On Sat, Jun 14, 2008 at 07:56:21PM -0700, Greg Egan wrote:
> 
> 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.

Not at all. What sparked our/my interest is that you seemed to have
interesting argument against the use of anthropic reasoning. However,
on reflection it seems to boil down to "there is no mysterious
pre-world of souls hanging around waiting the be born, so there is no
distribution of observers to be sampled from". I disagree with this syllogism.

...

> 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.

Assuming for the sake of argument that I can be viewed as a random
sample of the global population, how does this actually help to
distinguish theory A or B, unless I actually received less than X
kJ/day, which, by assumption is  not the case. I don't see how
anthropic reasoning makes a difference in this case.

> 
> 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.
> 

In only having superficial knowledge of the BB argument (largely
gleaned from New Scientist articles), I think I'll leave this one to
more knowledgable people to comment.

> > > 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".
> 

Again - I disagree.

> 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.

But we do this all the time. Why is it we reject crackpot claims that
the world will end on such and such a date for instance?

Of course, one day, one of these guys might be proven right :)

Good luck convincing the N-Category Cafe crowd.

Cheers

-- 

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A/Prof Russell Standish                  Phone 0425 253119 (mobile)
Mathematics                              
UNSW SYDNEY 2052                         [EMAIL PROTECTED]
Australia                                http://www.hpcoders.com.au
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