Year: 2005
Type: preprint
Abstract: Using the Autodialer thought experiment, we show that the Self-Sampling Assumption (SSA) is too general, and propose a revision to the assumption that limits its applicability to causally-independent observers. Under the revised assumption, the Doomsday Argument fails, and the paradoxes associated with the standard SSA are dispelled. We also consider the effects of the revised sampling assumption on tests of cosmological theories. There we find that, while we must restrict our attention to universes containing at least one observer, the total number of observers predicted in each universe is irrelevant to the confirmation of a theory. The Doomsday Argument (Bostrom 1997, 2002; Leslie 1989, 1996) concludes that the prior probability we assign to the short-term extinction of humanity is greatly magnified by our observation that we exist at the present time in human history. Before we discuss the Doomsday Argument itself, it is instructive to examine one of the thought experiments that is held up as its analogue. The following experiment, Cubicles, is a minor variation of the original Incubator described by Bostrom (2002). Cubicles One hundred cubicles are numbered 1 to 100. A coin is flipped to determine how many people will be placed in the cubicles. If the result is heads, one person is placed in all 100 cubicles. If the result is tails, only the first 10 cubicles are occupied. Each person who enters a cubicle is led in blindfolded so they cannot tell which cubicle they are placed in, nor can they tell how many other people have been placed in cubicles. Initially, you find yourself in a cubicle, but you do not know which one. You are asked to estimate the probability that the coin toss was tails. You have no additional information, so you answer 50%. Next, you learn that you are in cubicle #5. What is the posterior probability that the coin flip was tails? The revised probability of the coin flip having been tails can be computed using Bayes ' theorem: p(tails|#5) = p(#5|tails) p(tails) / (p(#5|tails) p(tails) + p(#5|heads) p(heads)) (1)
Author: Ivan Phillips
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W68575130