RE: my objection to the Doomsday argument

From: gts (gts_2000@yahoo.com)
Date: Tue Apr 29 2003 - 14:03:46 MDT

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    Ramez Naam wrote:

    > George Dvorsky wrote:
    >
    >> You pull a ball from one of them, and you get
    >> the number 4. Any reasonable person would therefore assume
    >> that they pulled the ball from the 10-ball machine.
    >
    > This analogy breaks down from the viewpoint of the balls. If
    > you're a ball, and you see that you have a #4 painted on you,
    > then it may seem to you that there's a 50% chance that you're
    > from the machine with 10 balls and a 50% chance that you're
    > from the machine with 1 million balls. After all, you're one
    > of two such balls, and you have no information that suggests
    > you're from one machine or the other (you can never see balls
    > that come later in number than you).

    I don't believe the analogy breaks down for the reason you cite. All you
    know initially is that 1) you are a ball, that 2) there are two sequences of
    balls, one long and one short, and that 3) you come from one of those two
    sequences. You look at your birth order and see that you are ball #4 in your
    sequence. The question then is: "Am I from the short sequence or from the
    long sequence?"

    It is reasonable to conclude that you came probably from the short sequence,
    because the probability of finding yourself to be the 4th ball in the long
    sequence is small by comparison.

    There is a key idea in my last sentence, that of "finding oneself." You
    "found yourself" to be #4 in your sequence. Implicit in the idea of finding
    yourself to be #4 is the assumption that *in principle* you could have found
    yourself to have been any number in either sequence, i.e., that your
    observation of your birth order is a random sample of birth order
    observations taken from the population of observations from which yours is
    drawn. This is the Self-Sampling Assumption (SSA) upon with all of DA theory
    rests. If SSA is false then DA fails immediately, but then so do a lot of
    common sense ideas that we take as obvious fact. And therein lies the rub.

    -gts

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