The Unexpected Hanging

[Gandalf the White]

I can sort of understand the arguments flying around about rour friendly infinite demons. However I still cannot get my head round the solution to the Hanging puzzle. Could someone who understands how the paradox is broken explain it better? Thanks.

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How many Grey Labryntians does it take to change a lightbulb?

Precisely 0.99999...

[ZenBeam]

I think Gandalf means this puzzle.

[Rhino]

I have trouble getting my head around anything as I have quite the massive cranium

I only saw the unexpected hanging puzzle after it had been solved...I don't even remember the answer I had in my head before I looked at the official solution. But I am a believer.

The prisoner didn't know when the execution would be. The logic of his defense limited the number of days the execution could take place, thereby reducing the surprise. But he couldn't just apply that logic selectively so that he would have only one possible time of execution, he had to apply it to everything, eliminating all possible days.

Bottom Line: He still did not know when the execution would occur.

Actually, he was confident in his defense, so he did not even know the execution would occur. Even if he did know that the execution was still on, he could not say when it would occur

[This message has been edited by Rhino (edited 05-18-2000).]

[CrystyB]

[CrystyB]

So where am i wrong??? Anyone???

[HappyMutant]

If he follows that logic, he thinks others think that he expects to be hanged, and therefore will not get hanged. If he goes by this logic, he will not expect to be hanged. Therefore, if he doesn't expect to be hanged, it'd be a surprise.

[Eddie Murphy]

Look, Nawton, I know that you know that I know that you wanna hang me. So hang me!

[ZenBeam]

I think I just figured out what CrystyB means: the prisoner always assumes he will be hanged that day, so it will never be a surprise, as the Judge said it must be. This hinges on te "surprise" part of the rulling, not on the "which day of the week" part.

A way around that, for the judge, is to have the prisoner drugged Wednesday night, and kept asleep all day Thursday. The prisoner can then be told at 11:00 am on Friday that he will be hanged "today", and he will be surprised to find that "today" is Friday, not Thursday.

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It is so clear, and so it is hard to see.

[Kerinsky]

I have several things to point out

1) I think the base issue here is actually a defenition of the word "suprise". I think the following deals with any defenition of the word (that I would find reasonable)

Breaking the prisoners logic down you get a statement such as "There is no day that you can execute me on that would suprise me, therefore you cannot execute me". The resolution is simple. Execute him on Tuesday, he'll be suprised won't he?

2) Of course reading the puzzle it seems to me that the judge gives a defenition, or clarification, of what he means by suprise.

"It is the decision of this court that the day of the hanging be a surprise to the prisoner; you shall not know for certain what day you will be hanged until one hour before the execution."

Now set up a computer with a psuedo-random number generator to pick a number from 1 to 5, run it and then at 11 AM each morning have it tell the warden to execute the prisoner or not. By this time the prisoner knows his appeal has been rejected so he "knows" that he will be executed that day every day. Run through the seven possibilites and on average his "knowledge" is correct 1/4th of the time, definetly not a certainty. He also can't make a reverse argument (i.e. based on the logic of what I've gone through above they can't execute me on the first day, and then regressing) because he doesn't know for certain that he will be executed on monday, if he is it's simply a lucky guess that he came to be seemingly logical means (Guessing a coin toss corectly does not indicate you had any knowledge)

Perhaps stating this another way, in the above scenerio he cannot "know" for certain what day he will be killed because that "decision" is made by a machine that he cannot observe, therfore he cannot have knowledge of it.

Finally, I present what I consider to be the most compelling arguement.

The prisoners logical is based on an asumption (or 7) as follows: "I will be executed on Monday, or Tuesday, or Wednesday, or Thursday or Friday or Saturday or Sunday" Based on the above he reasons that he cannot be executed on Sunday, because after noon on Saterday he can be certain that he will be executed on Sunday. Wrong.

His very own arguement shows that his assumption is wrong because there is another possibility, that he won't be executed! Thus even at 10 AM Friday morning he cannot "know" or "be certain" that he will be executed that day, because there is always a finite chance that something will happen that would keep him from being executed. If he can't be certain that he'll be executed on the final day then his entire arguement, obviously, falls apart.

I guess in the end it all comes down to this. The prisoner was hung, and he was suprised, therefore his logic was flawed somewhere. It's a matter of interpretation
as to where and how it failed...

[Ewan]

I think It failed becuase he wasnt the prisoner that he postulated.

prinsoner thinks:

imagine a prisoner thinking about getting execututed by surprise......

but the prisoner he thinks about is not him, the prisoner he postulates dosnt carry the reasoning on as far as the real prisoner dose. and hence the theorem dosnt match real life. ie. the postulated prisoner believes he will be executed on the last day on the penultimate day, but the rela one believe he will go free