The backwards induction argument assumes the time of execution is a discrete variable.
However, at least as far as we know, time seems to be continuous.
Unexpected hanging paradox
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Re: Unexpected hanging paradox
#12The backwards induction argument assumes the time of execution is a discrete variable. However, at least as far as we know, time seems to be continuous.
What about a scenario that describes an event occurring during a discrete amount of time during a set length of time? For example: A teacher says that he will give the class a surprise pop quiz at the beginning of class some day next week. How does reverse induction fail here?
Re: Unexpected hanging paradox
#13[deleted]
Re: Unexpected hanging paradox
#14Of all those paradoxical thought experiments, this is still my favorite, or really high up at least. Maybe because I've heard it at a young age and my little brain was all flabbergasted. The impression must have lasted.
> Maybe because I've heard it at a young age and my little brain was all flabbergasted. The impression must have lasted.
That rhyme definitely wasn't something I would've forecasted...
Re: Unexpected hanging paradox
#15I enjoy the math versions. "Theorem" version: Every integer is interesting. (Otherwise, one number would be the smallest uninteresting integer. And that would be of notable interest.) "Paradox" version: What is the largest number that cannot be described in fewer than 100 characters? Or even the classic paradox by Russell https://en.wikipedia.org/wiki/Russell%27s_paradox Does the set of all sets that do not include t…
> the largest number that cannot be described in fewer than 100 characters
Almost certainly you mean the smallest number (= positive integer), no? (One doesn't automatically expect that the existence of some positive integer satisfying a property means that there is a largest such.)
Re: Unexpected hanging paradox
#16If the prisoner convinces himself on each day, “I will be hanged today,” then it is not be possible to surprise him. Paradoxes like this tend to make implicit use of assumptions regarding perfect rationality, deduction, and common knowledge, and I think the underlying problem here comes from a violation regarding these.
Re: Unexpected hanging paradox
#17[deleted]
Re: Unexpected hanging paradox
#18It just seems to me it is impossible to be surprised by a bounded random variable in this context. If the death sentence were carried out x days from now, where x is drawn from an exponential distribution, that would fulfill the surprising criterion. The source of the paradox is that the “surprising” aspect is fundamentally incompatible with the bounded nature of the sentence.
Re: Unexpected hanging paradox
#19I've never understood why the resolution to this paradox isn't because of his confidence he expected not to be hung, thus any hanging would be unexpected/a suprise.
Dosent seem terribly paradoxical to me.
Re: Unexpected hanging paradox
#20I enjoy the math versions. "Theorem" version: Every integer is interesting. (Otherwise, one number would be the smallest uninteresting integer. And that would be of notable interest.) "Paradox" version: What is the largest number that cannot be described in fewer than 100 characters? Or even the classic paradox by Russell https://en.wikipedia.org/wiki/Russell%27s_paradox Does the set of all sets that do not include t…
> the largest number that cannot be described in fewer than 100 characters Almost certainly you mean the smallest number (= positive integer), no? (One doesn't automatically expect that the existence of some positive integer satisfying a property means that there is a largest such.)
Oops.
Yeah, smallest.