Paradox Answers

[kentonio]

The answer I prefer is that the hangman or electrocutioner or whatever flips a coin each day - heads the prisoner dies, tails his execution is deferred. The executioner doesn't know on which day the prisoner will be executed so neither can the prisoner know, and there is only a very minute chance that the hangman will need to lie (either by deferring the execution til the following week or else by automatically doing the execution on Saturday without the coin flip), and this chance can be further reduced by flipping multiple coins (if either coin comes up heads then the prisoner is executed)

Why would it matter if the executioner knew? The only information presented is that a) it will be a day next week at noon & b) the prisoner won't know in advance. Apart from the reason for it not being Saturday (which is logical as long as you consider Saturday the last day of the week), there appears to be no reason at all why he couldn't be killed on any other day.

[loinburger]

Why would it matter if the executioner knew?

Because if the executioner doesn't know then it's very difficult to make the argument that the prisoner would know

[kentonio]

Because if the executioner doesn't know then it's very difficult to make the argument that the prisoner would know

Why would the executioner knowing mean the prisoner knew? The prisoner is the only one who isn't allowed to know in advance.

[loinburger]

If the executioner knows the date of the execution in advance then the prisoner's reasoning is sound - on Thursday afternoon he'll know in advance that he's going to be executed on Friday because he has correctly concluded that he can't be executed on Saturday without knowing in advance the date of his execution. However, if the executioner doesn't know the date of his execution either then the prisoner can't apply this reasoning because the executioner's coins might actually dictate that the prisoner be executed on Saturday (which would make the executioner incorrect, but there is a much higher probability that he will be correct than incorrect)

Anyway, an alternative is that the prisoner's logic is self-defeating, because if he concludes that he can't be executed on Saturday then boy won't he be surprised when he's executed on Saturday

[Dinner]

Hearts of Iron IV was released on the 72nd anniversary of the Normandy landings

If it follows Paradox's usual pattern it will be buggy and incomplete upon release but by the time the second expansion pack comes out it will be a great game.

[kentonio]

If the executioner knows the date of the execution in advance then the prisoner's reasoning is sound - on Thursday afternoon he'll know in advance that he's going to be executed on Friday because he has correctly concluded that he can't be executed on Saturday without knowing in advance the date of his execution. However, if the executioner doesn't know the date of his execution either then the prisoner can't apply this reasoning because the executioner's coins might actually dictate that the prisoner be executed on Saturday (which would make the executioner incorrect, but there is a much higher probability that he will be correct than incorrect)

No, his logic is still fatally flawed, you only need two consecutive 'possible' days. Saturday is definitely out, as is Friday. Thursday is eliminated but only because both Saturday and Friday are. Wednesday however is firmly in play (as are all previous days), because on Wednesday at 11:59 he has no idea whether the execution date is Wednesday or Thursday. He can't rule out Thursday without actually reaching Thursday morning. He won't know its Thursday (and therefore impossible) until 12:01, by which time he could already be dead.

Thinking about it, Thursday might still be possible for the same reason.

[giblets]

A prisoner is told that he is to be executed on the following week at noon, but he will not know in advance the day on which he is to be executed. The prisoner reasons that he can't be executed on Saturday, because after noon on Friday he'll know that he's going to be executed on Saturday. By the same reasoning he can't be executed on Friday, because after noon on Thursday he'll know that he is going to be executed on Friday (because he can't be executed on Saturday). Applying this reasoning to every other day leads the prisoner to the conclusion that he can't be executed on the following week.

On the following week he was executed on Wednesday. Did the warden lie to the prisoner, or was the prisoner's reasoning fallacious?

(A less grim version of this paradox exists in which a teacher says that she will give a pop quiz next week and the students won't know on which day they'll have the quiz)

The executioner was right, so the prisoner's reasoning was wrong.

[Aeson]

As a defensive measure, the prisoner should have adopted the multiverse theory and thus known that he would be killed on each day of the week.

[Ben Kenobi]

Achilles is in a race with a tortoise - he runs ten times faster than the tortoise but the tortoise has a 10 meter head start. After Achilles runs ten meters the tortoise will have run one meter; after Achilles runs one meter the tortoise will have run one tenth of a meter; after Achilles runs one tenth of a meter the tortoise will have run one hundredth of a meter. Achilles realizes that he can never catch the tortoise, because whenever he attempts to close the distance the tortoise will have extended the distance.

We know that he could catch the tortoise at 20 metres, because he would have run 20 metres and the tortoise would only have run 12. At 12 metres, the tortoise would have run 11.2 metres. So we know that at some point between 10 and 12 metres the runner has to have passed the tortoise.

[loinburger]

That reasoning is sloppy - he catches the tortoise after running exactly 100/9 meters

[Aeson]

Then the tortoise will bite him in the heel, and go on to an easy victory ...

[loinburger]

Agreed, this must be one helluva turtle if it's only ten times slower than Achilles

[The Mad Monk]

Not necessarily; Achilles always did have that tendon problem.

[Aeson]

With Achilles taken down by the turtle, Hector repulses the Greek armies and isn't fooled by the wooden horse. Troy never falls, and thus Rome is never founded. With no Rome, Jesus isn't crucified. So without Rome or Christianity, Europe remains backwards, pagan, and divided, easily picked apart and conquered by Muslims in later centuries. The Muslims have no need for an alternate route to India, and indeed don't even want one found so as to continue to control the nexus of trade, so the new world remains undiscovered until much later. The Iroquois use this time to spread across the continent thus spreading their myth of the Great Turtle across the land ... and so, by defeating Achilles, the turtle becomes a god!

[The Mad Monk]

...but without Jesus to spread the concept of monotheism beyond Judaism, Mohamed can never be inspired! Clearly, the Golden Horde conquers all!