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Good morning, ladies and gentlemen.
女士们先生们 早上好
My name is Art Benjamin, and I am a "mathemagician."
我叫阿瑟 本杰明 是一名“数学魔术师”
What that means is, I combine my loves of math and magic to do something I call "mathemagics."
我把我所热爱的数学跟魔术结合了起来我将其称为‘数学魔术’
But before I get started, I have a quick question for the audience.
但是在开始我的表演之前 我给大家准备了一个快问快答
By any chance, did anyone happen to bring with them this morning a calculator?
有人碰巧身边带着计算器吗
Seriously, if you have a calculator with you, raise your hand.
如果你带了计算器 麻烦举下手
Raise your hand. Did your hand go up?
举下手 你是不是举手了
Now bring it out, bring it out. Anybody else?
现在把他拿出来 拿出来 还有人也带了吗
I see, I see one way in the back.
我看到了 看到了 坐在后面的那个
You sir, that's three. And anybody on this side here?
是你 先生 现在共有三个了 这边的有谁带了？
OK, over there on the aisle.
好的 那边角落有一个
Would the four of you please bring out your calculators, then join me up on stage.
麻烦你们四个拿出你们的计算器然后到台上来配合我表演
Let's give them a nice round of applause. That's right.
大家掌声有请（这四位）好的
Now, since I haven't had the chance to work with these calculators, I need to make sure that they are all working properly.
现在 由于我从没有机会检查这几台计算器所以我必须确保它们都可以正常工作
Would somebody get us started by giving us a two-digit number, please?
开始前 麻烦来个人给个2位数
How about a two-digit number? 22.
给个2位数怎么样？22
Multiply 22 times 47, make sure you get 1,034, or the calculators are not working.
Do all of you get 1,034? 1,034? No.
你们都得到1034了是吧？1034？不是
她是594 让我们给予另外3位以热烈的掌声
Would you like to try a more standard calculator, just in case? OK, great.
以防万一 你愿意试试标准计算器吗 好的
What I'm going to try and do then I notice it took some of you a little bit of time to get your answer. That's OK.
接下来我要尝试做的是 我发现你得花点时间才能得到答案 没关系
I'll give you a shortcut for multiplying even faster on the calculator.
我会给你个妙招 让你比计算器乘的更快
There is something called the square of a number, which most of you know is taking a number and multiplying it by itself.
我们都知道一个数的平方就是把一个数和它自身相乘
For instance, five squared would be 25.
比如说 5的平方是什么 25
is by taking the number, such as five, hitting "times" and then "equals," and on most calculators that will give you the square.
像这样用一个数字 比如说5 按下“乘”再按一下“等于”计算机上就会显示这个数的平方
On some of these ancient RPN calculators, you've got an "x squared" button on it, will allow you to do the calculation even faster.
在一些老式的RPN计算器上你会看到一个平方键让你能算得更快
What I'm going to try and do now is to square, in my head,
现在我要尝试做的是在我的脑子里算平方
four two-digit numbers faster than they can do on their calculators, even using the shortcut method.
4个2位数的数字 比计算器还要快即使计算器用了快捷方式
What I'll use is the second row this time, and I'll get four of you to each yell out a two-digit number,
我需要第二排的观众需要请你们中的四位 每人喊出一个两位数字
and if you would square the first number, and if you would square the second, the third and the fourth,
请你计算第一个数字的平方请你计算二个 你第三个 你第四个
I will try and race you to the answer. OK?
我会和你比赛谁得到答案的速度快 好吗？
So quickly, a two-digit number please. 37. 37 squared, OK. 23. 23 squared, OK. 59.
来快一点 请说一个两位数字 37 37的平方 好的 23 23的平方 好的 59
Let me try to take this one step further.
让我们尝试更进一步
I'm going to try to square some three-digit numbers this time.
我这次将计算一些三位数字的平方
I won't even write these down I'll just call them out as they're called out to me.
甚至不会把这些写下来而是在他们喊出数字后直接喊出答案
Anyone I point to, call out a three-digit number.
我点到谁 谁就说一个三位数字
Anyone on our panel, verify the answer.
在台上的各位 帮忙确认下答案
Just give some indication if it's right.
如果是对的 请示意我
A three-digit number, sir, yes 987. 987 squared is 974,169. Yes? Good.
先生请说一个三位数的数字 987 987 的平方等于974169 对吗？好的
Another three-digit another three-digit number, sir? 457.
下一个三位数先生请说另外一个三位数字 457
OK, another, another three-digit number, sir? 321. 321 is 103,041. 103,041.
好的，另一个三位数字 321 321的平方是103041 103041
Yes? One more three-digit number please. Oh, 722. 722 is 500, that's a harder one.
下一个三位数字 722 722的平方是500 这个有点难
Is that 513,284? Yes. Yes? Oh, one more, one more three-digit number please. 162.
是513284吗？是的 好的 再来一个三位数字 162
Let me try to take this one step further.
接下来我要挑战更有难度的
I'm going to try to square a four-digit number this time.
这一次我要计算一个四位数的平方
You can all take your time on this; I will not beat you to the answer on this one, but I will try to get the answer right.
这次你们可以慢慢来因为我可能没有你们算的快但是我会尽量保证答案正确
To make this a little bit more random, let's take the fourth row this time, let's say, one, two, three, four.
为了使这个四位数产生的更随机一些 我将会请四个人比如说1234
If each of you would call out a single digit between zero and nine, that will be the four-digit number that I'll square.
你们中的每一个人说一个0到9之间的个数 组成这个四位数 我再来计算它的平方
Nine. Seven. Five. Eight. 9,758, this will take me a little bit of time, so bear with me.
九 七 五 八 9758 请再给我一点时间
Now, I would attempt to square a five-digit number and I can but unfortunately, most calculators cannot.
现在 我来挑战一个5位数的平方我能做到但不幸的是 大部分计算器都不能做到
Eight-digit capacity -- don't you hate that?
八位数的计算量——难道你不讨厌这个吗？
So, since we've reached the limits of our calculators what's that?
好的 既然我们已经达到了我们计算器的极限怎么啦？
Does yours go higher? I don't know. Oh, yours does?
你的计算器能够进行更高位的计算吗 我不知道 你的呢？
I can probably do it. I'll talk to you later.
我的可以做到 好的 我一会儿再跟你说
In the meanwhile, let me conclude the first part of my show by doing something a little trickier.
同时让我总结一下我的第一部分魔术表演
Let's take the largest number on the board here, 8649.
我们用屏幕上最大的数字8649
Would you each enter that on your calculator?
都输入到你们计算器上了吗？
And instead of squaring it this time, I want you to take that number and multiply it by any three-digit number that you want,
这次不要平方我要你们用那个数去乘任意一个三位数
but don't tell me what you're multiplying by just multiply it by any random three-digit number.
但不要告诉我你所乘的数是几就乘任意一个三位数字
So you should have as an answer either a six-digit or probably a seven-digit number.
所以你的最终结果是一个六位到七位之间的数字
How many digits do you have, six or seven? Seven, and yours? Seven? Seven?
你得到了几位数 六还是七 七 你的呢 7 7
And, uncertain. Seven. Is there any possible way that I could know what seven-digit numbers you have?
不确定 7 你们觉得有可能我会知道 你的七位数是几吗？
Say "No." Good, then I shall attempt the impossible or at least the improbable.
说“不可能” 好的 现在我要做到不可能的事情至少看上去是不太可能的事
What I'd like each of you to do is to call out for me any six of your seven digits, any six of them, in any order you'd like.
我希望你们每个人大声念出你们七位数中的任意六位用你喜欢的任何顺序都可以
One digit at a time, I shall try and determine the digit you've left out.
一次念一位数我将说出剩下的那个数字
Starting with your seven-digit number, call out any six of them please. 1, 9, 7, 0, 4, 2.
从你的七位数开始吧请说出其中的任意六位 197042
Did you leave out the number 6? Good, OK, that's one.
你是没说六吗 好的 好的 就是这个
You have a seven-digit number, call out any six of them please. 4, 4, 8, 7, 5.
你有一个七位的数字 请大声念出其中的任意六位 44875
I think I only heard five numbers. I wait 44875 did you leave out the number 6
我好像只听到了五位数字 等一下...是44875吗 剩下的数字是不是六
Same as she did, OK.
是的 和她的数字一样
You've got a seven-digit number call out any six of them loud and clear. 0, 7, 9, 0, 4, 4.
你有一个七位数字大声并且清晰的念出其中的任意六位 079044
I think you left out the number 3 That's three.
剩下的那个数字是3吗 是3
The odds of me getting all four of these right by random guessing would be one in 10,000: 10 to the fourth power.
我猜对这些随机数字的几率是万分之一也就是十的四次方
OK, any six of them.
好的 请说出其中的任意六位
Really scramble them up this time, please. 2, 6, 3, 9, 7, 2.
请打乱它们的顺序 263972
Did you leave out the number 7?
阿瑟:剩下的一个是不是数字7？
And let's give all four of these people a nice round of applause. Thank you very much.
掌声鼓励他们四个 十分感谢
For my next number while I mentally recharge my batteries,
为了我接下来的数字我已经给自己充满了电
I have one more question for the audience.
还有一个问题要问大家
By any chance, does anybody here happen to know the day of the week that they were born on?
有人恰巧知道自己生日那天是星期几吗？
If you think you know your birth day, raise your hand.
如果你知道你是星期几出生的 请举手
Let's see, starting with -- let's start with a gentleman first.
我们来看一下--从这位先生开始
What year was it, first of all?
先生你是哪一年出生的？
That's why I pick a gentleman first. 1953. 1953, and the month November what
这是我选择这位先生的原因 1953 1953年 哪个月 11月 11月几号
I haven't seen any women's hands up.
我好像没有看到哪位女士举手
OK, how about you, what year?
好的你是哪一年出生的？
Yes! I'll go way to the back right now, how about you?
是的我现在要走到后面去找一位观众 您是什么时候生的？
Yell it out, what year 1959. 1959, OK and the month February. February what?
大声的说出来 您是哪一年出生的 1959 1959好的哪一个月 二月 二月几号？
Sixth was that a Friday Yes. Good, how about the person behind her?
6号，那是不是星期五？是的。很好，在她后面的那个人要不要试试？
Call out, what year was it 1947. 1947, and the month? May. May what?
把你的生日年份大声的说出来 1947 1947年哪个月？五月 五月几号？
Seventh would that be a Wednesday? Yes. Thank you very much.
七号 那是星期三吗 是的 非常感谢
Anybody here who'd like to know the day of the week they were born?
谁想要知道自己是星期几出生的？
We can do it that way.
我可以帮助你们
Of course, I could just make up an answer and you wouldn't know, so I come prepared for that.
当然我会告诉你一个答案但是你可能无法判断它是不是对的因此我预备了一下
I brought with me a book of calendars.
我随身携带了一本日历
It goes as far back into the past as 1800, because you never know.
这本日历最远能够翻到1800年 在座的你们肯定都不知道
I didn't mean to look at you, sir you were just sitting there.
先生 我不是故意盯着你看的正好你坐在这而已
Anyway, Chris, you can help me out here, if you wouldn't mind.
无论如何克里斯会帮主助我的
This is a book of calendars. Who wanted to know their birth day?
这是一本日历 谁想知道自己的生日在星期几？
What year was it, first of all? 1966. 66 turn to the calendar with 1966.
首先你是哪一年的 1966 66 年 把日历本翻到1966年
And what month April. April what 17th. I believe that was a Sunday.
哪个月 四月几号 十七号 我知道那是星期天
Can you confirm, Chris Yes. I'll tell you what, Chris:
克里斯能帮我证实吗 是的 克里斯我告诉你
as long as you have that book in front of you,
把你面前的这本日历
do me a favor, turn to a year outside of the 1900s,
翻翻二十世纪以外的年份
either into the 1800s or way into the 2000s
无论是十九世纪或者是21世纪都可以
that'll be a much greater challenge for me.
这将对我是更大的挑战
What year would you like 1824. 1824, OK. And what month? June.
你选择的是哪一年 1824年 1824 好的 哪个月 六月
June what? Sixth. Was that a Sunday?
六月几号 六号 那是星期天吗
It was. And it was cloudy Good, thank you very much.
是的 那一天是多云天气吗 好的 非常感谢
But I'd like to wrap things up now by alluding to something from earlier in the presentation.
我们现在来把思绪整理一下从刚才到现在的整个过程
There was a gentleman up here who had a 10 digit calculator.
先前台上有位带10位数计算器的先生
Where is he, would you stand up, 10 digit guy?
他在哪儿 你能站起来示意一下吗 十位数的男人？
OK, stand up for me just for a second, so I can see where you are.
好的 请站一会儿好让我可以看到你在哪里
You have a 10 digit calculator, sir, as well?
好的 你也有一个10位数的计算器？
OK, what I'm going to try and do, is to square in my head a five-digit number requiring a 10-digit calculator.
好的 接下来我要做的事用我的大脑计算一个五位数的平方 我们需要一个十位数的计算器
But to make my job more interesting for you, as well as for me, I'm going to do this problem thinking out loud.
为了使我的表演更加有意思我要把思考问题的过程大声的说出来
So you can actually, honestly hear what's going on in my mind while I do a calculation of this size.
你就可以听到当我在计算一个数的平方的时候我是怎么想的
Now, I have to apologize to our magician friend Lennart Green.
现在我要对我的魔术师朋友雷纳德·格林说声对不起
I know as a magician we're not supposed to reveal our secrets,
知道作为一个魔术师我们不应该泻露自己的秘密
but I'm not too afraid that people are going to start doing my show next week, so I think we're OK.
但是我并不怎么害怕下个星期人们开始相互间表演我的魔术所以我觉得没问题
So, let's see, let's take a different row of people, starting with you.
好的让我们拭目以待重新选择一些人来说出数字 从你开始吧
I'll get five digits: one, two, three, four. Oh, I did this row already.
我需要一个五位数：1234 哦 人已经满了
Let's do the row before you, starting with you: one, two, three, four, five.
这次报数到你之前截止从你开始：12345
Call out a single digit that will be the five-digit number that I will try to square, go ahead.
每人喊出一位数字那我们将会有一个五位数 我会试着计算它的平方 开始吧
Five. Seven. Six. Eight. Three. 57,683 squared. Yuck.
五 七 六 八 三 57683 把它平方哦太讨厌了
Let me explain to you how I'm going to attempt this problem.
让我来告诉你我会怎么计算
I'm going to break the problem down into three parts.
我会把这个问题分成3部分
I'll do 57,000 squared, plus 683 squared, plus 57,000 times 683 times two.
我会先做57000的平方 然后加上683的平方加上57000乘以683乘以2
Add all those numbers together, and with any luck, arrive at the answer.
把所有的这些数字都加起来很快我们就能得到答案
Now, let me recap. Thank you.
再让我重新讲一遍 谢谢你
While I explain something else I know, that you can use, right?
好的我要需要解释一下其他东西我知道你的计算器可以算对吗？
While I do these calculations, you might hear certain words, as opposed to numbers, creep into the calculation.
当我在计算这些数字的时候 你可能会听到一些特定的不同于数字的单词加入了计算过程
Let me explain what that is.
让我来解释一下
This is a phonetic code, a mnemonic device that I use, that allows me to convert numbers into words.
这是一种语音编码 把它作为一个辅助记忆的仪器加以使用我把数字转化成单词
I store them as words, and later on retrieve them as numbers.
我以单词的形式将它们存储得到答案之后再把它们恢复成数字
I know it sounds complicated; it's not.
我知道这听起来非常复杂 但实际上恰恰相反
I don't want you to think you're seeing something out of "Rain Man."
我不希望你们看着表演像是“雨人”
There's definitely a method to my madness definitely, definitely. Sorry.
绝对有种办法来解释我疯狂的表演绝对有肯定有 抱歉
If you want to talk to me about ADHD afterwards, you can talk to me then.
如果你想找我谈论小儿多动症的话我很乐意谈谈
By the way, one last instruction, for my judges with the calculators
顺便提下 这是最后一个我和手持计算器的你们之间的挑战
you know who you are there is at least a 50 percent chance that I will make a mistake here.
你们知道自己是谁 我犯错的概率至少是50%
If I do, don't tell me what the mistake is;
如果算错了 不要告诉我哪里错了
just say, "you're close," or something like that, and I'll try and figure out the answer which could be pretty entertaining in itself.
只要说“你非常接近了”这样的话就行了我会努力算出这个有意思的答案
If, however, I am right, whatever you do, don't keep it to yourself, OK?
如果我对了的话无论如何 你都不要自己留着结果把它告诉大家好吗？
Make sure everybody knows that I got the answer right, because this is my big finish, OK.
确保每个人知道我得到了正确的答案因为这是我的收官之作
So, without any more stalling, here we go.
好的 接下来不会再有停顿我们开始吧
I'll start the problem in the middle, with 57 times 683.
我会先解决中间这个计算 用57乘以683
that's 38,760 plus 171, 38,760 plus 171 is 38,931.
用38760加上171 38760加上171是38931
cookie fission is 77,822.
‘cookie fission’ 是77822
That seems right, I'll go on. Cookie fission, OK.
好像没错 继续 'cookie fission’好的
Next, I do 57 squared, which is 3,249, so I can say, three billion.
接下来我要做57的平方 答案是3249也就是三十亿
Take the 249, add that to cookie, 249, oops, but I see a carry coming 249
用249加上'cookie' 哦，答案是'carry' 249
add that to cookie, 250 plus 77, is 327 million
加上 'cookie' 250加上77 等于3亿2千7百万
fission, fission, OK, finally, we do 683 squared,
答案是'fission' 好的最后我们做983的平方
that's 700 times 666, plus 17 squared is 466,489, rev up if I need it,
相当于700乘以666，再加上17的平方是466489
rev up, take the 466, add that to fission, to get, oh gee 328,489. Yeah! Good.
放大 用466 再加上'fission' 呃 答案是328489 太棒了 好的
Thank you very much. I hope you enjoyed mathemagics. Thank you.
非常感谢大家 希望你们喜欢我的数学魔术 感谢
