Almost the right answer. In fact, if you download the population of countries from the US Census bureau, throw them into a histogram, you will find that the distribution is best fit with a power law, with exponent -1 (my best fit was actually -1.05, but it was -1 within error). This implies that the reduced chance of appearing in a lower population country is exactly counterbalanced by the effect of their being more lower population countries. Hence anthropic arguments cannot tell us what our nationality should be.

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The interesting aside from this is that any arbitrary category (citizenship is obviously rather arbitrary) should follow Zipf's law (x^{-1}), which indeed many such categories do (eg frequencies of English words etc). I've never heard of this justification of Zipf's law before - has anyone else? (Note it may not be phrased in anthropic terminology). You are right in saying this is like the SIA argument. However I am fairly inconvinced by this argument - it seems to work against John Gott III's version of the DA, but does not explain why we seem to be living at the beginning of an exponential population growth (it is a fact that the population trend through the 20th century is atypical with the rest of history - again see the US Census bureau for historical figures). Now to conscious ants. I originally posted this argument at msg03660 (Google seems to find this URL: http://www.mail-archive.com/everything-list@eskimo.com/msg03660.html) The problem is that ants (or amoebae) is a rather arbitrary category, corresponding to thousands of species. To an ant, all of those species might be as distinct as chimpanzees or giraffes are to us. An alternative way of phrasing this is to ask what is the expected body mass of a conscious individual. Biologist do know something about the distribution of body masses of biological organisms. There is something called Damuth's law, named after a chap who wrote about this in 1981 in Nature, which states that the density of a species (individuals per square metre) is inversely proportional to its body mass raised to the power of 3/4, or in symbols: d = A m^{-3/4} The trouble is that this result is not quite the probability distribution that we're after. We need to settle the measure with which this law is calculated. My guess is that the error (or bin size, if you like) of any individual point in the distribution is some fixed proportion of the organisms mass, ie that a logarithmic measure is used. ie P(m<M) \propto \int^M m^{-3/4}d(ln m) = \int^M m^{-7/4} dm Then the d is the density of a fixed species. If the range of different species overlaps more greatly the smaller an individual is, we would expect an even faster fall off as m->\infty. I really need to dig out Damuth's paper. Anyway, regardless of what it is, it does look the the distribution is a power law with exponent less than -1. The interesting thing about power law distributions is that they have no mean, or more accurately the mean reflects the value of the cutoffs: <x> = \int_{x_0}^{x_1} x x^s \approx x_1 (if s>-1) \approx x_0 (if s<-1) assuming x_0 << x_1 (Exercise for the interested reader) So we can conclude with Damuth's law and anthropic reasoning that the expected body mass to be close to the minimum body mass for consciousness - ie dogs and chimpanzees may be conscious, but ants are not. Cheers On Mon, Jun 20, 2005 at 10:39:42PM +0200, Saibal Mitra wrote: > > I don't think so, because most people on Earth are not Chinese. The correct > refutation of the Doomsday Paradox was given by D. Dieks and involves the > Self Indicating Axiom. The definition of the reference class defines the set > of observers that you consider to be you. The DA involves applying Bayes's > theorem and to do that correctly you have then to use the correct a priori > probability which is also fixed by the choice of the reference class. The > two effects cancel and there is no Doomsday Problem. This is all explained > here: > > > http://arxiv.org/abs/gr-qc/0009081 > > > > Saibal > > > ------------------------------------------------- > Defeat Spammers by launching DDoS attacks on Spam-Websites: > http://www.hillscapital.com/antispam/ > > > -- *PS: A number of people ask me about the attachment to my email, which is of type "application/pgp-signature". Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics 0425 253119 (") UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 ----------------------------------------------------------------------------

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