I think the actual situation is even more underspecified and moot than 
Greg Egan or anyone else would have it.
The entire discussion is fundamentally flawed because everyone assumes 
that their cosmology has involved the prediction of an (scientific) 
observer and what that scientific observation actually entails. 

This is done without reference to neuroscience.

Until a cosmology predicts the necessary structure of a brain that 
results in human scientific observation occuring ..(ie .. that it 'be 
like a human scientist observing X when doing science to describe X) the 
entire discussion is just a lot of  empty waffle.

Cosmology should /not/ be explaining what we observe!

Cosmology's job is to explain *observation itself. ....*That is.... the 
mere existence of an observer, not merely what such an observer will 

*That done, everything else follows.

_Side issue:_ Based on the discussion in the original post (below) - 
What I see is a re-discovery-in-progress of the "No Free Lunch" theorem 
of machine learning:

Wolpert, D. H. (1996) The lack of A priori distinctions between learning 
algorithms. Neural Computation. 8, 7, 1341-1390.
Wolpert, D. H. (1996) The existence of A priori distinctions between 
learning algorithms. Neural Computation. 8, 7, 1391-1420.
Koppen, M., D. H. Wolpert, and W. G. Macready (2001) Remarks on a recent 
paper on the ''No free lunch'' theorems. IEEE Transactions on 
Evolutionary Computation. 5, 3, 295-296.

Machine learning folks gave up the very thing cosmologists are doing 
over a decade ago. Maybe a few cosmologists should have a look at the 
NFL theorem - it may save a lot of angst. To apply it to science, all 
you have to do is replace the machine with a human using only boundary 
I/O (not qualia) to do 'observation'. The job is done.

IMO the route of the discussion emanates from a failure to realise that 
what cosmology is trying to do is the "mother of all inverse ( or 
'ill-defined') problems" by assuming that what is derived includes the 
physics basis of observation when all they are doing is generating a 
model for observations by an assumed observer without having any idea of 
how the observation actually happens.  'Scientific observation' (the 
facts of observation in general) and 'measurement' (an abstracted 
particular observation) are being confused.

*Re: Bayes*
Any a-priori posit assumes an observer exists already (for how is a 
conditional to be formulated?), when the object of the whole exercise is 
to explain observation itself...you have failed the moment you write 
down your conditional. The assumption of a conditional is equivalent to 
supervised learning in a situation _when there is no supervisor_. In 
supplying a conditional you have implicitly added a supervisor: YOU. All 
of these discussions where any sort of posit of an observer occurs are 
doomed to fail, for they assume observation is explained. Everything 
that flows from such posits is empty in the garbage-in/garbage-out sense.

The universe we live in manages to produce an endogenous observer (a 
human scientist) intrinsically using innate properties that must exist 
for human science to be possible. Human science is enabled by very 
specific, highly localised brain material activity that delivers 
scientific observation that have been repeatedly verified over and over 
for more than a century. Human science is critically dependent in the 
most verifiable way on the delivery of observation - in particular the 
visual scene delivered by occipital lobes. The scene is the visual 
experience you are currently having whilst reading this email. When you 
embed your brain in the causality chain inclusing the the studied 
phenomenon ... voila! scientific observation occurs.

/When are cosmologists going to take a look at the neuroscience? When is 
the 'mathematics-rapture' era going to end?/

Until a cosmological theory predicts/explains how human brain material 
makes a scientist possible (and 'appearances' do /not/ do that), 
cosmology is just off in the weeds, deluding itself. That is, a true 
cosmology should make predictions in brain material that shall be 
otherwise unavailable. Only when such predictions are found shall signs 
of a real explanation (of scientists) be created. None of the 
discussions in cosmology do that nor have they ever done that.


Colin Hales

Greg Egan wrote:
> On Jun 13, 9:25 am, Russell Standish <[EMAIL PROTECTED]> wrote:
>> 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're able to extract the following (somewhat 
>> fanciful) predictions:  theory A implies that in the entire history of
>> the universe, there will be 10^50 observers* of class 1 and 10^5000 
>> observers of class 2, while theory B implies that in the entire history of
>> the universe, there will be 10^5000 observers of class 1 and 10^50 observers 
>> of class 2."
> Hi Russell
> 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.
> 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 could argue that this ought to be somewhat higher than 10^10,
> depending on how we classify our ancestors, but the point is that any
> reasonable number we pick will be less than 10^50.  And of course this
> whole scenario is just a toy model for the sake of having a concrete
> example to discuss.)
> We then have:
> P(H|A) = P(H|B) = 1
> P(A) = P(B) = 1/2
> P(H) = P(A) P(H|A) + P(B) P(H|B) = 1
> P(A|H) = P(H|A) P(A) / P(H) = 1/2
> P(B|H) = P(H|B) P(B) / P(H) = 1/2
> In other words, the data we have, expressed in the observation H, does
> nothing to discriminate between theory A and theory B, and leaves the
> initial prior probabilities unchanged.
> We, in the here and now, have no access to any process that randomly
> samples the set of all observers in the history of the universe.  Of
> course it's possible to construct various sums over the set of *all*
> observers and seek to maximise some kind of global average, and to ask
> questions such as "What strategy, if adopted uniformly by every single
> observer in the history of the universe, would maximise the
> expectation value for the number of observers in the history of the
> universe who correctly guessed whether A or B was the true description
> of the universe."  But whether or not there are any plausible
> scenarios in which maximising that number could be a desirable
> goal ... the fact remains that if we're discussing the *information*
> available to *us* -- the human population of Earth at the present
> moment -- we do not have access to the probabilities p(1|A), p(2|A),
> p(1|B), p(2|B) that you describe.
> The context in which I was discussing this at the N-Category Café is
> the claim by some cosmologists that we ought to favour A-type
> cosmological theories in which class 2 observers like us, with a clear
> Darwinian history, will not be outnumbered (over the whole history of
> the universe) by class 1 observers (Boltzmann brains).  My contention
> is that we have no empirical data at the present time that tells us
> anything at all about the relative frequencies (over the whole history
> of the universe) of class 1 and class 2 observers, and that our own
> existence should not be mistaken for the outcome of a random sampling
> of that whole-of-spacetime population.  These issues are discussed in
> more detail in:
> "Are We Typical?" by James Hartle and Mark Srednicki, 
> http://arxiv.org/abs/0704.2630
> >

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