Applying the SSA, the colour of the light when you first find yourself
in the room is more likely to be the high measure state than the low
measure state. (You didn't state what that colour was, but hopefully
the fictional prisoner can remember it).
With the RSSA, subsequent states tell you no information whatsoever
about which state is high measure. With the ASSA, you would expect
that the light remains in one state most of the time (googol out of
googol+1). So the fact that the light is alternating (and that you
trust that the letter is in fact true) implies that the ASSA does not
apply in this thought experiment.
Cheers
On Fri, Jun 17, 2005 at 12:12:59AM +1000, Stathis Papaioannou wrote:
>
> 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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Received on Thu Jun 16 2005 - 21:04:16 PDT