Arthur Benjamin does "Mathemagic" آرثر بنجامين يؤدي أغنية "سحر الرياضيات" Arthur Benjamin macht "Mathemagie" Ο Arthur Benjamin κάνει "Mathemagic" Arthur Benjamin hace "Matemagia" Arthur Benjamin fait de la "mathématique" アーサー・ベンジャミンが "Mathemagic "をする。 Arthur Benjamin wykonuje "Mathemagic" Arthur Benjamin faz "Mathemagic" Артур Бенджамин делает "Математическую магию" Arthur Benjamin "Mathemagic" yapıyor 阿瑟·本杰明创作《数学魔法》

Well, good morning ladies and gentlemen. Bom dia, senhoras e senhores.

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." To znamená, že spojuji svou lásku k matematice a magii a dělám něco, čemu říkám „matemagie“. But before I get started, I have a quick question for the audience. Ale než začnu, mám rychlou otázku pro diváky. By any chance, did anyone happen to bring with them this morning a calculator? By any chance, did anyone happen to bring with them this morning a calculator? ひょっとして、たまたま今朝電卓を持ってきた人はいませんか？ Seriously, if you have a calculator with you, raise your hand, raise your hand. Sério, se você tiver uma calculadora, levante a mão, levante a mão. I -- was -- your hand go up? 私は - でした - あなたの手が上がりますか？

Now bring it out, bring it out. Teď to vynes, vynes to ven. Und jetzt raus damit, raus damit. さあ、出して、出して。 Agora traga para fora, traga para fora. Anybody else? Kdokoliv jiný? I see, I see one way in the back. Vidím, vidím jednu cestu dozadu. なるほど、奥に一本道があるんですね。 You sir, that’s three, And anybody on this side here? Vy, pane, to jsou tři, A je tu někdo na této straně? こちら側には誰かいる？ OK, you over there on the aisle. OK、あなたは通路にいます。 Would the four of you with calculators please bring out your calculators, then join me up on stage. 電卓をお持ちの4人の方は電卓をお持ちになって、ステージに上がってください。 And let’s give these volunteers a nice round of applause. そして、このボランティアたちに、素敵な拍手を送りましょう。 (Applause)

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. さて、これらの計算機を使用する機会がなかったので、それらがすべて正しく機能していることを確認する必要があります。 Would somebody get us started by giving us a two-digit number please? 誰か 2 桁の番号を教えてください。 How about a two-digit number? 2桁の数字はどうでしょう。 Audience: 22.

Arthur Benjamin: 22.

And another two-digit number, Sir? Audience: 47.

AB: Multiply 22 times 47, make sure you get 1,034, or the calculators are not working. AB: 22 かける 47 を掛けて、必ず 1,034 になるようにしてください。そうしないと、電卓が機能しません。

Do all of you get 1,034? みなさんは1,034点取れますか？ 1,034? Woman: No.

AB: 594.

Let’s give three of them a nice round of applause there. そこで3人に素敵な拍手を送りましょう。 (Applause)

Would you like to try a more standard calculator, just in case? 念のため、より標準的な電卓を試してみますか？

OK, great. What I’m going to try and do then -- I notice that took some of you a little bit of time to get your answer. 私がこれからやろうとしていること - 回答を得るのに少し時間がかかった人もいることを知りました。 That’s OK. I’ll give you a shortcut for multiplying even faster on the calculator. 電卓でさらに速く乗算するためのショートカットを紹介します。 There is something called the square of a number, which most of you know is taking a number and multiplying it by itself. 数の二乗と呼ばれるものがあります。これは、ほとんどの人が知っている数を取り、それ自体を乗算することです。 For instance, five squared would be? 例えば、5の2乗は？ Audience: 25.

AB: 25.

Now, 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. さて、ほとんどの電卓で二乗ができる方法ですが、この電卓で実演してみますと、5などの数字をとって「倍」、そして「等しい」と打つと、ほとんどの電卓で二乗が出ます。 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. これらの古代の RPN 計算機の一部には、「x 二乗」ボタンがあり、計算をさらに高速に行うことができます。 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. 私がこれからやろうとしていることは、頭の中で 4 つの 2 桁の数字を 2 乗することです。ショートカット法を使っても、電卓でできるよりも速くできます。 What I’ll use is the second row this time, and I’ll get four of you -- one, two, three, four -- 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. 今回は2列目を使います。4人の方（1、2、3、4）にそれぞれ2桁の数字を叫んでもらい、最初の数字を2乗、2、3、4乗してもらえば、答えを競うことにします。 OK? So quickly -- a two-digit number please. Audience: 37.

AB: 37 squared, OK.

Audience: 23.

AB: 23 squared, OK.

Audience: 59.

AB: 59 squared, OK, and finally?

Audience: 93.

AB: 93 squared.

Would you call out your answers, please? Woman: 1369.

AB: 1369. Woman: 529.

AB: 529.

Man: 3481.

AB: 3481.

Man: 8649.

AB: Thank you very much.

(Applause)

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. 書き出すこともなく、ただ呼ばれたままに呼びかけるだけです。 Anyone I point to, call out a three-digit number. Anyone on our panel, verify the answer. パネルの誰でもいいので、答えを検証してください。 Just give some indication if it’s right. ただ、それが正しいかどうか、何らかの指示を出してください。 A three-digit number, sir, yes? 3桁の数字です、はい？ Audience: 987.

AB: 987 squared is 974,169.

(Laughter)

Yes?

Good.

Another, another three-digit -- (Applause) -- another three-digit number, sir? Audience: 457.

AB: 457 squared is 205,849.

205,849? Yes?

OK, another, another three-digit number, sir? Audience: 321.

AB: 321 is 103,041. 103,041. Yes?

One more three-digit number please. Audience: Oh, 722.

AB: 722 is 500 -- ooh, that’s a harder one. AB：722は500--おお、これは難しいな。 Is that 513,284? Woman: Yes.

AB: Yes?

Oh, one more, one more three-digit number please. Audience: 162.

162 squared is 26,244. Thank you very much.

(Applause)

Let me try to take this one step further. もう一歩踏み込んで考えてみます。

(Laughter)

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

Now 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. Audience: Nine.

AB: Nine.

Audience: Seven.

AB: Seven.

Audience: Five.

AB: Five. Audience: Eight.

AB: Eight. 9,758, this will take me a little bit of time, so bear with me. 9,758、これはちょっと時間がかかるので、我慢してください。 95,218,564? Woman: Yes.

AB: Thank you very much.

(Applause)

Now, I would attempt to square a five-digit number -- and I can -- but unfortunately most calculators cannot. さて、私は5桁の数字を2乗しようと思うのですが、残念ながらほとんどの電卓は2乗することができません。 (Laughter)

Eight-digit capacity -- don’t you hate that? 8桁の容量--嫌じゃないですか？

So, since we’ve reached the limits of our calculators -- what’s that? Does yours go -- Woman: I don’t know.

AB: Does yours go higher?

Oh -- yours does? Man: I can probably do it.

AB: I’ll talk to you later.

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. 今回は二乗する代わりに、その数字を好きな3桁の数字に掛けてみてほしい。 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? Seven, and yours?

Woman: Seven. AB: Seven?

Seven?

And, uncertain. Man: Yeah.

AB: Seven.

Is there any possible way that I could know what seven digit numbers you have? 7桁の数字を知ることができる方法はないでしょうか？ Say "No. (Laughter)

Good.

Then I shall attempt the impossible -- or at least the improbable. Dann werde ich das Unmögliche versuchen - oder zumindest das Unwahrscheinliche. 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. 皆さんにやっていただきたいのは、7桁の数字のうち、好きな6桁を好きな順番で私に呼びかけていただくことです。 (Laughter)

One digit at a time, I shall try and determine the digit you’ve left out.

So, starting with your seven-digit number, call out any six of them please. Woman: One, OK, 197042.

AB: Did you leave out the number 6?

Woman: Yes, AB: Good, OK, that’s one.

You have a seven-digit number, call out any six of them please. Woman: 44875.

AB: I think I only heard five numbers.

I -- wait -- 44875 -- did you leave out the number 6? Woman: Yes.

AB: Same as she did, OK. You’ve got a seven-digit number -- call out any six of them loud and clear. 7桁の数字があるのですが、そのうちの6桁を大きな声で呼びかけてください。 Man: 079044.

AB: I think you left out the number 3?

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. Really scramble them up this time, please. Man: 263972.

AB: 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.

For my next number -- (Laughter) while I mentally recharge my batteries, I have one more question for the audience. 次の質問は......（笑）、精神的な充電をしながら、もう1つ、会場の皆さんに質問させてください。 By any chance, does anybody here happen to know the day of the week that they were born on? ひょっとして、この中に自分の生まれた曜日をご存知の方はいらっしゃいますか？ If you think you know your birth day, raise your hand. Se você acha que conhece seu dia de nascimento, levante a mão. Let’s see, starting with -- let’s start with a gentleman first, OK sir, what year was it, first of all? That’s why I start with a gentleman first. What year? Audience: 1953.

AB: 1953, and the month?

Audience: November.

AB: November what? Audience: 23rd.

AB: 23rd -- was that a Monday?

Audience: Yes.

Yes, good. somebody else? Who else would like -- see I don’t -- haven’t seen any women’s hands up. 他にどなたか......そういえば、女性の手が上がっているのを見たことがないですね。 OK, it’s -- how about you, what year? Audience: 1949.

AB: 1949, and the month? Audience: October.

AB: October what? Audience: Fifth.

AB: Fifth -- was that a Wednesday?

Yes, my -- I’ll go way to the back right now, how about you? Yell it out, what year? Audience: 1959. AB: 1959, OK -- and the month?

Audience: February.

AB: February what?

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

Audience: Yes.

Good, how about the person behind her? よかった、後ろの人はどうなんだろう？ Call -- call -- what year was it? Audience: 1947.

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

AB: May what? Audience: Seventh.

AB: Seventh -- would that be a Wednesday? Audience: Yes.

AB: Thank you very much.

(Applause)

Anybody here who’d like to know the day of the week they were born? 自分の生まれた曜日を知りたい人はいるかな？

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, 'cause you never know. (Laughter)

I didn’t mean to look at you, sir -- you were just sitting there. Anyway, Chris, you can help me out here, if you wouldn’t mind. This is a book of calendars, and I’ll ask -- who was it that wanted to know their birth day? You sir? OK.

What year was it, first of all? Audience: 1966.

AB: '66 -- turn to the calendar with 1966 -- and what month? AB：66年--1966年のカレンダーをめくってみて、何月か？

Audience: April.

AB: April what? Audience: 17th.

AB: 17th -- I believe that was a Sunday. Can you confirm, Chris? Chris Anderson: Yes.

AB: Yeah, OK. 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. クリス：その本が目の前にある限り、お願いだから1900年代以外の年、つまり1800年代や2000年代の年号に目を向けてほしいんだ。 What year, Chris, would you like? CA: 1824.

AB: 1824, OK.

And what month? CA: June. AB: June what?

CA: Sixth. AB: Sixth -- was that a Sunday?

CA: It was.

AB: And it was cloudy. Good, thank you very much. (Applause)

But I’d like to wrap things up now by alluding to something from earlier in the presentation. しかし、ここで、先ほどのプレゼンテーションの内容を引用して、話をまとめたいと思います。 There was a gentleman up here who had a 10-digit calculator. この上に10桁の電卓を持っている紳士がいた。 Where is he, would you stand up, 10-digit guy? OK, well stand up for me just for a second, so I can see where you are. では、ちょっとだけ立ってください、どこにいるかわかりますから。 OK, oh, OK -- you have a 10-digit calculator, sir, as well? OK, oh, OK -- 10桁の電卓もお持ちなのですね、先生？ OK, what I’m going to try and do, is to square in my head a five-digit number requiring a 10-digit calculator. じゃあ、試しに、5桁の数字を頭の中で2乗して、10桁の電卓を必要とするようにしてみようか。 But to make my job more interesting for you, as well as for me, I’m going to do this problem thinking out loud. しかし、あなただけでなく、私にとっても仕事を面白くするために、この問題思考を声に出してやってみることにします。 So you can actually, honestly hear what’s going on in my mind while I do a calculation of this size. だから、この規模の計算をするときに、私の頭の中で何が起こっているのか、実際に、正直に聞くことができるのです。 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. マジシャンとして秘密は明かさない方がいいとは思いますが、来週から私の番組をやる人が出てきてもあまり怖くないので--大丈夫だと思います。 So, let’s see, let’s take a -- let’s take a different row of people, starting with you. それでは、......あなたから順番に、違う列の人たちを取り上げてみましょうか。 I’ll get five digits: one, two, three, four -- oh, I did this row already. 1、2、3、4と5桁の数字が出ます--あ、この列はもうやりました。 Let’s do the row before you, starting with you sir: one, two, three, four, five. あなたの前の列を、あなたから順に、1、2、3、4、5とやってみましょう。 Call out a single digit -- that will be the five-digit number that I will try to square. 一桁の数字を呼んでください。それが、私が二乗しようとする5桁の数字になります。 Go ahead. Audience: Five.

AB: Five. Audience: Seven.

AB: Seven.

Audience: Six.

AB: Six. Audience: Eight.

AB: Eight. Audience: Three.

AB: Three. 57,683 squared. Yuck. Que nojo. Let me explain to you how I’m going to attempt this problem. この問題にどう挑むか、説明しよう。 Deixe-me explicar como vou tentar esse problema. I’m going to break the problem down into three parts. 問題を3つに分解して考えてみる。 I’ll do 57,000 squared, plus 683 squared, plus 57,000 times 683 times two. 57,000の2乗、プラス683の2乗、プラス57,000の683倍の2乗をする。 Add all those numbers together, and with any luck, arrive at the answer. Now, let me recap. さて、おさらいです。 Thank you. While I explain something else -- -- I know, that you can use, right? 私が他のことを説明する間に......私が知っている、あなたが使えるもの、ですね？ While I do these calculation, you might hear certain words, as opposed to numbers, creep into the calculation. このような計算をしていると、数字とは違う、ある言葉が計算の中に入り込んでくることがあるんです。 Let me explain what that is. それが何なのか、説明させてください。 This is a phonetic code, a mnemonic device that I use, that allows me to convert numbers into words. これは、私が使っているフォネティックコードというニモニックデバイスで、数字を言葉に変換することができるのです。 I store them as words, and later on retrieve them as numbers. I know it sounds complicated; it’s not -- I just don’t want you to think you’re seeing something out of "Rain Man" here. 複雑そうに聞こえるかもしれませんが、そうではなく、『レインマン』のようなものを見ていると思われないようにしたいのです。 (Laughter)

There’s definitely a method to my madness -- definitely, definitely. 私の狂気には間違いなく方法がある--間違いなく、間違いなく。 Sorry. (Laughter)

If you want to talk to me about ADHD afterwards, you can talk to me then. その後、ADHDについて相談したいことがあれば、その時に相談すればいい。

All right -- by the way, one last instruction, for my judges with the calculators -- OK, you know who you are -- there is at least a 50 percent chance that I will make a mistake here. ところで、計算機を持っているジャッジの皆さん、ご存知でしょうが、少なくとも50パーセントの確率で私が間違えますよ。 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. もしそうなったら、間違いは言わずに、「惜しいね」とか言ってくれれば、答え合わせをしてみる。 Se sim, não me diga qual é o erro; diga apenas "você está perto" ou algo assim, e tentarei descobrir a resposta - que pode ser bastante divertida em si mesma. If, however, I am right, whatever you do, don’t keep it to yourself, OK? しかし、もし私が正しいのであれば、何をするにしても、一人で抱え込まないこと、いいね？ (Laughter)

Make sure everybody knows that I got the answer right, because this is my big finish, OK. 私が正解したことをみんなに知らせてね。これが私の大きな仕上げなんだから。

So, without any more stalling, here we go. I’ll start the problem in the middle, with 57 times 683. 真ん中の57回683回から問題を始めます。 Now, 57 times 68 is 3,400, plus 476 is 3876, that’s 38,760 plus 171, 38,760 plus 171 is 38,931. さて、57×68は3400、プラス476は3876、これで38,760＋171で38,931となります。 38,931; double that to get 77,862. 38,931、2倍にすると77,862になります。 77,862 becomes cookie fission, cookie fission is 77,822. 77,862がクッキーフィクションになり、クッキーフィクションが77,822になる。 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. 次に57の2乗をすると3,249になるので、30億と言えますね。 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. 249を取り、それをクッキーに足すと、249、おっとっと、でもキャリーが来るぞ、249、それをクッキーに足すと、250＋77で3億2700万、分裂、分裂、OK、最後に、683の2乗、つまり666の700倍、それに17の2乗で466，489、必要ならレブアップ、466を取って分裂に足したら、なんと、328，489。 Audience: Yeah!

AB: Good.

(Applause)

Thank you very much.

I hope you enjoyed mathemagics. Thank you. (Applause)