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. 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? JDG _______________________________________________ http://www.mccmedia.com/mailman/listinfo/brin-l
