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现场表演“数学魔术”

Lightning calculation and other "mathemagic" | Arthur Benjamin

早上好 女士们先生们
Good morning, ladies and gentlemen.
我叫阿瑟 本杰明 我是一名‘数学魔术师’
My name is Art Benjamin, and I am a “mathemagician.”
我把我所热爱的数学跟魔术结合了起来
What that means is, I combine my loves of math and magic
我将其称为‘数学魔术’
to do something I call “mathemagics.”
在表演开始前我有个小问题想问下观众们
But before I get started, I have a quick question for the audience.
有人碰巧身边带着
By any chance, did anyone happen
计算器吗?
to bring with them this morning a calculator?
如果你带了计算器 麻烦举下手
Seriously, if you have a calculator with you, raise your hand.
举下手 你是不是举手了?
Raise your hand. Did your hand go up?
现在把他拿出来 拿出来 还有人也带了吗?
Now bring it out, bring it out. Anybody else?
我看到了 看到了 坐在后面的那个
I see, I see one way in the back.
是你 先生 现在共有三个了
You sir, that’s three.
这边的有谁带了?
And anybody on this side here?
好的 那边角落有一个
OK, over there on the aisle.
麻烦你们四个拿出你们的计算器
Would the four of you please bring out your calculators,
然后到台上来配合我表演
then join me up on stage.
大家掌声有请(这四位)
Let’s give them a nice round of applause.
(鼓掌)
(Applause)
好的
That’s right.
现在 由于我从没有机会检查这几台计算器
Now, since I haven’t had the chance to work with these calculators,
所以我必须确保它们都可以正常工作
I need to make sure that they are all working properly.
开始前 麻烦来个人给个2位数
Would somebody get us started by giving us a two-digit number, please?
给个2位数怎么样?
How about a two-digit number?
观众:22
Audience: 22.
阿瑟本杰明:22好的 另一个两位数呢?
AB: 22. And another two-digit number, sir?
观众:47
Audience: 47.
阿瑟本杰明:22 乘以47 确认下计算器是否得到的是1034
AB: Multiply 22 times 47, make sure you get 1,034,
如果不是那就是计算器坏了
or the calculators are not working.
你们都得到1034了是吧?1034?
Do all of you get 1,034? 1,034?
女士:不是
Volunteer: No.
阿瑟本杰明:她是594 让我们给予另外3位以热烈的掌声
AB: 594. Let’s give three of them a nice round of applause there.
(掌声)
(Applause)
以防万一 你愿意试试标准计算器吗?
Would you like to try a more standard calculator, just in case?
好的
OK, great.
接下来我要尝试做的是
What I’m going to try and do then —
我发现你得花点时间才能得到答案
I notice it took some of you a little bit of time to get your answer.
没关系
That’s OK.
我会给你个妙招 让你比计算器乘的更快
I’ll give you a shortcut for multiplying even faster on the calculator.
我们都知道一个数的平方
There is something called the square of a number,
就是把一个数和它自身相乘
which most of you know is taking a number and multiplying it by itself.
比如说 5的平方是什么?
For instance, five squared would be?
观众:25
Audience: 25.
阿瑟:25 大部分的计算器上 我们都这样做平方——
AB: 25. The way we can square on most calculators —
拿一个来示范下
let me demonstrate with this one —
像这样用一个数字 比如说5
is by taking the number, such as five,
按下“乘”再按一下“等于”
hitting “times” and then “equals,”
计算机上就会显示这个数的平方
and on most calculators that will give you the square.
在一些老式的RPN计算器上
On some of these ancient RPN calculators,
你会看到一个平方键
you’ve got an “x squared” button on it,
让你能算得更快
will allow you to do the calculation even faster.
现在我要尝试做的是在我的脑子里算平方
What I’m going to try and do now is to square, in my head,
4个2位数的数字
four two-digit numbers
比计算器还要快
faster than they can do on their calculators,
即使计算器用了快捷方式
even using the shortcut method.
我需要第二排的观众
What I’ll use is the second row this time,
需要请你们中的四位
and I’ll get four of you
每人喊出一个两位数字
to each yell out a two-digit number,
请你计算第一个数字的平方
and if you would square the first number,
请你计算二个 你第三个 你第四个
and if you would square the second, the third and the fourth,
我会和你比赛谁得到答案的速度快 好吗?
I will try and race you to the answer. OK?
来快一点 请说一个两位数字
So quickly, a two-digit number please.
观众:37
Audience: 37.
阿瑟 本杰明:37的平方 好的
Arthur Benjamin: 37 squared, OK.
观众:23
Audience: 23.
阿瑟:23的平方 好的
AB: 23 squared, OK.
观众:59
Audience: 59.
阿瑟:59的平方 好的 最后一个?
AB: 59 squared, OK, and finally?
观众:93
Audience: 93.
阿瑟:93的平方
AB: 93 squared.
请你们说出你的答案好吗?
Would you call out your answers, please?
志愿者:1369阿瑟:1369
Volunteer: 1369. AB: 1369.
志愿者:529阿瑟:529
Volunteer: 529. AB: 529.
志愿者:3481阿瑟:3481
Volunteer: 3481. AB: 3481.
志愿者:8649
Volunteer: 8649.
阿瑟:非常感谢
AB: Thank you very much.
(掌声)
(Applause)
让我们尝试更进一步
Let me try to take this one step further.
我这次将计算一些三位数字的平方
I’m going to try to square some three-digit numbers this time.
甚至不会把这些写下来
I won’t even write these down —
而是在他们喊出数字后直接喊出答案
I’ll just call them out as they’re called out to me.
我点到谁 谁就说一个三位数字
Anyone I point to, call out a three-digit number.
在台上的各位 帮忙确认下答案
Anyone on our panel, verify the answer.
如果是对的 请示意我
Just give some indication if it’s right.
先生请说一个三位数的数字
A three-digit number, sir, yes?
观众:987
Audience: 987.
阿瑟:987 的平方等于974169
AB: 987 squared is 974,169.
(笑声)
(Laughter)
阿瑟:对吗?好的
AB: Yes? Good.
下一个三位数
Another three-digit —
(掌声)
(Applause)
先生请说另外一个三位数字?
— another three-digit number, sir?
观众:457
Audience: 457.
阿瑟:457的平方是205849
AB: 457 squared is 205,849.
205849?
205,849?
对吗?
AB: Yes?
好的,另一个三位数字?
OK, another, another three-digit number, sir?
观众:321
Audience: 321.
321的平方是103041
AB: 321 is 103,041.
103041
103,041.
下一个三位数字
Yes? One more three-digit number please.
观众:722
Audience: Oh, 722.
722的平方是500 这个有点难
AB: 722 is 500, that’s a harder one.
是513284吗?
Is that 513,284?
是的
Volunteer: Yes.
好的 再来一个三位数字
AB: Yes? Oh, one more, one more three-digit number please.
观众:162
Audience: 162.
162的平方是26244
162 squared is 26,244.
志愿者:是的
Volunteer: Yes.
非常感谢
Thank you very much.
(掌声)
(Applause)
(掌声结束)
(Applause ends)
接下来我要挑战更有难度的
Let me try to take this one step further.
(笑声)
(Laughter)
这一次我要计算一个四位数的平方
I’m going to try to square a four-digit number this time.
这次你们可以慢慢来
You can all take your time on this;
因为我可能没有你们算的快
I will not beat you to the answer on this one,
但是我会尽量保证答案正确
but I will try to get the answer right.
为了使这个四位数产生的更随机一些 我将会请四个人
To make this a little bit more random, let’s take the fourth row this time,
比如说1234
let’s say, one, two, three, four.
你们中的每一个人说一个0到9之间的个数
If each of you would call out a single digit between zero and nine,
组成这个四位数 我再来计算它的平方
that will be the four-digit number that I’ll square.

Nine.

Seven.

Five.

Eight.
9758 请再给我一点时间
9,758, this will take me a little bit of time, so bear with me.
9500万
95 million —
(吸气)
(Sighs)
218564
218,564?
志愿者:对
Volunteer: Yes!
非常谢谢
AB: Thank you very much.
(掌声)
(Applause)
(掌声结束)
(Applause ends)
现在 我来挑战一个5位数的平方
Now, I would attempt to square a five-digit number —
我能做到
and I can —
但不幸的是 大部分计算器都不能做到
but unfortunately, most calculators cannot.
(笑声)
(Laughter)
八位数的计算量——难道你不讨厌这个吗?
Eight-digit capacity — don’t you hate that?
好的 既然我们已经达到了我们计算器的极限
So, since we’ve reached the limits of our calculators —
怎么啦?
what’s that?
你的计算器能够进行更高位的计算吗?
Does yours go higher?
志愿者:我不知道
Volunteer: I don’t know.
阿瑟:你的呢?
AB: Oh, yours does?
志愿者:我的可以做到阿瑟:好的 我一会儿再跟你说
Volunteer: I can probably do it. AB: I’ll talk to you later.
同时让我总结一下
In the meanwhile, let me conclude
我的第一部分魔术表演
the first part of my show by doing something a little trickier.
我们用屏幕上最大的数字8649
Let’s take the largest number on the board here, 8649.
都输入到你们计算器上了吗?
Would you each enter that on your calculator?
这次不要平方
And instead of squaring it this time,
我要你们用那个数去乘
I want you to take that number and multiply it
任意一个三位数
by any three-digit number that you want,
但不要告诉我你所乘的数是几
but don’t tell me what you’re multiplying by —
就乘任意一个三位数字
just multiply it by any random three-digit number.
所以你的最终结果
So you should have as an answer either
是一个六位到七位之间的数字
a six-digit or probably a seven-digit number.
你得到了几位数 六还是七?
How many digits do you have, six or seven?
七 你的呢?
Seven, and yours?
7?7?
Seven? Seven?
不确定?
And, uncertain.
7
Seven.
你们觉得有可能我会知道
Is there any possible way that I could know
你的七位数是几吗?
what seven-digit numbers you have?
说“不可能”
Say “No.”
(笑声)
(Laughter)
好的 现在我要做到不可能的事情
Good, then I shall attempt the impossible —
至少看上去是不太可能的事
or at least the improbable.
我希望你们每个人大声念出
What I’d like each of you to do is to call out for me
你们七位数中的任意六位
any six of your seven digits, any six of them,
用你喜欢的任何顺序都可以
in any order you’d like.
(笑声)
(Laughter)
一次念一位数
One digit at a time,
我将说出剩下的那个数字
I shall try and determine the digit you’ve left out.
从你的七位数开始吧
Starting with your seven-digit number,
请说出其中的任意六位
call out any six of them please.
志愿者:197042
Volunteer: 1, 9, 7, 0, 4, 2.
你是没说六吗?
AB: Did you leave out the number 6?
好的 好的 就是这个
Good, OK, that’s one.
你有一个七位的数字 请大声念出其中的任意六位
You have a seven-digit number, call out any six of them please.
志愿者:44875
Volunteer: 4, 4, 8, 7, 5.
我好像只听到了五位数字 等一下…是44875吗?
I think I only heard five numbers. I — wait — 44875 —
剩下的数字是不是六?
did you leave out the number 6?
是的 和她的数字一样
Same as she did, OK.
你有一个七位数字
You’ve got a seven-digit number —
大声并且清晰的念出其中的任意六位
call out any six of them loud and clear.
志愿者:079044
Volunteer: 0, 7, 9, 0, 4, 4.
剩下的那个数字是3吗?
I think you left out the number 3?
阿瑟本杰明:是3
AB: That’s three.
我猜对这些随机数字的几率是万分之一
The odds of me getting all four of these right by random guessing
也就是十的四次方
would be one in 10,000: 10 to the fourth power.
好的 请说出其中的任意六位
OK, any six of them.
(笑声)
(Laughter)
请打乱它们的顺序
Really scramble them up this time, please.
志愿者:263972
Volunteer: 2, 6, 3, 9, 7, 2.
阿瑟:剩下的一个是不是数字7?
Did you leave out the number 7?
掌声鼓励他们四个
And let’s give all four of these people a nice round of applause.
十分感谢
Thank you very much.
(掌声)
(Applause)
(掌声结束)
(Applause ends)
为了我接下来的数字–
For my next number —
(笑声)
(Laughter)
我已经给自己充满了电
while I mentally recharge my batteries,
还有一个问题要问大家
I have one more question for the audience.
有人恰巧知道
By any chance, does anybody here happen to know
自己生日那天是星期几吗?
the day of the week that they were born on?
如果你知道你是星期几出生的 请举手
If you think you know your birth day, raise your hand.
我们来看一下–从这位先生开始
Let’s see, starting with — let’s start with a gentleman first.
先生你是哪一年出生的?
What year was it, first of all?
这是我选择这位先生的原因
That’s why I pick a gentleman first.
观众:1953
Audience: 1953.
阿瑟: 1953年 哪个月?
1953, and the month?
观众:11月阿瑟:11月几号?
November what?
观众:23号阿瑟:那是星期一吗?
23rd — was that a Monday?
观众:是的
Audience: Yes.
好的 下一个?
Good. Somebody else?
我好像没有看到哪位女士举手
I haven’t seen any women’s hands up.
好的你是哪一年出生的?
OK, how about you, what year?
1949 哪一个月?
1949, and the month?
十月几号?
October what?
阿瑟: 5号 — 那是不是星期3?
Fifth — was that a Wednesday?
是的我现在要走到后面去找一位观众 您是什么时候生的?
Yes! I’ll go way to the back right now, how about you?
大声的说出来 您是哪一年出生的?
Yell it out, what year?
观众:1959
Audience: 1959.
1959好的哪一个月?
1959, OK — and the month?
观众:二月
Audience: February.
二月几号?
February what?
阿瑟: 6号,那是不是星期五?观众:是的。
Sixth — was that a Friday? Audience: Yes.
很好,在她后面的那个人要不要试试?
Good, how about the person behind her?
把你的生日年份大声的说出来
Call out, what year was it?
观众:1947阿瑟本杰明:1947年哪个月?
Audience: 1947. AB: 1947, and the month?
观众:五月阿瑟本杰明:五月几号?
Audience: May. AB: May what?
七号–那是星期三吗?
Seventh — would that be a Wednesday?
观众:是的阿瑟本杰明:非常感谢
Audience: Yes. AB: Thank you very much.
(掌声)
(Applause)
谁想要知道自己是星期几出生的?
Anybody here who’d like to know the day of the week they were born?
我可以帮助你们
We can do it that way.
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
Of course, I could just make up an answer and you wouldn’t know,
因此我预备了一下
so I come prepared for that.
我带来了一本日历
I brought with me a book of calendars.
这本日历是1800年的 在座的你们肯定都不知道
It goes as far back into the past as 1800, because you never know.
(笑声)
(Laughter)
先生 我不是故意盯着你看的正好你坐在这而已
I didn’t mean to look at you, sir — you were just sitting there.
(笑声)
(Laughter)
无论如何克里斯会帮主助我的
Anyway, Chris, you can help me out here, if you wouldn’t mind.
这是一本日历
This is a book of calendars.
谁想知道自己的生日在星期几?
Who wanted to know their birth day?
首先你是哪一年的?
What year was it, first of all?
观众:1966
Audience: 1966.
66–把日历本翻到1966年
66 — turn to the calendar with 1966.
哪个月?
And what month?
观众:四月阿瑟本杰明:四月几号?
Audience: April. AB: April what?
观众:十七号
Audience: 17th.
我知道那是星期天
I believe that was a Sunday.
克里斯能帮我证实吗?
Can you confirm, Chris?
克里斯亚当斯:是的
Chris Anderson: Yes.
阿瑟本杰明:克里斯我告诉你
AB: I’ll tell you what, Chris:
把你面前的这本日历
as long as you have that book in front of you,
翻翻二十世纪以外的年份
do me a favor, turn to a year outside of the 1900s,
无论是十九世纪或者是21世纪都可以
either into the 1800s or way into the 2000s —
这将对我是更大的挑战
that’ll be a much greater challenge for me.
阿瑟本杰明:你选择的是哪一年?克里斯亚当斯:1824年
AB: What year would you like? CA: 1824.
阿瑟: 1824 好的
AB: 1824, OK.
阿瑟本杰明:那个月?
AB: And what month?
克里斯亚当斯:六月
CA: June.
阿瑟本杰明:六月几号?克里斯亚当斯:六号
AB: June what? CA: Sixth.
阿瑟本杰明:那是星期天吗?
AB: Was that a Sunday?
克里斯亚当斯:是的阿瑟本杰明:那一天是多云天气吗?
CA: It was. AB: And it was cloudy.
(笑声)
(Laughter)
好的 非常感谢
Good, thank you very much.
(掌声)
(Applause)
(掌声结束)
(Applause ends)
我们现在来把思绪整理一下
But I’d like to wrap things up now
从刚才到现在的整个过程
by alluding to something from earlier in the presentation.
先前台上有位带10位数计算器的先生
There was a gentleman up here who had a 10-digit calculator.
他在哪儿 你能站起来示意一下吗?
Where is he, would you stand up,
十位数的男人?
10-digit guy?
好的 请站一会儿
OK, stand up for me just for a second,
好让我可以看到你在哪里
so I can see where you are.
好的 — 你也有一个10位数的计算器?
You have a 10-digit calculator, sir, as well?
好的 接下来我要做的事
OK, what I’m going to try and do, is to square in my head
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
a five-digit number requiring a 10-digit calculator.
为了使我的表演更加有意思
But to make my job more interesting for you, as well as for me,
我要把思考问题的过程大声的说出来
I’m going to do this problem thinking out loud.
你就可以听到
So you can actually, honestly hear
当我在计算一个数的平方的时候我是怎么想的
what’s going on in my mind while I do a calculation of this size.
现在我要对我的魔术师朋友雷纳德·格林说声对不起
Now, I have to apologize to our magician friend Lennart Green.
知道作为一个魔术师我们不应该泻露自己的秘密
I know as a magician we’re not supposed to reveal our secrets,
但是我并不怎么害怕
but I’m not too afraid
下个星期人们开始相互间表演我的魔术
that people are going to start doing my show next week, so —
所以我觉得没问题
I think we’re OK.
(笑声)
(Laughter)
(掌声)
(Applause)
好的让我们拭目以待
So, let’s see,
重新选择一些人来说出数字 从你开始吧
let’s take a different row of people, starting with you.
我需要一个五位数:1234
I’ll get five digits: one, two, three, four.
哦 人已经满了
Oh, I did this row already.
这次报数到你之前截止
Let’s do the row before you,
从你开始:12345
starting with you: one, two, three, four, five.
每人喊出一位数字
Call out a single digit —
那我们将会有一个五位数 我会试着计算它的平方 开始吧
that will be the five-digit number that I will try to square, go ahead.

Five.

Seven.

Six.

Eight.

Three.
57683
57,683 —
把它平方
squared.
哦太讨厌了
Yuck.
让我来告诉你我会怎么计算
Let me explain to you how I’m going to attempt this problem.
我会把这个问题分成3部分
I’m going to break the problem down into three parts.
我会先做57000的平方
I’ll do 57,000 squared,
然后加上683的平方
plus 683 squared,
加上57000乘以683乘以2
plus 57,000 times 683 times two.
把所有的这些数字都加起来
Add all those numbers together,
很快我们就能得到答案
and with any luck, arrive at the answer.
再让我重新讲一遍
Now, let me recap.
(笑声)
(Laughter)
谢谢你
Thank you.
(笑声)
(Laughter)
好的我要需要解释一下其他东西
While I explain something else —
(笑声)
(Laughter)
我知道你的计算器可以算对吗?
— I know, that you can use, right?
(笑声)
(Laughter)
当我在计算这些数字的时候
While I do these calculations,
你可能会听到一些特定的不同于数字的单词
you might hear certain words,
加入了计算过程
as opposed to numbers, creep into the calculation.
让我来解释一下
Let me explain what that is.
这是一种语音编码
This is a phonetic code,
把它作为一个辅助记忆的仪器加以使用
a mnemonic device that I use,
我把数字转化成单词
that allows me to convert numbers into words.
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 store them as words, and later on retrieve them as numbers.
我知道这听起来非常复杂 但实际上恰恰相反
I know it sounds complicated; it’s not.
我不希望你们看着表演像是“雨人”
I don’t want you to think you’re seeing something out of “Rain Man.”
(笑声)
(Laughter)
绝对有种办法来解释我疯狂的表演 —
There’s definitely a method to my madness —
绝对有肯定有
definitely, definitely.
抱歉
Sorry.
(笑声)
(Laughter)
如果你想找我谈论小儿多动症的话
If you want to talk to me about ADHD afterwards,
我很乐意谈谈
you can talk to me then.
顺便提下 这是最后一个
By the way, one last instruction,
我和手持计算器的你们之间的挑战
for my judges with the calculators —
你们知道自己是谁
you know who you are —
我犯错的概率至少是50%
there is at least a 50 percent chance that I will make a mistake here.
如果算错了 不要告诉我哪里错了
If I do, don’t tell me what the mistake is;
只要说“你非常接近了”这样的话就行了
just say, “you’re close,” or something like that,
我会努力算出这个
and I’ll try and figure out the answer —
有意思的答案
which could be pretty entertaining in itself.
如果我对了的话
If, however, I am right,
无论如何 你都不要自己留着结果把它告诉大家好吗?
whatever you do, don’t keep it to yourself, OK?
(笑声)
(Laughter)
确保每个人知道我得到了正确的答案
Make sure everybody knows that I got the answer right,
因为这是我的收官之作
because this is my big finish, OK.
好的 接下来不会再有停顿
So, without any more stalling,
我们开始吧
here we go.
我会先解决中间这个计算 用57乘以683
I’ll start the problem in the middle, with 57 times 683.
57乘以68是3400再加上476是3876
57 times 68 is 3,400, plus 476 is 3876,
用38760加上171
that’s 38,760 plus 171,
38760加上171是38931
38,760 plus 171 is 38,931.
38931:它的两倍是77862
38,931; double that to get 77,862.
77862变成‘cookie fission’
77,862 becomes cookie fission,
‘cookie fission’ 是77822
cookie fission is 77,822.
好像没错 继续 ‘cookie fission’好的
That seems right, I’ll go on. Cookie fission, OK.
接下来我要做57的平方 答案是3249
Next, I do 57 squared, which is 3,249, so I can say,
也就是三十亿
three billion.
用249加上’cookie’
Take the 249, add that to cookie, 249,
哦,答案是’carry’
oops, but I see a carry coming —
249 —
249 —
加上 ‘cookie’ 250加上77
add that to cookie, 250 plus 77,
等于3亿2千7百万 —
is 327 million —
答案是’fission’ 好的最后我们做983的平方
fission, fission, OK, finally, we do 683 squared,
相当于700乘以666,再加上17的平方
that’s 700 times 666, plus 17 squared
是466489
is 466,489, rev up if I need it,
放大 用466
rev up, take the 466,
再加上’fission’
add that to fission, to get,
呃…
oh gee —
答案是328489
328,489.
观众:太棒了阿瑟本杰明:好的
Audience: Yeah! AB: Good.
非常感谢大家
Thank you very much.
(掌声)
(Applause)
希望你们喜欢我的数学魔术
I hope you enjoyed mathemagics.
感谢
Thank you.
(掌声)
(Applause)

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视频概述

该视频是“数学魔术”的现场表演,魔术师挑战计算器的速度和位数极限,演出最后揭秘了自己计算平方数的方法

听录译者

收集自网络

翻译译者

与光同尘

审核员

知易行难

视频来源

https://www.youtube.com/watch?v=M4vqr3_ROIk

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