# Re: Cosmology and Boltzmann brains

```On Thu, Jun 12, 2008 at 11:43:26PM +0200, Günther Greindl wrote:
>
> Hi all,
>
> someone on another list alerted me to this post, there is a very
> interesting discussion going on on that blog related to Observer Moments:
>
> http://golem.ph.utexas.edu/category/2008/06/urban_myths_in_contemporary_co.html
>
> Greg Egan has posted too; and has some very interesting things to say.
> Specifically, he says the right things why DA fails:```
```
I'm not sure his application of Bayes is correct. Given the facts of
his hypothetical scenario, and writing e=10^{-4050}

p(1|A) = e
p(2|A) = 1-e
p(1|B) = 1-e
p(2|B) = e

This is my translation of:

"Now suppose that (somehow) we\u2019re able to extract the following (somewhat
fanciful) predictions:  theory A implies that in the entire history of the
universe, there will be 1050 observers* of class 1 and 105000 observers of
class 2, while theory B implies that in the entire history of the universe,
there will be 105000 observers of class 1 and 1050 observers of class 2."

Now we further suppose there is no reason to prefer theory A over B,
ie p(A)=p(B).

Then we need to compute the likelihood of theory A given the fact that
we're an observer of class 2, ie:

p(A|2) = p(A & 2) / p(2) = p(2|A) p(A) / p(2)   ... (1)

and

p(B|2) = p(B & 2) / p(2) = p(2|B) p(B) / p(2)   ... (2)

dividing (1) by (2) gives

p(A|2) / p(B|2) = p(2|A) / p(2|B) = (1-e) / e = 10^{4050}

ie Bayes' theorem most definitely implies theory A is overwhelmingly
supported.

Have I missed something, or is Greg Egan wrong?

In a later posting, he gives absurd example of some extremely
improbably theory A, and applying the above reasoning. Yet the above
reasoning assumes p(A)=p(B), which is not the case in his absurd
example. It may be relevant to the BB argument though. If theory A was
"we are a statistical fluctuation (ie Boltzmann brains)", and theory B
was "evolved by Darwinian evolution", then p(A) << p(B). One cannot
comment on whether one should prefer A or B, since the numerical
values are just pulled out of a hat in any case.

--

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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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