The
Doomsday Argument is based on
Bayes' Theorem. Stated most
simply in terms of balls in
urns, as all things
probabilistic: If you are a purple ball, and you know you've been selected from either an urn with many
puse balls and few purple balls, or an urn with few puse balls and many purple balls. Then it is most likely that you were
selected from the urn with many purple balls.
So applying this model to myself, I look at all the possible times to choose a me. Assuming that a me is interchangeable with a you and an everyone-else-that-ever-lived-or-ever-will, the time that I am most likely to be chosen is when the population of me-interchangables is greatest. If we assume geometric human population growth, and accept that the way humans find a generation is the same way a ball finds an urn, then my being alive and Bayes being smart, means that we don't have much time left.
How about this model though? Are individuals randomly selected without replacement as the model in the Doomsday Argument suggests? Is it any less reasonable to think that they are popped off a stack, or dependent upon preexisting factors? Did selecting a you depend on who your parents were, or would you be you even if you had different genes?
Because the Doomsday Argument is a very crude mathematical model, and because the choice of model is rooted in complex philosophical issues such as free will and determinism, it feel that it is unreasonable even to proceede with the arithmetic.
Reason be damned. Where's my calculator?