Discussion: The Prisoner’s Paradox and Gödel’s Incompleteness Theorem
From the forum: Sam's Essays
This thread was started by: joxn.
Discussion start time: 2011-02-28 19:17:50.
From the forum: Sam's Essays
This thread was started by: joxn.
Discussion start time: 2011-02-28 19:17:50.
From: joxn.
Subj: The Prisoner’s Paradox and Gödel’s Incompleteness Theorem
Date: 2011-02-28 19:17:50.
Subj: The Prisoner’s Paradox and Gödel’s Incompleteness Theorem
Date: 2011-02-28 19:17:50.
Here's a link to the post under discussion: <a href="http://www.xamuel.com/prisoners-paradox/">The Prisoner’s Paradox and Gödel’s Incompleteness Theorem</a>.
You left off my favorite part of the story, which is the punchline: So, Friday rolls around, and the executioner and two guards show up at the prisoner's door. "Ready to go? It's time to get your head chopped off!" "But ... but ... it can't be! I proved that the execution could never take place!"
"SURPRISE!"
You left off my favorite part of the story, which is the punchline: So, Friday rolls around, and the executioner and two guards show up at the prisoner's door. "Ready to go? It's time to get your head chopped off!" "But ... but ... it can't be! I proved that the execution could never take place!"
"SURPRISE!"
From: Glowing Face Man.
Subj: Re: The Prisoner�s Paradox and Gödel�s Incompleteness Theorem
Date: 2011-02-28 21:09:56.
Subj: Re: The Prisoner�s Paradox and Gödel�s Incompleteness Theorem
Date: 2011-02-28 21:09:56.
From: yourfriendrick.
Subj: Re: The Prisoner's Paradox and Godel's Incompleteness Theorem
Date: 2011-03-04 01:02:28.
Subj: Re: The Prisoner's Paradox and Godel's Incompleteness Theorem
Date: 2011-03-04 01:02:28.
The Turing Test (recently a subject of discussion at:
http://www.xamuel.com/guessability-turing-test/
reminds me of the Prisoner's Dilemma.
Think of it this way: Turing, who was gay, introduced the test as a variation on a gender test. A person with an epicene voice would be hidden behind a screen and folks were supposed to guess whether the voice was that of a man or a woman.
Obviously, to Turing, this kind of guessing had a lot to do with intimacy issues, and therefore with trust.
Likewise, the iterated Prisoner's Dilemma is a question of trust.
When we evaluate people's outputs, over time, we are always asking ourselves, "Is this the kind of person that I can trust?"
The Turing article linked above made the point: 'both terminals should eventually appear human. If a terminal spouts human-text about half the time and machine-text about half the time, then it cannot be produced by a machine (assuming we humans are not ourselves machines). Programming a computer to appear human about half the time is no easier than programming it to appear human all the time. Thus, neither terminal is purely machine, and Player A should eventually begin to suspect as much, at which point he can safely stop ever changing his mind, confident that both other players are human and thus that his guess is trivially correct and doesn’t need changing.'
Put that into the context of trust versus distrust. Eventually, when people behave unreliably, one doesn't have any enemies - everyone is a frenemy. Everyone can be cooperated with in the short term, or betrayed in the blink of an eye.
http://www.xamuel.com/guessability-turing-test/
reminds me of the Prisoner's Dilemma.
Think of it this way: Turing, who was gay, introduced the test as a variation on a gender test. A person with an epicene voice would be hidden behind a screen and folks were supposed to guess whether the voice was that of a man or a woman.
Obviously, to Turing, this kind of guessing had a lot to do with intimacy issues, and therefore with trust.
Likewise, the iterated Prisoner's Dilemma is a question of trust.
When we evaluate people's outputs, over time, we are always asking ourselves, "Is this the kind of person that I can trust?"
The Turing article linked above made the point: 'both terminals should eventually appear human. If a terminal spouts human-text about half the time and machine-text about half the time, then it cannot be produced by a machine (assuming we humans are not ourselves machines). Programming a computer to appear human about half the time is no easier than programming it to appear human all the time. Thus, neither terminal is purely machine, and Player A should eventually begin to suspect as much, at which point he can safely stop ever changing his mind, confident that both other players are human and thus that his guess is trivially correct and doesn’t need changing.'
Put that into the context of trust versus distrust. Eventually, when people behave unreliably, one doesn't have any enemies - everyone is a frenemy. Everyone can be cooperated with in the short term, or betrayed in the blink of an eye.
From: Glowing Face Man.
Subj: Re: The Prisoner�s Paradox and Gödel�s Incompleteness Theorem
Date: 2011-03-04 20:19:54.
Subj: Re: The Prisoner�s Paradox and Gödel�s Incompleteness Theorem
Date: 2011-03-04 20:19:54.
Hmmm, I suppose gender tests are also nonguessable. The same sort of paradox would apply to those too. Say Player A is trying to detect a non-male speaker (as far as he knows, both speakers might be non-male). The truth is, one speaker is male and one is female. The operator is being obnoxious and switching the terminals so that as soon as A's guesses become correct, they are rendered incorrect. Then locally, A will change his mind infinitely often, assuming that he can eventually detect males and females minus the operator's prank. But globally, both dialogues appear to be about half-male and about half-female, which bizarre behavior is definitely non-male, and if A can eventually discern as much, he can safely stop changing his mind-- a paradox.