Lightning calculation and other "mathemagic" | Arthur Benjamin

翻译人员: jianfeng liu 校对人员: Cai Yu

Good morning, ladies and gentlemen.

早上好，先生们女士们。

My name is Art Benjamin, and I am a "mathemagician."

我叫阿瑟 本杰明，我是一名‘数学魔术师。’

What that means is, I combine my loves of math and magic

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。’

to do something I call "mathemagics."

给它取名叫‘数学魔术。’

But before I get started, I have a quick question for the audience.

在表演开始前我有个问题想问下观众们。

By any chance, did anyone happen

有没有人今天早上恰巧

to bring with them this morning a calculator?

有带计算器过来的？

Seriously, if you have a calculator with you, raise your hand.

说真的，如果你有带计算器的话，举起你的手，举起你的手。

Raise your hand. Did your hand go up?

我 -- 是 -- 你举的手吗？

Now bring it out, bring it out. Anybody else?

拿出来，把它拿出来。还有谁带了？

I see, I see one way in the back.

我看到，我看到后面有一个。

You sir, that's three.

是你，先生，共有三个了。

And anybody on this side here?

这边的有谁带了？

OK, over there on the aisle.

好的，在过道旁边的那位。

Would the four of you please bring out your calculators,

请你们4位带着计算器到台上来。

then join me up on stage.

Let's give them a nice round of applause.

让我们给这些自愿者予热烈的掌声。

(Applause)

（掌声）

That's right.

很好。因为我还...

Now, since I haven't had the chance to work with these calculators,

没用过这些计算器，所以现在我要确认下

I need to make sure that they are all working properly.

这些计算器是否能正常运算。

Would somebody get us started by giving us a two-digit number, please?

有谁能给出一个...

2位数的数字作为开始？

How about a two-digit number?

给个2位数的数字？

Audience: 22.

观众：22

AB: 22. And another two-digit number, sir?

阿瑟 本杰明：22。 再来一个，先生？

Audience: 47.

观众：47。

AB: Multiply 22 times 47, make sure you get 1,034,

阿瑟：把22 乘以47，确认下计算器是否得到1034，

or the calculators are not working.

否则它工作不正常。你们都算出1034了吗? 1034?

Do all of you get 1,034? 1,034?

Volunteer: No.

女士：不是

AB: 594. Let's give three of them a nice round of applause there.

阿瑟: 是594。 让我们给那边的3位予热烈的掌声。

(Applause)

（掌声）

Would you like to try a more standard calculator, just in case?

你要换个标准的计算器吗，以防万一？

好的，很好

OK, great.

What I'm going to try and do then --

接下来我要做的 --

I notice it took some of you a little bit of time to get your answer.

我想你们中有人会花点时间才能得到答案。

That's OK.

没有关系。我会帮你们算出乘法

I'll give you a shortcut for multiplying even faster on the calculator.

快过计算器。

There is something called the square of a number,

有种乘法是平方一个数。

which most of you know is taking a number and multiplying it by itself.

也就是众所周知的把一个数

乘以它本身。

For instance, five squared would be?

举个例子，5的平方会等于？

Audience: 25.

观众：25。

AB: 25. The way we can square on most calculators --

阿瑟: 25。 现在，我们计算平方的方式在大多计算器上 --

let me demonstrate with this one --

还是让我来演示下这个 --

is by taking the number, such as five,

选个数字，比如说5.

hitting "times" and then "equals,"

点击 ‘乘号’然后 ‘等号。’

and on most calculators that will give you the square.

然后大多数计算器会算出平方。

On some of these ancient RPN calculators,

在一些老式的RPN 计算器上，

you've got an "x squared" button on it,

会有一个‘X 平方’的按键。

will allow you to do the calculation even faster.

用这个快捷键会算得更快。

What I'm going to try and do now is to square, in my head,

现在我要尝试的是在我的脑子里算平方，

four two-digit numbers

4个2位数的数字

faster than they can do on their calculators,

快过他们用计算器，即便是用快捷键。

even using the shortcut method.

What I'll use is the second row this time,

这次我选第二排的4个观众 --

and I'll get four of you

1个，2个，3个，4个 -- 每人喊出一个2位数的数字，

to each yell out a two-digit number,

and if you would square the first number,

然后你来平方第一个数字，

and if you would square the second, the third and the fourth,

你来平方第二个，以此类推，第三个和第四个。

我们来比看谁算得快，好吗？

I will try and race you to the answer. OK?

So quickly, a two-digit number please.

那么赶快 -- 请给出一个2位数的数字。

Audience: 37.

观众：37。

Arthur Benjamin: 37 squared, OK.

阿瑟：37的平方，好的。

Audience: 23.

观众：23。

AB: 23 squared, OK.

阿瑟：23的平方，好的。

Audience: 59.

AB: 59 squared, OK, and finally?

观众：59。

阿瑟：59的平方，好的，最后一个？

Audience: 93.

观众：93。

AB: 93 squared.

Would you call out your answers, please?

阿瑟：93的平方。你们可以大声说出答案了吗？

Volunteer: 1369. AB: 1369.

女士: 1369。 阿瑟: 1369。

Volunteer: 529. AB: 529.

女士: 529。

阿瑟：529。

Volunteer: 3481. AB: 3481.

男士：3481。

阿瑟：3481。

Volunteer: 8649.

男士：8649。

AB: Thank you very much.

阿瑟：非常感谢。

(Applause)

（掌声）

Let me try to take this one step further.

我再来试下更有难度的。

I'm going to try to square some three-digit numbers this time.

我接下来要计算一些3位数数字的平方。

I won't even write these down --

我甚至不把它们写下来 --

I'll just call them out as they're called out to me.

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.

被我指到的人，请喊出一个3位数的数字。

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.

如果正确的话给下提示。

A three-digit number, sir, yes?

给一个3位数，这位先生，好吗？

Audience: 987.

观众：987。

AB: 987 squared is 974,169.

阿瑟：987 的平方等于974169。

(Laughter)

（笑声）

AB: Yes? Good.

对吧？好的。

Another three-digit --

再来，再来个3位数 --

(Applause)

（掌声）

-- 再来个3位数数字，这位先生？

-- another three-digit number, sir?

Audience: 457.

观众：457。

AB: 457 squared is 205,849.

阿瑟：457的平方等于205849。

205,849?

205849？

AB: Yes?

对吗？

OK, another, another three-digit number, sir?

好的，再来，再来个3位数数字，这位先生？

Audience: 321.

AB: 321 is 103,041.

观众：321。

阿瑟：321 等于103041。 103041。

103,041.

对吗？请再喊出一个3位数数字。

Yes? One more three-digit number please.

观众：哦，722。

Audience: Oh, 722.

AB: 722 is 500, that's a harder one.

阿瑟：722等于500 -- 哦，这个有点难。

Is that 513,284?

是等于513284吗？

Volunteer: Yes.

女士：没错。

AB: Yes? Oh, one more, one more three-digit number please.

阿瑟：没错吗？哦，再来个，请再来个3位数数字。

Audience: 162.

观众：162。

162 squared is 26,244.

162的平方等于26244。

Volunteer: Yes.

非常感谢。

Thank you very much.

(Applause)

（掌声）

(Applause ends)

Let me try to take this one step further.

我再来试下更有难度的。

(Laughter)

（笑声）

I'm going to try to square a four-digit number this time.

我这次要计算个4位数的平方。

You can all take your time on this;

这次你们可以慢慢来；这次我不会抢在你们前面回答，

I will not beat you to the answer on this one,

但我会尽力给出正确的答案。

but I will try to get the answer right.

为了看起来更随机点，这次让我们选第四排的，

To make this a little bit more random, let's take the fourth row this time,

那我们开始吧，1个，2个，3个，4个。

let's say, one, two, three, four.

If each of you would call out a single digit between zero and nine,

你们每个人大声说出一个数字从0到9，

那样我就有个4位数可以计算。

that will be the four-digit number that I'll square.

观众：9。

Nine.

阿瑟：9。

Seven.

观众：7。 阿瑟: 7。

Five.

观众：5。阿瑟：5。

观众：8。阿瑟:8。

Eight.

9,758, this will take me a little bit of time, so bear with me.

9758, 这个要花点时间，所以请大家耐心。

95 million --

是95218564吗？

(Sighs)

218,564?

Volunteer: Yes!

女士：是的。

AB: Thank you very much.

阿瑟: 非常感谢。

(Applause)

（掌声）

(Applause ends)

Now, I would attempt to square a five-digit number --

现在，我很想试着平方一个5位数 --

and I can --

我可以 --

but unfortunately, most calculators cannot.

但可惜大多数计算器不能。

(Laughter)

（笑声）

Eight-digit capacity -- don't you hate that?

最多只能8位 -- 你们不讨厌吗？

So, since we've reached the limits of our calculators --

好吧，既然我们已经超越计算器的计算能力 --

what's that?

什么？你的可以 --

Does yours go higher?

女士：我不知道。

阿瑟：你的可以算吗？

Volunteer: I don't know.

AB: Oh, yours does?

哦 -- 是你的可以吗？

Volunteer: I can probably do it. AB: I'll talk to you later.

男士：好像可以。

阿瑟：我等会儿再找你。

In the meanwhile, let me conclude

与此同时，让我来用些更巧妙的把戏来小结

the first part of my show by doing something a little trickier.

我的第一部分表演。

Let's take the largest number on the board here, 8649.

让我们用这块板上最大的一个数字，8649。

Would you each enter that on your calculator?

你们每个人可否在计算器上输入这个数？

And instead of squaring it this time,

这次不要平方，

I want you to take that number and multiply it

我要你们用那个数乘以

by any three-digit number that you want,

任何3位数，

but don't tell me what you're multiplying by --

但不要告诉我你所乘的数 --

just multiply it by any random three-digit number.

只要乘以任何一个3位数。

So you should have as an answer either

那么你得到的答案可能会是

a six-digit or probably a seven-digit number.

一个六位数或者七位数。

How many digits do you have, six or seven?

你的是几位，6还是7？

Seven, and yours?

7，你的呢？女士：7。

Seven? Seven?

阿瑟：7？7吗？

不确定。

And, uncertain.

Seven.

男士：是的。

Is there any possible way that I could know

阿瑟: 7。 有没有办法会让我知道

what seven-digit numbers you have?

你所得到的7位数？应该不可能。

Say "No."

(Laughter)

（笑声）

Good, then I shall attempt the impossible --

很好。那我应该来挑战下这个不可能 --

or at least the improbable.

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

接下来我想让你们告诉我

any six of your seven digits, any six of them,

7位数里面的任意6位数字。

in any order you'd like.

任意顺序都可以。

(Laughter)

（笑声）

每次一位数，我会试着算出剩下的数。

One digit at a time,

I shall try and determine the digit you've left out.

那么，从你开始吧。

Starting with your seven-digit number,

请喊出任意6位数字。

call out any six of them please.

Volunteer: 1, 9, 7, 0, 4, 2.

女士：1，哦，197042。

AB: Did you leave out the number 6?

阿瑟：你是不是漏说了6？

Good, OK, that's one.

女士：是的，阿瑟:很好，好的，没错。

You have a seven-digit number, call out any six of them please.

你的是7位数，请大声说出其中任意的六个数。

女士：44875。

Volunteer: 4, 4, 8, 7, 5.

阿瑟: 我好像只听到5个数字。我 -- 等下 -- 44875 --

I think I only heard five numbers. I -- wait -- 44875 --

did you leave out the number 6?

你是不是漏说了数字6？

Same as she did, OK.

女士：是的。 阿瑟:跟她的一样，好的。你得到的是一个7位数 --

You've got a seven-digit number --

大声清晰地说出其中的任意6个数字。

call out any six of them loud and clear.

Volunteer: 0, 7, 9, 0, 4, 4.

男：079044.

I think you left out the number 3?

阿瑟:我想你漏说了数字3？

AB: That's three.

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

The odds of me getting all four of these right by random guessing

将会是万分之一。10的负四次方。

would be one in 10,000: 10 to the fourth power.

OK, any six of them.

好了，任意6位数字。

(Laughter)

Really scramble them up this time, please.

这次请把它们搅乱一下。

Volunteer: 2, 6, 3, 9, 7, 2.

男：263972。

Did you leave out the number 7?

阿瑟:你是不是漏说了数字7？

And let's give all four of these people a nice round of applause.

现在让我们给这四位观众予热烈的掌声。

非常感谢。

Thank you very much.

(Applause)

(Applause ends)

我的下一个数 --

For my next number --

(Laughter)

（笑声）

while I mentally recharge my batteries,

在给我脑袋充电期间

我有个问题要问下观众们。

I have one more question for the audience.

By any chance, does anybody here happen to know

有可能的话，在场的有谁刚好知道

the day of the week that they were born on?

你生日的那天是星期几？

If you think you know your birth day, raise your hand.

如果你觉得知道的话，举下手。

Let's see, starting with -- let's start with a gentleman first.

让我们看看，从 -- 从男士开始，

What year was it, first of all?

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。

That's why I pick a gentleman first.

哪年？

Audience: 1953.

观众：1953。

1953, and the month?

阿瑟: 1953，哪个月？

November what?

观众：11月。阿瑟：11月几号？

观众:23号。

23rd -- was that a Monday?

阿瑟: 23号 -- 是不是星期一？观众：是的。

Audience: Yes.

没错，很好。还有人吗？还有谁想要 --

Good. Somebody else?

I haven't seen any women's hands up.

呃，还没，我还没看到有女士举手。

OK, how about you, what year?

啊，很好，你呢，哪年？

1949, and the month?

观众：1949. 阿瑟: 1949， 哪月？

October what?

观众： 十月。阿瑟: 十月几号？

观众： 5号。

Fifth -- was that a Wednesday?

阿瑟: 5号 -- 那是不是星期3？

Yes! I'll go way to the back right now, how about you?

没错，现在我从后面选，你怎样？

Yell it out, what year?

大声说出来，哪年？观众：1959。

Audience: 1959.

1959, OK -- and the month?

阿瑟:1959， 好的 -- 哪月？

观众：二月。

Audience: February.

February what?

阿瑟: 2月几号？ 观众：6号。

Sixth -- was that a Friday? Audience: Yes.

阿瑟: 6号，那是不是星期五？观众：是的。

Good, how about the person behind her?

很好，在她后面的那个人要不要试试？

Call out, what year was it?

喊出 -- 哪一年？

Audience: 1947. AB: 1947, and the month?

观众：1947. 阿瑟: 1947，哪月？

Audience: May. AB: May what?

观众：5月。阿瑟: 5月几号？

Seventh -- would that be a Wednesday?

观众：7号。阿瑟:7号 -- 那是不是星期三？

Audience: Yes. AB: Thank you very much.

观众：是的。

阿瑟:非常感谢。

(Applause)

（掌声）

Anybody here who'd like to know the day of the week they were born?

在场的哪一位想知道自己的生日是在星期几的？

We can do it that way.

我们也可以这么做。

Of course, I could just make up an answer and you wouldn't know,

当然，这样的话我乱编一个你也不会知道，

所以我事先有准备了下。

so I come prepared for that.

I brought with me a book of calendars.

我带了一个日历。

It goes as far back into the past as 1800, because you never know.

可以查回到1800年，谁知道会不会用得着呢？哈。

(Laughter)

（笑声）

I didn't mean to look at you, sir -- you were just sitting there.

我不是故意看着你，先生 --

你只是恰巧坐在那边。

(Laughter)

Anyway, Chris, you can help me out here, if you wouldn't mind.

不管怎样，Chris,你可以帮我下，如果你不介意的话。

This is a book of calendars.

这是一本日历，然后我会问 --

Who wanted to know their birth day?

是谁想知道他的生日的，是你吗，先生？好的。

What year was it, first of all?

先问下哪一年？

Audience: 1966.

观众：1966。

66 -- turn to the calendar with 1966.

阿瑟: 66年 -- 翻到日历的1966年 --

And what month?

阿瑟: 哪月？

Audience: April. AB: April what?

观众：4月。 阿瑟: 4月几号？

Audience: 17th.

观众：17号。 阿瑟: 17号 -- 我确信那是个星期天。

I believe that was a Sunday.

Can you confirm, Chris?

你能否确认下，Chris？

Chris: 是的。阿瑟: 很好，我跟你说

Chris Anderson: Yes.

AB: I'll tell you what, Chris:

chris，用你面前的那本书，

as long as you have that book in front of you,

do me a favor, turn to a year outside of the 1900s,

帮我下忙，翻到1900s以外的，

either into the 1800s or way into the 2000s --

翻到页面1800s 或者2000s --

that'll be a much greater challenge for me.

那样对我来说会更有挑战性。

AB: What year would you like? CA: 1824.

你喜欢哪年，Chris？

Chris: 1824.

AB: 1824, OK.

阿瑟: 1824, 好的。

AB: And what month?

哪月呢？Chris: 六月。

CA: June.

哪月呢？Chris: 六月

AB: June what? CA: Sixth.

AB: Was that a Sunday?

6号 -- 是不是星期天？

CA: It was. AB: And it was cloudy.

Chris:没错。 阿瑟:并且是阴天。

(Laughter)

Good, thank you very much.

很好，非常感谢。

(Applause)

（掌声）

(Applause ends)

But I'd like to wrap things up now

但是现在我想来个总结

by alluding to something from earlier in the presentation.

再次回到

我之前的表演

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,

现在在哪里，你能站起来一下吗？

10-digit guy?

10位数的伙计？

OK, stand up for me just for a second,

好的，请站起来下，

so I can see where you are.

好让我可以看到你在哪里。

You have a 10-digit calculator, sir, as well?

好，哦，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

很好，我接下来要做的是，心算平方

a five-digit number requiring a 10-digit calculator.

一个5位数的数字，这需要个10位数的计算器。

But to make my job more interesting for you, as well as for me,

为了给大家和我自己增加点乐趣，

I'm going to do this problem thinking out loud.

我会把心算过程

大声的念出来。

So you can actually, honestly hear

这样你们就可以实际上听到

what's going on in my mind while I do a calculation of this size.

我心算时的具体过程

当我计算这样大的数字的时候。

Now, I have to apologize to our magician friend Lennart Green.

现在，我得向我们的魔术师朋友 Lennart Green道下歉。

I know as a magician we're not supposed to reveal our secrets,

我知道作为一个魔术师本不应该泄漏我们的秘密，

but I'm not too afraid

但我并不是很担心其他人

that people are going to start doing my show next week, so --

会在下个星期开始模仿我的表演，所以 --

I think we're OK.

我想没有什么问题。

(Laughter)

(Applause)

So, let's see,

那么，让我们开始吧，

let's take a different row of people, starting with you.

让我们选另一排的观众，就从你开始吧。

I'll get five digits: one, two, three, four.

我将得到5位数：1，2，3，4 --

Oh, I did this row already.

哦，我已经选过这排了。那就选你前面的这排观众，

Let's do the row before you,

starting with you: one, two, three, four, five.

从你开始先生：1，2，3，4，5。

Call out a single digit --

（每个人）喊出一个一位数 -- 这样就组成一个5位数的数字

that will be the five-digit number that I will try to square, go ahead.

我会心算这个数的平方。开始吧。

观众：5。阿瑟：5。

Five.

Seven.

观众：7。阿瑟：7。

观众：6。阿瑟：6。

Six.

观众：8。阿瑟：8。

Eight.

Three.

观众：3。阿瑟：3。

57,683 --

57683

squared.

Yuck.

平方。惨啦。

Let me explain to you how I'm going to attempt this problem.

让我来给大家解释下

我接下来要怎么算。

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,

我先算57000的平方，

plus 683 squared,

然后加上683的平方，

plus 57,000 times 683 times two.

加上57000乘以

683乘以2。

Add all those numbers together,

把所有的结果加起来，

and with any luck, arrive at the answer.

幸运的话，就可以得出答案。

Now, let me recap.

现在，让我先想一下（合上笔帽）。（一语双关）

(Laughter)

Thank you.

谢谢。

(Laughter)

While I explain something else --

当我讲一些其他的 --

(Laughter)

-- I know, that you can use, right?

-- 我知道，你可以利用这个，对吧？

(Laughter)

While I do these calculations,

当我心算的时候，在计算的过程中

you might hear certain words,

你会听到某些词语，

来对应一些数字，融入到计算当中。

as opposed to numbers, creep into the calculation.

Let me explain what that is.

让我来解释下是什么。

This is a phonetic code,

这是语音代码，

a mnemonic device that I use,

相当于一个记忆用的设备，

that allows me to convert numbers into words.

这个设备能帮我把数字转换成单词。

I store them as words, and later on retrieve them as numbers.

我先存为单词，然后再转回成数字。

I know it sounds complicated; it's not.

我知道这听起来有点复杂；（实际上）一点也不 --

I don't want you to think you're seeing something out of "Rain Man."

我不想让你们以为自己看到了‘雨人’。

（笑声）

(Laughter)

There's definitely a method to my madness --

这其中绝对有种方法来解释我疯狂的表演 --

definitely, definitely.

一定的，一定的。不好意思。

Sorry.

(Laughter)

（笑声）

If you want to talk to me about ADHD afterwards,

如果你想找我谈论小儿多动症的话，

you can talk to me then.

你可以找我谈谈。好吧 --

By the way, one last instruction,

顺便提下，

for my judges with the calculators --

给我那个有计算器的裁判最后一个说明

you know who you are --

至少有一半的机会

there is at least a 50 percent chance that I will make a mistake here.

我会犯错。

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,

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 --

and I'll try and figure out the answer --

这样会更有趣点。

which could be pretty entertaining in itself.

If, however, I am right,

如果，我对了的话，

whatever you do, don't keep it to yourself, OK?

无论如何，你都不要自己留着结果，好吗？

(Laughter)

（笑声）

Make sure everybody knows that I got the answer right,

确保让大家知道我算对了，

因为这对我来说是个完美的收场。

because this is my big finish, OK.

So, without any more stalling,

好吧，闲话少说，

here we go.

我们开始吧。

I'll start the problem in the middle, with 57 times 683.

我会从问题的中间部分开始，先算57乘以683。

现在，57乘以68等于3400，加上476等于3876，

57 times 68 is 3,400, plus 476 is 3876,

那是38760加上171，

that's 38,760 plus 171,

38,760 plus 171 is 38,931.

38760加上171等于38931。

38,931; double that to get 77,862.

38931；翻一倍得到77862。

77,862 becomes cookie fission,

77862变成‘cookie fission’，

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,

接下来，我算57的平方等于3249，那么应该是，

three billion.

30亿。用249加上'cookie',249，

Take the 249, add that to cookie, 249,

oops, but I see a carry coming --

哦，但是我看到有一个包过来了 --

249 --

249 --

add that to cookie, 250 plus 77,

加上 'cookie'，250加上77，

is 327 million --

等于3亿2千7百万 --

fission, fission, OK, finally, we do 683 squared,

'fission, fission,' 好的，总算可以算683的平方了，

that's 700 times 666, plus 17 squared

相当于700乘以666，再加上17的平方

is 466,489, rev up if I need it,

等于466489，我需要的时候转起来，

rev up, take the 466,

放大，用466，

add that to fission, to get,

加上'fission'，得到，

哦老天 --

oh gee --

328,489.

328489。

Audience: Yeah! AB: Good.

观众：没错！

阿瑟：很好。

Thank you very much.

（掌声）

(Applause)

非常感谢。

I hope you enjoyed mathemagics.

希望你们能喜欢数学魔术。谢谢大家。

Thank you.

(Applause)

（掌声）