On 12 Oct 2006, at 4:33PM, jdiebremse wrote:
Case I
If N(blue) = 0, then every native exists in:
State 1: Sees only red dots, but doesn't know if N(blue) = 0 or N
(blue)
=1
This case obviously doesn't apply to the given example.
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**\
*
Case II
If N(blue) = 1, then:
State 1: One native sees only red dots, but doesn't know if N
(blue) = 0
or N(blue) =1
State 2: All other natives see one blue dot, but don't know if N
(blue)
= 1 or N(blue) = 2
Moreover, in this case All Natives know that each and every Native
knows
that each of them is either in State 1 or State 2.
In this case, the anthropologist imparts information to the one native
in State 1, causing the cascade.
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*
Case III
If N(blue) = 2
State 2: Two natives see one blue dot, but don't know if N(blue) =
1 or
N(blue) = 2
State 3: All other natives see two blue dots, but don't know if N
(blue)
= 2 or N(blue) = 3
Moreover, in this case All Natives know that each and every Native
knows
that each of them is either in State 2 or State 3.
But they don't. The two blue-dot natives don't know if the other blue
dot sees one blue dot or *none*.
In this case, the anthropologist doesn't impart any information to
anyone. Everyone knows that N(blue) >= 1. So, presuming that the
island existed in a steady state before the anthropologist's arrival,
then her arrival with the announcement that N(blue) >= 1 has no
effect.
It tells each of the two blue-dots that the other blue-dot now has
enough information to kill himself if he is the only blue-dot. When
neither does, both can deduce they are blue-dots the next day. All
the reds follow the day after.
Possibly Maru
--
William T Goodall
Mail : [EMAIL PROTECTED]
Web : http://www.wtgab.demon.co.uk
Blog : http://radio.weblogs.com/0111221/
If you listen to a UNIX shell, can you hear the C?
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