another puzzzle

From: Stathis Papaioannou <stathispapaioannou.domain.name.hidden>
Date: Fri, 17 Jun 2005 00:12:59 +1000

You find yourself in a locked room with no windows, and no memory of how you
got there. The room is sparsely furnished: a chair, a desk, pen and paper,
and in one corner a light. The light is currently red, but in the time you
have been in the room you have observed that it alternates between red and
green every 10 minutes. Other than the coloured light, nothing in the room
seems to change. Opening one of the desk drawers, you find a piece of paper
with incredibly neat handwriting. It turns out to be a letter from God,
revealing that you have been placed in the room as part of a philosophical
experiment. Every 10 minutes, the system alternates between two states. One
state consists of you alone in your room. The other state consists of 10^100
exact copies of you, their minds perfectly synchronised with your mind, each
copy isolated from all the others in a room just like yours. Whenever the
light changes colour, it means that God is either instantaneously creating
(10^100 - 1) copies, or instantaneously destroying all but one randomly
chosen copy.

Your task is to guess which colour of the light corresponds with which state
and write it down. Then God will send you home.

Having absorbed this information, you reason as follows. Suppose that right
now you are one of the copies sampled randomly from all the copies that you
could possibly be. If you guess that you are one of the 10^100 group, you
will be right with probability (10^100)/(10^100+1) (which your calculator
tells you equals one). If you guess that you are the sole copy, you will be
right with probability 1/(10^100+1) (which your calculator tells you equals
zero). Therefore, you would be foolish indeed if you don't guess that you in
the 10^100 group. And since the light right now is red, red must correspond
with the 10^100 copy state and green with the single copy state.

But just as you are about to write down your conclusion, the light changes
to green...

What's wrong with the reasoning here?

--Stathis Papaioannou

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