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

    歡迎來到我們正式推出的新頻道《數字狂》,今天是第一集

  • 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

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

歡迎來到我們正式推出的新頻道《數字狂》,今天是第一集

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【數字狂】你知道11.11.11有什麼樣不同的意思嗎? 11.11.11 - Numberphile

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