## アーサー・ベンジャミンが行う「数学手品」

Arthur Benjamin: A performance of "Mathemagic"

（興味があれば読んでください）

## 英文日本語訳資料

Well, 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."

But before I get started, I have a quick question for the audience.
しかし始める前に、皆様に質問があります

By any chance, did anyone happen to bring with them this morning a calculator?
こののなかで、今朝、 たまたま電卓を持ってきた方はいらっしゃいますか？

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

I -- was -- your hand go up? Now bring it out, bring it out.

Anybody else? I see, I see one way in the back.
そうです　他に誰か？ 見えた、後ろに一人 貴方です、

You sir, that's three, And anybody on this side here? OK,
これで3人 こちら側にいる方はどうですか？ OK、

you over there on the aisle.
そこの通路側にいる人

Would the four of you with calculators please bring out your calculators,
これで電卓を持っている人が4人になりました

then join me up on stage.

And let's give these volunteers a nice round of applause.
そして、ボランティアの皆さんに皆様拍手を

(Applause)
（拍手）

That's right. Now, since I haven't had the chance to work with these calculators,
そう　それでは、これらの電卓をまだ 使ったことは無いので、

I need to make sure that they are all working properly.
ちゃんと動くかどうか 確かめなければなりません

Would somebody get us started by giving us a two-digit number please?
どなたか2桁の数値を言って 始めさせてもらえませんか？

How about a two-digit number?
2桁の数値をどうぞ

Audience: 22.

Arthur Benjamin: 22. And another two-digit number, Sir?
Arthur Benjamin (AB): 22　そして他の2桁の数値は、あなた？

Audience: 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?
AB: 22掛ける47は、1,034 になったでしょうか でなければ電卓は正しく動いておりません　皆様 1,034 ですか？ 1,034？

Woman: No.

AB: 594. Let's give three of them a nice round of applause there.
AB: 594　ではここにいる3人に拍手を

(Applause)
（拍手）

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

What I'm going to try and do then --
それでは これから私のすることは

I notice that took some of you a little bit of time to get your answer.
-- 答えを計算するのに少しだけ時間がかかっていた様ですね

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,
ある数字の二乗というのがあり、

which most of you know is taking a number and multiplying it by itself.
それは ここにいる皆様の殆どがご存知の様に 　ある数値を同じ数値で掛ける事です

For instance, five squared would be?

Audience: 25.

AB: 25. Now, the way we can square on most calculators
AB: 25　それでは、どうやって殆どの電卓で二乗を計算するか

-- let me demonstrate with this one
-- これで試させて下さい

-- is by taking the number, such as five,
-- 例えば5という数字を打って

hitting "times" and then "equals,"
「×」ボタンの次に「＝」ボタンを押すと、

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.
これで更に早く計算する事ができます

What I'm going to try and do now is to square,in my head,
これから私が行うのは

four two-digit numbers faster than they can do on their calculators,
4つある2桁の数の 二乗を 彼らの電卓よりも

even using the shortcut method.
たとえショートカットを使ったとしても、早く出すというものです

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,
ここの4人 1、2、3、4 　-- それぞれ2桁の数を言って下さい

and if you would square the first number, and if you would square the second,
あなたが最初の数を二乗して 2つ目の数を二乗し、

the third and the fourth, I will try and race you to the answer.
3つ目、4つ目も同じ様に、 どちらか早いか試してみましょう

OK? So quickly, a two-digit number please.

Audience: 37.

AB: 37 squared, OK.
AB: 37の二乗、OK

Audience: 23.

AB: 23 squared, OK.
AB: 23の二乗、OK

Audience: 59.

AB: 59 squared, OK, and finally?
AB: 59の二乗、OK、そして最後は？

Audience: 93.

AB: 93 squared. Would you call out your answers, please?
AB: 93の二乗　答えを言ってみて下さい

Woman: 1369. AB: 1369.

Woman: 529.

AB: 529.
AB: 529

Man: 3481.

AB: 3481.
AB: 3481

Man: 8649.

AB: Thank you very much.
AB: どうもありがとうございます

(Applause)
（拍手）

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.
ステージにいる人は、答えを検証して下さい

Just give some indication if it's right.
それが正しいか教えて下さい

A three-digit number, sir, yes?
3桁の数字をどうぞ、はい？

Audience: 987.

AB: 987 squared is 974,169.
AB: 987の二乗は974,169

(Laughter)
（笑）

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?
457の二乗は 205,849 205,849ですか？ 良い？ OK、別の、別の3桁の数字は、はい？

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. Is that 513,284?

Woman: Yes.

AB: Yes? Oh, one more, one more three-digit number please.
AB: そう？それでは、もう1つ、もう1つ3桁の数字をお願いします

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

(Applause)
（拍手）

Let me try to take this one step further.

(Laughter)
（笑）

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,
これはさすがに計算機にはかないません

but I will try to get the answer right.
しかし正しい答えを出す様に頑張ります

To make this a little bit more random, let's take the fourth row this time,
もう少しランダムにする為に、今度は4列目の中の、そうですね、

let's say, one, two, three, four.
1、2、3、4 各人が

If each of you would call out a single digit between zero and nine,
0から9の間の1つの数字を言う事で、

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

Audience: Nine.

AB: Nine.
AB: 9

Audience: Seven. AB: Seven.

Audience: Five. AB: Five.
AB: 5　AB: 5

Audience: Eight. AB: Eight. 9,758,

this will take me a little bit of time,
これは少し時間がかかりますが、

so bear with me. 95,218,564?

Woman: Yes.

AB: Thank you very much.
AB: どうもありがとう

(Applause)
（拍手）

Now, I would attempt to square a five-digit number
さて、5桁の数字を二乗しようと思いますが -

-- and I can -- but unfortunately most calculators cannot.
- そしてそれもできるのですが -- 残念な事に普通の電卓ではできません

(Laughter)
（笑）

Eight-digit capacity -- don't you hate that?
8桁表示の電卓 -- 嫌ですよねぇ

So, since we've reached the limits of our calculators -- what's that? Does yours go --
それで、電卓の限界に来てしまったので -- 何ですか？あなたのは --

Woman: I don't know.

AB: Does yours go higher? Oh -- yours does?
AB: あなたの電卓ではできると？ おぉ -- できますか？

Man: I can probably do it.

AB: I'll talk to you later.
AB: 後で話しましょう

In the meanwhile,let me conclude the first part of my show by doing something a little trickier.
ひとまずは　ショーの最初のパートを もう少しトリッキーなもので締めくくらせて下さい

Let's take the largest number on the board here, 8649.
ボードにある一番大きな数字を取ります　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,
その数値を、あなたの好きな3桁の数値で 掛けてください

but don't tell me what you're multiplying by
どの数値で掛けているかは言わないで下さい

-- just multiply it by any random three-digit number.
-- ランダムな3桁の数字で掛けて下さい

So you should have as an answer either a six-digit or probably a seven-digit number.
それで、その答えは 6桁か、多分7桁の数字になるはずです

How many digits do you have, six or seven?
何桁でしょうか？6桁ですか、7桁ですか？

Seven, and yours? Woman: Seven.
7、そしてあなたは？　女性: 7

AB: Seven? Seven? And, uncertain.
AB: 7桁？7桁？ そして、分からない

Man: Yeah.

AB: Seven. Is there any possible way that I could know what seven digit numbers you have? Say "No."
AB: 7桁　私がその7桁の数字を知る事は できるでしょうか？　「No」と言って下さい

(Laughter)
（笑）

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,
私がこれからしてもらいたい事は、7桁のうちの 6桁を言ってもらう事です

any six of them,in any order you'd like.
6つのうちのどれでも 好きな順序で構いません

(Laughter)
（笑）

One digit at a time, I shall try and determine the digit you've left out.
1回に1桁、残っている数字を当ててみたいと思います

So, starting with your seven-digit number, call out any six of them please.
それでは、あなたの7桁の数字から、6桁の数字の どれでも言ってみて下さい

Woman: One, OK, 197042.

AB: Did you leave out the number 6?
AB: 残っているのは6ですね？

Woman: Yes, AB: Good, OK, that's one.

You have a seven-digit number, call out any six of them please.
これで1つ 7桁の数字のうちの、6つの数を教えて下さい

Woman: 44875.

AB: I think I only heard five numbers.
AB: 5桁しか聞いていないと思いますが

I -- wait -- 44875 -- did you leave out the number 6?
-- ちょっと待って -- 44875 -- 残っているのは6ですね？

Woman: Yes. AB: Same as she did, OK.

You've got a seven-digit number -- call out any six of them loud and clear.
あなたは7桁の数字ですね -- 6桁の数字をはっきりとお願いします

Man: 079044.

AB: I think you left out the number 3?
AB: 残っているのは3ではないですか？

That's three.
3ですね

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,
10の4乗です OK

any six of them. Really scramble them up this time, please.
6桁の数字を 今度はごちゃまぜにしてください、どうぞ

Man: 263972.

AB: Did you leave out the number 7?
AB: 残っているのは7ですね？

And let's give all four of these people a nice round of applause.
ここにいる4人の皆さんに拍手をお願いします

Thank you very much. (Applause)
どうもありがとう

For my next number -- (Laughter)
次の数は -- （笑）

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?
もしかしてこの中のどなたか偶然、 自分の生まれた曜日を知っていらっしゃいますか？

If you think you know your birth day, raise your hand. Let's see,

starting with -- let's start with a gentleman first, OK sir, what year was it,
それでは、そこの男性から始めましょう　OK、

first of all?
まず初めに、何年でしたか？

That's why I start with a gentleman first. What year?

Audience: 1953.

AB: 1953, and the month?
AB: 1953年、それで何月？

Audience: November. AB: November what?

Audience: 23rd.

AB: 23rd -- was that a Monday? Audience: Yes. Yes, good. Somebody else?
AB: 23日 -- は月曜日ですね？　観客: そうです そう、宜しい　他に誰か？

Who else would like -- see I don't -- haven't seen any women's hands up. 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?
AB: 5日 -- は水曜日ですね？

Yes, my -- I'll go way to the back right now, how about you?
そう、次は後ろの方にいこうと思います、あなたはいかがですか？

Yell it out, what year? Audience: 1959.
言って下さい、何年ですか？　観客: 1959

AB: 1959, OK -- and the month?
AB: 1959、OK -- それで何月？

Audience: February.

AB: February what? Audience: Sixth.
AB: 2月の何日？　観客: 6日です

AB: Sixth -- was that a Friday?
AB: 6日 -- は金曜日ですね？

Audience: Yes.　Good, how about the person behind her? 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.
AB: どうもありがとう

(Applause)
（拍手）

Anybody here who'd like to know the day of the week they were born?
この中で自分が生まれた日の曜日を知りたい型はいらっしゃいますか？

We can do it that way.
こういう風にやることもできます

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.
なので準備をしてきました　カレンダーの本を持ってきました　勿論、答えを勝手に言ったとしても、それが正しいか分からないでしょう

It goes as far back into the past as 1800, 'cause you never know.
1800年の過去まで遡れます、何があるか分かりませんからね

(Laughter)
（笑）

I didn't mean to look at you, sir -- you were just sitting there.
あなたを見ていた訳ではありませんよ ただそこにいただけです

Anyway, Chris, you can help me out here, if you wouldn't mind.
とにかく、クリス、もしよかったら手伝ってもらえますか？

This is a book of calendars, and I'll ask -- who was it that wanted to know their birth day? You sir?
これがカレンダーの本で -- どなたか 生まれた曜日を知りたい人はいますか？

OK. What year was it, first of all?
あなた？　OK 最初に、何年でしたか？

Audience: 1966.

AB: '66 -- turn to the calendar with 1966 -- and what month?
AB: 66年 -- 1966年のページを開いて下さい それで何月？

Audience: April. AB: April what?

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

Chris Anderson: Yes.
クリス・アンダーソン (CA): そうです

AB: Yeah, OK. I'll tell you what,
AB: OK　こうしましょう

Chris: as long as you have that book in front of you,
クリス: その本を使って、やってもらいたい事が あります

do me a favor, turn to a year outside of the 1900s,
1900年代以外のページを、

either into the 1800s or way into the 2000s --
1800年代か、2000年代か、開いて下さい

that'll be a much greater challenge for me. What year, Chris, would you like?
-- もっと難しくなりますから クリス、何年が良いですか？

CA: 1824.
CA: 1824年

AB: 1824, OK. And what month? CA: June.
AB: 1824、OK それで何月？　CA: 6月

AB: June what? CA: Sixth.
AB: 6月の何日？　CA: 6日

AB: Sixth -- was that a Sunday?
AB: 6日 -- は日曜日ですね？

CA: It was.
CA: そうです

AB: And it was cloudy. Good, thank you very much.
AB: で、曇りだった 良いですね、どうもありがとう

(Applause)
（拍手）

But I'd like to wrap things up now by alluding to something from earlier in the presentation.
さて、この辺でこの講演の 前の方で出てきたものに 立ち返って幕を閉じたいと思います

There was a gentleman up here who had a 10-digit calculator
10桁の電卓を持っていた男性がいましたね

Where is he, would you stand up, 10-digit guy? OK,

well stand up for me just for a second,
10桁の男性？ OK、ちょっとの間だけ立ち上がって下さい

so I can see where you are. OK, oh, OK -- you have a 10-digit calculator, sir, as well?　OK,
それで何処にいるか分かりますから OK、あなたも10桁の電卓を持っているのですか？　OK、

what I'm going to try and do, is to square in my head a five-digit number requiring a 10-digit calculator.
これから私が挑戦する事は、10桁の電卓が必要な 5桁の数字の二乗の暗算です

But to make my job more interesting for you, as well as for me,
でもこれを、あなたにとっても 私にとっても、もっと楽しくする為に

I'm going to do this problem thinking out loud.
この問題は、考えている事を 話しながら行います

So you can actually,
それであなたは実際に、

honestly hear what's going on in my mind while I do a calculation of this size.
このレベルの 計算をしている間、私の頭の中で 何が起きているのか分かるわけです

Now, I have to apologize to our magician friend Lennart Green.
さて、私は友人の手品師 レナート グリーン に謝らなければなりません

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
ここにいる人達が来週から私のショーを やり始めるとは考えていません

-- I think we're OK. So, let's see, let's take a
なので -- これも大丈夫だと思います

-- let's take a different row of people, starting with you.
それでは、 別の列を使いましょう

I'll get five digits: one, two, three, four -- oh, I did this row already.
あなたから 5つの数字を下さい: 1、2、3、4 -- あら、この列では既にやりましたね

Let's do the row before you,
その前の列でやりましょう

starting with you sir: one, two, three, four, five. 　Call out a single digit
あなたからスタートして:　1、2、3、4、5 1つの数字を言って下さい

-- that will be the five-digit number that I will try to square. Go ahead.
-- それが私が二乗する 5桁の数字になります

Audience: Five. AB: Five.

Audience: Seven. AB: Seven.

Audience: Six. AB: Six.

Audience: Eight. AB: Eight.

Audience: Three. AB: Three. 57,683 squared. Yuck.

Let me explain to you how I'm going to attempt this problem.
この問題をどうやって 攻略するか説明させて下さい

I'm going to break the problem down into three parts.
この問題を3つのパートに分解します

I'll do 57,000 squared, plus 683 squared, plus 57,000 times 683 times two.
まずは 57,000 の二乗を それに 683 の二乗と、 57,000 × 683 × 2 を 加えるのです

Add all those numbers together,
これらの数字を足し合わせると

and with any luck, arrive at the answer.

Now, let me recap. Thank you.
それでは、蓋を閉めて ありがとう

While I explain something else

-- -- I know, that you can use, right?
-- -- これを使っても良い事は知ってますよ、でしょ？

While I do these calculation[s], you might hear certain words, as opposed to numbers,　creep into the calculation.
これらの計算をしながら 数字以外の別の単語が 計算に出てくるのを耳にするかも知れません

Let me explain what that is.
それが何なのか説明します

This is a phonetic code, a mnemonic device that I use,
それは通話表で、 私が使う記憶を助ける方法であり

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
難しいと感じるかも知れませんが、そうではありません

-- I just don't want you to think you're seeing something out of "Rain Man" here.
-- ここで「レインマン」を見ているわけではないと言うのを伝えたかったのです

(Laughter)
（笑）

There's definitely a method to my madness -- definitely, definitely. Sorry.

(Laughter)
（笑）

If you want to talk to me about ADHD afterwards, you can talk to me then.

All right -- by the way, one last instruction,
それでは -- ところで、最後のお願いですが、

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.
ここでは少なくとも50パーセントの 確率で私は間違いを犯します

If I do, don't tell me what the mistake is;
その場合、何が間違っているのかは言わないで下さい;

just say, "you're close," or something like that,
「近い」とか、そういうことを言って下さい、

and I'll try and figure out the answer
それで答えを出しますから

-- which could be pretty entertaining in itself.
-- そしてそれも楽しかったりします

If, however, I am right, whatever you do, don't keep it to yourself, OK?
しかしもし、私が正しければ 何をするにしても、自分だけではしないでください、良いですか？

(Laughter)
（笑）

Make sure everybody knows that I got the answer right,

because this is my big finish, OK.
これが大きな幕引きなのですから、OK

So, without any more stalling, here we go.
それでは、お喋りはこれぐらいにして 始めましょう

I'll start the problem in the middle, with 57 times 683.
まずは真ん中の問題から、57×683

Now, 57 times 68 is 3,400, plus 476 is 3876,
57×68の3,400に476を足して3876

that's 38,760 plus 171, 38,760 plus 171 is 38,931. 38,931;
これは38,760足すの171 38,760足す171は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.
これで良さそう、続けます

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,
クッキーに足す、249 おっと、

but I see a carry coming -- 249 -- add that to cookie,
でも繰り上げが来て　-- 249 -- それをクッキーに足す

250 plus 77, is 327 million --
250足す77 は 327百万

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.

Audience: Yeah!

AB: Good.
AB: よしっ

(Applause)
（拍手）

Thank you very much. I hope you enjoyed mathemagics. Thank you.
どうもありがとう 数学手品を楽しんで頂けたでしょうか　ありがとう

(Applause)
（拍手）

## 単語

Seriously

indication

bear with me
ちょっと待ってください。

conclude

call out

a round of applause

Yell

allude

presentation

creep

complicate

afterwards
あとで

you're close

rev up