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

Možete li riješiti slavno tešku zelenooku logičku zagonetku? - Alex Gendler

Prevoditelj: Martina Valković Recezent: Ivan Stamenković

Imagine an island where 100 people,

Zamislite otok gdje je sto ljudi,

all perfect logicians, are imprisoned by a mad dictator.

sve savršeni logičari, zarobio ludi diktator.

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

Ne postoji izlaz, osim jednog čudnog pravila.

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

Svaki zatvorenik može prići čuvarima tijekom noći i zatražiti da ga se pusti.

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

Ako imaju zelene oči, bit će pušteni.

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

Ako ne, bit će bačeni u vulkan.

As it happens, all 100 prisoners have green eyes,

Svih sto zatvorenika ima zelene oči,

but they've lived there since birth,

no živjeli su ondje od rođenja,

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

a diktator je osigurao da ne mogu saznati svoju vlastitu boju očiju.

There are no reflective surfaces,

Nema reflektivnih površina,

all water is in opaque containers,

sva je voda u neprozirnim posudama,

and most importantly,

i, najvažnije,

they're not allowed to communicate among themselves.

nije im dozvoljeno da međusobno komuniciraju.

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

Iako mogu vidjeti jedni druge tijekom jutarnjeg prebrojavanja.

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

Ipak, svi znaju da nitko nikada ne bi riskirao i pokušao otići,

without absolute certainty of success.

a da nije apsolutno siguran da će uspjeti.

After much pressure from human rights groups,

Nakon pritisaka grupa za zaštitu ljudskih prava,

the dictator reluctantly agrees to let you visit the island

diktator nerado pristane dozvoliti vam da posjetite otok

and speak to the prisoners under the following conditions:

i obratite se zatvorenicima pod sljedećim uvjetima:

you may only make one statement,

imate pravo na samo jednu izjavu,

and you cannot tell them any new information.

i ne smijete im pružiti nikakvu novu informaciju.

What can you say to help free the prisoners

Što možete reći kako bi pomogli oslobađanju zatvorenika

without incurring the dictator's wrath?

bez da izazovete diktatorovu srdžbu?

After thinking long and hard,

Nakon dugog i napornog razmišljanja,

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

kažete okupljenima, "Barem jedan od vas ima zelene oči".

The dictator is suspicious

Diktator je sumnjičav,

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

no umiri se mišlju da vaša izjava nije mogla ništa promijeniti.

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

Vi odete, a život na otoku se, naizgled, nastavlja kao i ranije.

But on the hundredth morning after your visit,

No, stotog jutra nakon vašeg posjeta,

all the prisoners are gone,

svi su zatvorenici nestali,

each having asked to leave the previous night.

svaki od njih je zatražio oslobođenje noć ranije.

So how did you outsmart the dictator?

Pa, kako ste nadmudrili diktatora?

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

Možda pomaže ako shvatite da je broj zatvorenika arbitraran.

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

Pojednostavimo stvari zamišljajući tek dvoje, Adriju i Billa.

Each sees one person with green eyes,

Svaki vidi osobu sa zelenim očima,

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.

Prvu noć nijedno ne reagira.

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

No, kad sljedeće jutro vide da su oboje još tu,

they gain new information.

dobiju novu informaciju.

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

Adria shvati da, da je Bill vidio ne-zelenooku osobu pored sebe,

he would have left the first night

otišao bi prve noći

after concluding the statement could only refer to himself.

nakon što bi zaključio da se izjava mogla odnositi samo na njega.

Bill simultaneously realizes the same thing about Adria.

Bill istovremeno shvati istu stvar o Adriji.

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 oči moraju biti zelene.

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

I, sljedećeg jutra, oboje su otišli.

Now imagine a third prisoner.

Sada zamislite trećeg zatvorenika.

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

Adria, Bill i Carl svaki vide dvoje zelenookih ljudi,

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

no nisu sigurni vidi li također i svaki drugi zatvorenik dvoje zelenookih ljudi,

or just one.

ili samo jednoga.

They wait out the first night as before,

Čekaju prvu večer kao i prije,

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

no sljedećeg jutra i dalje ne mogu biti sigurni.

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

Carl misli, "ako imam ne-zelene oči,

Adria and Bill were just watching each other,

Adria i Bill su samo gledali jedno drugo,

and will now both leave on the second night."

i sad će oboje otići sljedeće noći".

But when he sees both of them the third morning,

No, kada ih vidi oboje sljedećeg jutra,

he realizes they must have been watching him, too.

shvati da su, također, gledali i njega.

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

Adria i Bill su oboje prolazili kroz isti misaoni proces,

and they all leave on the third night.

i oni svi odlaze treće noći.

Using this sort of inductive reasoning,

Koristeći ovakvu vrstu induktivnog

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

zaključivanja, vidimo da će se obrazac ponavljati bez obzira koliko osoba dodali.

The key is the concept of common knowledge,

Ključ je u konceptu zajedničkog znanja,

coined by philosopher David Lewis.

kojeg je skovao filozof David Lewis.

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 njenom kazivanju svima istovremeno.

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

Sada, osim što zna da barem jedan od njih ima zelene oči,

each prisoner also knows that everyone else is keeping track

svaki zatvorenik također zna i da svaki drugi prati

of all the green-eyed people they can see,

sve zelenooke ljude koje vidi,

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

i da svaki od njih također to zna, i tako dalje.

What any given prisoner doesn't know

Ono što nijedan zatvorenik ne zna

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

jest je li on sam jedan od zelenookih ljudi

the others are keeping track of

koje drugi prate,

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

sve dok nije prošlo toliko noći koliko je zatvorenika na otoku.

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

Naravno, mogli ste poštediti zatvorenike 98 dana na otoku

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

tako što biste im rekli da barem 99 od njih ima zelene oči,

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

no kad su ludi diktatori uključeni, bolje je biti oprezan.