Talk:Unexpected hanging paradox/Archive 2

Archive 1

Archive 2

You Cannot Say You Are Not Surprised After The Process of Giving Surprise Starts and You Observe It

The problem here is because of the elongation of time in the process of giving surprise to the prisoner. Consider Bob has 5 balls in his bag (red, green, blue, yellow, purple) and he says to Alice that he's going to give her the bag with one of these balls (like you'll be hanged) but which ball that would be is a surprise for her (like the day of the week). At this moment, it is indeed going to be a surprise for Alice which ball she gets. Now Bob starts removing ball from the bag one by one... and Alice observes it, so after 4 balls are removed (and say purple one is left there), she cannot say, "you see, I know now that it is purple ball there, so it is no surprise for me!" She already had a surprise by the time 4 balls are taken out. Similarly the prisoner already had a surprise if he has not been hanged for first four days. How can you have the same surprise again? Which day it would be is a surprise at the time sentence was announced but cannot be once the process of giving surprise is initiated and each day is eliminated one by one.

So if a prisoner says that his hanging on Friday is not a surprise for him, he is flawed in his statement, as he came to know about it just after Thursday noon, of course, surprisingly, as he could have been hanged on Thursday as well. If he says that before the start of the week (that he knows he is going to be hanged on Friday), then it is agreeable that it's not going to be a surprise for him.

So even if the prisoner is hanged on Friday, it is a surprise for him. That the surprise was revealed for him just after Thursday noon is another thing. It's just that there is some time gap before the surprise was open for him and he is hanged. But it is nevertheless, a surprise. If prisoner's argument is bought then there can be no surprises in the world, as just after any surprise is revealed (and before some act related to the surprise is completed), it can be said that now that we know it, it's not a surprise. Mani Sareen (talk) 07:29, 16 December 2012 (UTC)

It doesn't matter that the prisoner decides he will escape

The judge makes 2 claims:

1) The prisoner will be hung on a weekday in the coming week

2) The prisoner will be surprised when summoned to the hanging

The prisoner's reasoning (in deciding that no day will be a surprise) is sound and it leads to the conclusion that claims 1 and 2 cannot both be true. But, why does that make the prisoner assume that claim 1 is false? Common sense would tell us that 2 is false, but 1 is true. If he accepts 1 as true (and accepts that he will be hung), and 2 as false, the prisoner no longer has reason to expect to be hung every day, because that theory was based on the presumption that 2 was true. He is therefore just as surprised to hear the knock at his door at noon on Wednesday as if the judge never said claim 2. The contradiction is removed, and the judge was right all along.

173.23.82.190 (talk) 11:24, 4 January 2014 (UTC)

Please see WP:NOTFORUM and WP:OR. If you want to suggest changes to the article, please state what should be changed, and which reliable sources support the change. Paradoctor (talk) 12:50, 4 January 2014 (UTC)

The View from 30,000 feet

The "paradox" here is because two contradictory things are asserted. Both can't be true. Here is a "resolution", light on "rigor" but heavy on "intuition".

By "complete information" I mean anything that the prisoner knows will happen with probability 1.

Thing 1: The prisoner has "complete information" about being hanged. When the prisoner is told "you will be hanged sometime next week", he has "complete information".

Thing 2: The prisoner does not have "complete information" about being hanged. When the prisoner is told "you will not know whether you will be hanged today", he does not have "complete information".

I don't have "complete information" if I will win the lotto today, even though it is possible I will. There is a small probability (say 1 in a billion trillion) I will suddenly have an urge to buy a lotto ticket that will win, but I do not know anything with probability 1. Similarly telling the prisoner "you may or may not hang today" implied lack of "complete information".

The "solution" for the paradox is that you can't both have and not have "complete information".

If you define the "events" rigorously using probability (measure theory etc.), define rigorously what it means to be "surprised" etc. etc. etc., any paradox goes away.

JS (talk) 19:04, 10 January 2014 (UTC)

WP:TPG: "Article talk pages should not be used by editors as platforms for their personal views on a subject." If you want to suggest changes to the article, please state what should be changed, and which reliable sources support the change. Paradoctor (talk) 19:07, 10 January 2014 (UTC)

this article should be deleted for lack of notability of the subject matter

This so-called paradox is not well known enough to warrant having its own article. Tweedledee2011 (talk) 01:02, 11 January 2014 (UTC)

WP:AfD, though you might want to check the weather report first, it might WP:Snow. Or read the article. Paradoctor (talk) 02:34, 11 January 2014 (UTC)

Lame Duck

I can't believe people are arguing this at all.

This "logic problem" is about as idiotic as the "arrow moves half the distance" problem. Anyone with half a brain realizes that there is no paradox, they just might not be able to articulate exactly why.

This problem breaks down the minute the timeframe is longer than 2 days. It's always a surprise except on the last day. This is exactly a case of the gambler's fallacy. Nothing more. Odds don't change due to expectations. If the Judge draws a random lot to choose the day (which is implied) then any expectations the prisoner makes are pure fantasy. He will be surprised by the day, in fact, he makes himself more surprised by the very concept of believing he can outwit the judge.

Think about it.

Lajekahr 15:15, 12 May 2007 (UTC)

Of course paradoxes do not exist, not in mathematics at least, but the point is to find situations which would be very hard to believe to not be paradoxical. The Unexpected Hanging Paradox is an excellent example in my opinion. To solve a "paradox" means to find an error in it. The point is not to decide whether the prisoner can outwit the judge, but to find where the prisoner made a mistake. By the way, the case of 2 days is no different from the case of 5 days, if the prisoner is to be hanged on the first. People are arguing, i think, because there are many possible solutions, but the explanation Lajekahr has given is not a complete solution. Do you think the prisoner made a mistake when he concluded that he would not be hanged on Thursday, but with Friday his conclusion was valid? Think about it. --Cokaban (talk) 15:30, 8 December 2007 (UTC)

I don't understand why this is considered a paradox at all. If he's alive on Thursday night, he would have to be hanged Friday, which means he expects it, which means it can't be the day. If he's alive Wednesday night, then the day can't be Thursday, because if it wasn't Thursday, it would have to be Friday, which he would expect, etc. However, on Monday morning, how does he know if it's going to be Monday, or Tuesday? Can't be Thursday because at 12:01 PM on Wednesday he would KNOW it's Thursday because it can't be Friday. If he's alive on Monday night, it could be Tuesday or Wednesday, which means they could kill him Monday and he would be surprised. — Preceding unsigned comment added by 207.199.253.60 (talk) 19:43, 18 February 2014 (UTC)