Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


quasi
Posts:
12,047
Registered:
7/15/05


Re: Maximisation problem
Posted:
Jul 27, 2013 5:30 AM


pepstein5 wrote: >Peter Percival wrote: >> Paul wrote: >> >> >Let n be a fixed integer > 1. n logicians walk into a bar. >> >The barwoman says "Do all of you want a beer?" The first >> >logician says "I don't know." The second logician says >> >"I don't know." ... The n1st logician says "I don't know." >> >The nth logician says "Yes please." >> >> That doesn't answer the question correctly. >... > >Please could you state your objection? Everyone is narrowly >focusing on the yes/no question: "Do all of the n logicians >want a beer?"
It's not exactly a yes/no question since some of the answers have been "I don't know".
>Everyone saying "I don't know" clearly wants a beer because, >if they didn't want a beer, they would know that not everyone >wants a beer and would answer "no" instead of "I don't know."
The joke has the implicit assumption that each logician would answer yes or no if asked individually as whether or not they want a beer. With that assumption, together with infinitely many levels of recursion about that assumption, the logic of the joke works.
To eliminate that issue, the joke could be stated as follows.
BEGIN JOKE
Let n be a fixed integer > 1. n logicians walk into a bar. The barwoman says "Do all of you want a beer?"
Assume that
(A1) Each logician either wants a beer or doesn't want a beer.
(A2) Each logician knows that each of the others either wants a beer or doesn't want a beer.
(A3) Each logician knows that each logician knows that ...
and so on, for infinitely many levels.
(B1) Also assume that each logician will answer either "Yes","No", or "I don't know", and will only answer "I don't know" if they can't deduce the preferences of the others.
(B2) Each logician knows that each logician will answer either "Yes","No", or "I don't know", and will only answer "I don't know" if they can't deduce the preferences of the others.
(B3) Each logician knows that each logician knows that each logician will answer ...
and so on, for infinitely many levels.
With those assumptions,
The first logician says "I don't know." The second logician says "I don't know." ... The n1st logician says "I don't know." The nth logician says "Yes please".
END JOKE
Of course, the joke should be left as it is, so as not to ruin it. The goal is humor, not precision.
quasi



