Original Message: ----------------- From: John D. Giorgis [EMAIL PROTECTED] Date: Thu, 12 Oct 2006 21:43:28 -0400 To: brin-l@mccmedia.com Subject: RE: Paradox, or, Breaking the mind of logic
Based on the explanations of Dan and Alberto, let me give this another crack: ********************************************************************* >Case I > >If N(blue) = 0, then every native exists in: > > >State 1: > -Sees only red dots > -Doesn't know if N(blue) = 0 or N(blue)=1 > -Doesn't know if everyone else is existing in State 1 or State 2 > >This case obviously doesn't apply to the given example. > > >********************************************************************* > >Case II > >If N(blue) = 1, then: > >State 1: One native > -Sees only red dots > -Doesn't know if N(blue) = 0 or N(blue) =1 > -Doesn't know if everyone else is existing in State 1 or State 2 > >State 2: All other natives > -See one blue dot, > -Don't know if N(blue)= 1 or N(blue) = 2 > -Don't know if native with blue dot is in State 1 or State 2 > -Don't know if All other natives are in State 2 or State 3 > >In this case, the anthropologist imparts information to the one native >in State 1 that N(blue) = 1. That native commits suicide on the first >day, everyone else goes on the second day. > >************************************************************************ > >Case III > >If N(blue) = 2 > >State 1: (No Natives) > -Sees only red dots > >State 2: Two Natives > -See one blue dot, > -Don't know if N(blue)= 1 or N(blue) = 2 > -Don't know if native with blue dot is in State 1 or State 2 > -Don't know if all other natives are in State 2 or State 3 > >State 3: All Other Natives > -See two blue dots > -Don't know if N(blue) = 2 or N(blue) = 3 > -Don't know if the two natives with blue dots are in State 2 or State 3 > -Don't know if all other natives are in State 3 or State 4 > >In this case, the anthropologist imparts second-order knowledge. The >two natives in State 2 don't know if the other one is blissfully living >in State 1 - believing that it is one happy island of red dots. When >the other one does not commit suicide on the 1sst day, they then realize >that it is because the other sees one blue dot - their own. They die >that night, and the rest die the next night. > >************************************************************************ >****************************** > >Case IV > > >If N(blue) = 3 > >State 1: (No Natives) > -Sees only red dots > >State 2: (No Natives) > -Sees one blue dot >State 3: Three Natives > -See two blue dots > -Don't know if N(blue) = 2 or N(blue) = 3 > -Don't know if the two natives with blue dots are in State 2 or State 3 > -Don't know if all other natives are in State 3 or State 4 >State 4: All Other Natives > -See three blue dots > -Don't know if N(blue) = 3 or N(blue) = 4 > -Don't know if the three natives with blue dots are in State 3 or >State 4 > -Don't know if all other natives are in State 4 or State 5 >I'm still not sure what the anthropologist imparts in this situation. Using your termonology, third order knowledge. You have shown, in Case III, that if there are two people with blue dots, then they will each deduce that on day two. Gor knows that too. >Every native knows that every other already sees at least one blue dot. >Thinking about the case of the three natives in State 3 - let's call >them Gor, Kull, and Tar as Alberto suggested. >Day 1: >Gor thinks: If I am red, then Kull and Tar each see one blue dot Kull >and Tar don't know if I see one blue dot or two blue dots. >Gor thinks: If I am blue, the Kull and Tar each see two blue dots. >Kull and Tar don't know if I see one blue dot or two blue dots. >In both cases, the anthropologist imparts no new information to anyone, >so no one commits suicide. >Day 2: >Gor thinks: Neither Kull nor Tar kicked the bucket last night. That is >because they each saw at least one blue dot - just as the anthropologist >said. But I knew *yesterday* that they each saw one blue dot. How is >today any different? Moreover, Kull and Tar see that I am still >around, so I must see at least one blue dot - but they knew that >yesterday too. Again, how is today any different? Day 3: Gor thinks, Kull and Tar did not both kick the bucket last night. That means neither one of them deduced that they were in state 2, one of two natives with blue dots. If they each only saw one blue dot, then they would have deduced that by yesterday. Thus, I must have a blue dot....and kill myself along with Kull and Tar tonight. Dan M. _______________________________________________ http://www.mccmedia.com/mailman/listinfo/brin-l -------------------------------------------------------------------- mail2web - Check your email from the web at http://mail2web.com/ . _______________________________________________ http://www.mccmedia.com/mailman/listinfo/brin-l
