## [0704.2630] Are We Typical?

 Authors: James B. Hartle, Mark Srednicki Abstract: Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by some physical process, despite the absence of any evidence for such a process, or any observational evidence favoring our typicality. It is possible to favor theories in which we are typical by appropriately choosing their prior probabilities, but such assumptions should be made explicit to avoid confusion. [PDF]  [PS]  [BibTex]  [Bookmark]

Discussion related to specific recent arXiv papers
Antony Lewis
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### [0704.2630] Are We Typical?

This paper argues that the correct datum for comparing cosmological theories is There exists at least one observing system with our observations. This seems to be essentially the same as 'full non-indexical conditioning' advocated in considerably more detail in arXiv:math/0608592. It is certainly reasonably compelling, at least for finite theories. One feature is that it favours models with larger volume (because usually the probability for an observer to exist with all our observations is proportional to volume), which is the 'presumptuous philosopher' objection (which is an objection based purely on intuition and does not mean it is necessarily wrong; e.g. see gr-qc/0009081).

The main problem is that it seems to be unclear how to apply this kind of reasoning in infinite theories where all observations exist at least once. e.g. regarding Boltzmann brains: it's true that brains with different observations are irrelevant; however any infinite theory with Boltzmann brains will have my observations an infinite number of times, and so using this reasoning alone a theory with only brains cannot be distinguished from a more 'physical' theory where my brain evolved. [note that in a Boltzmann brain theory the Earth and other cosmologists are just fake memories in by brain, so the entire information, gathering and utilizing system is just my brain]

Mark Srednicki
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### [0704.2630] Are We Typical?

Pretty cool that this board (apparently automatically) sent an email telling me that our paper was under discussion ...

Jim Hartle and I were not previously aware of Neal's paper (which does not seem to be cross-listed on either hep-th or gr-qc). It presents a very thorough and cogent analysis; however, Neal always assumes that the probability of our complete data set (everything we've ever observed) is much less than 1/N, where N is the number of universes. We discuss this case at the beginning of page 5 of our paper. Neal argues that, if this is not the case, we should reason as if it is. In that case, his "full non-indexical conditioning" gives different results than our "there exists at least one observing system with our observations".