# Re: another puzzzle

From: rmiller <rmiller.domain.name.hidden>
Date: Thu, 16 Jun 2005 09:30:45 -0500

At 09:12 AM 6/16/2005, 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.

RM: You've just described me at work in my office.

>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.

RM. . .at my annual New Years' party.

>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?

RM: Nothing wrong with the premise or the reasoning IMHO. Happens to me
every day---while sitting at a traffic light alone in my car(s) all 10^100
of me come up with a great idea---I try to write it down and the light
changes to green.

>--Stathis Papaioannou
>
>_________________________________________________________________