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

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