most recent 30 from http://mathoverflow.net 2013-05-18T18:54:47Z http://mathoverflow.net/feeds/user/6940 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/28861/mathematics-of-the-anthropic-principle/28915#28915 Zack M. Davis 2010-06-21T05:09:52Z 2010-06-21T05:09:52Z

<p>I agree with Chapman and Clark that this isn't really a math question: anthropics is the epistemological problem about how to <i>interpret</i> probability theory; the theorems themselves are not in doubt.</p> <p>However, since this question hasn't been closed, I might as well make my first post and answer it: if you're interested in anthropic reasoning, I recommend checking out the work of <a href="http://www.nickbostrom.com/" rel="nofollow">Nick Bostrom</a>, who has written a book (<a href="http://www.anthropic-principle.com/book/" rel="nofollow"><i>Anthropic Bias: Observation Selection Effects in Science and Philosophy</i>, available free online</a>) and a number of papers on the subject. I hasten to mention again that these are primarily works of philosophy and not mathematics, but they do include equations where relevant.</p> <p>The first example you mention is known as the <a href="http://en.wikipedia.org/wiki/Doomsday_argument" rel="nofollow">doomsday argument</a> (because if half of all observers that will ever exist have already been born and population grows exponentially, then we should expect the end of the world to come quite soon!). Bostrom discusses the doomsday argument in chapters six and seven of his book and argues that it has not been refuted (!).</p>