你也會得到 11 的加乘

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

以這本書為例，這是 11 的平方，也就是 11 乘以 11

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

不論你的答案是哪個數字，它都會是 11 的多次方

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

這是人為設計的數字排列方式，以便於偵測

there's been an error.

數字排列有否錯誤

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

如果你輸入條碼錯誤，如果你不小心將 2 個數字

digits over by mistake, it will be

互相調換，這系統

able to detect a problem.

可以及時偵測到這問題

It's called an error detection code.

這方法稱為錯誤偵測條碼

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

通常最後一個數字決定這偵測方法的成功

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

最後一個數字可以是 0 到 10

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

書號上呈現前面 9 位數字都不會是個問題

0, 1, 2, 3, 4, 5.

0，1，2，3，4，5

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

但對於最後一個數字 10

a single digit for a 10.

我們沒有一個數字就能代表 10

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

所以你會看到英文字母 X，代表的是

numeral for 10.

羅馬數字的 10

That's used for 10 instead.

用以代表數字 10

So this part, well, that could be anything that

所以這部分可以是任何數字

they want it to be.

只要他們想要

But this number is completely engineered to make this work,

但最後的數字必須是由程式去挑選

to make a multiple of 11.

才會是 11 的多次方

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

如果你的書籍是使用 13 位數字的索書碼

a slightly different operation.

運算的程式略有不同

It's actually based on the number 10 instead

它是用 10 為基礎，而非

of the number 11.

11 為基礎去運算

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

這便是 11,11,11 的其中一個說法

The number 11 is used for these error correction codes.

數字 11 可以作為錯誤偵測條碼之用途

But error correction code, that idea is used

不過錯誤偵測條碼的用途

all over the place.

非常之廣

It's used with computers.

可以用在電腦

It's used with mobile phones if you're

也可以用在手機，當你試著

trying to send a message.

傳送一則簡訊

And, well, in transmission, you can

當然傳送訊息的過程中，你會

lose some of the message.

遺失部分內容

So you want to be able to reconstruct the message

所以你會希望能重新建立訊息

without having to send it all over again.

卻能不用重新寄送簡訊

And you can do this yourself.

你可以靠自己就能完成

Again, this is with a CD.

我這裡有片 CD

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

如果你要燒錄一片 CD，把 CD 拿到光亮處

can even see where the tracks are.

你可以看到其中的軌跡

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

假設使用一隻黑色麥克筆，我現在

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

在 CD 上用筆弄一個黑點，把這黑點視作

something like dirt or a scratch.

灰塵或是刮痕

And this will still play.

這片 CD 還是可以播放

It can compensate for this missing information.

它可以自動修復遺漏的訊息

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

我們知道書碼的數字可能有誤

There's something we can do.

我們還有辦法補救

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

CD 片的方程式透過

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

各種數字，你可以利用方程式來找出

number is missing and what it is.

遺漏的數字，以及是什麼數字

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

我們現在就要用我的 CD 在我的電腦做這件事

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

我要播送一首歌給你們聽，是一首有關數字的歌曲

I thought it would be an appropriate choice.

我想這是不錯的選擇

You can hear it does still play.

你可以聽到 CD 正常播放音樂

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

我現在直接拿出 CD，這比黑色麥克筆畫點

marker pen.

更嚴重

We actually drilled a hole through the CD.

事實上，我們剛才在 CD 上鑽了一個洞

So the data is actually literally missing.

所以這部分的資料是真的不見了

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

不是一個黑點，而是我們真的把資料取出來

Yet the CD player can reconstruct it and still play

但 CD 播放機仍然可以自動修復，而且繼續播放音樂

the song because it will use this error detection

因為它可以透過錯誤偵測科技來修正

technology, this mathematics that reconstructs the missing

數學運算方式可以重新建構遺失的

information.

訊息

In fact, this hole is about 2 millimeters.

這洞約有 2 毫米

You can go up to about 2.5.

你可以鑽一個 2.5 毫米的洞

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

如果我再鑽更大洞，大概是 3 毫米大小

3-millimeter hole.

一個 3 毫米的洞

This hole is too big.

這洞真的非常大

Let's try it out.

我們現在再試一次

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

我來試試看可否播放

You'll notice the difference.

你會發現其中的差別

[MUSIC SKIPPING]

〔音樂跳針〕

It's trying.

它正在試著修復

It's trying its best.

它正在用盡全力試著修復

It doesn't play.

它不能播放了

Too much missing information.

太多遺失的資訊

So 11 was just our starting point into a world of

11 只是我們踏入數學世界的

mathematics and error correction code, something

起始點，錯誤偵測條碼的用途

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

隨處可見，可以讓 CD 正常運轉

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

讓手機正常運作，其中當然包括讓書籍背後的

on the back of a book work.

書碼數字排列正常

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

Brady 堅持要我提醒你們 11

the number of players in a football team.

是一個足球隊伍裡足球員的總數