Hi Russell, thanks very much for your reply.

It's possible that I'm arguing at cross-purposes here, because I
gather that the whole reason for this list is to discuss models of the
universe that are very different from standard cosmology, but I hope
you won't mind if I pursue a defence of my specific claims at the N-
Category Café, which are intended to apply to reasoning about standard
cosmology.

On Jun 15, 8:45 am, Russell Standish <[EMAIL PROTECTED]> wrote:
> On Fri, Jun 13, 2008 at 09:28:07PM -0700,Greg Egan wrote:
> > The p(2|A) you give above is the probability for selecting one
> > observer at random from the totality of all observers throughout the
> > history of the universe, and finding that he/she/it belongs to class 2
> > (given theory A).  But no such selection process has taken place.
>
> There may be no physical process doing the sampling like pulling balls
> from an urn, but it is nevertheless a sampling. My attributes (eg
> height, weight and so on) are all drawn from distributions of such
> attributes. Why not some hypothetical property like "observer class"
> as set up in this toy problem?

Your height and weight can be understood as arising from a complicated
sequence of local, causal processes and a set of assumptions about
your initial conditions (at the very least, including the assumption
that you are human).  Whether some health statistician samples a sub-
population to which you belong, or whether you, in the process of
living your life, sample various probabilistic influences, the
relevant distribution needs to be *accessible* for this way of looking
at things to make sense.

For example, suppose an Australian health statistician is forbidden to
leave Australia or to access data collected elsewhere, and that there
is no migration between countries.  Then the *global* distributions of
human height and weight become completely invisible to her, and
completely irrelevant to a child growing up in Australia.

Suppose theory A claims that children who receive less than X
kilojoules a day will all have a height of less than 120 cm at age 15,
while theory B claims that half of these malnourished children will
nonetheless exceed 120 cm at age 15.  I currently have no reason to
prefer theory A over theory B, but I'd like to gather some empirical
data to see which one is right.

But suppose I have access only to data about Australia, and it so
happens than in Australia, there are *no* children who receive less
than X kilojoules a day.  Then it doesn't matter what I do or how I
reason, I am never going to have a justification to distinguish
between theory A and theory B.  Noticing, say, that my own height
would have different relative frequencies in the global population
under the two theories is not informative, because there is no
relevant sense in which I can be viewed as a random sample of the
global population.

A cosmologist who hopes to distinguish between cosmological theories
based on their predictions about future populations of Boltzmann
brains is in exactly the same situation.  The data to which she has
access does not discriminate between the theories.  It is pointless
for her to note that one theory implies that the overwhelming majority
of observers in the history of the universe will be Boltzmann brains,
while another theory reverses the proportions; she simply does not
have access to the global populations in question.

> > Given that humans are class 2 observers, all we have is the fact H:
>
> >    H := "The number of class 2 observers in the history of the
> > universe is at least of the order 10^10."
>
> We also have the fact that I am of class 2.

But there is no "also" here, because it is a necessary consequence of
H that someone exists who says "I am of class 2".   To say "I am of
class 2" means no more and no less than:  "The number of class 2
observers in the history of the universe is at least 1."  It does
*not* mean "Someone was picked at random from the set of all observers
who have ever lived, or ever will live, and was found to be class 2".

Ultimately this boils down to locality.  I, here and now, do not know
the future, so of course I can't discriminate between rival theories
that make identical predictions about the present but different
predictions about the future.
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