TED2005
Arthur Benjamin: A performance of "Mathemagic"
Arthur Benjamin - matemagičar!
Filmed:
Readability: 3.2
9,599,588 views
Arthur Benjamin u ovom živahnom nastupu pokušava biti brži od kalkulatora u izračunu kvadrata troznamenkastih brojeva, napamet rješava izuzetno tešku jednadžbu i pogađa rođendane. Reći će čak i kako to izvodi.
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.
0
1000
1000
Dobro jutro dame i gospodo.
00:14
My name is Art Benjamin, and I am a "mathemagician."
1
2000
3000
Zovem se Arthur Benjamin i ja sam "matemagičar".
00:18
What that means is, I combine my loves of math and magic
2
6000
3000
Značenje toga je da kombiniram svoju ljubav za matematikom i mađioničarskim trikovima
00:21
to do something I call "mathemagics."
3
9000
2000
u nešto što zovem "matemagijom".
00:24
But before I get started, I have a quick question for the audience.
4
12000
3000
Ali prije nego započnem, imam kratko pitanje za publiku.
00:27
By any chance, did anyone happen
5
15000
2000
Da li je netko slučajno
00:29
to bring with them this morning a calculator?
6
17000
4000
ponio sa sobom kalkulator?
00:33
Seriously, if you have a calculator with you, raise your hand, raise your hand.
7
21000
4000
Ozbiljno, ako imate kalkulator kod sebe, dignite ruku, samo dignite ruku.
00:37
I -- was -- your hand go up?
8
25000
2000
Mislio sam... vi ste digli ruku?
00:39
Now bring it out, bring it out. Anybody else?
9
27000
2000
Izvadite te ga, izvadite ga. Još netko?
00:41
I see, I see one way in the back.
10
29000
2000
Vidim, vidim nekog tamo iza.
00:43
You sir, that's three,
11
31000
2000
Vi gospodine... to je već tri.
00:45
And anybody on this side here?
12
33000
3000
Netko možda na ovoj strani?
00:48
OK, you over there on the aisle. Would the four of you with calculators
13
36000
2000
OK, I vi tamo kraj prolaza. Možete li vas četvoro sa kalkulatorima
00:50
please bring out your calculators, then join me up on stage.
14
38000
3000
izvaditi ih i pridružiti mi se na pozornici?
00:53
And let's give these volunteers a nice round of applause.
15
41000
2000
I dajmo ovim dobrovoljcima jedan lijepi pljesak!
00:55
(Applause)
16
43000
3000
(pljesak)
00:58
That's right. Now, since I haven't had the chance
17
46000
3000
Odlično. Sada, pošto nisam prije imao prilike
01:01
to work with these calculators, I need to make sure
18
49000
3000
koristiti ove vaše kalkulatore, moram provjeriti
01:04
that they are all working properly.
19
52000
2000
da li svi rade ispravno.
01:06
Would somebody get us started by giving us a
20
54000
2000
Molim nekoga da započne tako da nam kaže
01:08
two-digit number please?
21
56000
3000
jedan dvoznamenkasti broj?
01:11
How about a two-digit number?
22
59000
2000
Može jedan dvoznamenkasti broj?
01:13
Audience: 22.
23
61000
1000
Publika: 22.
01:14
Arthur Benjamin: 22. And another two-digit number, Sir?
24
62000
2000
Arthur Benjamin: 22. I može još jedan dvoznamenkasti broj gospodine?
01:16
Audience: 47.
25
64000
1000
Publika: 47.
01:17
AB: Multiply 22 times 47, make sure you get 1,034,
26
65000
4000
AB: Pomnožite kalkulatorima 22 puta 47, provjerite da li ste dobili 1,034
01:21
or the calculators are not working. Do all of you get 1,034? 1,034?
27
69000
5000
jer ako niste, kalkulatori vam ne rade. Da li su svi dobili 1,034? 1,034?
01:26
Woman: No.
28
74000
1000
Žena: Ne.
01:27
AB: 594. Let's give three of them a nice round of applause there.
29
75000
4000
AB: 594. Dajmo im svim jedan pljesak ovdje!
01:31
(Applause)
30
79000
2000
(pljesak)
01:33
Would you like to try a more standard calculator, just in case?
31
81000
2000
Želite li možda neki običniji kalkulator za svaki slučaj?
01:35
OK, great.
32
83000
2000
Ok, super.
01:37
What I'm going to try and do then --
33
85000
2000
Želim pokušati nešto --
01:39
I notice that took some of you a little bit of time to get your answer.
34
87000
3000
Primjećujem da je nekima od vas trebalo vremena da dođete do rješenja.
01:42
That's OK. I'll give you a shortcut for multiplying
35
90000
3000
To je OK. Dati ću vam prečac za množenje
01:45
even faster on the calculator.
36
93000
2000
koje će na kalkulatorima biti brže.
01:47
There is something called the square of a number,
37
95000
2000
Postoji nešto zvano "kvadrat broja,"
01:49
which most of you know is taking a number
38
97000
2000
za što većina vas zna da je broj
01:51
and multiplying it by itself.
39
99000
2000
pomnožen sa samim sobom.
01:53
For instance, five squared would be?
40
101000
2000
Na primjer, pet na kvadrat bi bilo?
01:55
Audience: 25.
41
103000
1000
Publika: 25.
01:56
AB: 25. Now, the way we can square on most calculators --
42
104000
2000
AB: 25. Pogledajte, način na koji možemo kvadrirati brojeve na većini kalkulatora --
01:58
let me demonstrate with this one --
43
106000
2000
da vam pokažem na ovome --
02:00
is by taking the number, such as five,
44
108000
2000
je da upišemo broj, na primjer pet,
02:02
hitting "times" and then "equals,"
45
110000
3000
pritisnemo "puta" i onda "jednako,"
02:05
and on most calculators that will give you the square.
46
113000
3000
što će na većini kalkulatora dati kvadrat broja.
02:08
On some of these ancient RPN calculators,
47
116000
2000
Na nekim starim RPN kalkulatorima,
02:10
you've got an "x squared" button on it,
48
118000
2000
postoji posebna naredba "x na kvadrat",
02:12
will allow you to do the calculation even faster.
49
120000
3000
koja vam omogućuje da izračunate ovo još brže.
02:15
What I'm going to try and do now is to square, in my head,
50
123000
3000
Ono što ću sada pokušati je kvadrirati, napamet
02:18
four two-digit numbers
51
126000
2000
četiri dvoznamenkasta broja
02:20
faster than they can do on their calculators, even using the shortcut method.
52
128000
4000
brže nego što oni mogu na svojim kalkulatorima, čak i sa ovom bržom metodom.
02:24
What I'll use is the second row this time, and I'll get four of you --
53
132000
2000
Sada ću koristiti drugi red, i vas četvoro --
02:26
one, two, three, four -- to each yell out a two-digit number,
54
134000
3000
jedan, dva, tri, četiri -- ćete mi doviknuti dvoznamenkasti broj,
02:29
and if you would square the first number,
55
137000
4000
a vi ćete kvadrirati prvi broj,
02:33
and if you would square the second, the third and the fourth,
56
141000
2000
i vi ćete kvadrirati drugi broj, pa treći i četvrti,
02:35
I will try and race you to the answer. OK?
57
143000
3000
a ja ću se utrkivati s vama tko će brže do rješenja. OK?
02:38
So quickly, a two-digit number please.
58
146000
3000
Pa brzo -- molim jedan dvoznamenkasti broj.
02:41
Audience: 37.
59
149000
1000
Publika: 37.
02:42
AB: 37 squared, OK.
60
150000
1000
AB: 37 na kvadrat, OK.
02:44
Audience: 23.
61
152000
1000
Publika: 23.
02:45
AB: 23 squared, OK.
62
153000
2000
AB: 23 na kvadrat, OK.
02:47
Audience: 59.
63
155000
1000
Publika: 59.
02:48
AB: 59 squared, OK, and finally?
64
156000
1000
AB: 59 na kvadrat, OK, i na kraju?
02:49
Audience: 93.
65
157000
2000
Publika: 93.
02:51
AB: 93 squared. Would you call out your answers, please?
66
159000
2000
AB: 93 na kvadrat. Hoćete li molim vas reći vaša rješenja?
02:54
Woman: 1369. AB: 1369.
67
162000
2000
Žena: 1369. AB: 1369.
02:56
Woman: 529.
68
164000
1000
Žena: 529.
02:57
AB: 529.
69
165000
1000
AB: 529.
02:58
Man: 3481.
70
166000
1000
Muškarac: 3481.
02:59
AB: 3481.
71
167000
1000
AB: 3481.
03:00
Man: 8649.
72
168000
1000
Muškarac: 8649.
03:01
AB: Thank you very much.
73
169000
1000
AB: Puno hvala svima!
03:02
(Applause)
74
170000
5000
(pljesak)
03:07
Let me try to take this one step further.
75
175000
3000
Dopustite mi da ovo dovedem korak dalje.
03:10
I'm going to try to square some three-digit numbers this time.
76
178000
3000
Ovaj put ću pokušati kvadrirati troznamenkaste brojeve.
03:13
I won't even write these down --
77
181000
2000
Ove neću niti zapisati.
03:15
I'll just call them out as they're called out to me.
78
183000
2000
Samo ću izvikavati rezultate kada čujem brojeve.
03:17
Anyone I point to, call out a three-digit number.
79
185000
3000
Molio bih da oni u publici u koje pokažem doviknu troznamenkasti broj
03:20
Anyone on our panel, verify the answer.
80
188000
2000
Neka netko od izabranih provjeri rezultat na kalkulatoru.
03:22
Just give some indication if it's right.
81
190000
2000
Samo recite da li je točan.
03:24
A three-digit number, sir, yes?
82
192000
2000
Gospodine, može troznamenkasti broj?
03:27
Audience: 987.
83
195000
1000
Publika: 987.
03:28
AB: 987 squared is 974,169.
84
196000
3000
AB: 987 na kvadrat je 974,169
03:31
(Laughter)
85
199000
2000
(smijeh)
03:33
Yes? Good.
86
201000
2000
Je? Dobro.
03:35
Another, another three-digit --
87
203000
2000
Slijedeći, slijedeći troznamenkasti --
03:37
(Applause)
88
205000
1000
(pljesak)
03:38
-- another three-digit number, sir?
89
206000
3000
-- slijedeći troznamenkasti broj gospodine?
03:41
Audience: 457.
90
209000
1000
Publika: 457.
03:42
AB: 457 squared is 205,849.
91
210000
3000
AB: 457 na kvadrat je 205,849.
03:45
205,849?
92
213000
2000
205,849?
03:47
Yes?
93
215000
2000
Je?
03:49
OK, another, another three-digit number, sir?
94
217000
3000
OK, slijedeći, slijedeći troznamenkasti broj gospodine?
03:52
Audience: 321.
95
220000
1000
Publika: 321.
03:53
AB: 321 is 103,041. 103,041.
96
221000
3000
AB: 321 je 103,041... 103,041.
03:56
Yes? One more three-digit number please.
97
224000
3000
Je? Još jedan troznamenkasti broj molim.
03:59
Audience: Oh, 722.
98
227000
2000
Publika: Oh, 722.
04:01
AB: 722 is 500 -- ooh, that's a harder one.
99
229000
3000
AB: 722 je 500 -- uh taj je teži
04:04
Is that 513,284?
100
232000
3000
Možda je 513,284?
04:07
Woman: Yes.
101
235000
1000
Žena: Je.
04:08
AB: Yes? Oh, one more, one more three-digit number please.
102
236000
3000
AB: Je? Oh molim još jedan, još jedan troznamenkasti broj?
04:11
Audience: 162.
103
239000
1000
Publika: 162.
04:12
162 squared is 26,244.
104
240000
4000
162 na kvadrat je 26,244.
04:16
Thank you very much.
105
244000
2000
Puno vam hvala!
04:18
(Applause)
106
246000
6000
(pljesak)
04:25
Let me try to take this one step further.
107
253000
3000
Dopustite da odem još dalje s ovim.
04:28
(Laughter)
108
256000
2000
(smijeh)
04:30
I'm going to try to square a four-digit number this time.
109
258000
3000
Ovaj puta ću pokušati kvadrirati četveroznamenkasti broj.
04:33
Now you can all take your time on this; I will not beat you to the answer on this one,
110
261000
3000
Ne morate se žuriti s ovima; neću moći biti brži od vas,
04:36
but I will try to get the answer right.
111
264000
2000
ali pokušati ću doći do točnog odgovora.
04:38
To make this a little bit more random, let's take the fourth row this time,
112
266000
3000
Da uvedemo još malo slučajnosti, sada ćemo uzeti četvrti red publike,
04:41
let's say, one, two, three, four.
113
269000
3000
recimo jedan, dva, tri, četiri.
04:44
If each of you would call out a single digit between zero and nine,
114
272000
2000
Ako svatko od vas kaže jednu znamenku od nula do devet,
04:46
that will be the four-digit number that I'll square.
115
274000
3000
to će biti četveroznamenkasti broj koji ću kvadrirati.
04:49
Audience: Nine.
116
277000
1000
Publika: Devet.
04:50
AB: Nine.
117
278000
1000
AB: Devet.
04:51
Audience: Seven. AB: Seven.
118
279000
1000
Publika: Sedam. AB: Sedam.
04:52
Audience: Five. AB: Five.
119
280000
1000
Publika: Pet, AB: Pet.
04:53
Audience: Eight. AB: Eight.
120
281000
1000
Publika: Osam, AB: Osam.
04:55
9,758, this will take me a little bit of time, so bear with me.
121
283000
3000
9,758, ovo će malo potrajati pa budite strpljivi.
04:58
95,218,564?
122
286000
9000
95,218,564?
05:07
Woman: Yes.
123
295000
1000
Žena: Da.
05:08
AB: Thank you very much.
124
296000
2000
AB: Puno vam hvala!
05:10
(Applause)
125
298000
7000
(pljesak)
05:18
Now, I would attempt to square a five-digit number --
126
306000
3000
Sada bi pokušao kvadrirati peteroznamenkasti broj --
05:21
and I can --
127
309000
2000
i mogu to --
05:23
but unfortunately most calculators cannot.
128
311000
2000
ali nažalost većina kalkulatora ne može.
05:25
(Laughter)
129
313000
2000
(smijeh)
05:27
Eight-digit capacity -- don't you hate that?
130
315000
3000
Kalkulatori s osam znamenaka - ne mrzite li to?
05:30
So, since we've reached the limits of our calculators --
131
318000
3000
Pa kako smo došli do granica mogućnosti naših kalkulatora --
05:33
what's that? Does yours go --
132
321000
3000
što ste rekli? Da li vaš ide do --
05:36
Woman: I don't know.
133
324000
1000
Žena: ne znam.
05:37
AB: Does yours go higher?
134
325000
2000
AB: da li vaš ima više?
05:39
Oh -- yours does?
135
327000
2000
Oh -- vaš ide?
05:41
Man: I can probably do it.
136
329000
1000
Muškarac: Vjerojatno bi mogao.
05:42
AB: I'll talk to you later.
137
330000
2000
AB: Pričati ću s vama kasnije.
05:44
In the meanwhile, let me conclude
138
332000
2000
U međuvremenu, završio bih
05:46
the first part of my show by doing something a little trickier.
139
334000
3000
prvi dio mog nastupa sa nečim malo težim.
05:49
Let's take the largest number on the board here, 8649.
140
337000
3000
Uzmimo najveći broj na ovoj ploči, 8649.
05:52
Would you each enter that on your calculator?
141
340000
3000
Hoćete ga molim upisati u kalkulatore?
05:55
And instead of squaring it this time,
142
343000
2000
I sada umjesto da ga kvadrirate,
05:57
I want you to take that number and multiply it
143
345000
2000
želim da taj broj pomnožite
05:59
by any three-digit number that you want,
144
347000
3000
sa bilo kojim troznamenkastim brojem koji želite,
06:02
but don't tell me what you're multiplying by --
145
350000
2000
ali nemojte mi reći s čim ga množite --
06:04
just multiply it by any random three-digit number.
146
352000
3000
Samo ga pomnožite sa bilo kojim troznamenkastim brojem.
06:07
So you should have as an answer either
147
355000
2000
Vaš rezultati bi trebao biti ili
06:09
a six-digit or probably a seven-digit number.
148
357000
4000
ili šesteroznamenkasti ili vjerojatno sedmeroznamenkasti broj.
06:13
How many digits do you have, six or seven?
149
361000
1000
Koliko brojki imate, šest ili sedam?
06:14
Seven, and yours? Woman: Seven.
150
362000
2000
Sedam, a vi? Žena: Sedam.
06:16
AB: Seven? Seven?
151
364000
3000
AB: Sedam? Sedam?
06:19
And, uncertain.
152
367000
2000
I možda.
06:21
Man: Yeah.
153
369000
1000
Muškarac: Da.
06:22
AB: Seven. Is there any possible way that I could know
154
370000
2000
AB: Sedam. Ima li neki način na koji bi mogao znati
06:24
what seven digit numbers you have? Say "No."
155
372000
3000
kojih sedam brojeva imate? Recite "Ne."
06:27
(Laughter)
156
375000
2000
(smijeh)
06:29
Good. Then I shall attempt the impossible --
157
377000
2000
Dobro. Sada ću pokušati nemoguće --
06:31
or at least the improbable.
158
379000
2000
ili barem nevjerojatno.
06:33
What I'd like each of you to do is to call out for me
159
381000
2000
Želim da mi svatko od vas dovikne
06:35
any six of your seven digits, any six of them,
160
383000
3000
bilo kojih šest od vaših sedam znamenaka, bilo kojih šest,
06:38
in any order you'd like.
161
386000
2000
u bilo kojem redoslijedu.
06:40
(Laughter)
162
388000
1000
(smijeh)
06:41
One digit at a time, I shall try and determine the digit you've left out.
163
389000
5000
Jednu po jednu znamenku, a ja ću pokušati pogoditi koju znamenku ste izostavili.
06:46
So, starting with your seven-digit number,
164
394000
2000
Počevši sa vašim sedmeroznamenkastim brojem,
06:48
call out any six of them please.
165
396000
2000
molim recite bilo kojih šest.
06:50
Woman: One, OK, 197042.
166
398000
6000
Žena: Jedan, OK, 197042.
06:56
AB: Did you leave out the number 6?
167
404000
1000
AB: Jeste izostavili šest?
06:57
Woman: Yes, AB: Good, OK, that's one.
168
405000
2000
Žena: Da, AB: Dobro, OK, to je prvi
06:59
You have a seven-digit number, call out any six of them please.
169
407000
2000
Vi imate sedmeroznamenkasti broj, izvikujte bilo kojih šest znamenki.
07:01
Woman: 44875.
170
409000
3000
Žena: 44875.
07:04
AB: I think I only heard five numbers. I -- wait -- 44875 --
171
412000
5000
AB: Mislim da sam čuo samo pet znamenki. Mislim -- čekajte -- 44875 --
07:09
did you leave out the number 6?
172
417000
2000
jeste izostavili broj 6?
07:11
Woman: Yes. AB: Same as she did, OK. You've got a seven-digit number --
173
419000
2000
Žena: Da. AB: Isto kao i ona, OK. Vi imate semeroznamenkasti broj --
07:13
call out any six of them loud and clear.
174
421000
3000
izvikujte bilo kojih šest jasno i glasno.
07:16
Man: 079044.
175
424000
4000
Muškarac: 079044.
07:20
AB: I think you left out the number 3?
176
428000
2000
AB: Mislim da ste izostavili 3?
07:22
That's three. The odds of me getting all four of these right by random guessing
177
430000
4000
To je tri. Vjerojatnost da sam pogađao ove četiri znamenke umjesto računanja je
07:26
would be one in 10,000: 10 to the fourth power.
178
434000
3000
jedan u 10,000: 10 na četvrtu
07:29
OK, any six of them.
179
437000
2000
OK, bilo kojih šest
07:32
Really scramble them up this time, please.
180
440000
2000
Molim da ih stvarno stavite u slučajni redoslijed ovaj put.
07:34
Man: 263972.
181
442000
4000
Čovjek: 263972.
07:38
AB: Did you leave out the number 7?
182
446000
2000
Jeste izostavili sedam?
07:40
And let's give all four of these people a nice round of applause.
183
448000
2000
I dajmo im svim jedan lijepo pljesak!
07:42
Thank you very much. (Applause)
184
450000
2000
Hvala puno svima.
07:52
For my next number --
185
460000
2000
Za slijedeću točku --
07:54
(Laughter)
186
462000
2000
(smijeh)
07:57
while I mentally recharge my batteries,
187
465000
2000
dok mentalno napunim baterije
07:59
I have one more question for the audience.
188
467000
3000
Imam još jedno pitanje za publiku.
08:02
By any chance, does anybody here happen to know
189
470000
5000
Zna li netko ovdje slučajno
08:07
the day of the week that they were born on?
190
475000
3000
u kojem danu u tjednu je rođen?
08:10
If you think you know your birth day, raise your hand.
191
478000
4000
Ako mislite da znate svoj dan rođenja, dignite ruku.
08:14
Let's see, starting with -- let's start with a gentleman first,
192
482000
3000
Da vidim, počinjemo sa -- idemo započeti prvo sa gospodinom,
08:17
OK sir, what year was it, first of all? That's why I start with a gentleman first.
193
485000
3000
OK gospodine, prvo recite koja je godina? Zato porvo počinjem s gospodinom.
08:20
What year?
194
488000
1000
Koja godina?
08:21
Audience: 1953.
195
489000
1000
Publika: 1953.
08:22
AB: 1953, and the month?
196
490000
2000
AB: 1953, a mjesec?
08:24
Audience: November. AB: November what?
197
492000
1000
Publika: Studeni. AB: Kojeg studenog?
08:25
Audience: 23rd.
198
493000
1000
Publika: 23.
08:26
AB: 23rd -- was that a Monday? Audience: Yes.
199
494000
2000
AB: 23. -- je li to bio ponedjeljak? Publika: Da.
08:28
Yes, good. Somebody else? Who else would like --
200
496000
2000
Da, dobro, još netko? Tko bi još htio --
08:30
see I don't -- haven't seen any women's hands up.
201
498000
2000
vidite nema -- nisam još vidio da žene dižu ruke.
08:32
OK, it's -- how about you, what year?
202
500000
2000
OK, to je -- možemo vas, koja godina?
08:34
Audience: 1949. AB: 1949, and the month?
203
502000
2000
Publika: 1949. AB: 1949, a mjesec?
08:36
Audience: October. AB: October what?
204
504000
1000
Publika: Listopad. AB: Listopad koji?
08:37
Audience: Fifth.
205
505000
1000
Publika: Petog.
08:38
AB: Fifth -- was that a Wednesday?
206
506000
2000
AB: Peti -- je li to bila srijeda?
08:40
Yes, my -- I'll go way to the back right now, how about you?
207
508000
2000
Da, moja -- Sada ću nekoga odozada, možda vi?
08:42
Yell it out, what year? Audience: 1959.
208
510000
2000
Vičite, koja godina? Publika: 1959.
08:44
AB: 1959, OK -- and the month?
209
512000
2000
AB: 1959, OK -- a mjesec?
08:46
Audience: February.
210
514000
2000
Veljača.
08:48
AB: February what? Audience: Sixth.
211
516000
2000
Kojeg veljače?
08:50
AB: Sixth -- was that a Friday? Audience: Yes.
212
518000
2000
AB: Šestog -- je li to bio Petak? Publika: Da.
08:52
Good, how about the person behind her?
213
520000
2000
Dobro, može sada osoba iza nje?
08:54
Call -- call -- what year was it?
214
522000
2000
Recite -- recite -- koja je bila godina?
08:56
Audience: 1947. AB: 1947, and the month?
215
524000
2000
Publika: 1947. AB: 1947, a mjesec?
08:58
Audience: May. AB: May what?
216
526000
2000
Publika: Svibanj. AB: Koji svibnja?
09:00
Audience: Seventh. AB: Seventh -- would that be a Wednesday?
217
528000
2000
Publika: Sedmog. AB: Sedmi -- to bi bila srijeda?
09:02
Audience: Yes.
218
530000
1000
Publika: Da.
09:03
AB: Thank you very much.
219
531000
2000
AB: Puno hvala!
09:05
(Applause)
220
533000
3000
(pljesak)
09:09
Anybody here who'd like to know the day of the week they were born?
221
537000
3000
Želi li netko ovdje znati kojeg dana u tjednu je rođen?
09:12
We can do it that way.
222
540000
2000
Možemo i tako.
09:14
Of course, I could just make up an answer and you wouldn't know,
223
542000
2000
Naravno, mogao bih izmisliti odgovor i ne biste primjetili,
09:16
so I come prepared for that.
224
544000
2000
pa sam došao pripremljen.
09:18
I brought with me a book of calendars.
225
546000
2000
Donio sam knjigu kalendara
09:21
It goes as far back into the past as 1800, 'cause you never know.
226
549000
4000
Ima podatke sve do 1800. jer nikad se ne zna
09:25
(Laughter)
227
553000
2000
(smijeh)
09:27
I didn't mean to look at you, sir --
228
555000
2000
Nisam namjerno gledao u vas gospodine --
09:29
you were just sitting there.
229
557000
2000
Slučajno ste sjedili ovdje.
09:31
Anyway, Chris, you can help me out here, if you wouldn't mind.
230
559000
3000
Bilo kako bilo, Chris, možeš mi pomoći ovdje?
09:34
This is a book of calendars, and I'll ask --
231
562000
2000
Ovo je knjiga s kalendarima i pitati ću --
09:36
who was it that wanted to know their birth day? You sir? OK.
232
564000
2000
tko je ono bio da je htio znati svoj dan rođenja? Vi gospodine? OK.
09:38
What year was it, first of all?
233
566000
2000
Prvo recite koja je to bila godina?
09:40
Audience: 1966.
234
568000
1000
Publika: 1966.
09:41
AB: '66 -- turn to the calendar with 1966 --
235
569000
2000
AB: 66.-ta -- okreni na kalendar od 1966. --
09:43
and what month?
236
571000
2000
i koji mjesec?
09:45
Audience: April. AB: April what?
237
573000
2000
Publika: Travanj. AB: Travanj koji?
09:47
Audience: 17th. AB: 17th -- I believe that was a Sunday.
238
575000
2000
Publika: 17. AB: 17. -- mislim da je to bila nedjelja.
09:50
Can you confirm, Chris?
239
578000
2000
Chris, možeš li potvrditi?
09:52
Chris Anderson: Yes. AB: Yeah, OK. I'll tell you what, Chris:
240
580000
2000
Chris Anderson: Je. AB: Da, OK. Recimo ovako, Chris:
09:54
as long as you have that book in front of you,
241
582000
3000
kada već držiš tu knjigu ispred sebe,
09:57
do me a favor, turn to a year outside of the 1900s,
242
585000
4000
napravi mi uslugu, okreni na godinu izvan 1900tih
10:01
either into the 1800s or way into the 2000s --
243
589000
3000
ili u 1800te ili skroz u 2000te --
10:04
that'll be a much greater challenge for me.
244
592000
1000
tako će mi biti veći izazov
10:06
What year, Chris, would you like?
245
594000
1000
Koju godinu bi ti htio?
10:07
CA: 1824.
246
595000
1000
CA: 1824
10:08
AB: 1824, OK.
247
596000
3000
AB: 1824, OK
10:11
And what month? CA: June.
248
599000
2000
i koji mjesec? CA: Lipanj.
10:13
AB: June what? CA: Sixth.
249
601000
1000
AB: Lipanj koji? CA:: šestog.
10:15
AB: Sixth -- was that a Sunday?
250
603000
2000
AB: Šesti -- to je bila nedjelja?
10:17
CA: It was. AB: And it was cloudy.
251
605000
2000
CA: bila je. AB: I bilo je oblačno.
10:20
Good, thank you very much.
252
608000
2000
Odlično, puno hvala!
10:22
(Applause)
253
610000
6000
(pljesak)
10:28
But I'd like to wrap things up now
254
616000
2000
Ali htio bih sada završiti
10:30
by alluding to something
255
618000
3000
pozivajući se na nešto
10:33
from earlier in the presentation.
256
621000
2000
ranije u mojoj prezentaciji.
10:35
There was a gentleman up here who had a 10-digit calculator.
257
623000
3000
Bio je gospodin sa kalkulatorom sa deset znamenaka.
10:38
Where is he, would you stand up,
258
626000
2000
Gdje je, možete li ustati?
10:42
10-digit guy?
259
630000
2000
Čovjek s 10 znamenki?
10:44
OK, well stand up for me just for a second,
260
632000
3000
Ok, možete li mi nakratko ustati,
10:47
so I can see where you are.
261
635000
2000
da vidim gdje ste.
10:49
OK, oh, OK -- you have a 10-digit calculator, sir, as well?
262
637000
3000
OK, oh, OK -- vi isto imate kalkulator s 10 znamenki?
10:52
OK, what I'm going to try and do, is to square in my head
263
640000
4000
OK, ono što ću pokušati napraviti je kvadrirati napamet
10:56
a five-digit number requiring a 10-digit calculator.
264
644000
3000
broj sa pet znamenki, za što je potreban kalkulator s 10 znamenki.
10:59
But to make my job more interesting for you, as well as for me,
265
647000
5000
Ali da to bude zanimljivije za vas i za mene,
11:04
I'm going to do this problem
266
652000
2000
ovo ću riješiti
11:06
thinking out loud.
267
654000
2000
govoreći što mislim.
11:08
So you can actually, honestly hear
268
656000
3000
Tako da možete zapravo čuti
11:11
what's going on in my mind
269
659000
2000
što se događa u mojoj glavi
11:13
while I do a calculation of this size.
270
661000
2000
dok računam ovako veliki broj.
11:15
Now, I have to apologize to our magician friend Lennart Green.
271
663000
3000
Sad, morao bih se ispričati našem mađioničaru Lennartu Greenu,
11:18
I know as a magician we're not supposed to reveal our secrets,
272
666000
4000
jer znam da kao mađioničar ne bi trebao odavati naše tajne,
11:22
but I'm not too afraid that people are going
273
670000
2000
ali ne bojim se previše da će ljudi
11:24
to start doing my show next week, so --
274
672000
2000
početi izvoditi moju točku slijedeći tjedan pa--
11:26
I think we're OK.
275
674000
2000
mislim da je to OK.
11:30
So, let's see, let's take a --
276
678000
3000
Pa da vidimo, uzmimo --
11:33
let's take a different row of people, starting with you.
277
681000
2000
uzmimo neki drugi red ljudi, počevši od vas.
11:35
I'll get five digits: one, two, three, four --
278
683000
3000
Dobiti ću pet znamenki: jedan, dva, tri, četiri --
11:38
oh, I did this row already. Let's do the row before you,
279
686000
2000
a, vas sam već pitao. Uzmimo red prije vas,
11:40
starting with you sir: one, two, three, four, five.
280
688000
3000
počevši od vas gospodine: jedan, dva, tri, četiri, pet.
11:43
Call out a single digit -- that will be the five-digit number
281
691000
3000
Izvikujte jednu znamenku -- biti će to peteroznamenkasti broj
11:46
that I will try to square. Go ahead.
282
694000
2000
kojeg ću pokušati kvadrirati. Počnite.
11:48
Audience: Five. AB: Five.
283
696000
2000
Publika: Pet, AB: Pet.
11:50
Audience: Seven. AB: Seven.
284
698000
1000
Publika: Sedam. AB: Sedam.
11:51
Audience: Six. AB: Six.
285
699000
1000
Publika: Šest. AB: Šest.
11:52
Audience: Eight. AB: Eight.
286
700000
2000
Publika: Osam. AB: Osam.
11:54
Audience: Three. AB: Three.
287
702000
2000
Publika: Tri. AB: Tri.
11:56
57,683
288
704000
3000
57,683
12:01
squared. Yuck.
289
709000
2000
na kvadrat. Bljak.
12:03
Let me explain to you how
290
711000
2000
Da vam objasnim kako
12:05
I'm going to attempt this problem.
291
713000
3000
ću pokušati riješiti taj problem.
12:08
I'm going to break the problem down into three parts.
292
716000
3000
Razdijeliti ću ga u tri dijela.
12:11
I'll do 57,000 squared,
293
719000
2000
Prvo ću kvadrirati 57,000,
12:13
plus 683 squared,
294
721000
3000
plus 683 na kvadrat,
12:17
plus 57,000 times
295
725000
3000
plus 57,000 puta
12:20
683 times two.
296
728000
2000
683 puta 2.
12:22
Add all those numbers together,
297
730000
2000
Zbrojite sve te brojeve zajedno,
12:24
and with any luck, arrive at the answer.
298
732000
3000
iz uz nešto sreće dođete do rezultata.
12:28
Now, let me recap.
299
736000
2000
Ponovimo.
12:31
Thank you.
300
739000
2000
Hvala.
12:34
While I explain something else --
301
742000
2000
Da vam još nešto objasnim --
12:37
-- I know, that you can use, right?
302
745000
2000
-- znam, nešto što ćevam koristiti, jeli?
12:40
While I do these calculation[s],
303
748000
2000
Dok računam,
12:42
you might hear certain words,
304
750000
2000
možda ćete čuti neke riječi,
12:44
as opposed to numbers, creep into the calculation.
305
752000
4000
koje nisu brojevi, kako dolaze usred računanja.
12:48
Let me explain what that is.
306
756000
1000
Objasniti ću vam o čemu se radi.
12:49
This is a phonetic code,
307
757000
2000
To je fonetski kod,
12:51
a mnemonic device that I use,
308
759000
2000
mnemonički način pamćenja kojeg koristim,
12:53
that allows me to convert numbers into words.
309
761000
3000
koji mi dozvoljava da pretvorim brojeve u riječi.
12:56
I store them as words, and later on retrieve them as numbers.
310
764000
3000
Pamtim ih kao riječi i kasnije vraćam kao brojeve.
12:59
I know it sounds complicated; it's not --
311
767000
2000
Znam da zvuči komplicirano ali nije.
13:01
I just don't want you to think you're seeing something out of "Rain Man" here.
312
769000
3000
Samo ne bi htio da mislite da gledate nešto kao u "Kišnom čovjeku."
13:04
(Laughter)
313
772000
2000
(smijeh)
13:06
There's definitely a method to my madness --
314
774000
2000
Sigurno ima plana u mojoj ludosti --
13:08
definitely, definitely. Sorry.
315
776000
2000
Sigurno, sigurno. Ispričavam se.
13:10
(Laughter)
316
778000
3000
(smijeh)
13:14
If you want to talk to me about ADHD afterwards,
317
782000
2000
Ako želite kasnije pričati samnom o ADHD-u,
13:16
you can talk to me then. All right --
318
784000
2000
možemo o tome kasnije. U redu --
13:18
by the way, one last instruction,
319
786000
2000
naposlijetku, zadnja uputa
13:20
for my judges with the calculators -- OK, you know who you are --
320
788000
3000
za moje sudce sa kalkulatorima -- OK, znate koji ste --
13:23
there is at least a 50 percent chance
321
791000
3000
postoji barem 50% šanse
13:26
that I will make a mistake here.
322
794000
3000
da ću negdje pogriješiti.
13:29
If I do, don't tell me what the mistake is;
323
797000
3000
Ako pogriješim, nemojte mi reći gdje je greška;
13:32
just say, "you're close," or something like that, and I'll try and figure out the answer --
324
800000
3000
samo recite "blizu ste" ili nešto slično, i pokušati ću sam doći do rješenja --
13:35
which could be pretty entertaining in itself.
325
803000
3000
što će biti vrlo zabavno ako se dogodi.
13:39
If, however, I am right,
326
807000
2000
S druge strane, ako sam u pravu,
13:41
whatever you do, don't keep it to yourself, OK?
327
809000
3000
nemojte to ni slučajno tajiti, OK?
13:44
(Laughter)
328
812000
1000
(smijeh)
13:45
Make sure everybody knows that I got the answer right,
329
813000
2000
Budite sigurni da svi znaju da sam točno izračunao, u redu?
13:47
because this is my big finish, OK.
330
815000
3000
jer to mi je veliko finale, OK.
13:50
So, without any more stalling,
331
818000
3000
Pa bez daljnjeg odugovlačenja,
13:53
here we go.
332
821000
3000
krenimo.
13:56
I'll start the problem in the middle, with 57 times 683.
333
824000
2000
Početi ću sa problemom u sredini, sa 57 puta 683.
13:58
Now, 57 times 68 is 3,400, plus 476 is 3876,
334
826000
3000
Sad, 57 puta 68 je 3,400, plus 476 je 3876,
14:01
that's 38,760 plus 171,
335
829000
3000
to je 38,760 plus 171,
14:04
38,760 plus 171 is 38,931.
336
832000
3000
38,760 plus 171 je 38,931,
14:07
38,931; double that to get 77,862.
337
835000
4000
38,931; duplo od toga je 77,862.
14:11
77,862 becomes cookie fission,
338
839000
2000
77,862 je "cookie" i "fission",
14:13
cookie fission is 77,822.
339
841000
4000
"cookie fission" je 77,822.
14:17
That seems right, I'll go on. Cookie fission, OK.
340
845000
2000
To mi izgleda dobro, pa ću nastaviti. "Cookie fission", OK
14:19
Next, I do 57 squared, which is 3,249, so I can say,
341
847000
4000
Slijedeće, 57 na kvadrat je 3,249, pa mogu reći,
14:23
three billion. Take the 249, add that to cookie, 249,
342
851000
5000
tri milijarde. Uzmimo 249, dodamo to u "cookie", 249,
14:28
oops, but I see a carry coming --
343
856000
2000
oops, vidim da će mi doći prelijev --
14:30
249 --
344
858000
2000
249 --
14:32
add that to cookie, 250 plus 77,
345
860000
2000
dodaj to u "ookie", 250 plus 77,
14:34
is 327 million --
346
862000
4000
je 327 miliona --
14:38
fission, fission, OK, finally, we do 683 squared,
347
866000
2000
"fission", "fission", OK, na kraju kvadriramo 683,
14:41
that's 700 times 666, plus 17 squared
348
869000
2000
to je 700 puta 666 plus 17 na kvadrat
14:43
is 466,489, rev up if I need it,
349
871000
3000
je 466,489, treba mi to brže,
14:46
rev up, take the 466,
350
874000
2000
brže, uzmi 466,
14:48
add that to fission, to get,
351
876000
2000
dodaj u "fission" i dobiješ
14:50
oh gee --
352
878000
2000
a da --
14:54
328,489.
353
882000
4000
328,489.
14:58
Audience: Yeah!
354
886000
1000
Publika: Je!
14:59
AB: Good.
355
887000
1000
AB: Dobro.
15:00
(Applause)
356
888000
1000
(pljesak)
15:01
Thank you very much.
357
889000
2000
Puno vam hvala!
15:03
I hope you enjoyed mathemagics. Thank you.
358
891000
2000
Nadam se da ste uživali u matemagici. Hvala vam.
15:05
(Applause)
359
893000
4000
(pljesak)
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