Can you solve the famously difficult green-eyed logic puzzle? - Alex Gendler

Možete li da rešite čuvenu tešku logičku zagonetku zelenih očiju? - Aleks Džendler (Alex Gendler)

Prevodilac: Marija Kojić Lektor: Ivana Krivokuća

Imagine an island where 100 people,

Zamislite ostrvo na kojem je 100 ljudi,

all perfect logicians, are imprisoned by a mad dictator.

sve savršene logičare, zatvorio ludi diktator.

Nema izlaza, osim jednog čudnog pravila.

There's no escape, except for one strange rule.

Any prisoner can approach the guards at night and ask to leave.

Bilo koji zatvorenik može noću prići stražarima, i tražiti da ode.

Ako imaju zelene oči, biće pušteni.

If they have green eyes, they'll be released.

If not, they'll be tossed into the volcano.

Ako nemaju, biće bačeni u vulkan.

As it happens, all 100 prisoners have green eyes,

Igrom slučaja,

svih 100 zatvorenika ima zelene oči,

but they've lived there since birth,

ali, žive ovde od rođenja,

and the dictator has ensured they can't learn their own eye color.

i diktator se postarao da ne mogu da saznaju svoju boju očiju.

There are no reflective surfaces,

Ne postoje reflektujuće površine,

all water is in opaque containers,

sva voda je u neprozirnim posudama,

i, što je najvažnije,

and most importantly,

they're not allowed to communicate among themselves.

nije im dozvoljeno da komuniciraju jedni sa drugima,

Though they do see each other during each morning's head count.

mada mogu da vide jedni druge prilikom jutarnjih prozivki.

Nevertheless, they all know no one would ever risk trying to leave

Ipak, svi oni znaju da niko nikada ne bi rizikovao da pokuša da ode

without absolute certainty of success.

a da ne bude potpuno siguran u uspeh.

After much pressure from human rights groups,

Posle mnogo pritiska grupa za ljudska prava,

diktator preko volje pristaje da vam dozvoli da posetite ostrvo

the dictator reluctantly agrees to let you visit the island

i razgovarate sa zatvorenicima pod sledećim uslovima:

and speak to the prisoners under the following conditions:

you may only make one statement,

možete dati samo jednu izjavu,

and you cannot tell them any new information.

i ne smete im dati nijednu novu informaciju.

What can you say to help free the prisoners

Šta možete reći da pomognete da se oslobode zatvorenici

without incurring the dictator's wrath?

a da ne izazovete diktatorov bes?

Nakon dugog i pažljivog razmišljanja,

After thinking long and hard,

you tell the crowd, "At least one of you has green eyes."

kažete gomili:

„Najmanje jedno od vas ima zelene oči.”

The dictator is suspicious

Diktator je sumnjičav

but reassures himself that your statement couldn't have changed anything.

ali se teši da vaša izjava nije mogla ništa da promeni.

You leave, and life on the island seems to go on as before.

Vi odete, i život na ostrvu se naizgled nastavlja kao i do sada.

But on the hundredth morning after your visit,

Ali, stoto jutro posle vaše posete,

all the prisoners are gone,

svi zatvorenici su nestali,

jer su svi prošle noći pitali da odu.

each having asked to leave the previous night.

So how did you outsmart the dictator?

Dakle, kako ste nadmudrili diktatora?

It might help to realize that the amount of prisoners is arbitrary.

Moglo bi vam pomoći da shvatite da je broj zatvorenika proizvoljan.

Hajde da pojednostavimo stvari

Let's simplify things by imagining just two, Adria and Bill.

tako što ćemo zamisliti samo dva zatvorenika, Adriju i Bila.

Oboje vide jednu osobu sa zelenim očima,

Each sees one person with green eyes,

and for all they know, that could be the only one.

i koliko oni znaju, to bi mogla biti jedina takva osoba.

For the first night, each stays put.

Prve noći, nijedno ne preduzima ništa.

But when they see each other still there in the morning,

Ali, kada vide da je ona druga osoba još uvek tu sledećeg jutra,

they gain new information.

dobijaju novu informaciju.

Adria realizes that if Bill had seen a non-green-eyed person next to him,

Adrija shvata,

da bi Bil, da je pored sebe video osobu koja nema zelene oči,

he would have left the first night

otišao prve noći

after concluding the statement could only refer to himself.

posle zaključka da se izjava odnosi samo na njega.

Bil istovremeno shvata istu stvar o Adriji

Bill simultaneously realizes the same thing about Adria.

The fact that the other person waited

Činjenica da je druga osoba čekala

tells each prisoner his or her own eyes must be green.

govori svakom zatvoreniku da njegove ili njene oči mora da su zelene boje.

I drugog jutra, oboje odlaze.

And on the second morning, they're both gone.

Now imagine a third prisoner.

Sada, zamislite trećeg zatvorenika.

Adria, Bill and Carl each see two green-eyed people,

Adrija, Bil i Karl - svako od njih vidi dve osobe koje imaju zelene oči,

but aren't sure if each of the others is also seeing two green-eyed people,

ali nisu sigurni da svako od njih isto vidi dve osobe koje imaju zelene oči,

or just one.

ili vide samo jednu osobu.

They wait out the first night as before,

Sačekaju prvu noć, kao u prošlom primeru,

but the next morning, they still can't be sure.

ali, sledećeg jutra, ioš uvek ne mogu da budu sigurni.

Karl misli: „Ako ja nemam zelene oči,

Carl thinks, "If I have non-green eyes,

Adria and Bill were just watching each other,

Adrija i Bil su se upravo posmatrali,

and will now both leave on the second night."

i oboje će otići druge noći.”

But when he sees both of them the third morning,

Ali, kada ih Karl oboje vidi trećeg jutra,

he realizes they must have been watching him, too.

shvata da mora biti da su i njega takođe posmatrali.

Adrija i Bil su takođe prošli kroz isti proces razmišljanja,

Adria and Bill have each been going through the same process,

and they all leave on the third night.

i svi odlaze treće noći.

Using this sort of inductive reasoning,

Koristeći ovaj vid induktivnog zaključivanja,

we can see that the pattern will repeat no matter how many prisoners you add.

vidimo da će se obrazac ponavljati bez obzira koliko zatvorenika dodamo.

The key is the concept of common knowledge,

Ključ je koncept zajedničkog znanja

coined by philosopher David Lewis.

koji je iskovao filozof Dejvid Luis.

The new information was not contained in your statement itself,

Nova informacija nije bila sadržana u samoj vašoj izjavi,

but in telling it to everyone simultaneously.

već u tome što ste je izrekli svima u isto vreme.

Now, besides knowing at least one of them has green eyes,

Pored toga što znaju da najmanje jedna osoba ima zelene oči,

each prisoner also knows that everyone else is keeping track

svaki zatvorenik takođe zna da svi drugi prate

of all the green-eyed people they can see,

sve zelenooke osobe koje mogu da vide

and that each of them also knows this, and so on.

i da svako od njih takođe to zna, i tako dalje.

What any given prisoner doesn't know

Ono što svaki zatvorenik ne zna

is whether they themselves are one of the green-eyed people

jeste da li i oni sami spadaju među ljude koji imaju zelene oči

the others are keeping track of

a koje drugi posmatraju,

until as many nights have passed as the number of prisoners on the island.

sve dok ne prođe isti broj noći koliko ima zatvorenika na ostrvu.

Of course, you could have spared the prisoners 98 days on the island

Naravno, mogli ste da poštedite zatvorenike 98 dana na ostrvu

da ste im rekli da najmanje 99 njih ima zelene oči,

by telling them at least 99 of you have green eyes,

but when mad dictators are involved, you're best off with a good headstart.

ali kada se radi o ludim diktatorima, bolje da se dobro obezbedite.