In the Laplace’s sunrise problem the question is: what are the chances that Sun will rise again after it has raised 5000 previous day. Let’s reframe the problem: what are the chances that a catastrophe will not happen in the year 5001 given that it didn’t happen in the previous 5000 years. Laplace gives chances of no catastrophe as 1 − 1/(5000 +2). ’+2″ appears here because we are a) speaking about discrete events, and the next year is 5001.
So simplifying we get that Laplace gives 1/(5000) chances of catastrophe for the next year after 5000 year of no-catastrophe.
If we take Gott’s equation for Doomsday argument, it also gives probability of catastrophe 1/(5000) for the situation when I survived 5000 years without a catastrophe BUT was randomly selected from that period. Laplace and Gott achieved basically the same equation but using different methods.
I do not see Laplace’s problem as problematic, it is another version of Doomsday argument and both are correct. But is shows us that “random sampling’ is not a necessary condition of for having Doomsday argument.
In the Laplace’s sunrise problem the question is: what are the chances that Sun will rise again after it has raised 5000 previous day. Let’s reframe the problem: what are the chances that a catastrophe will not happen in the year 5001 given that it didn’t happen in the previous 5000 years. Laplace gives chances of no catastrophe as 1 − 1/(5000 +2). ’+2″ appears here because we are a) speaking about discrete events, and the next year is 5001.
So simplifying we get that Laplace gives 1/(5000) chances of catastrophe for the next year after 5000 year of no-catastrophe.
If we take Gott’s equation for Doomsday argument, it also gives probability of catastrophe 1/(5000) for the situation when I survived 5000 years without a catastrophe BUT was randomly selected from that period. Laplace and Gott achieved basically the same equation but using different methods.
I do not see Laplace’s problem as problematic, it is another version of Doomsday argument and both are correct. But is shows us that “random sampling’ is not a necessary condition of for having Doomsday argument.