Good morning, ladies and gentlemen. My name is Art Benjamin, and I am a "mathemagician." What that means is, I combine my loves of math and magic to do something I call "mathemagics."
早上好,先生们女士们。 我叫阿瑟 本杰明,我是一名‘数学魔术师。’ 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。’ 给它取名叫‘数学魔术。’
But before I get started, I have a quick question for the audience. By any chance, did anyone happen to bring with them this morning a calculator? Seriously, if you have a calculator with you, raise your hand. Raise your hand. Did your hand go up? Now bring it out, bring it out. Anybody else? I see, I see one way in the back. You sir, that's three. And anybody on this side here? OK, over there on the aisle. Would the four of you please bring out your calculators, then join me up on stage. Let's give them a nice round of applause.
在表演开始前我有个问题想问下观众们。 有没有人今天早上恰巧 有带计算器过来的? 说真的,如果你有带计算器的话,举起你的手,举起你的手。 我 -- 是 -- 你举的手吗? 拿出来,把它拿出来。还有谁带了? 我看到,我看到后面有一个。 是你,先生,共有三个了。 这边的有谁带了? 好的,在过道旁边的那位。 请你们4位带着计算器到台上来。 让我们给这些自愿者予热烈的掌声。 (掌声)
(Applause)
很好。因为我还...
That's right. Now, since I haven't had the chance to work with these calculators, I need to make sure that they are all working properly. Would somebody get us started by giving us a two-digit number, please? How about a two-digit number?
没用过这些计算器,所以现在我要确认下 这些计算器是否能正常运算。 有谁能给出一个... 2位数的数字作为开始? 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, or the calculators are not working. Do all of you get 1,034? 1,034?
阿瑟:把22 乘以47,确认下计算器是否得到1034, 否则它工作不正常。你们都算出1034了吗? 1034?
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? OK, great. 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. I'll give you a shortcut for multiplying even faster on the calculator. There is something called the square of a number, which most of you know is taking a number and multiplying it by itself. For instance, five squared would be?
你要换个标准的计算器吗,以防万一? 好的,很好 接下来我要做的 -- 我想你们中有人会花点时间才能得到答案。 没有关系。我会帮你们算出乘法 快过计算器。 有种乘法是平方一个数。 也就是众所周知的把一个数 乘以它本身。 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 -- let me demonstrate with this one -- is by taking the number, such as five, hitting "times" and then "equals," and on most calculators that will give you the square. 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. What I'm going to try and do now is to square, in my head, four two-digit numbers faster than they can do on their calculators, even using the shortcut method. 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, and if you would square the first number, and if you would square the second, the third and the fourth, I will try and race you to the answer. OK? So quickly, a two-digit number please.
阿瑟: 25。 现在,我们计算平方的方式在大多计算器上 -- 还是让我来演示下这个 -- 选个数字,比如说5. 点击 ‘乘号’然后 ‘等号。’ 然后大多数计算器会算出平方。 在一些老式的RPN 计算器上, 会有一个‘X 平方’的按键。 用这个快捷键会算得更快。 现在我要尝试的是在我的脑子里算平方, 4个2位数的数字 快过他们用计算器,即便是用快捷键。 这次我选第二排的4个观众 -- 1个,2个,3个,4个 -- 每人喊出一个2位数的数字, 然后你来平方第一个数字, 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? 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.
观众:59。
AB: 59 squared, OK, and finally?
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。
Volunteer: 3481. AB: 3481.
阿瑟:529。
男士:3481。
Volunteer: 8649.
阿瑟:3481。
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. I'm going to try to square some three-digit numbers this time. I won't even write these down -- I'll just call them out as they're called out to me. Anyone I point to, call out a three-digit number. Anyone on our panel, verify the answer. Just give some indication if it's right. A three-digit number, sir, yes?
我再来试下更有难度的。 我接下来要计算一些3位数数字的平方。 我甚至不把它们写下来 -- 而是在他们喊出数字后直接喊出答案。 被我指到的人,请喊出一个3位数的数字。 在台上的各位,帮忙确认下答案。 如果正确的话给下提示。 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. Another three-digit --
对吧?好的。 再来,再来个3位数 --
(Applause) -- another three-digit number, sir?
(掌声) -- 再来个3位数数字,这位先生?
Audience: 457.
观众:457。
AB: 457 squared is 205,849. 205,849? AB: Yes? OK, another, another three-digit number, sir?
阿瑟:457的平方等于205849。 205849? 对吗? 好的,再来,再来个3位数数字,这位先生?
Audience: 321.
观众:321。
AB: 321 is 103,041. 103,041. Yes? One more three-digit number please.
阿瑟:321 等于103041。 103041。 对吗?请再喊出一个3位数数字。 观众:哦,722。
Audience: Oh, 722.
阿瑟:722等于500 -- 哦,这个有点难。
AB: 722 is 500, that's a harder one. Is that 513,284?
是等于513284吗? 女士:没错。
Volunteer: Yes.
阿瑟:没错吗?哦,再来个,请再来个3位数数字。
AB: Yes? Oh, one more, one more three-digit number please.
观众:162。
Audience: 162. 162 squared is 26,244.
162的平方等于26244。
Volunteer: Yes.
非常感谢。
Thank you very much.
(掌声)
(Applause)
(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. 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. To make this a little bit more random, let's take the fourth row this time, let's say, one, two, three, four. 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.
我这次要计算个4位数的平方。 这次你们可以慢慢来;这次我不会抢在你们前面回答, 但我会尽力给出正确的答案。 为了看起来更随机点,这次让我们选第四排的, 那我们开始吧,1个,2个,3个,4个。 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。 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. 95 million --
9758, 这个要花点时间,所以请大家耐心。 是95218564吗?
(Sighs) 218,564?
女士:是的。
Volunteer: Yes!
阿瑟: 非常感谢。
AB: Thank you very much.
(掌声)
(Applause)
(Applause ends)
Now, I would attempt to square a five-digit number -- and I can -- but unfortunately, most calculators cannot.
现在,我很想试着平方一个5位数 -- 我可以 -- 但可惜大多数计算器不能。
(Laughter)
(笑声)
Eight-digit capacity -- don't you hate that? So, since we've reached the limits of our calculators -- what's that? Does yours go higher?
最多只能8位 -- 你们不讨厌吗? 好吧,既然我们已经超越计算器的计算能力 -- 什么?你的可以 -- 女士:我不知道。
Volunteer: I don't know.
阿瑟:你的可以算吗?
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。
In the meanwhile, let me conclude the first part of my show by doing something a little trickier. Let's take the largest number on the board here, 8649. Would you each enter that on your calculator? 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, but don't tell me what you're multiplying by -- just multiply it by any random three-digit number. So you should have as an answer either a six-digit or probably a seven-digit number. How many digits do you have, six or seven?
阿瑟:我等会儿再找你。 与此同时,让我来用些更巧妙的把戏来小结 我的第一部分表演。 让我们用这块板上最大的一个数字,8649。 你们每个人可否在计算器上输入这个数? 这次不要平方, 我要你们用那个数乘以 任何3位数, 但不要告诉我你所乘的数 -- 只要乘以任何一个3位数。 那么你得到的答案可能会是 一个六位数或者七位数。 你的是几位,6还是7?
Seven, and yours?
7,你的呢?女士:7。
Seven? Seven? And, uncertain.
阿瑟:7?7吗? 不确定。
Seven. Is there any possible way that I could know what seven-digit numbers you have? Say "No."
男士:是的。 阿瑟: 7。 有没有办法会让我知道 你所得到的7位数?应该不可能。 (笑声)
(Laughter)
Good, then I shall attempt the impossible -- or at least the improbable. 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.
很好。那我应该来挑战下这个不可能 -- 至少看上去是不太可能的事。 接下来我想让你们告诉我 7位数里面的任意6位数字。 任意顺序都可以。
(Laughter)
(笑声)
One digit at a time, I shall try and determine the digit you've left out. Starting with your seven-digit number, call out any six of them please.
每次一位数,我会试着算出剩下的数。 那么,从你开始吧。 请喊出任意6位数字。 女士:1,哦,197042。
Volunteer: 1, 9, 7, 0, 4, 2.
AB: Did you leave out the number 6?
阿瑟:你是不是漏说了6?
Good, OK, that's one. You have a seven-digit number, call out any six of them please.
女士:是的,阿瑟:很好,好的,没错。 你的是7位数,请大声说出其中任意的六个数。
Volunteer: 4, 4, 8, 7, 5.
女士:44875。
I think I only heard five numbers. I -- wait -- 44875 -- did you leave out the number 6?
阿瑟: 我好像只听到5个数字。我 -- 等下 -- 44875 -- 你是不是漏说了数字6?
Same as she did, OK. You've got a seven-digit number -- call out any six of them loud and clear.
女士:是的。 阿瑟:跟她的一样,好的。你得到的是一个7位数 -- 大声清晰地说出其中的任意6个数字。 男:079044.
Volunteer: 0, 7, 9, 0, 4, 4.
阿瑟:我想你漏说了数字3?
I think you left out the number 3?
AB: That's three. The odds of me getting all four of these right by random guessing would be one in 10,000: 10 to the fourth power. OK, any six of them.
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 将会是万分之一。10的负四次方。 好了,任意6位数字。
(Laughter)
这次请把它们搅乱一下。
Really scramble them up this time, please.
男:263972。
Volunteer: 2, 6, 3, 9, 7, 2.
Did you leave out the number 7? And let's give all four of these people a nice round of applause. Thank you very much.
阿瑟:你是不是漏说了数字7? 现在让我们给这四位观众予热烈的掌声。 非常感谢。
(Applause)
(Applause ends) For my next number --
我的下一个数 --
(Laughter)
(笑声)
while I mentally recharge my batteries, I have one more question for the audience. By any chance, does anybody here happen to know the day of the week that they were born on? If you think you know your birth day, raise your hand. Let's see, starting with -- let's start with a gentleman first. What year was it, first of all? That's why I pick a gentleman first.
在给我脑袋充电期间 我有个问题要问下观众们。 有可能的话,在场的有谁刚好知道 你生日的那天是星期几? 如果你觉得知道的话,举下手。 让我们看看,从 -- 从男士开始, 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。 哪年?
Audience: 1953.
观众:1953。
1953, and the month? November what?
阿瑟: 1953,哪个月? 观众:11月。阿瑟:11月几号?
23rd -- was that a Monday?
观众:23号。 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. OK, how about you, what year? 1949, and the month? October what? Fifth -- was that a Wednesday? Yes! I'll go way to the back right now, how about you? Yell it out, what year?
呃,还没,我还没看到有女士举手。 啊,很好,你呢,哪年? 观众:1949. 阿瑟: 1949, 哪月? 观众: 十月。阿瑟: 十月几号? 观众: 5号。 阿瑟: 5号 -- 那是不是星期3? 没错,现在我从后面选,你怎样? 大声说出来,哪年?观众:1959。
Audience: 1959.
阿瑟:1959, 好的 -- 哪月?
1959, OK -- and the month?
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? Call out, what year was it?
很好,在她后面的那个人要不要试试? 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。
(Applause)
阿瑟:非常感谢。
(掌声)
Anybody here who'd like to know the day of the week they were born? We can do it that way. Of course, I could just make up an answer and you wouldn't know, so I come prepared for that. I brought with me a book of calendars. It goes as far back into the past as 1800, because you never know.
在场的哪一位想知道自己的生日是在星期几的? 我们也可以这么做。 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。 我带了一个日历。 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 --
(Laughter)
你只是恰巧坐在那边。
Anyway, Chris, you can help me out here, if you wouldn't mind. This is a book of calendars. Who wanted to know their birth day? What year was it, first of all?
不管怎样,Chris,你可以帮我下,如果你不介意的话。 这是一本日历,然后我会问 -- 是谁想知道他的生日的,是你吗,先生?好的。 先问下哪一年?
Audience: 1966.
观众:1966。
66 -- turn to the calendar with 1966. And what month?
阿瑟: 66年 -- 翻到日历的1966年 -- 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 Anderson: Yes.
Chris: 是的。阿瑟: 很好,我跟你说
AB: I'll tell you what, Chris: as long as you have that book in front of you, do me a favor, turn to a year outside of the 1900s, either into the 1800s or way into the 2000s -- that'll be a much greater challenge for me. AB: What year would you like? CA: 1824.
chris,用你面前的那本书, 帮我下忙,翻到1900s以外的, 翻到页面1800s 或者2000s -- 那样对我来说会更有挑战性。 你喜欢哪年,Chris?
AB: 1824, OK.
Chris: 1824.
AB: And what month?
阿瑟: 1824, 好的。 哪月呢?Chris: 六月。
CA: June.
哪月呢?Chris: 六月
AB: June what? CA: Sixth.
6号 -- 是不是星期天?
AB: Was that a Sunday?
Chris:没错。 阿瑟:并且是阴天。
CA: It was. AB: And it was cloudy.
(Laughter)
很好,非常感谢。
Good, thank you very much.
(掌声)
(Applause)
(Applause ends)
但是现在我想来个总结
But I'd like to wrap things up now by alluding to something from earlier in the presentation. There was a gentleman up here who had a 10-digit calculator. Where is he, would you stand up, 10-digit guy? OK, stand up for me just for a second, so I can see where you are. You have a 10-digit calculator, sir, as well? OK, what I'm going to try and do, is to square in my head a five-digit number requiring a 10-digit calculator. But to make my job more interesting for you, as well as for me, I'm going to do this problem thinking out loud. So you can actually, honestly hear what's going on in my mind while I do a calculation of this size.
再次回到 我之前的表演 先前台上有位带10位数计算器的先生。 现在在哪里,你能站起来一下吗? 10位数的伙计? 好的,请站起来下, 好让我可以看到你在哪里。 好,哦,好的 -- 你也有一个10位数的计算器? 很好,我接下来要做的是,心算平方 一个5位数的数字,这需要个10位数的计算器。 为了给大家和我自己增加点乐趣, 我会把心算过程 大声的念出来。 这样你们就可以实际上听到 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. I know as a magician we're not supposed to reveal our secrets, but I'm not too afraid that people are going to start doing my show next week, so -- I think we're OK.
现在,我得向我们的魔术师朋友 Lennart Green道下歉。 我知道作为一个魔术师本不应该泄漏我们的秘密, 但我并不是很担心其他人 会在下个星期开始模仿我的表演,所以 -- 我想没有什么问题。
(Laughter)
(Applause)
那么,让我们开始吧,
So, let's see, let's take a different row of people, starting with you. I'll get five digits: one, two, three, four. Oh, I did this row already. Let's do the row before you, starting with you: one, two, three, four, five. Call out a single digit -- that will be the five-digit number that I will try to square, go ahead.
让我们选另一排的观众,就从你开始吧。 我将得到5位数:1,2,3,4 -- 哦,我已经选过这排了。那就选你前面的这排观众, 从你开始先生:1,2,3,4,5。 (每个人)喊出一个一位数 -- 这样就组成一个5位数的数字 我会心算这个数的平方。开始吧。
Five.
观众:5。阿瑟:5。
Seven.
观众:7。阿瑟:7。
Six.
观众:6。阿瑟:6。
Eight.
观众:8。阿瑟:8。
Three. 57,683 -- squared. Yuck.
观众:3。阿瑟:3。 57683 平方。惨啦。
Let me explain to you how I'm going to attempt this problem. I'm going to break the problem down into three parts. I'll do 57,000 squared, plus 683 squared, plus 57,000 times 683 times two. Add all those numbers together, and with any luck, arrive at the answer. Now, let me recap.
让我来给大家解释下 我接下来要怎么算。 我会把这个问题分成3部分。 我先算57000的平方, 然后加上683的平方, 加上57000乘以 683乘以2。 把所有的结果加起来, 幸运的话,就可以得出答案。 现在,让我先想一下(合上笔帽)。(一语双关)
(Laughter)
谢谢。
Thank you.
(Laughter)
当我讲一些其他的 --
While I explain something else --
(Laughter)
-- 我知道,你可以利用这个,对吧?
-- I know, that you can use, right?
(Laughter)
当我心算的时候,在计算的过程中
While I do these calculations, you might hear certain words, as opposed to numbers, creep into the calculation. Let me explain what that is. This is a phonetic code, a mnemonic device that I use, that allows me to convert numbers into words. I store them as words, and later on retrieve them as numbers. I know it sounds complicated; it's not. I don't want you to think you're seeing something out of "Rain Man."
你会听到某些词语, 来对应一些数字,融入到计算当中。 让我来解释下是什么。 这是语音代码, 相当于一个记忆用的设备, 这个设备能帮我把数字转换成单词。 我先存为单词,然后再转回成数字。 我知道这听起来有点复杂;(实际上)一点也不 -- 我不想让你们以为自己看到了‘雨人’。
(Laughter)
(笑声)
There's definitely a method to my madness -- definitely, definitely. Sorry.
这其中绝对有种方法来解释我疯狂的表演 -- 一定的,一定的。不好意思。 (笑声)
(Laughter)
If you want to talk to me about ADHD afterwards, you can talk to me then. By the way, one last instruction, for my judges with the calculators -- you know who you are -- there is at least a 50 percent chance that I will make a mistake here. If I do, don't tell me what the mistake is; 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. If, however, I am right, whatever you do, don't keep it to yourself, OK?
如果你想找我谈论小儿多动症的话, 你可以找我谈谈。好吧 -- 顺便提下, 给我那个有计算器的裁判最后一个说明 至少有一半的机会 我会犯错。 如果算错了,不要告诉我哪里错了; 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 -- 这样会更有趣点。 如果,我对了的话, 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, because this is my big finish, OK. So, without any more stalling, here we go. I'll start the problem in the middle, with 57 times 683. 57 times 68 is 3,400, plus 476 is 3876, that's 38,760 plus 171, 38,760 plus 171 is 38,931. 38,931; double that to get 77,862. 77,862 becomes cookie fission, cookie fission is 77,822. That seems right, I'll go on. Cookie fission, OK. Next, I do 57 squared, which is 3,249, so I can say, three billion. Take the 249, add that to cookie, 249, oops, but I see a carry coming -- 249 -- add that to cookie, 250 plus 77, is 327 million -- fission, fission, OK, finally, we do 683 squared, that's 700 times 666, plus 17 squared is 466,489, rev up if I need it, rev up, take the 466, add that to fission, to get, oh gee -- 328,489.
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。 好吧,闲话少说, 我们开始吧。 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, 那是38760加上171, 38760加上171等于38931。 38931;翻一倍得到77862。 77862变成‘cookie fission’, ‘cookie fission’ 是77822。 好像没错,继续。'cookie fission’,好的。 接下来,我算57的平方等于3249,那么应该是, 30亿。用249加上'cookie',249, 哦,但是我看到有一个包过来了 -- 249 -- 加上 'cookie',250加上77, 等于3亿2千7百万 -- 'fission, fission,' 好的,总算可以算683的平方了, 相当于700乘以666,再加上17的平方 等于466489,我需要的时候转起来, 放大,用466, 加上'fission',得到, 哦老天 -- 328489。
Audience: Yeah! AB: Good.
观众:没错!
Thank you very much.
阿瑟:很好。
(掌声)
(Applause) I hope you enjoyed mathemagics.
非常感谢。 希望你们能喜欢数学魔术。谢谢大家。
Thank you.
(掌声)
(Applause)