TED2005
Arthur Benjamin: A performance of "Mathemagic"
Arthur Benjamin face "Matemagie"
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Într-o prezentare vioaie, matemagicianul Arthur Benjamin se întrece cu un grup de calculatoare pentru a găsi rădăcinile unor numere din 3 cifre, rezolva o dificilă ecuație mentală și ghicește câteva zile de naștere. Cum face toate astea? Vă va spune chiar el.
Arthur Benjamin - Mathemagician
Using daring displays of algorithmic trickery, lightning calculator and number wizard Arthur Benjamin mesmerizes audiences with mathematical mystery and beauty. Full bio
Using daring displays of algorithmic trickery, lightning calculator and number wizard Arthur Benjamin mesmerizes audiences with mathematical mystery and beauty. Full bio
Double-click the English transcript below to play the video.
00:13
Well, good morning ladies and gentlemen.
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Bună ziua doamnelor și domnilor.
00:14
My name is Art Benjamin, and I am a "mathemagician."
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Ma numesc Art Benjamin si sunt un "matemagician"
00:18
What that means is, I combine my loves of math and magic
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Asta inseamna ca eu combin doua pasiuni - matematica si magia,
00:21
to do something I call "mathemagics."
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pentru a realiza ceea ce eu numesc "matemagie"
00:24
But before I get started, I have a quick question for the audience.
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Inainte sa incepem, am o intrebare scurta pentru public.
00:27
By any chance, did anyone happen
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Din intamplare,
00:29
to bring with them this morning a calculator?
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a adus cineva in aceasta dimineata un calculator?
00:33
Seriously, if you have a calculator with you, raise your hand, raise your hand.
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Serios, daca aveti un calculator la voi, ridicati mana, ridicati mana.
00:37
I -- was -- your hand go up?
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Ma -- gandeam -- mana ta e sus?
00:39
Now bring it out, bring it out. Anybody else?
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Adu-l aici, adu-l aici. Altcineva?
00:41
I see, I see one way in the back.
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Vad ... vad o mana ridicata departe in spate.
00:43
You sir, that's three,
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Dumneavoastra domnule, acum avem trei,
00:45
And anybody on this side here?
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Si cineva din partea aceasta?
00:48
OK, you over there on the aisle. Would the four of you with calculators
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Da, tu cel de la margine. As vrea ca voi patru cu calculatoare
00:50
please bring out your calculators, then join me up on stage.
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va rog, aduceti-va calculatoarele, apoi veniti langa mine pe scena.
00:53
And let's give these volunteers a nice round of applause.
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Sa le oferim voluntarilor un rand generos de aplauze.
00:55
(Applause)
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(Aplauze)
00:58
That's right. Now, since I haven't had the chance
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Asa. Acum, pentru ca nu am avut ocazia
01:01
to work with these calculators, I need to make sure
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sa lucrez cu aceste calculatoare, trebuie sa ma asigur
01:04
that they are all working properly.
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ca toate functioneaza corect.
01:06
Would somebody get us started by giving us a
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Pentru inceput ar putea cineva sa ne dea
01:08
two-digit number please?
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un numar din doua cifre, va rog?
01:11
How about a two-digit number?
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Cine are un numar de doua cifre?
01:13
Audience: 22.
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Audienta: 22.
01:14
Arthur Benjamin: 22. And another two-digit number, Sir?
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Arthur Benjamin: 22. Si inca un numar de doua cifre, domnule?
01:16
Audience: 47.
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Audienta: 47.
01:17
AB: Multiply 22 times 47, make sure you get 1,034,
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AB: Inmultiti 22 cu 47 si verificati sa va dea 1,034,
01:21
or the calculators are not working. Do all of you get 1,034? 1,034?
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sau calculatoarele nu functioneaza. Aveti toti 1,034? 1,034?
01:26
Woman: No.
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Femeia: Nu.
01:27
AB: 594. Let's give three of them a nice round of applause there.
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AB: 594. Sa le oferim celor trei un rand de aplauze.
01:31
(Applause)
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(Aplauze)
01:33
Would you like to try a more standard calculator, just in case?
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Vreti sa incercati cu un calculator standard, in orice caz?
01:35
OK, great.
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Bine, perfect.
01:37
What I'm going to try and do then --
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Ce urmeaza sa fac --
01:39
I notice that took some of you a little bit of time to get your answer.
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Am observat ca v-a luat ceva timp pentru a ajunge la rezultat.
01:42
That's OK. I'll give you a shortcut for multiplying
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Dar este in regula. Am sa va dau o scurtatura pentru
01:45
even faster on the calculator.
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inmultirea mai rapida pe calculator.
01:47
There is something called the square of a number,
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Exista radacina la patrat a unui numar,
01:49
which most of you know is taking a number
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ceea ce inseamna, dupa cum stiti, numarul
01:51
and multiplying it by itself.
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imnultit cu el insusi.
01:53
For instance, five squared would be?
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De exemplu, cinci la patrat ar fi?
01:55
Audience: 25.
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Audienta: 25.
01:56
AB: 25. Now, the way we can square on most calculators --
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AB: 25. Acum, felul in care ridicam la patrat cu majoritatea calculatoarelor --
01:58
let me demonstrate with this one --
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am sa va arat cu acesta --
02:00
is by taking the number, such as five,
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este tastarea numarului, adica cinci,
02:02
hitting "times" and then "equals,"
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apasand "inmultit" si apoi "egal",
02:05
and on most calculators that will give you the square.
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iar pe multe calculatoare ar trebui sa va dea radacina.
02:08
On some of these ancient RPN calculators,
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Pe unele calculatoare mai vechi,
02:10
you've got an "x squared" button on it,
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aveti un buton "x la patrat" pe el,
02:12
will allow you to do the calculation even faster.
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va va permite sa calculati chiar mai repede.
02:15
What I'm going to try and do now is to square, in my head,
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Ceea ce voi incerca acum, este sa ridic la patrat, in cap,
02:18
four two-digit numbers
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patru numere de doua cifre
02:20
faster than they can do on their calculators, even using the shortcut method.
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mai rapid decat pot ei calcula, chiar folosind metoda rapida.
02:24
What I'll use is the second row this time, and I'll get four of you --
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Voi folosi al doilea rand de aceasta data, si as dori de la voi --
02:26
one, two, three, four -- to each yell out a two-digit number,
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unu, doi, trei, patru -- sa strigati cate un numar de doua cifre,
02:29
and if you would square the first number,
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si as vrea ca tu sa ridici la patrat primul numar,
02:33
and if you would square the second, the third and the fourth,
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tu al doilea, al treilea si al patrulea,
02:35
I will try and race you to the answer. OK?
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iar eu voi incerca sa va intrec. In regula?
02:38
So quickly, a two-digit number please.
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Deci repede -- un numar de doua cifre, va rog.
02:41
Audience: 37.
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Audienta: 37.
02:42
AB: 37 squared, OK.
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AB: 37 la patrat, da.
02:44
Audience: 23.
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Audienta: 23.
02:45
AB: 23 squared, OK.
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AB: 23 la patrat, da.
02:47
Audience: 59.
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Audienta: 59.
02:48
AB: 59 squared, OK, and finally?
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AB: 59 la patrat, da, iar ultimul?
02:49
Audience: 93.
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Audienta: 93.
02:51
AB: 93 squared. Would you call out your answers, please?
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AB: 93 la patrat. Imi puteti spune raspunsurile, va rog?
02:54
Woman: 1369. AB: 1369.
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Femeia: 1369. AB: 1369.
02:56
Woman: 529.
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Femeia: 529.
02:57
AB: 529.
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AB: 529.
02:58
Man: 3481.
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Barbatul: 3481.
02:59
AB: 3481.
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AB: 3481.
03:00
Man: 8649.
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Barbatul: 8649.
03:01
AB: Thank you very much.
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AB: Va multumesc foarte mult.
03:02
(Applause)
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(Aplauze)
03:07
Let me try to take this one step further.
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Haideti sa mergem un pas mai departe.
03:10
I'm going to try to square some three-digit numbers this time.
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Am sa ridic la patrat niste numere de trei cifre acum.
03:13
I won't even write these down --
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Nici nu o sa le mai scriu --
03:15
I'll just call them out as they're called out to me.
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o sa le scriu direct cand mi se spun.
03:17
Anyone I point to, call out a three-digit number.
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Cel spre care arat cu degetul, striga un numar de trei cifre.
03:20
Anyone on our panel, verify the answer.
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Oricine din juriu, verifica raspunsul.
03:22
Just give some indication if it's right.
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Doar spuneti-mi daca e bine.
03:24
A three-digit number, sir, yes?
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Un numar din trei cifre, doumnule?
03:27
Audience: 987.
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Audienta: 987.
03:28
AB: 987 squared is 974,169.
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AB: 987 ridicat la patrat e 974,169.
03:31
(Laughter)
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(Rasete)
03:33
Yes? Good.
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Da? Bun.
03:35
Another, another three-digit --
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Inca un numar de trei cifre --
03:37
(Applause)
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(Aplauze)
03:38
-- another three-digit number, sir?
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-- inca un numar de trei cifre, domnule?
03:41
Audience: 457.
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Audienta: 457.
03:42
AB: 457 squared is 205,849.
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AB: 457 ridicat la patrat este 205,849.
03:45
205,849?
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205,849?
03:47
Yes?
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Da?
03:49
OK, another, another three-digit number, sir?
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Bun, inca, inca un numar de trei cifre, domnule?
03:52
Audience: 321.
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Audienta: 321.
03:53
AB: 321 is 103,041. 103,041.
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AB: 321 este 103,041. 103, 041.
03:56
Yes? One more three-digit number please.
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Da? Inca un numar de trei cifre, va rog.
03:59
Audience: Oh, 722.
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Audienta: umm, 722.
04:01
AB: 722 is 500 -- ooh, that's a harder one.
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AB: 722 este 500 -- uf, acesta e mai greu.
04:04
Is that 513,284?
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raspunsul este 513,284?
04:07
Woman: Yes.
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Femeia: Da.
04:08
AB: Yes? Oh, one more, one more three-digit number please.
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AB: Da? Inca unul, inca un numar de trei cifre, va rog.
04:11
Audience: 162.
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Audienta: 162.
04:12
162 squared is 26,244.
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162 ridicat la patrat este 26,244.
04:16
Thank you very much.
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Va multumesc foarte mult.
04:18
(Applause)
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(Aplauze)
04:25
Let me try to take this one step further.
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Hai sa incercam un pas mai departe.
04:28
(Laughter)
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(Rasete)
04:30
I'm going to try to square a four-digit number this time.
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Am sa ridic la patrat un numar de patru cifre, acum.
04:33
Now you can all take your time on this; I will not beat you to the answer on this one,
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Puteti sa calculati linistiti; nu va voi da raspunsul mai rapid,
04:36
but I will try to get the answer right.
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dar am sa incerc sa va dau raspunsul corect.
04:38
To make this a little bit more random, let's take the fourth row this time,
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Pentru a face mai aleatorie alegerea, am sa iau al patrulea rand acum,
04:41
let's say, one, two, three, four.
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sa spunem, unu, doi, trei, patru.
04:44
If each of you would call out a single digit between zero and nine,
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Spuneti va rog cate un singur numar de la zero la noua,
04:46
that will be the four-digit number that I'll square.
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acesta va fi numarul nostru din patru cifre pe care il voi ridica la patrat.
04:49
Audience: Nine.
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Audienta: Noua.
04:50
AB: Nine.
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AB: Noua.
04:51
Audience: Seven. AB: Seven.
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Audienta: Sapte. AB: Sapte.
04:52
Audience: Five. AB: Five.
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Audienta: Cinci. AB: Cinci.
04:53
Audience: Eight. AB: Eight.
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Audienta: Opt. AB: Opt.
04:55
9,758, this will take me a little bit of time, so bear with me.
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9,758, imi va lua ceva timp, asteptati putin.
04:58
95,218,564?
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95,218,564?
05:07
Woman: Yes.
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Femeia: Da.
05:08
AB: Thank you very much.
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AB: Va multumesc foarte mult.
05:10
(Applause)
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(Aplauze)
05:18
Now, I would attempt to square a five-digit number --
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Acum, as incerca sa ridic la patrat un numar din cinci cifre --
05:21
and I can --
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si pot --
05:23
but unfortunately most calculators cannot.
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dar din pacate multe calculatoare nu pot.
05:25
(Laughter)
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(Rasete)
05:27
Eight-digit capacity -- don't you hate that?
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Spatiu pe opt biti -- nu urati asta?
05:30
So, since we've reached the limits of our calculators --
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Deci, cum am ajuns la limita calculatoarelor noastre --
05:33
what's that? Does yours go --
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poftim? Al tau merge --
05:36
Woman: I don't know.
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Femeia: Nu stiu.
05:37
AB: Does yours go higher?
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AB: Al tau merge mai sus?
05:39
Oh -- yours does?
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Ah -- al tau?
05:41
Man: I can probably do it.
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Barbatul: Cel mai probabil pot.
05:42
AB: I'll talk to you later.
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AB: O sa vorbim noi mai tarziu.
05:44
In the meanwhile, let me conclude
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Intre timp, as termina
05:46
the first part of my show by doing something a little trickier.
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prima parte a spectacolului meu prin a face ceva mai greu.
05:49
Let's take the largest number on the board here, 8649.
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Hai sa luam cel mai mare numar de pe plansa, 8649.
05:52
Would you each enter that on your calculator?
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Puteti introduce fiecare asta in calculator?
05:55
And instead of squaring it this time,
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Dar in loc sa ridicati la patrat acum,
05:57
I want you to take that number and multiply it
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As vrea sa luati numarul si sa il inmultiti
05:59
by any three-digit number that you want,
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cu orice numar din trei cifre doriti,
06:02
but don't tell me what you're multiplying by --
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dar nu imi spuneti cu ce numar il inmultiti --
06:04
just multiply it by any random three-digit number.
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doar inmultiti-l cu orice numar aleatoriu de trei cifre.
06:07
So you should have as an answer either
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Ar trebui sa aveti ca raspuns fie
06:09
a six-digit or probably a seven-digit number.
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un numar format din 6 cifre, sau poate 7.
06:13
How many digits do you have, six or seven?
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Cate cifre are al tau, sase sau sapte?
06:14
Seven, and yours? Woman: Seven.
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Sapte, iar al tau? Femeia: Sapte.
06:16
AB: Seven? Seven?
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AB: Sapte? Sapte?
06:19
And, uncertain.
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Deci, nesigur.
06:21
Man: Yeah.
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Barbatul: Da.
06:22
AB: Seven. Is there any possible way that I could know
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AB: Sapte. Ar fi cumva posibil sa stiu
06:24
what seven digit numbers you have? Say "No."
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ce numar de sapte cifre aveti? Spuneti "Nu."
06:27
(Laughter)
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(Rasete)
06:29
Good. Then I shall attempt the impossible --
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Bun. Atunci am sa incerc imposibilul --
06:31
or at least the improbable.
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sau cel putitn improbabilul.
06:33
What I'd like each of you to do is to call out for me
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Ce as dori ca fiecare sa imi spuna
06:35
any six of your seven digits, any six of them,
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oricare sase dintre cele sapte cifre, oricare sase,
06:38
in any order you'd like.
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in ce ordine doriti.
06:40
(Laughter)
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(Rasete)
06:41
One digit at a time, I shall try and determine the digit you've left out.
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Cate o cifra pe rand, iar eu am sa incerc sa gasesc ultima cifra.
06:46
So, starting with your seven-digit number,
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Deci, incepand cu numarul de sapte cifre,
06:48
call out any six of them please.
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spune-mi oricare sase cifre, te rog.
06:50
Woman: One, OK, 197042.
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Femeia: Unu, da, 197042
06:56
AB: Did you leave out the number 6?
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Ai omis cumva cifra 6?
06:57
Woman: Yes, AB: Good, OK, that's one.
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Femeia: Da, AB: Bun, primul.
06:59
You have a seven-digit number, call out any six of them please.
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Tu ai un numar de sapte cifre, spune-mi oricare sase te rog.
07:01
Woman: 44875.
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Femeia: 44875.
07:04
AB: I think I only heard five numbers. I -- wait -- 44875 --
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AB: Cred ca am auzit doar cinci numere. 44875...
07:09
did you leave out the number 6?
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ai omis numarul sase?
07:11
Woman: Yes. AB: Same as she did, OK. You've got a seven-digit number --
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Femeia: Da. AB: La fel ca ea, bun. Tu ai un numar de sapte cifre --
07:13
call out any six of them loud and clear.
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spune-mi oricare sase tare si clar.
07:16
Man: 079044.
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Barbatul: 079044.
07:20
AB: I think you left out the number 3?
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AB: Cred ca ai omis numarul 3?
07:22
That's three. The odds of me getting all four of these right by random guessing
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Asta-l al treilea. Sansele ca eu sa ghicesc toate patru numerele corect
07:26
would be one in 10,000: 10 to the fourth power.
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ar fi una din 10,000: 10 la puterea a patra.
07:29
OK, any six of them.
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Bun, oricare sase dintre ele.
07:32
Really scramble them up this time, please.
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Amesteca-le bine de data aceasta, te rog.
07:34
Man: 263972.
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Barbatul: 263972.
07:38
AB: Did you leave out the number 7?
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AB: Ai omis numarul 7?
07:40
And let's give all four of these people a nice round of applause.
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Haideti sa le acordam acestor oameni un rand de aplauze.
07:42
Thank you very much. (Applause)
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Va multumesc foarte mult.
07:52
For my next number --
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Pentru numarul urmator --
07:54
(Laughter)
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(Rasete)
07:57
while I mentally recharge my batteries,
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pana imi incarc bateriile,
07:59
I have one more question for the audience.
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am o intrebare pentru audienta,
08:02
By any chance, does anybody here happen to know
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Din intamplare, isi cunoaste cineva
08:07
the day of the week that they were born on?
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ziua saptamanii in care s-a nascut?
08:10
If you think you know your birth day, raise your hand.
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Daca va cunoasteti ziua de nastere, ridicati mana.
08:14
Let's see, starting with -- let's start with a gentleman first,
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Hai sa vedem, incepem cu -- hai sa incepem cu un domn,
08:17
OK sir, what year was it, first of all? That's why I start with a gentleman first.
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Bun domnule, ce an a fost, in primul rand? De asta incep cu un domn.
08:20
What year?
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Ce an?
08:21
Audience: 1953.
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Audienta: 1953.
08:22
AB: 1953, and the month?
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AB: 1953, si luna?
08:24
Audience: November. AB: November what?
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Audienta: Noiembrie. AB: Noiembrie cat?
08:25
Audience: 23rd.
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Audienta: 23.
08:26
AB: 23rd -- was that a Monday? Audience: Yes.
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AB: 23 -- a fost cumva o zi de Luni? Audienta: Da.
08:28
Yes, good. Somebody else? Who else would like --
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Da, bun. altcineva? Cine mai vrea --
08:30
see I don't -- haven't seen any women's hands up.
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nu am vazut nicio doamna ridicand mana.
08:32
OK, it's -- how about you, what year?
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Bun, este -- dar tu, ce an?
08:34
Audience: 1949. AB: 1949, and the month?
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Audienta: 1949. AB: 1949, iar luna?
08:36
Audience: October. AB: October what?
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Audienta: Octombrie. AB: Octombrie cat?
08:37
Audience: Fifth.
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Audienta: Cinci.
08:38
AB: Fifth -- was that a Wednesday?
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AB: Cinci -- a fost o zi de Miercuri?
08:40
Yes, my -- I'll go way to the back right now, how about you?
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Da, -- hai sa mergem mult in spate, tu?
08:42
Yell it out, what year? Audience: 1959.
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Striga mai tare, ce an? Audienta: 1959.
08:44
AB: 1959, OK -- and the month?
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AB: 1959, bun -- iar luna?
08:46
Audience: February.
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Audienta: Februarie.
08:48
AB: February what? Audience: Sixth.
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AB: Februarie cat? Audienta: Sase.
08:50
AB: Sixth -- was that a Friday? Audience: Yes.
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AB: Sase -- a fost o zi de Vineri? Audienta: Da.
08:52
Good, how about the person behind her?
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Bun, ia sa vedem, persoana din spatele ei?
08:54
Call -- call -- what year was it?
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Spune -- spune -- in ce an?
08:56
Audience: 1947. AB: 1947, and the month?
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Audienta: 1947. AB: 1947, iar luna?
08:58
Audience: May. AB: May what?
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Audienta: Mai. AB: Mai cat?
09:00
Audience: Seventh. AB: Seventh -- would that be a Wednesday?
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Audienta: Sapte. AB: Sapte -- a fost cumva o zi de Miercuri?
09:02
Audience: Yes.
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Audienta: Da.
09:03
AB: Thank you very much.
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AB: Va multumesc foarte mult.
09:05
(Applause)
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(Aplauze)
09:09
Anybody here who'd like to know the day of the week they were born?
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Este cineva care ar dori sa stie ziua din saptamana cand s-a nascut?
09:12
We can do it that way.
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Putem face si asa.
09:14
Of course, I could just make up an answer and you wouldn't know,
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Bineinteles ca as putea inventa o zi, iar voi nu ati sti,
09:16
so I come prepared for that.
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asa ca am venit pregatit pentru asta.
09:18
I brought with me a book of calendars.
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Am adus cu mine un almanah al calendarelor.
09:21
It goes as far back into the past as 1800, 'cause you never know.
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Merge pana in anii 1800, pentru ca nu stii niciodata.
09:25
(Laughter)
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(Rasete)
09:27
I didn't mean to look at you, sir --
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Nu am vrut sa ma uit la tine, domnule --
09:29
you were just sitting there.
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doar stateai acolo.
09:31
Anyway, Chris, you can help me out here, if you wouldn't mind.
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Oricum, Chris, ai putea sa ma ajuti putin aici?
09:34
This is a book of calendars, and I'll ask --
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Acesta e un almanah al calendarelor, si am sa intreb --
09:36
who was it that wanted to know their birth day? You sir? OK.
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cine voia sa isi cunoasca ziua de nastere? Tu, domnule? Bun.
09:38
What year was it, first of all?
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Ce an a fost, in primul rand?
09:40
Audience: 1966.
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Audienta: 1966.
09:41
AB: '66 -- turn to the calendar with 1966 --
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AB: '66 -- da pagina la 1966 --
09:43
and what month?
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si ce luna?
09:45
Audience: April. AB: April what?
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Audienta: Aprilie. AB: Aprilie cat?
09:47
Audience: 17th. AB: 17th -- I believe that was a Sunday.
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Audienta: 17. AB: 17 -- cred ca a fost o Duminica.
09:50
Can you confirm, Chris?
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Poti sa ne confirmi, Chris?
09:52
Chris Anderson: Yes. AB: Yeah, OK. I'll tell you what, Chris:
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Chris Anderson: Da. AB: Da, bun. Hai sa vedem, Chris,
09:54
as long as you have that book in front of you,
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daca tot esti cu almanahul in fata,
09:57
do me a favor, turn to a year outside of the 1900s,
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ajuta-ma, da pagina la un an in afara 1900'
10:01
either into the 1800s or way into the 2000s --
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ori printre anii 1800 ori mult inspre 2000' --
10:04
that'll be a much greater challenge for me.
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ar fi o provocare mai mare pentru mine.
10:06
What year, Chris, would you like?
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Ce an, Chris?
10:07
CA: 1824.
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CA: 1824.
10:08
AB: 1824, OK.
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AB: 1824, bun.
10:11
And what month? CA: June.
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Si ce luna? CA: Iunie.
10:13
AB: June what? CA: Sixth.
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AB: Iunie cat? CA: Sase.
10:15
AB: Sixth -- was that a Sunday?
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AB: Sase -- era o zi de Duminica?
10:17
CA: It was. AB: And it was cloudy.
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CA: Da. AB: Si a fost innorat.
10:20
Good, thank you very much.
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Bun, va multumesc foarte mult.
10:22
(Applause)
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(Aplauze)
10:28
But I'd like to wrap things up now
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Dar as dori sa terminam
10:30
by alluding to something
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prin a reveni la ceva
10:33
from earlier in the presentation.
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ce am discutat mai devreme.
10:35
There was a gentleman up here who had a 10-digit calculator.
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Era un domn care avea un calculator pe 10-biti?
10:38
Where is he, would you stand up,
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Unde este, poate sa se ridice,
10:42
10-digit guy?
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tipul cu 10-biti?
10:44
OK, well stand up for me just for a second,
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Bun, stai in picioare pentru o secunda,
10:47
so I can see where you are.
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sa pot vedea unde esti.
10:49
OK, oh, OK -- you have a 10-digit calculator, sir, as well?
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Ah, bun -- si dumneavoastra aveti un calculator pe 10-biti, domnule?
10:52
OK, what I'm going to try and do, is to square in my head
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Bun, ceea ce am sa incerc acum, este sa ridic la patrat in minte
10:56
a five-digit number requiring a 10-digit calculator.
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un numar de cinci cifre, necesitand un calculator pe 10-biti.
10:59
But to make my job more interesting for you, as well as for me,
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Dar pentru a face totul mai interesant pentru voi, cat si pentru mine,
11:04
I'm going to do this problem
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Am sa rezolv aceasta problema
11:06
thinking out loud.
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gandind cu voce tare.
11:08
So you can actually, honestly hear
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Iar voi veti auzi, serios,
11:11
what's going on in my mind
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ceea ce imi trece mie prin cap
11:13
while I do a calculation of this size.
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in timp ce fac calcule de marimea aceasta.
11:15
Now, I have to apologize to our magician friend Lennart Green.
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Acum, as dori sa ii cer scuze magicianului nostru Lennart Green.
11:18
I know as a magician we're not supposed to reveal our secrets,
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Stiu ca un magician nu ar trebui sa isi arate secretele,
11:22
but I'm not too afraid that people are going
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dar nu cred ca oamenii vor incepe
11:24
to start doing my show next week, so --
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sa reproduca spectacolul meu intr-o saptamana, asadar --
11:26
I think we're OK.
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cred ca suntem in regula.
11:30
So, let's see, let's take a --
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Asadar, haideti sa vedem, sa luam un --
11:33
let's take a different row of people, starting with you.
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haideti sa luam un alt rand, incepand de la tine.
11:35
I'll get five digits: one, two, three, four --
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Am nevoie de cinci cifre: una, doua, trei, patru --
11:38
oh, I did this row already. Let's do the row before you,
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ah, am incercat deja pe randul asta. Hai sa luam randul din fata voastra,
11:40
starting with you sir: one, two, three, four, five.
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incepand cu tine: unu, doi, trei, patru, cinci.
11:43
Call out a single digit -- that will be the five-digit number
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Strigati cate o singura cifra -- acesta va fi numarul nostru de cinci cifre
11:46
that I will try to square. Go ahead.
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pe care il voi ridica la patrat. Haideti.
11:48
Audience: Five. AB: Five.
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Audienta: Cinci. AB: Cinci
11:50
Audience: Seven. AB: Seven.
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Audienta: Sapte: AB: Sapte.
11:51
Audience: Six. AB: Six.
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Audienta: Sase. AB: Sase.
11:52
Audience: Eight. AB: Eight.
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Audienta: Opt. AB: Opt.
11:54
Audience: Three. AB: Three.
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Audienta: Trei. AB: Trei.
11:56
57,683
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57,683
12:01
squared. Yuck.
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la patrat. Bleah.
12:03
Let me explain to you how
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Am sa incerc sa va explic
12:05
I'm going to attempt this problem.
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cum am sa abordez aceasta problema.
12:08
I'm going to break the problem down into three parts.
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Am sa incep prin a imparti problema in trei parti.
12:11
I'll do 57,000 squared,
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Am sa fac 57,000 la patrat,
12:13
plus 683 squared,
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plus 683 la patrat,
12:17
plus 57,000 times
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plus 57,000 inmultit cu
12:20
683 times two.
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683 inmultit cu doi.
12:22
Add all those numbers together,
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Adun toate aceste numere,
12:24
and with any luck, arrive at the answer.
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si cu putin noroc, voi ajunge la rezultat.
12:28
Now, let me recap.
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Acum, hai sa recapitulam.
12:31
Thank you.
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Multumesc.
12:34
While I explain something else --
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Intre timp am sa explic altceva --
12:37
-- I know, that you can use, right?
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-- stiu ca poti folosi, nu?
12:40
While I do these calculation[s],
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Cat timp fac aceste calcule,
12:42
you might hear certain words,
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veti auzi niste cuvinte cheie,
12:44
as opposed to numbers, creep into the calculation.
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care pe langa numere, vor aparea in calcule.
12:48
Let me explain what that is.
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Hai sa va explic ce inseamna.
12:49
This is a phonetic code,
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Reprezinta un cod fonetic,
12:51
a mnemonic device that I use,
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un dispozitiv mnemotic pe care il folosesc,
12:53
that allows me to convert numbers into words.
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care imi permite sa transform numere in cuvinte.
12:56
I store them as words, and later on retrieve them as numbers.
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Le memorez ca si cuvinte, iar apoi le transform in numere.
12:59
I know it sounds complicated; it's not --
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Stiu ca suna complicat; dar nu e --
13:01
I just don't want you to think you're seeing something out of "Rain Man" here.
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Vreau doar sa stiti ca nu vedeti o scena din "Rain Man" acum.
13:04
(Laughter)
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(Rasete)
13:06
There's definitely a method to my madness --
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Sigur exista o metoda in nebunia mea --
13:08
definitely, definitely. Sorry.
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sigur, sigur. Scuze.
13:10
(Laughter)
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(Rasete)
13:14
If you want to talk to me about ADHD afterwards,
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Daca doriti sa discutam despre sindromul ADHD dupa aceea,
13:16
you can talk to me then. All right --
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putem vorbi atunci. Asadar --
13:18
by the way, one last instruction,
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chiar, o ultima rugaminte,
13:20
for my judges with the calculators -- OK, you know who you are --
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pentru cei din juriu, cu calculatoarele -- bun, stiti cine suntet --
13:23
there is at least a 50 percent chance
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exista cel putin 50 la suta sansa
13:26
that I will make a mistake here.
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ca eu sa gresesc.
13:29
If I do, don't tell me what the mistake is;
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Daca gresesc, nu imi spuneti ce gresala am facut;
13:32
just say, "you're close," or something like that, and I'll try and figure out the answer --
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doar spuneti "pe aproape", sau ceva de genul acesta, iar eu am sa incerc sa rezolv --
13:35
which could be pretty entertaining in itself.
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ceea ce ar putea fi interesant.
13:39
If, however, I am right,
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Daca, totusi, am dreptate,
13:41
whatever you do, don't keep it to yourself, OK?
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orice ati face, nu tineti doar pentru voie, da?
13:44
(Laughter)
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(Rasete)
13:45
Make sure everybody knows that I got the answer right,
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Fiti siguri ca toata lumea stie ca am gasit raspunsul corect,
13:47
because this is my big finish, OK.
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pentru ca este marele meu final. Bun.
13:50
So, without any more stalling,
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Asadar, fara a mai trage de timp,
13:53
here we go.
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sa incepem.
13:56
I'll start the problem in the middle, with 57 times 683.
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Am sa incep cu problema din mijloc, cu 57 inmultit cu 683.
13:58
Now, 57 times 68 is 3,400, plus 476 is 3876,
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Acum, 57 inmultit cu 68 este 3,400, plus 476 da 3876,
14:01
that's 38,760 plus 171,
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adica 38,760 plus 171,
14:04
38,760 plus 171 is 38,931.
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38,760 plus 171 este 38,931.
14:07
38,931; double that to get 77,862.
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38,931; dublam asta si obtinem 77,862.
14:11
77,862 becomes cookie fission,
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77,862 devine "cookie fission",
14:13
cookie fission is 77,822.
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"cookie fission" este 77,822.
14:17
That seems right, I'll go on. Cookie fission, OK.
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Pare in regula, sa continuam. "Cookie fission", bun.
14:19
Next, I do 57 squared, which is 3,249, so I can say,
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Apoi, calculez 57 la patrat, care este 3,249, deci pot spune,
14:23
three billion. Take the 249, add that to cookie, 249,
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3 miliarde. Iau 249 si il adaug la "cookie", 249,
14:28
oops, but I see a carry coming --
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ups, dar vad un posibil rest --
14:30
249 --
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249 --
14:32
add that to cookie, 250 plus 77,
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adaug asta la "cookie", 250 plus 77,
14:34
is 327 million --
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este 327 de milioane --
14:38
fission, fission, OK, finally, we do 683 squared,
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"fission", "fission", bun, in sfarsit, facem 683 la patrat,
14:41
that's 700 times 666, plus 17 squared
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adica 700 inmultit cu 666 plus 17 la patrat,
14:43
is 466,489, rev up if I need it,
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adica 466,489, rotesc daca am nevoie,
14:46
rev up, take the 466,
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rotesc, iau 466,
14:48
add that to fission, to get,
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adaug asta la "fission" si obtin,
14:50
oh gee --
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of, vai --
14:54
328,489.
353
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328,489.
14:58
Audience: Yeah!
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Audienta: Daa!
14:59
AB: Good.
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AB: Bun.
15:00
(Applause)
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(Aplauze)
15:01
Thank you very much.
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Va multumesc foarte mult.
15:03
I hope you enjoyed mathemagics. Thank you.
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Sper ca v-a placut "matemagia". Va multumesc
15:05
(Applause)
359
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(Aplauze)
ABOUT THE SPEAKER
Arthur Benjamin - MathemagicianUsing daring displays of algorithmic trickery, lightning calculator and number wizard Arthur Benjamin mesmerizes audiences with mathematical mystery and beauty.
Why you should listen
Arthur Benjamin makes numbers dance. In his day job, he's a professor of math at Harvey Mudd College; in his other day job, he's a "Mathemagician," taking the stage in his tuxedo to perform high-speed mental calculations, memorizations and other astounding math stunts. It's part of his drive to teach math and mental agility in interesting ways, following in the footsteps of such heroes as Martin Gardner.
Benjamin is the co-author, with Michael Shermer, of Secrets of Mental Math (which shares his secrets for rapid mental calculation), as well as the co-author of the MAA award-winning Proofs That Really Count: The Art of Combinatorial Proof. For a glimpse of his broad approach to math, see the list of research talks on his website, which seesaws between high-level math (such as his "Vandermonde's Determinant and Fibonacci SAWs," presented at MIT in 2004) and engaging math talks for the rest of us ("An Amazing Mathematical Card Trick").
Arthur Benjamin | Speaker | TED.com