TED2005
Arthur Benjamin: A performance of "Mathemagic"
"Matemagija" Arthurja Benjamina
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Matematik Arthur Benjamin tokrat poskuša premagati kalkulatorje pri kvadriranju, uganjuje rojstne dneve in reši ogromno miselno uganko. Kako mu vse to uspe? Povedal vam bo.
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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Pozdravljeni, dame in gospodje.
00:14
My name is Art Benjamin, and I am a "mathemagician."
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Ime mi je Art Benjamin in sem "matematični čarovnik".
00:18
What that means is, I combine my loves of math and magic
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To pomeni, da združujem svojo ljubezen do matematike in magije,
00:21
to do something I call "mathemagics."
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da ustvarim tako imenovano "matemagijo".
00:24
But before I get started, I have a quick question for the audience.
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A preden začnem, imam kratko vprašanje za vas.
00:27
By any chance, did anyone happen
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Ima slučajno kdo
00:29
to bring with them this morning a calculator?
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s sabo kalkulator?
00:33
Seriously, if you have a calculator with you, raise your hand, raise your hand.
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Resno mislim, če imate kalkulator, dvignite roko.
00:37
I -- was -- your hand go up?
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Torej, ste dvignili roko?
00:39
Now bring it out, bring it out. Anybody else?
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Kar dvignite jih. Še kdo?
00:41
I see, I see one way in the back.
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Vidim eno tam zadaj.
00:43
You sir, that's three,
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Vi gospod, torej 3 roke.
00:45
And anybody on this side here?
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Še kdo na tej strani?
00:48
OK, you over there on the aisle. Would the four of you with calculators
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OK, še vi tam ob strani. Lahko vi s kalkulatorji
00:50
please bring out your calculators, then join me up on stage.
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pridete sedaj na oder?
00:53
And let's give these volunteers a nice round of applause.
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Zaploskajmo našim prostovoljcem.
00:55
(Applause)
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(Aplavz)
00:58
That's right. Now, since I haven't had the chance
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Torej, ker nisem še nikoli delal
01:01
to work with these calculators, I need to make sure
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s temi kalkulalatorji, se moram prepričati,
01:04
that they are all working properly.
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da vsi pravilno delujejo.
01:06
Would somebody get us started by giving us a
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Lahko kdo začne
01:08
two-digit number please?
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z dvoštevilčno številko?
01:11
How about a two-digit number?
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Torej eno dvomestno prosim?
01:13
Audience: 22.
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22.
01:14
Arthur Benjamin: 22. And another two-digit number, Sir?
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V redu, še kakšna?
01:16
Audience: 47.
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47.
01:17
AB: Multiply 22 times 47, make sure you get 1,034,
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Zmnožite 22 s 47, dobili boste 1034,
01:21
or the calculators are not working. Do all of you get 1,034? 1,034?
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razen seveda če kalkulatorji ne delajo. Ste vsi dobili 1034?
01:26
Woman: No.
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Ne.
01:27
AB: 594. Let's give three of them a nice round of applause there.
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594. No vseeno jim zaploskajmo.
01:31
(Applause)
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(Aplavz)
01:33
Would you like to try a more standard calculator, just in case?
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Bi raje poskusili z bolj preprostim kalkulatorjem?
01:35
OK, great.
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OK, super.
01:37
What I'm going to try and do then --
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Poskusil bom torej...
01:39
I notice that took some of you a little bit of time to get your answer.
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...opažam, da ste potrebovali kar nekaj časa za računanje.
01:42
That's OK. I'll give you a shortcut for multiplying
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Dal vam bom bližnjico za še hitrejše
01:45
even faster on the calculator.
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množenje s kalkulatorjem.
01:47
There is something called the square of a number,
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Obstaja nekaj, čemur pravimo kvadrat števila,
01:49
which most of you know is taking a number
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kot veste ga dobimo z množenjem
01:51
and multiplying it by itself.
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števila samega s seboj.
01:53
For instance, five squared would be?
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Torej, kvadrat od 5 bi bil?
01:55
Audience: 25.
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25.
01:56
AB: 25. Now, the way we can square on most calculators --
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25. Torej, kako lahko kvadriramo na kalkulatorju --
01:58
let me demonstrate with this one --
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bom pokazal na tem --
02:00
is by taking the number, such as five,
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vzamemo število, kot je 5
02:02
hitting "times" and then "equals,"
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pritisnemo gumb "krat", nato "je enako".
02:05
and on most calculators that will give you the square.
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Večina kalkulatorjev bo tako pokazala kvadrat.
02:08
On some of these ancient RPN calculators,
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Na nekaterih starinskih kalkulatorjih,
02:10
you've got an "x squared" button on it,
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imate gumb "x na kvadrat",
02:12
will allow you to do the calculation even faster.
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kar vam še pospeši računanje.
02:15
What I'm going to try and do now is to square, in my head,
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Sedaj bom poskušal na pamet kvadrirati
02:18
four two-digit numbers
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štiri dvomestna števila,
02:20
faster than they can do on their calculators, even using the shortcut method.
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hitreje kakor oni s kalkulatorji, tudi če si bodo pomagali z bližnjicami.
02:24
What I'll use is the second row this time, and I'll get four of you --
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Sedaj bom izbral drugo vrsto in poiskal 4 gledalce,
02:26
one, two, three, four -- to each yell out a two-digit number,
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da vsak od njih pove eno dvomestno število.
02:29
and if you would square the first number,
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Vi pa boste kvadrirali prvo število,
02:33
and if you would square the second, the third and the fourth,
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vi drugo, tretje in vi četrto.
02:35
I will try and race you to the answer. OK?
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Jaz pa vas bom poskušal prehiteti. V redu?
02:38
So quickly, a two-digit number please.
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Torej hitro -- dvomestno število prosim?
02:41
Audience: 37.
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37.
02:42
AB: 37 squared, OK.
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37 na kvadrat, OK.
02:44
Audience: 23.
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23.
02:45
AB: 23 squared, OK.
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23 na kvadrat, OK.
02:47
Audience: 59.
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59.
02:48
AB: 59 squared, OK, and finally?
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59 na kvadrat, in še?
02:49
Audience: 93.
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93.
02:51
AB: 93 squared. Would you call out your answers, please?
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93 na kvadrat. Bi lahko povedali rezultate prosim?
02:54
Woman: 1369. AB: 1369.
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1369. - 1369
02:56
Woman: 529.
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529.
02:57
AB: 529.
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529
02:58
Man: 3481.
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3481
02:59
AB: 3481.
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3481
03:00
Man: 8649.
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8649
03:01
AB: Thank you very much.
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Najlepša hvala.
03:02
(Applause)
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(Aplavz)
03:07
Let me try to take this one step further.
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Pa pojdimo še en korak naprej.
03:10
I'm going to try to square some three-digit numbers this time.
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Sedaj bom kvadriral trimestna števila.
03:13
I won't even write these down --
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Sploh jih ne bom zapisal --
03:15
I'll just call them out as they're called out to me.
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jih bom pač le izgovoril.
03:17
Anyone I point to, call out a three-digit number.
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Mi lahko kdo pove eno trimestno število?
03:20
Anyone on our panel, verify the answer.
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Nekdo tukaj pa naj preveri odgovor.
03:22
Just give some indication if it's right.
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Samo dajte mi znak, če je pravilen.
03:24
A three-digit number, sir, yes?
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Trimestno število torej?
03:27
Audience: 987.
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987.
03:28
AB: 987 squared is 974,169.
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987 na kvadrat je 974,169.
03:31
(Laughter)
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(Smeh)
03:33
Yes? Good.
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Je? Super.
03:35
Another, another three-digit --
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Še kakšno število?
03:37
(Applause)
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(Aplavz)
03:38
-- another three-digit number, sir?
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Še kakšno trimestno prosim?
03:41
Audience: 457.
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457.
03:42
AB: 457 squared is 205,849.
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457 na kvadrat je 205,849.
03:45
205,849?
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205,849?
03:47
Yes?
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Je?
03:49
OK, another, another three-digit number, sir?
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OK, še eno prosim?
03:52
Audience: 321.
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321.
03:53
AB: 321 is 103,041. 103,041.
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321 je 103,041. 103,041.
03:56
Yes? One more three-digit number please.
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Ja, še eno?
03:59
Audience: Oh, 722.
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722.
04:01
AB: 722 is 500 -- ooh, that's a harder one.
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722 je pa 500 ... uf ta je pa težka.
04:04
Is that 513,284?
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Je mogoče 513,284?
04:07
Woman: Yes.
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Je.
04:08
AB: Yes? Oh, one more, one more three-digit number please.
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Ja? OK še eno trimestno prosim?
04:11
Audience: 162.
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Občinstvo: 162.
04:12
162 squared is 26,244.
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162 na kvadrat je 26,244.
04:16
Thank you very much.
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Najlepša hvala.
04:18
(Applause)
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(Aplavz)
04:25
Let me try to take this one step further.
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No pa poskusimo iti še en korak naprej.
04:28
(Laughter)
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(Smeh)
04:30
I'm going to try to square a four-digit number this time.
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Kvadriral bom štirimestno število.
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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Tukaj ne bom hitrejši od vas,
04:36
but I will try to get the answer right.
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vendar bom pa poskusil pravilno odgovoriti.
04:38
To make this a little bit more random, let's take the fourth row this time,
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Pa vzemimo tokrat četrto vrsto, da bo bolj naključno,
04:41
let's say, one, two, three, four.
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recimo, prvi, drugi, tretji, četrti.
04:44
If each of you would call out a single digit between zero and nine,
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Če lahko vsak prosim pove eno enomestno številko,
04:46
that will be the four-digit number that I'll square.
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tako da bomo dobili štiri števke, ki jih bom kvadriral.
04:49
Audience: Nine.
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9.
04:50
AB: Nine.
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9.
04:51
Audience: Seven. AB: Seven.
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7.
04:52
Audience: Five. AB: Five.
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5
04:53
Audience: Eight. AB: Eight.
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8.
04:55
9,758, this will take me a little bit of time, so bear with me.
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Torej 9758, tukaj potrebujem nekaj časa, prosim počakajte.
04:58
95,218,564?
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Je 95,218,564?
05:07
Woman: Yes.
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Ja.
05:08
AB: Thank you very much.
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Najlepša hvala.
05:10
(Applause)
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(Aplavz)
05:18
Now, I would attempt to square a five-digit number --
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Sedaj pa bom kvadriral petmestno število --
05:21
and I can --
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in jaz to lahko --
05:23
but unfortunately most calculators cannot.
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a večina kalkulatorjev tega ne zmore.
05:25
(Laughter)
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(Smeh)
05:27
Eight-digit capacity -- don't you hate that?
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Osemštevilčna kapaciteta -- gotovo jo sovražite.
05:30
So, since we've reached the limits of our calculators --
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Torej, ker smo dosegli limit kalkulatorjev...
05:33
what's that? Does yours go --
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Kaj pravite? Gre vaš --
05:36
Woman: I don't know.
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Ne vem.
05:37
AB: Does yours go higher?
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Gre vaš še višje?
05:39
Oh -- yours does?
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O, vaš gre?
05:41
Man: I can probably do it.
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Gospod: Jaz bi verjetno zmogel.
05:42
AB: I'll talk to you later.
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Se pogovoriva kasneje.
05:44
In the meanwhile, let me conclude
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Medtem pa naj zaključim
05:46
the first part of my show by doing something a little trickier.
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prvi del predstave z nečim še malo težjim.
05:49
Let's take the largest number on the board here, 8649.
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Vzemimo največje število tukaj, torej 8649.
05:52
Would you each enter that on your calculator?
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Jo lahko vpišete v kalkulator?
05:55
And instead of squaring it this time,
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In namesto, da bi jo kvadrirali,
05:57
I want you to take that number and multiply it
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jo pomnožite s katerokoli trimestno
05:59
by any three-digit number that you want,
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številko, ki vam pride na misel.
06:02
but don't tell me what you're multiplying by --
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Ampak ne povejte mi, s katero ste množili --
06:04
just multiply it by any random three-digit number.
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samo zmnožite z naključno trimestno številko.
06:07
So you should have as an answer either
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Torej rezultat bo ali šestmestna
06:09
a six-digit or probably a seven-digit number.
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ali najbrž sedemmestna številka.
06:13
How many digits do you have, six or seven?
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Koliko mest ima vaša, šest ali sedem?
06:14
Seven, and yours? Woman: Seven.
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Sedem, vaša? Sedem.
06:16
AB: Seven? Seven?
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Sedem? Sedem?
06:19
And, uncertain.
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Aha, vi pa na veste.
06:21
Man: Yeah.
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Gospod: Ja.
06:22
AB: Seven. Is there any possible way that I could know
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Sedem. Obstaja kakšen način, kako bom vedel,
06:24
what seven digit numbers you have? Say "No."
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katero sedemmestno število ste dobili. Recite "ne".
06:27
(Laughter)
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(Smeh)
06:29
Good. Then I shall attempt the impossible --
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Dobro, torej bom poskusil nemogoče --
06:31
or at least the improbable.
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oziroma vsaj neverjetno.
06:33
What I'd like each of you to do is to call out for me
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Povejte mi katerihkoli šest števk izmed
06:35
any six of your seven digits, any six of them,
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vaših sedmih števk, v kakršnemkoli
06:38
in any order you'd like.
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vrstnem redu.
06:40
(Laughter)
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(Smeh)
06:41
One digit at a time, I shall try and determine the digit you've left out.
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In jaz bom poskusil ugotoviti, katero števko ste izpustili.
06:46
So, starting with your seven-digit number,
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Torej začnimo z vašim številom.
06:48
call out any six of them please.
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Povejte katerihkoli šest.
06:50
Woman: One, OK, 197042.
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Torej, 197042.
06:56
AB: Did you leave out the number 6?
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Ste izpustili 6?
06:57
Woman: Yes, AB: Good, OK, that's one.
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Gospa: Ja. Art: Dobro.
06:59
You have a seven-digit number, call out any six of them please.
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Vaša sedemmestnica, povejte šest števk.
07:01
Woman: 44875.
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44875.
07:04
AB: I think I only heard five numbers. I -- wait -- 44875 --
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Art: Slišal sem le pet števk. Am -- čakajte -- 44875...
07:09
did you leave out the number 6?
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Ste izpustili številko 6?
07:11
Woman: Yes. AB: Same as she did, OK. You've got a seven-digit number --
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Gospa: Ja. Art: Torej enako kot ona, OK. Še vaša sedemmestna --
07:13
call out any six of them loud and clear.
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povejte mi šest števk.
07:16
Man: 079044.
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079044.
07:20
AB: I think you left out the number 3?
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Mislim da ste izpustili 3?
07:22
That's three. The odds of me getting all four of these right by random guessing
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Torej imamo že tri. Možnost, da bi vse tole naključno uganil, je
07:26
would be one in 10,000: 10 to the fourth power.
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1 proti 10,000. Torej 10 na četrto.
07:29
OK, any six of them.
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OK, šest števk prosim.
07:32
Really scramble them up this time, please.
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Pa res jih premešajte, prosim.
07:34
Man: 263972.
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263972.
07:38
AB: Did you leave out the number 7?
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Ste izpustili 7?
07:40
And let's give all four of these people a nice round of applause.
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Zaploskajmo vsem štirim prostovoljcem.
07:42
Thank you very much. (Applause)
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Najlepša hvala.
07:52
For my next number --
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Za naslednjo številko --
07:54
(Laughter)
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(Smeh)
07:57
while I mentally recharge my batteries,
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medtem ko si odahnem možgane,
07:59
I have one more question for the audience.
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imam še eno vprašanje za občinstvo.
08:02
By any chance, does anybody here happen to know
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Slučajno kdo ve, na kateri dan
08:07
the day of the week that they were born on?
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v tednu se je rodil?
08:10
If you think you know your birth day, raise your hand.
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Če že veste, dvignite roko.
08:14
Let's see, starting with -- let's start with a gentleman first,
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No pa poglejmo, vi gospod
08:17
OK sir, what year was it, first of all? That's why I start with a gentleman first.
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OK, letnico prosim? Zato seveda začenjam z gospodom.
08:20
What year?
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Katerega leta?
08:21
Audience: 1953.
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1953.
08:22
AB: 1953, and the month?
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1953. Mesec?
08:24
Audience: November. AB: November what?
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November. - Kateri november?
08:25
Audience: 23rd.
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23.
08:26
AB: 23rd -- was that a Monday? Audience: Yes.
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23. november -- ponedeljek? - Ja.
08:28
Yes, good. Somebody else? Who else would like --
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Aha, dobro. Še kdo?
08:30
see I don't -- haven't seen any women's hands up.
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Ne vidim nobenih ženskih rok.
08:32
OK, it's -- how about you, what year?
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OK tukaj imamo -- katerega leta?
08:34
Audience: 1949. AB: 1949, and the month?
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1949. - In mesec?
08:36
Audience: October. AB: October what?
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Oktober. - Kateri oktober?
08:37
Audience: Fifth.
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Peti.
08:38
AB: Fifth -- was that a Wednesday?
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5. oktober -- je bila sreda?
08:40
Yes, my -- I'll go way to the back right now, how about you?
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Aha, grem še malo tja zadaj, kaj pa vi?
08:42
Yell it out, what year? Audience: 1959.
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Katerega leta? - 1959.
08:44
AB: 1959, OK -- and the month?
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OK, še mesec?
08:46
Audience: February.
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Februar.
08:48
AB: February what? Audience: Sixth.
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Kateri februar? - Šesti.
08:50
AB: Sixth -- was that a Friday? Audience: Yes.
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Šesti -- je bil mogoče petek? - Ja.
08:52
Good, how about the person behind her?
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Dobro, kaj pa gospa zadaj?
08:54
Call -- call -- what year was it?
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Katerega leta?
08:56
Audience: 1947. AB: 1947, and the month?
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1947. - Mesec?
08:58
Audience: May. AB: May what?
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Maj. - Kateri maj?
09:00
Audience: Seventh. AB: Seventh -- would that be a Wednesday?
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Sedmi. - Sedmi maj -- sreda kajne?
09:02
Audience: Yes.
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Ja.
09:03
AB: Thank you very much.
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Najlepša hvala.
09:05
(Applause)
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(Aplavz)
09:09
Anybody here who'd like to know the day of the week they were born?
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Bi kdo rad izvedel, katerega dne v tednu se je rodil?
09:12
We can do it that way.
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Lahko se gremo tudi tako.
09:14
Of course, I could just make up an answer and you wouldn't know,
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Seveda, lahko bi si samo izmislil odgovor, saj ne bi nihče vedel.
09:16
so I come prepared for that.
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A prišel sem pripravljen.
09:18
I brought with me a book of calendars.
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S sabo imam koledarje,
09:21
It goes as far back into the past as 1800, 'cause you never know.
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ki segajo do leta 1800. Nikoli ne veš.
09:25
(Laughter)
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(Smeh)
09:27
I didn't mean to look at you, sir --
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Nisem gledal vas, gospod,
09:29
you were just sitting there.
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samo tam pač sedite.
09:31
Anyway, Chris, you can help me out here, if you wouldn't mind.
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Kakorkoli že, Chris, če mi lahko prosim pomagaš.
09:34
This is a book of calendars, and I'll ask --
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To je knjiga koledarjev, torej
09:36
who was it that wanted to know their birth day? You sir? OK.
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kdo je hotel izvedeti, na kateri dan v tednu se je rodil? Vi gospod? OK.
09:38
What year was it, first of all?
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Torej, najprej, katerega leta?
09:40
Audience: 1966.
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1966.
09:41
AB: '66 -- turn to the calendar with 1966 --
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1966 -- obrni koledar na 1966,
09:43
and what month?
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še mesec?
09:45
Audience: April. AB: April what?
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April. - Kateri april?
09:47
Audience: 17th. AB: 17th -- I believe that was a Sunday.
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17. - To bo pa nedelja.
09:50
Can you confirm, Chris?
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Se strinjaš, Chris?
09:52
Chris Anderson: Yes. AB: Yeah, OK. I'll tell you what, Chris:
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Ja. - OK, poglej Chris.
09:54
as long as you have that book in front of you,
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Če že imaš to knjigo,
09:57
do me a favor, turn to a year outside of the 1900s,
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prosim, obrni jo nekam globoko v 19. stoletje,
10:01
either into the 1800s or way into the 2000s --
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ali pa v 21. stoletje --
10:04
that'll be a much greater challenge for me.
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to bo veliko večji izziv.
10:06
What year, Chris, would you like?
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Katero leto, Chris?
10:07
CA: 1824.
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1824.
10:08
AB: 1824, OK.
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OK.
10:11
And what month? CA: June.
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Še mesec? - Junij.
10:13
AB: June what? CA: Sixth.
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Kateri junij? - Šesti.
10:15
AB: Sixth -- was that a Sunday?
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Šesti -- je bila nedelja?
10:17
CA: It was. AB: And it was cloudy.
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Je. - In bilo je oblačno.
10:20
Good, thank you very much.
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Najlepša hvala.
10:22
(Applause)
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(Aplavz)
10:28
But I'd like to wrap things up now
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Zdaj pa bi rad počasi zaključil
10:30
by alluding to something
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z namigom na nekaj
10:33
from earlier in the presentation.
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z začetka predstave.
10:35
There was a gentleman up here who had a 10-digit calculator.
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Imeli smo možakarja z desetmestnim kalkulatorjem.
10:38
Where is he, would you stand up,
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Kje je, lahko vstane?
10:42
10-digit guy?
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Desetmestnik?
10:44
OK, well stand up for me just for a second,
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OK, vstanite za trenutek,
10:47
so I can see where you are.
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da vidim, kje ste.
10:49
OK, oh, OK -- you have a 10-digit calculator, sir, as well?
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OK -- imate vi tudi desetmestni kalkulator?
10:52
OK, what I'm going to try and do, is to square in my head
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OK, na pamet bom poskusil kvadrirati
10:56
a five-digit number requiring a 10-digit calculator.
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petmestno številko, kar zahteva desetmestni kalkulator.
10:59
But to make my job more interesting for you, as well as for me,
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A da bo moje delo bolj zanimivo,
11:04
I'm going to do this problem
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bom tokrat
11:06
thinking out loud.
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razmišljal naglas.
11:08
So you can actually, honestly hear
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Tako, da boste slišali,
11:11
what's going on in my mind
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kaj se dejansko dogaja v moji glavi,
11:13
while I do a calculation of this size.
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ko računam s takimi številkami.
11:15
Now, I have to apologize to our magician friend Lennart Green.
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Najprej se moram opravičiti čarovniku Lennartu Greenu.
11:18
I know as a magician we're not supposed to reveal our secrets,
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Vem, da kot čarovnik ne bi smel razkriti takih skrivnosti,
11:22
but I'm not too afraid that people are going
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a mislim, da me ljudje še ne bodo uspeli
11:24
to start doing my show next week, so --
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posnemati naslednji teden.
11:26
I think we're OK.
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Mislim da smo varni.
11:30
So, let's see, let's take a --
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No, da vidimo,
11:33
let's take a different row of people, starting with you.
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vzemimo še eno drugo vrsto ljudi, začnimo tu.
11:35
I'll get five digits: one, two, three, four --
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Dobiti moram pet števk: ena, dva, tri, štiri --
11:38
oh, I did this row already. Let's do the row before you,
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o, saj to vrsto sem že obdelal. Poglejmo raje to pred vami,
11:40
starting with you sir: one, two, three, four, five.
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vi gospod,: ena, dva, tri, štiri, pet.
11:43
Call out a single digit -- that will be the five-digit number
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Povejte po eno števko -- tako da bomo dobili petmestno
11:46
that I will try to square. Go ahead.
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številko, ki jo bom kvadriral.
11:48
Audience: Five. AB: Five.
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Pet. - Pet.
11:50
Audience: Seven. AB: Seven.
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Sedem. - Sedem.
11:51
Audience: Six. AB: Six.
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Šest. - Šest.
11:52
Audience: Eight. AB: Eight.
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Osem. - Osem.
11:54
Audience: Three. AB: Three.
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Tri. - Tri.
11:56
57,683
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57,683
12:01
squared. Yuck.
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kvadriramo. Ojoj.
12:03
Let me explain to you how
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Naj vam razložim,
12:05
I'm going to attempt this problem.
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kako se bom lotil.
12:08
I'm going to break the problem down into three parts.
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Problem razčlenim na tri dele.
12:11
I'll do 57,000 squared,
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Torej, kvadriram 57,000
12:13
plus 683 squared,
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temu prištejem kvadrat od 683.
12:17
plus 57,000 times
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Prištejem 57,000 krat
12:20
683 times two.
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683 krat dve.
12:22
Add all those numbers together,
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Ko seštejemo vse to,
12:24
and with any luck, arrive at the answer.
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z nekaj sreče dobimo odgovor.
12:28
Now, let me recap.
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Torej, naj povzamem.
12:31
Thank you.
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Hvala.
12:34
While I explain something else --
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Medtem pa naj še nekaj pojasnim --
12:37
-- I know, that you can use, right?
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nekaj, kar vam bo prišlo prav.
12:40
While I do these calculation[s],
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Medtem, ko to računam,
12:42
you might hear certain words,
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boste mogoče slišali nekaj besed
12:44
as opposed to numbers, creep into the calculation.
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namesto številk v mojih računih.
12:48
Let me explain what that is.
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Naj pojasnim.
12:49
This is a phonetic code,
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To je glasovna koda,
12:51
a mnemonic device that I use,
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mnemotehnika, ki jo uporabljam,
12:53
that allows me to convert numbers into words.
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ki omogoča, da pretvorim številke v besede.
12:56
I store them as words, and later on retrieve them as numbers.
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Zapomnim si jih kot besede, kasneje pa jih prikličem
12:59
I know it sounds complicated; it's not --
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kot številke. Sliši se zapleteno, a ni.
13:01
I just don't want you to think you're seeing something out of "Rain Man" here.
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A nočem, da mislite, da sem Rain Man.
13:04
(Laughter)
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(Smeh)
13:06
There's definitely a method to my madness --
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Zagotovo ima ta norost nek smisel --
13:08
definitely, definitely. Sorry.
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zagotovo, zagotovo. Oprostite.
13:10
(Laughter)
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(Smeh)
13:14
If you want to talk to me about ADHD afterwards,
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Če bi se radi pogovorili o hiperaktivnosti,
13:16
you can talk to me then. All right --
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me poiščite kasneje. Torej --
13:18
by the way, one last instruction,
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mimogrede, še zadnje navodilo
13:20
for my judges with the calculators -- OK, you know who you are --
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za moje sodnike s kalkulatorji -- saj veste, kdo ste.
13:23
there is at least a 50 percent chance
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Obstaja najmanj 50% možnosti,
13:26
that I will make a mistake here.
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da se bom zmotil.
13:29
If I do, don't tell me what the mistake is;
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Če se, mi ne povejte, kje je napaka.
13:32
just say, "you're close," or something like that, and I'll try and figure out the answer --
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Samo recite, da "sem blizu" ali kaj takega, pa bom že našel rešitev --
13:35
which could be pretty entertaining in itself.
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kar bo najbrž precej zabavno.
13:39
If, however, I am right,
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Če pa se ne bom zmotil,
13:41
whatever you do, don't keep it to yourself, OK?
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mi to povejte, ne držite tega zase. OK?
13:44
(Laughter)
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(Smeh)
13:45
Make sure everybody knows that I got the answer right,
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Vsi morajo vedeti, da sem pravilno izračunal,
13:47
because this is my big finish, OK.
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saj bo to moj veliki zaključek, OK.
13:50
So, without any more stalling,
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Torej, brez zavlačevanja,
13:53
here we go.
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pa pojdimo.
13:56
I'll start the problem in the middle, with 57 times 683.
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Začnimo kar na sredini. 57 krat 683.
13:58
Now, 57 times 68 is 3,400, plus 476 is 3876,
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57 krat 68 je 3,400, plus 476 je 3876,
14:01
that's 38,760 plus 171,
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to je 38,760 plus 171.
14:04
38,760 plus 171 is 38,931.
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To je 38,931.
14:07
38,931; double that to get 77,862.
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Podvojimo in dobimo 77,862.
14:11
77,862 becomes cookie fission,
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77,862 postane fizija piškotov,
14:13
cookie fission is 77,822.
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fizija piškotov je 77,822.
14:17
That seems right, I'll go on. Cookie fission, OK.
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To se sliši v redu, gremo naprej. OK.
14:19
Next, I do 57 squared, which is 3,249, so I can say,
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Sedaj pa kvadrirajmo 57, to je 3,249. Torej,
14:23
three billion. Take the 249, add that to cookie, 249,
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to so tri milijarde. Vzamemo 249, dodamo to piškotom.
14:28
oops, but I see a carry coming --
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Opa, ovira je na vidiku --
14:30
249 --
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249 --
14:32
add that to cookie, 250 plus 77,
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plus piškoti, 250 plus 77
14:34
is 327 million --
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je 327 milijonov.
14:38
fission, fission, OK, finally, we do 683 squared,
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Fizija, fizija. OK, kvadriramo še 683,
14:41
that's 700 times 666, plus 17 squared
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to je 700 krat 666 plus 17 na kvadrat
14:43
is 466,489, rev up if I need it,
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to je 466,489,
14:46
rev up, take the 466,
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vzamemo še to,
14:48
add that to fission, to get,
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dodamo fiziji, da dobimo
14:50
oh gee --
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ojoj --
14:54
328,489.
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328,489.
14:58
Audience: Yeah!
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Ja!
14:59
AB: Good.
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Dobro.
15:00
(Applause)
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(Aplavz)
15:01
Thank you very much.
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Najlepša hvala.
15:03
I hope you enjoyed mathemagics. Thank you.
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Upam, da ste uživali v matemagiji. Hvala.
15:05
(Applause)
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(Aplavz)
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