I am currently re-reading Stephen Baxter's "Time". In this book, he uses (not necessarily endorses) the so called Carter Catastrophe. As Baxter is an author who usually has his science right (if on the speculative side), his use of this doomsday argument - even as a plot device - is heckling me.
The argument runs as follows (extract from "The Doomsday Argument" on
www.anthropic-principle.com):
Quote:
Imagine that two big urns are put in front of you, and you know that one of them contains ten balls and the other a million, but you are ignorant as to which is which. You know the balls in each urn are numbered 1, 2, 3, 4 ... etc. Now you take a ball at random from the left urn, and it is number 7. Clearly, this is a strong indication that that urn contains only ten balls. [...]
But now consider the case where instead of the urns you have two possible human races, and instead of balls you have individuals, ranked according to birth order. As a matter of fact, you happen to find that your rank is about sixty billion. Now, say Carter and Leslie, we should reason in the same way as we did with the urns. That you should have a rank of sixty billion or so is much more likely if only 100 billion persons will ever have lived than if there will be many trillion persons. Therefore, by Bayes' theorem, you should update your beliefs about humankind’s prospects and realize that an impending doomsday is much more probable than you have hitherto thought.
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In Baxter's book, one character calculates based on this argument that Doomsday is 150, maximum 200 years away.
Deep in my gut I have the feeling that this argument is fundamentally flawed (read: rubbish), but I can't come up with a clean and neat rebuttal. The best I can come up with: As the human population has grown roughly exponentially in the known past, exactly the same argument has been valid for each and every generation before us - for instance also for the generation that lived, say, 300 years ago. And yet we are here, 300 years after an imminent doom.
What are your takes on this argument?