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


quasi
Posts:
11,311
Registered:
7/15/05


Re: Maximisation problem
Posted:
Jul 27, 2013 6:16 AM


pepstein wrote: >quasi wrote: >>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
I'm no longer so sure of my claim below about infinitely many levels of recursion.
>>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.
A1 and A2 seem necessary, but I don't now see any need for further levels. I don't know what I was thinking. >> >> (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.
Once again, as far as I can see, B1 and B2 are needed, but I don't see a need for further levels. Then again, right now I'm very tired, so maybe I'm not thinking it through all the way. >> (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, > >I agree with everything in your posting.
I think you agreed too quickly.
I now think the stuff about infinitely many levels is nonsense.
>Would you be so kind as to answer the question I opened the >thread with? Which value of n do you think makes the joke work >best?
I like n = 3 best.
n = 2 wraps up too quickly, with no suspense.
n = 4 or higher is too longwinded.
Leaving n unknown is too abstract, suggesting more conceptual depth than is actually there.
quasi



