Re: Doomsday Thereom
I don't look at this forum very often, so I just found this thread and realize that it pretty much died a month ago, but I'd like to try to explain why I think you are confused. A very very similar theorem appears in the book "Time Travel in Einstein's Universe: The Physical Possibilities of Travel Through Time" by J. Richard Gott. It's a good book - find it at amazon.com. What jimdmcevoy was trying to say was the following:
The number of people to ever exist will be some finite number, N. (Looks like we all agree that this might be a reasonable assumption).
Take each person and number them from 1 to N IN THE ORDER of their birth. I think we all understand this part too.
Now, the part that's confusing some people. Call YOUR number 'x'. EVERYONE who is currently alive will have a number close to 'x', and thus x will be close to the total number of people who have been alive up to the present. Jimdmcevoy says this number is approximately 50 billion, which is probably within an order of magnitude of the correct number. Thus x ~= 50 billion.
HOWEVER: You are just as likely to have been born at any time. There is no reason that you should have been born at the present, when x = 50 billion. You could just as easily have been born when x = 10 billion. x is therefore a random variable distributed from 1 to N. You may not agree that x is distributed randomly (since there are a higher number of births when x is larger), but THIS is what the original argument was saying. He didn't "magic" anything out of thin air. All he said was "I was born randomly, at any time between the beginning of human existence and the end. As it happens, I was the 50 billionth person born. This means that there is a 50% chance that only 100 billion people will ever be born."
Again, this theorem (or a very similar one) is explained in detail at the end of the book above. In the book, Gott uses the theorem to correctly predict the dates of the fall of the Berlin wall, as well as the death of several famous people from history.
~Magic_Man
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