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.

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/
> 
> >

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