In the Laplace’s sunrise problem you are not assuming that you are randomly sampled in time, but the prediction is basically the same as in Doomsday argument—if applied to the same period of time.
Typically the sunrise problem is applied only to the next day, and DA is applied to the time several times longer than the whole history of existence of qualified observers, and also sunrise problem is discrete. But if we apply them to the same period of time, they give the same probability.
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 you are not assuming that you are randomly sampled in time, but the prediction is basically the same as in Doomsday argument—if applied to the same period of time.
Typically the sunrise problem is applied only to the next day, and DA is applied to the time several times longer than the whole history of existence of qualified observers, and also sunrise problem is discrete. But if we apply them to the same period of time, they give the same probability.
Could you explain the resemblance between Laplace’s sunrise and Doomsday argument and why the Laplace’s sunrise prediction is problematic?
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.