ABOUT THE SPEAKER
Arthur Benjamin - Mathemagician
Using daring displays of algorithmic trickery, lightning calculator and number wizard Arthur Benjamin mesmerizes audiences with mathematical mystery and beauty.

Why you should listen

Arthur Benjamin makes numbers dance. In his day job, he's a professor of math at Harvey Mudd College; in his other day job, he's a "Mathemagician," taking the stage in his tuxedo to perform high-speed mental calculations, memorizations and other astounding math stunts. It's part of his drive to teach math and mental agility in interesting ways, following in the footsteps of such heroes as Martin Gardner.

Benjamin is the co-author, with Michael Shermer, of Secrets of Mental Math (which shares his secrets for rapid mental calculation), as well as the co-author of the MAA award-winning Proofs That Really Count: The Art of Combinatorial Proof. For a glimpse of his broad approach to math, see the list of research talks on his website, which seesaws between high-level math (such as his "Vandermonde's Determinant and Fibonacci SAWs," presented at MIT in 2004) and engaging math talks for the rest of us ("An Amazing Mathematical Card Trick").

More profile about the speaker
Arthur Benjamin | Speaker | TED.com
TED2005

Arthur Benjamin: A performance of "Mathemagic"

阿瑟 本杰明表演 ‘数学魔术’

Filmed:
9,599,588 views

在一场现场表演中,数学魔术师阿瑟本杰明与一组计算者比赛算3位数数字的平方,更演算了一系列高难度的方程式并且猜出观众的生日。他是怎么做到的呢?让他来告诉你吧。
- Mathemagician
Using daring displays of algorithmic trickery, lightning calculator and number wizard Arthur Benjamin mesmerizes audiences with mathematical mystery and beauty. Full bio

Double-click the English transcript below to play the video.

00:13
Well, good morning早上 ladies女士们 and gentlemen绅士.
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早上好,先生们女士们。
00:14
My name名称 is Art艺术 Benjamin本杰明, and I am a "mathemagicianmathemagician."
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我叫阿瑟 本杰明,我是一名‘数学魔术师。’
00:18
What that means手段 is, I combine结合 my loves of math数学 and magic魔法
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也就是说我把我所热爱的数学跟魔术结合起来,给它取名叫‘数学魔术。’
00:21
to do something I call "mathemagicsmathemagics."
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给它取名叫‘数学魔术。’
00:24
But before I get started开始, I have a quick question for the audience听众.
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在表演开始前我有个问题想问下观众们。
00:27
By any chance机会, did anyone任何人 happen发生
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有没有人今天早上恰巧
00:29
to bring带来 with them this morning早上 a calculator计算器?
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有带计算器过来的?
00:33
Seriously认真地, if you have a calculator计算器 with you, raise提高 your hand, raise提高 your hand.
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说真的,如果你有带计算器的话,举起你的手,举起你的手。
00:37
I -- was -- your hand go up?
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我 -- 是 -- 你举的手吗?
00:39
Now bring带来 it out, bring带来 it out. Anybody任何人 else其他?
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拿出来,把它拿出来。还有谁带了?
00:41
I see, I see one way in the back.
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我看到,我看到后面有一个。
00:43
You sir先生, that's three,
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是你,先生,共有三个了。
00:45
And anybody任何人 on this side here?
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这边的有谁带了?
00:48
OK, you over there on the aisle走道. Would the four of you with calculators计算器
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好的,在过道旁边的那位。
00:50
please bring带来 out your calculators计算器, then join加入 me up on stage阶段.
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请你们4位带着计算器到台上来。
00:53
And let's give these volunteers志愿者 a nice不错 round回合 of applause掌声.
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让我们给这些自愿者予热烈的掌声。
00:55
(Applause掌声)
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(掌声)
00:58
That's right. Now, since以来 I haven't没有 had the chance机会
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很好。因为我还...
01:01
to work with these calculators计算器, I need to make sure
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没用过这些计算器,所以现在我要确认下
01:04
that they are all working加工 properly正确.
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这些计算器是否能正常运算。
01:06
Would somebody get us started开始 by giving us a
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有谁能给出一个...
01:08
two-digit两位数 number please?
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2位数的数字作为开始?
01:11
How about a two-digit两位数 number?
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给个2位数的数字?
01:13
Audience听众: 22.
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观众:22
01:14
Arthur亚瑟 Benjamin本杰明: 22. And another另一个 two-digit两位数 number, Sir先生?
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阿瑟 本杰明:22。 再来一个,先生?
01:16
Audience听众: 47.
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观众:47。
01:17
ABAB: Multiply 22 times 47, make sure you get 1,034,
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阿瑟:把22 乘以47,确认下计算器是否得到1034,
01:21
or the calculators计算器 are not working加工. Do all of you get 1,034? 1,034?
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否则它工作不正常。你们都算出1034了吗? 1034?
01:26
Woman女人: No.
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女士:不是
01:27
ABAB: 594. Let's give three of them a nice不错 round回合 of applause掌声 there.
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阿瑟: 是594。 让我们给那边的3位予热烈的掌声。
01:31
(Applause掌声)
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(掌声)
01:33
Would you like to try a more standard标准 calculator计算器, just in case案件?
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你要换个标准的计算器吗,以防万一?
01:35
OK, great.
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好的,很好
01:37
What I'm going to try and do then --
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接下来我要做的 --
01:39
I notice注意 that took some of you a little bit of time to get your answer回答.
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我想你们中有人会花点时间才能得到答案。
01:42
That's OK. I'll give you a shortcut捷径 for multiplying乘以
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没有关系。我会帮你们算出乘法
01:45
even faster更快 on the calculator计算器.
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快过计算器。
01:47
There is something called the square广场 of a number,
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有种乘法是平方一个数。
01:49
which哪一个 most of you know is taking服用 a number
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也就是众所周知的把一个数
01:51
and multiplying乘以 it by itself本身.
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乘以它本身。
01:53
For instance, five squared平方 would be?
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举个例子,5的平方会等于?
01:55
Audience听众: 25.
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观众:25。
01:56
ABAB: 25. Now, the way we can square广场 on most calculators计算器 --
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阿瑟: 25。 现在,我们计算平方的方式在大多计算器上 --
01:58
let me demonstrate演示 with this one --
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还是让我来演示下这个 --
02:00
is by taking服用 the number, such这样 as five,
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选个数字,比如说5.
02:02
hitting "times" and then "equals等于,"
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点击 ‘乘号’然后 ‘等号。’
02:05
and on most calculators计算器 that will give you the square广场.
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然后大多数计算器会算出平方。
02:08
On some of these ancient RPNRPN calculators计算器,
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在一些老式的RPN 计算器上,
02:10
you've got an "x squared平方" button按键 on it,
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会有一个‘X 平方’的按键。
02:12
will allow允许 you to do the calculation计算 even faster更快.
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用这个快捷键会算得更快。
02:15
What I'm going to try and do now is to square广场, in my head,
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现在我要尝试的是在我的脑子里算平方,
02:18
four two-digit两位数 numbers数字
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4个2位数的数字
02:20
faster更快 than they can do on their calculators计算器, even using运用 the shortcut捷径 method方法.
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快过他们用计算器,即便是用快捷键。
02:24
What I'll use is the second第二 row this time, and I'll get four of you --
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这次我选第二排的4个观众 --
02:26
one, two, three, four -- to each yell叫喊 out a two-digit两位数 number,
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1个,2个,3个,4个 -- 每人喊出一个2位数的数字,
02:29
and if you would square广场 the first number,
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然后你来平方第一个数字,
02:33
and if you would square广场 the second第二, the third第三 and the fourth第四,
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你来平方第二个,以此类推,第三个和第四个。
02:35
I will try and race种族 you to the answer回答. OK?
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我们来比看谁算得快,好吗?
02:38
So quickly很快, a two-digit两位数 number please.
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那么赶快 -- 请给出一个2位数的数字。
02:41
Audience听众: 37.
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观众:37。
02:42
ABAB: 37 squared平方, OK.
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阿瑟:37的平方,好的。
02:44
Audience听众: 23.
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观众:23。
02:45
ABAB: 23 squared平方, OK.
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阿瑟:23的平方,好的。
02:47
Audience听众: 59.
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观众:59。
02:48
ABAB: 59 squared平方, OK, and finally最后?
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阿瑟:59的平方,好的,最后一个?
02:49
Audience听众: 93.
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观众:93。
02:51
ABAB: 93 squared平方. Would you call out your answers答案, please?
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阿瑟:93的平方。你们可以大声说出答案了吗?
02:54
Woman女人: 1369. ABAB: 1369.
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女士: 1369。 阿瑟: 1369。
02:56
Woman女人: 529.
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女士: 529。
02:57
ABAB: 529.
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阿瑟:529。
02:58
Man: 3481.
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男士:3481。
02:59
ABAB: 3481.
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阿瑟:3481。
03:00
Man: 8649.
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男士:8649。
03:01
ABAB: Thank you very much.
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阿瑟:非常感谢。
03:02
(Applause掌声)
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(掌声)
03:07
Let me try to take this one step further进一步.
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我再来试下更有难度的。
03:10
I'm going to try to square广场 some three-digit三位数 numbers数字 this time.
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我接下来要计算一些3位数数字的平方。
03:13
I won't惯于 even write these down --
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我甚至不把它们写下来 --
03:15
I'll just call them out as they're called out to me.
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而是在他们喊出数字后直接喊出答案。
03:17
Anyone任何人 I point to, call out a three-digit三位数 number.
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被我指到的人,请喊出一个3位数的数字。
03:20
Anyone任何人 on our panel面板, verify校验 the answer回答.
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在台上的各位,帮忙确认下答案。
03:22
Just give some indication迹象 if it's right.
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如果正确的话给下提示。
03:24
A three-digit三位数 number, sir先生, yes?
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给一个3位数,这位先生,好吗?
03:27
Audience听众: 987.
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观众:987。
03:28
ABAB: 987 squared平方 is 974,169.
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阿瑟:987 的平方等于974169。
03:31
(Laughter笑声)
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(笑声)
03:33
Yes? Good.
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对吧?好的。
03:35
Another另一个, another另一个 three-digit三位数 --
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再来,再来个3位数 --
03:37
(Applause掌声)
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(掌声)
03:38
-- another另一个 three-digit三位数 number, sir先生?
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-- 再来个3位数数字,这位先生?
03:41
Audience听众: 457.
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观众:457。
03:42
ABAB: 457 squared平方 is 205,849.
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阿瑟:457的平方等于205849。
03:45
205,849?
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205849?
03:47
Yes?
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对吗?
03:49
OK, another另一个, another另一个 three-digit三位数 number, sir先生?
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好的,再来,再来个3位数数字,这位先生?
03:52
Audience听众: 321.
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观众:321。
03:53
ABAB: 321 is 103,041. 103,041.
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阿瑟:321 等于103041。 103041。
03:56
Yes? One more three-digit三位数 number please.
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对吗?请再喊出一个3位数数字。
03:59
Audience听众: Oh, 722.
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观众:哦,722。
04:01
ABAB: 722 is 500 -- ooh, that's a harder更难 one.
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阿瑟:722等于500 -- 哦,这个有点难。
04:04
Is that 513,284?
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是等于513284吗?
04:07
Woman女人: Yes.
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女士:没错。
04:08
ABAB: Yes? Oh, one more, one more three-digit三位数 number please.
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阿瑟:没错吗?哦,再来个,请再来个3位数数字。
04:11
Audience听众: 162.
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观众:162。
04:12
162 squared平方 is 26,244.
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162的平方等于26244。
04:16
Thank you very much.
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非常感谢。
04:18
(Applause掌声)
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(掌声)
04:25
Let me try to take this one step further进一步.
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我再来试下更有难度的。
04:28
(Laughter笑声)
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(笑声)
04:30
I'm going to try to square广场 a four-digit四位数 number this time.
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我这次要计算个4位数的平方。
04:33
Now you can all take your time on this; I will not beat击败 you to the answer回答 on this one,
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这次你们可以慢慢来;这次我不会抢在你们前面回答,
04:36
but I will try to get the answer回答 right.
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但我会尽力给出正确的答案。
04:38
To make this a little bit more random随机, let's take the fourth第四 row this time,
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为了看起来更随机点,这次让我们选第四排的,
04:41
let's say, one, two, three, four.
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那我们开始吧,1个,2个,3个,4个。
04:44
If each of you would call out a single digit数字 between之间 zero and nine,
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你们每个人大声说出一个数字从0到9,
04:46
that will be the four-digit四位数 number that I'll square广场.
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那样我就有个4位数可以计算。
04:49
Audience听众: Nine.
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观众:9。
04:50
ABAB: Nine.
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阿瑟:9。
04:51
Audience听众: Seven. ABAB: Seven.
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观众:7。 阿瑟: 7。
04:52
Audience听众: Five. ABAB: Five.
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观众:5。阿瑟:5。
04:53
Audience听众: Eight. ABAB: Eight.
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观众:8。阿瑟:8。
04:55
9,758, this will take me a little bit of time, so bear with me.
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9758, 这个要花点时间,所以请大家耐心。
04:58
95,218,564?
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是95218564吗?
05:07
Woman女人: Yes.
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女士:是的。
05:08
ABAB: Thank you very much.
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阿瑟: 非常感谢。
05:10
(Applause掌声)
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(掌声)
05:18
Now, I would attempt尝试 to square广场 a five-digit五位数 number --
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现在,我很想试着平方一个5位数 --
05:21
and I can --
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我可以 --
05:23
but unfortunately不幸 most calculators计算器 cannot不能.
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但可惜大多数计算器不能。
05:25
(Laughter笑声)
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(笑声)
05:27
Eight-digit八位 capacity容量 -- don't you hate讨厌 that?
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最多只能8位 -- 你们不讨厌吗?
05:30
So, since以来 we've我们已经 reached到达 the limits范围 of our calculators计算器 --
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好吧,既然我们已经超越计算器的计算能力 --
05:33
what's that? Does yours你的 go --
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什么?你的可以 --
05:36
Woman女人: I don't know.
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女士:我不知道。
05:37
ABAB: Does yours你的 go higher更高?
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阿瑟:你的可以算吗?
05:39
Oh -- yours你的 does?
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哦 -- 是你的可以吗?
05:41
Man: I can probably大概 do it.
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男士:好像可以。
05:42
ABAB: I'll talk to you later后来.
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阿瑟:我等会儿再找你。
05:44
In the meanwhile与此同时, let me conclude得出结论
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与此同时,让我来用些更巧妙的把戏来小结
05:46
the first part部分 of my show显示 by doing something a little trickier棘手.
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我的第一部分表演。
05:49
Let's take the largest最大 number on the board here, 8649.
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让我们用这块板上最大的一个数字,8649。
05:52
Would you each enter输入 that on your calculator计算器?
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你们每个人可否在计算器上输入这个数?
05:55
And instead代替 of squaring现蕾 it this time,
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这次不要平方,
05:57
I want you to take that number and multiply it
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我要你们用那个数乘以
05:59
by any three-digit三位数 number that you want,
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任何3位数,
06:02
but don't tell me what you're multiplying乘以 by --
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但不要告诉我你所乘的数 --
06:04
just multiply it by any random随机 three-digit三位数 number.
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只要乘以任何一个3位数。
06:07
So you should have as an answer回答 either
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那么你得到的答案可能会是
06:09
a six-digit六位数 or probably大概 a seven-digit七位数 number.
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一个六位数或者七位数。
06:13
How many许多 digits数字 do you have, six or seven?
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你的是几位,6还是7?
06:14
Seven, and yours你的? Woman女人: Seven.
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7,你的呢?女士:7。
06:16
ABAB: Seven? Seven?
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阿瑟:7?7吗?
06:19
And, uncertain不确定.
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不确定。
06:21
Man: Yeah.
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男士:是的。
06:22
ABAB: Seven. Is there any possible可能 way that I could know
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阿瑟: 7。 有没有办法会让我知道
06:24
what seven digit数字 numbers数字 you have? Say "No."
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你所得到的7位数?应该不可能。
06:27
(Laughter笑声)
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(笑声)
06:29
Good. Then I shall attempt尝试 the impossible不可能 --
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很好。那我应该来挑战下这个不可能 --
06:31
or at least最小 the improbable难以置信.
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至少看上去是不太可能的事。
06:33
What I'd like each of you to do is to call out for me
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接下来我想让你们告诉我
06:35
any six of your seven digits数字, any six of them,
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7位数里面的任意6位数字。
06:38
in any order订购 you'd like.
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任意顺序都可以。
06:40
(Laughter笑声)
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(笑声)
06:41
One digit数字 at a time, I shall try and determine确定 the digit数字 you've left out.
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每次一位数,我会试着算出剩下的数。
06:46
So, starting开始 with your seven-digit七位数 number,
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那么,从你开始吧。
06:48
call out any six of them please.
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请喊出任意6位数字。
06:50
Woman女人: One, OK, 197042.
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女士:1,哦,197042。
06:56
ABAB: Did you leave离开 out the number 6?
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阿瑟:你是不是漏说了6?
06:57
Woman女人: Yes, ABAB: Good, OK, that's one.
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女士:是的,阿瑟:很好,好的,没错。
06:59
You have a seven-digit七位数 number, call out any six of them please.
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你的是7位数,请大声说出其中任意的六个数。
07:01
Woman女人: 44875.
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女士:44875。
07:04
ABAB: I think I only heard听说 five numbers数字. I -- wait -- 44875 --
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阿瑟: 我好像只听到5个数字。我 -- 等下 -- 44875 --
07:09
did you leave离开 out the number 6?
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你是不是漏说了数字6?
07:11
Woman女人: Yes. ABAB: Same相同 as she did, OK. You've got a seven-digit七位数 number --
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女士:是的。 阿瑟:跟她的一样,好的。你得到的是一个7位数 --
07:13
call out any six of them loud and clear明确.
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大声清晰地说出其中的任意6个数字。
07:16
Man: 079044.
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男:079044.
07:20
ABAB: I think you left out the number 3?
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阿瑟:我想你漏说了数字3?
07:22
That's three. The odds可能性 of me getting得到 all four of these right by random随机 guessing揣测
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就是3. 要是我随便猜到话,那么我猜中其中4位数字的概率
07:26
would be one in 10,000: 10 to the fourth第四 power功率.
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将会是万分之一。10的负四次方。
07:29
OK, any six of them.
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好了,任意6位数字。
07:32
Really scramble争夺 them up this time, please.
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这次请把它们搅乱一下。
07:34
Man: 263972.
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男:263972。
07:38
ABAB: Did you leave离开 out the number 7?
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阿瑟:你是不是漏说了数字7?
07:40
And let's give all four of these people a nice不错 round回合 of applause掌声.
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现在让我们给这四位观众予热烈的掌声。
07:42
Thank you very much. (Applause掌声)
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非常感谢。
07:52
For my next下一个 number --
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我的下一个数 --
07:54
(Laughter笑声)
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(笑声)
07:57
while I mentally精神上 recharge充值 my batteries电池,
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在给我脑袋充电期间
07:59
I have one more question for the audience听众.
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我有个问题要问下观众们。
08:02
By any chance机会, does anybody任何人 here happen发生 to know
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有可能的话,在场的有谁刚好知道
08:07
the day of the week that they were born天生 on?
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你生日的那天是星期几?
08:10
If you think you know your birth分娩 day, raise提高 your hand.
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如果你觉得知道的话,举下手。
08:14
Let's see, starting开始 with -- let's start开始 with a gentleman绅士 first,
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让我们看看,从 -- 从男士开始,
08:17
OK sir先生, what year was it, first of all? That's why I start开始 with a gentleman绅士 first.
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好的先生,先说下是哪一年?这就是为什么我要先从男士开始。
08:20
What year?
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哪年?
08:21
Audience听众: 1953.
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观众:1953。
08:22
ABAB: 1953, and the month?
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阿瑟: 1953,哪个月?
08:24
Audience听众: November十一月. ABAB: November十一月 what?
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观众:11月。阿瑟:11月几号?
08:25
Audience听众: 23rdRD.
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观众:23号。
08:26
ABAB: 23rdRD -- was that a Monday星期一? Audience听众: Yes.
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阿瑟: 23号 -- 是不是星期一?观众:是的。
08:28
Yes, good. Somebody else其他? Who else其他 would like --
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没错,很好。还有人吗?还有谁想要 --
08:30
see I don't -- haven't没有 seen看到 any women's女士的 hands up.
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呃,还没,我还没看到有女士举手。
08:32
OK, it's -- how about you, what year?
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啊,很好,你呢,哪年?
08:34
Audience听众: 1949. ABAB: 1949, and the month?
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观众:1949. 阿瑟: 1949, 哪月?
08:36
Audience听众: October十月. ABAB: October十月 what?
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观众: 十月。阿瑟: 十月几号?
08:37
Audience听众: Fifth第五.
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观众: 5号。
08:38
ABAB: Fifth第五 -- was that a Wednesday星期三?
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阿瑟: 5号 -- 那是不是星期3?
08:40
Yes, my -- I'll go way to the back right now, how about you?
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没错,现在我从后面选,你怎样?
08:42
Yell叫喊 it out, what year? Audience听众: 1959.
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大声说出来,哪年?观众:1959。
08:44
ABAB: 1959, OK -- and the month?
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阿瑟:1959, 好的 -- 哪月?
08:46
Audience听众: February二月.
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观众:二月。
08:48
ABAB: February二月 what? Audience听众: Sixth第六.
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阿瑟: 2月几号? 观众:6号。
08:50
ABAB: Sixth第六 -- was that a Friday星期五? Audience听众: Yes.
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阿瑟: 6号,那是不是星期五?观众:是的。
08:52
Good, how about the person behind背后 her?
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很好,在她后面的那个人要不要试试?
08:54
Call -- call -- what year was it?
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喊出 -- 哪一年?
08:56
Audience听众: 1947. ABAB: 1947, and the month?
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观众:1947. 阿瑟: 1947,哪月?
08:58
Audience听众: May可能. ABAB: May可能 what?
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观众:5月。阿瑟: 5月几号?
09:00
Audience听众: Seventh第七. ABAB: Seventh第七 -- would that be a Wednesday星期三?
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观众:7号。阿瑟:7号 -- 那是不是星期三?
09:02
Audience听众: Yes.
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观众:是的。
09:03
ABAB: Thank you very much.
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阿瑟:非常感谢。
09:05
(Applause掌声)
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(掌声)
09:09
Anybody任何人 here who'd谁愿意 like to know the day of the week they were born天生?
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在场的哪一位想知道自己的生日是在星期几的?
09:12
We can do it that way.
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我们也可以这么做。
09:14
Of course课程, I could just make up an answer回答 and you wouldn't不会 know,
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当然,这样的话我乱编一个你也不会知道,
09:16
so I come prepared准备 for that.
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所以我事先有准备了下。
09:18
I brought with me a book of calendars日历.
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我带了一个日历。
09:21
It goes as far back into the past过去 as 1800, 'cause'原因 you never know.
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可以查回到1800年,谁知道会不会用得着呢?哈。
09:25
(Laughter笑声)
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(笑声)
09:27
I didn't mean to look at you, sir先生 --
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我不是故意看着你,先生 --
09:29
you were just sitting坐在 there.
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你只是恰巧坐在那边。
09:31
Anyway无论如何, Chris克里斯, you can help me out here, if you wouldn't不会 mind心神.
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不管怎样,Chris,你可以帮我下,如果你不介意的话。
09:34
This is a book of calendars日历, and I'll ask --
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这是一本日历,然后我会问 --
09:36
who was it that wanted to know their birth分娩 day? You sir先生? OK.
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是谁想知道他的生日的,是你吗,先生?好的。
09:38
What year was it, first of all?
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先问下哪一年?
09:40
Audience听众: 1966.
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观众:1966。
09:41
ABAB: '66 -- turn to the calendar日历 with 1966 --
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阿瑟: 66年 -- 翻到日历的1966年 --
09:43
and what month?
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阿瑟: 哪月?
09:45
Audience听众: April四月. ABAB: April四月 what?
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观众:4月。 阿瑟: 4月几号?
09:47
Audience听众: 17th. ABAB: 17th -- I believe that was a Sunday星期日.
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观众:17号。 阿瑟: 17号 -- 我确信那是个星期天。
09:50
Can you confirm确认, Chris克里斯?
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你能否确认下,Chris?
09:52
Chris克里斯 Anderson安德森: Yes. ABAB: Yeah, OK. I'll tell you what, Chris克里斯:
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Chris: 是的。阿瑟: 很好,我跟你说
09:54
as long as you have that book in front面前 of you,
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chris,用你面前的那本书,
09:57
do me a favor偏爱, turn to a year outside of the 1900s,
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帮我下忙,翻到1900s以外的,
10:01
either into the 1800s or way into the 2000s --
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翻到页面1800s 或者2000s --
10:04
that'll那会 be a much greater更大 challenge挑战 for me.
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那样对我来说会更有挑战性。
10:06
What year, Chris克里斯, would you like?
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你喜欢哪年,Chris?
10:07
CACA: 1824.
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Chris: 1824.
10:08
ABAB: 1824, OK.
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阿瑟: 1824, 好的。
10:11
And what month? CACA: June六月.
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哪月呢?Chris: 六月。
10:13
ABAB: June六月 what? CACA: Sixth第六.
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哪月呢?Chris: 六月
10:15
ABAB: Sixth第六 -- was that a Sunday星期日?
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6号 -- 是不是星期天?
10:17
CACA: It was. ABAB: And it was cloudy多云的.
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Chris:没错。 阿瑟:并且是阴天。
10:20
Good, thank you very much.
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很好,非常感谢。
10:22
(Applause掌声)
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(掌声)
10:28
But I'd like to wrap things up now
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但是现在我想来个总结
10:30
by alluding暗指 to something
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再次回到
10:33
from earlier in the presentation介绍.
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我之前的表演
10:35
There was a gentleman绅士 up here who had a 10-digit-数字 calculator计算器.
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先前台上有位带10位数计算器的先生。
10:38
Where is he, would you stand up,
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现在在哪里,你能站起来一下吗?
10:42
10-digit-数字 guy?
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10位数的伙计?
10:44
OK, well stand up for me just for a second第二,
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好的,请站起来下,
10:47
so I can see where you are.
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好让我可以看到你在哪里。
10:49
OK, oh, OK -- you have a 10-digit-数字 calculator计算器, sir先生, as well?
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好,哦,好的 -- 你也有一个10位数的计算器?
10:52
OK, what I'm going to try and do, is to square广场 in my head
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很好,我接下来要做的是,心算平方
10:56
a five-digit五位数 number requiring要求 a 10-digit-数字 calculator计算器.
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一个5位数的数字,这需要个10位数的计算器。
10:59
But to make my job工作 more interesting有趣 for you, as well as for me,
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为了给大家和我自己增加点乐趣,
11:04
I'm going to do this problem问题
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我会把心算过程
11:06
thinking思维 out loud.
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大声的念出来。
11:08
So you can actually其实, honestly老老实实 hear
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这样你们就可以实际上听到
11:11
what's going on in my mind心神
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我心算时的具体过程
11:13
while I do a calculation计算 of this size尺寸.
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当我计算这样大的数字的时候。
11:15
Now, I have to apologize道歉 to our magician魔术师 friend朋友 Lennart伦纳特 Green绿色.
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现在,我得向我们的魔术师朋友 Lennart Green道下歉。
11:18
I know as a magician魔术师 we're not supposed应该 to reveal揭示 our secrets秘密,
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我知道作为一个魔术师本不应该泄漏我们的秘密,
11:22
but I'm not too afraid害怕 that people are going
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但我并不是很担心其他人
11:24
to start开始 doing my show显示 next下一个 week, so --
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会在下个星期开始模仿我的表演,所以 --
11:26
I think we're OK.
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我想没有什么问题。
11:30
So, let's see, let's take a --
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那么,让我们开始吧,
11:33
let's take a different不同 row of people, starting开始 with you.
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让我们选另一排的观众,就从你开始吧。
11:35
I'll get five digits数字: one, two, three, four --
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我将得到5位数:1,2,3,4 --
11:38
oh, I did this row already已经. Let's do the row before you,
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哦,我已经选过这排了。那就选你前面的这排观众,
11:40
starting开始 with you sir先生: one, two, three, four, five.
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从你开始先生:1,2,3,4,5。
11:43
Call out a single digit数字 -- that will be the five-digit五位数 number
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(每个人)喊出一个一位数 -- 这样就组成一个5位数的数字
11:46
that I will try to square广场. Go ahead.
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我会心算这个数的平方。开始吧。
11:48
Audience听众: Five. ABAB: Five.
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观众:5。阿瑟:5。
11:50
Audience听众: Seven. ABAB: Seven.
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观众:7。阿瑟:7。
11:51
Audience听众: Six. ABAB: Six.
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观众:6。阿瑟:6。
11:52
Audience听众: Eight. ABAB: Eight.
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观众:8。阿瑟:8。
11:54
Audience听众: Three. ABAB: Three.
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观众:3。阿瑟:3。
11:56
57,683
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57683
12:01
squared平方. Yuck.
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平方。惨啦。
12:03
Let me explain说明 to you how
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让我来给大家解释下
12:05
I'm going to attempt尝试 this problem问题.
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我接下来要怎么算。
12:08
I'm going to break打破 the problem问题 down into three parts部分.
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我会把这个问题分成3部分。
12:11
I'll do 57,000 squared平方,
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我先算57000的平方,
12:13
plus 683 squared平方,
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然后加上683的平方,
12:17
plus 57,000 times
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加上57000乘以
12:20
683 times two.
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683乘以2。
12:22
Add all those numbers数字 together一起,
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把所有的结果加起来,
12:24
and with any luck运气, arrive到达 at the answer回答.
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幸运的话,就可以得出答案。
12:28
Now, let me recap概括.
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现在,让我先想一下(合上笔帽)。(一语双关)
12:31
Thank you.
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谢谢。
12:34
While I explain说明 something else其他 --
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当我讲一些其他的 --
12:37
-- I know, that you can use, right?
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-- 我知道,你可以利用这个,对吧?
12:40
While I do these calculation计算[s],
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当我心算的时候,在计算的过程中
12:42
you might威力 hear certain某些 words,
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你会听到某些词语,
12:44
as opposed反对 to numbers数字, creep爬行 into the calculation计算.
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来对应一些数字,融入到计算当中。
12:48
Let me explain说明 what that is.
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让我来解释下是什么。
12:49
This is a phonetic拼音 code,
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这是语音代码,
12:51
a mnemonic助记符 device设备 that I use,
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相当于一个记忆用的设备,
12:53
that allows允许 me to convert兑换 numbers数字 into words.
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这个设备能帮我把数字转换成单词。
12:56
I store商店 them as words, and later后来 on retrieve取回 them as numbers数字.
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我先存为单词,然后再转回成数字。
12:59
I know it sounds声音 complicated复杂; it's not --
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我知道这听起来有点复杂;(实际上)一点也不 --
13:01
I just don't want you to think you're seeing眼看 something out of "Rain Man" here.
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我不想让你们以为自己看到了‘雨人’。
13:04
(Laughter笑声)
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(笑声)
13:06
There's definitely无疑 a method方法 to my madness疯狂 --
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这其中绝对有种方法来解释我疯狂的表演 --
13:08
definitely无疑, definitely无疑. Sorry.
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一定的,一定的。不好意思。
13:10
(Laughter笑声)
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(笑声)
13:14
If you want to talk to me about ADHD多动症 afterwards之后,
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如果你想找我谈论小儿多动症的话,
13:16
you can talk to me then. All right --
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你可以找我谈谈。好吧 --
13:18
by the way, one last instruction指令,
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顺便提下,
13:20
for my judges法官 with the calculators计算器 -- OK, you know who you are --
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给我那个有计算器的裁判最后一个说明
13:23
there is at least最小 a 50 percent百分 chance机会
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至少有一半的机会
13:26
that I will make a mistake错误 here.
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我会犯错。
13:29
If I do, don't tell me what the mistake错误 is;
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如果算错了,不要告诉我哪里错了;
13:32
just say, "you're close," or something like that, and I'll try and figure数字 out the answer回答 --
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只要说,‘接近了,’或者类似的,然后我会再试着算出正确的答案 --
13:35
which哪一个 could be pretty漂亮 entertaining娱乐 in itself本身.
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这样会更有趣点。
13:39
If, however然而, I am right,
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如果,我对了的话,
13:41
whatever随你 you do, don't keep it to yourself你自己, OK?
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无论如何,你都不要自己留着结果,好吗?
13:44
(Laughter笑声)
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(笑声)
13:45
Make sure everybody每个人 knows知道 that I got the answer回答 right,
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确保让大家知道我算对了,
13:47
because this is my big finish, OK.
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因为这对我来说是个完美的收场。
13:50
So, without any more stalling失速,
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好吧,闲话少说,
13:53
here we go.
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我们开始吧。
13:56
I'll start开始 the problem问题 in the middle中间, with 57 times 683.
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我会从问题的中间部分开始,先算57乘以683。
13:58
Now, 57 times 68 is 3,400, plus 476 is 3876,
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现在,57乘以68等于3400,加上476等于3876,
14:01
that's 38,760 plus 171,
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那是38760加上171,
14:04
38,760 plus 171 is 38,931.
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38760加上171等于38931。
14:07
38,931; double that to get 77,862.
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38931;翻一倍得到77862。
14:11
77,862 becomes cookie曲奇饼 fission分裂,
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77862变成‘cookie fission’,
14:13
cookie曲奇饼 fission分裂 is 77,822.
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‘cookie fission’ 是77822。
14:17
That seems似乎 right, I'll go on. Cookie曲奇饼 fission分裂, OK.
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好像没错,继续。'cookie fission’,好的。
14:19
Next下一个, I do 57 squared平方, which哪一个 is 3,249, so I can say,
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接下来,我算57的平方等于3249,那么应该是,
14:23
three billion十亿. Take the 249, add that to cookie曲奇饼, 249,
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30亿。用249加上'cookie',249,
14:28
oops哎呀, but I see a carry携带 coming未来 --
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哦,但是我看到有一个包过来了 --
14:30
249 --
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249 --
14:32
add that to cookie曲奇饼, 250 plus 77,
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加上 'cookie',250加上77,
14:34
is 327 million百万 --
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等于3亿2千7百万 --
14:38
fission分裂, fission分裂, OK, finally最后, we do 683 squared平方,
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'fission, fission,' 好的,总算可以算683的平方了,
14:41
that's 700 times 666, plus 17 squared平方
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相当于700乘以666,再加上17的平方
14:43
is 466,489, rev up if I need it,
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等于466489,我需要的时候转起来,
14:46
rev up, take the 466,
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放大,用466,
14:48
add that to fission分裂, to get,
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加上'fission',得到,
14:50
oh gee哎呀 --
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哦老天 --
14:54
328,489.
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328489。
14:58
Audience听众: Yeah!
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观众:没错!
14:59
ABAB: Good.
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阿瑟:很好。
15:00
(Applause掌声)
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(掌声)
15:01
Thank you very much.
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非常感谢。
15:03
I hope希望 you enjoyed享受 mathemagicsmathemagics. Thank you.
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希望你们能喜欢数学魔术。谢谢大家。
15:05
(Applause掌声)
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(掌声)
Translated by jianfeng liu
Reviewed by Cai Yu

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ABOUT THE SPEAKER
Arthur Benjamin - Mathemagician
Using daring displays of algorithmic trickery, lightning calculator and number wizard Arthur Benjamin mesmerizes audiences with mathematical mystery and beauty.

Why you should listen

Arthur Benjamin makes numbers dance. In his day job, he's a professor of math at Harvey Mudd College; in his other day job, he's a "Mathemagician," taking the stage in his tuxedo to perform high-speed mental calculations, memorizations and other astounding math stunts. It's part of his drive to teach math and mental agility in interesting ways, following in the footsteps of such heroes as Martin Gardner.

Benjamin is the co-author, with Michael Shermer, of Secrets of Mental Math (which shares his secrets for rapid mental calculation), as well as the co-author of the MAA award-winning Proofs That Really Count: The Art of Combinatorial Proof. For a glimpse of his broad approach to math, see the list of research talks on his website, which seesaws between high-level math (such as his "Vandermonde's Determinant and Fibonacci SAWs," presented at MIT in 2004) and engaging math talks for the rest of us ("An Amazing Mathematical Card Trick").

More profile about the speaker
Arthur Benjamin | Speaker | TED.com