JDG wrote: > > But how does this work for N(blue) = 4? > The key point is that the natives are omniintelligent and know that all other natives are also omniintelligent.
> The initial state is that each native has two cases: > > 1) There are three blue-dot natives, and each blue dot native sees > two blue dot natives. > > 2) There are four blue-dot natives, including himself, and each blue > dot native sees three blue dot natives. > > In this case, I don't see how the naturalist provides any additional > information. In the initial state, every native knows that every other > native knows that there is at least one blue dot. > He does. Because of the omniintelligence hypothesis, each native can reason like this: (a) If there is only one blue dotted native, then, seeing that everybody else is red dotted, this native will commit ritual suicide in the first night. Induction Hypothesis: (b) Suppose that there are (N+1) blue dotted natives. Then, each of these natives, noticing that the other (N) blue dotted natives didn't commit suicide in the N-th night, will commit ritual suicide in the (N+1)-th night The naturalist provides information because he starts the process, by forcing step (a) of the induction. Alberto Monteiro _______________________________________________ http://www.mccmedia.com/mailman/listinfo/brin-l
