Re: Cosmology and Boltzmann brains

2008-06-19 Thread Bruno Marchal


On 19 Jun 2008, at 02:51, Brent Meeker wrote:


 Günther Greindl wrote:
 Brent,

 scientific theory.  Occams razor is a vague desiderata. You can  
 justify
 almost anything by choosing your definition of complex, e.g.   
 theists
 say, God did it. is the simplest possible theory.

 no you can't:
 http://www.overcomingbias.com/2007/09/occams-razor.html

 [...]
 But I agree that the problem with God or The Witch as a theory is  
 that they
 can explain anything and so fail to explain at all.



It all depends of your theory or theology. If by God you mean the  
creationist God who build the world 6000 years ago, then you get an ad  
hoc theory, which nevertheless can be taken as a falsifiable  
explanation. This is exactly Vic's Stenger point and I agree with him.  
Not only such a theory is falsifiable, but it can be considered as  
having been falsified and has been wisely abandoned by any reasonable  
scientist since. This is where I agree again with Vic Stenger.
[aparte: ... and given that some creationist asks for a course on  
creationism at school, then I think that creationnism should indeed  
be taught at school in the introduction to biology and evolution so  
that the failure of that theory is well explained, and here Vic  
Stenger's book can be very useful indeed. The creationist God is not  
supported by the facts].

If by God you mean the physical universe, and by it, the physical  
universe, then indeed, as a theory, this explains the existence of the  
physical universe in a trivial way, so this does not explain the  
existence of the physical universe.

If by God you mean the physical universe, and by it you mean  
consciousness, then you get a falsifiable theory, which is indeed  
falsified in all the computationalist theories (by UDA).

If by God you mean arithmetical or mathematical truth then you get a  
falsifiable theory of both consciousness and of the conscious  
appearance of physical (observable) universes. The theory predicts the  
existence of non trivial third person sharable probabilistic  
interfering dreams (subjective experiences) and is today well  
sustained by facts and logic. Indeed QM confirms its most counter- 
intuitive statements. But tomorrow it could been falsified as well.  
That is not obvious at all, but follows again by UDA.

Bruno

http://iridia.ulb.ac.be/~marchal/




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Re: Cosmology and Boltzmann brains

2008-06-18 Thread Brent Meeker

Russell Standish wrote:
 On Tue, Jun 17, 2008 at 09:24:21PM -0700, Brent Meeker wrote:
   
 scientific theories (doing so by definition). The reason it is
 rejected is because of the arbitrary nature of the date makes it a
 more complex theory (in the Occam's razor sense).
   
 And it is not POVI.

 Brent Meeker

 

 True, but then POVI is a specialised version of Occams razor.

   
It is more specific and as Vic argues it is sine qua non for a 
scientific theory.  Occams razor is a vague desiderata. You can justify 
almost anything by choosing your definition of complex, e.g.  theists 
say, God did it. is the simplest possible theory.

Brent

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Re: Cosmology and Boltzmann brains

2008-06-18 Thread Günther Greindl

Brent,

 scientific theory.  Occams razor is a vague desiderata. You can justify 
 almost anything by choosing your definition of complex, e.g.  theists 
 say, God did it. is the simplest possible theory.

no you can't:
http://www.overcomingbias.com/2007/09/occams-razor.html

most relevant quote from the above post:

This lets us see clearly the problem with using The lady down the 
street is a witch; she did it to explain the pattern in the sequence 
0101010101.  If you're sending a message to a friend, trying to 
describe the sequence you observed, you would have to say:  The lady 
down the street is a witch; she made the sequence come out 0101010101. 
  Your accusation of witchcraft wouldn't let you shorten the rest of the 
message; you would still have to describe, in full detail, the data 
which her witchery caused.

Witchcraft may fit our observations in the sense of qualitatively 
permitting them; but this is because witchcraft permits everything, like 
saying Phlogiston!  So, even after you say witch, you still have to 
describe all the observed data in full detail.  You have not compressed 
the total length of the message describing your observations by 
transmitting the message about witchcraft; you have simply added a 
useless prologue, increasing the total length.

The real sneakiness was concealed in the word it of A witch did it. 
  A witch did what?

QUOTE END

same goes for god did it

Cheers,
Günther

-- 
Günther Greindl
Department of Philosophy of Science
University of Vienna
[EMAIL PROTECTED]
http://www.univie.ac.at/Wissenschaftstheorie/

Blog: http://dao.complexitystudies.org/
Site: http://www.complexitystudies.org

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Re: Cosmology and Boltzmann brains

2008-06-18 Thread Brent Meeker

Günther Greindl wrote:
 Brent,
 
 scientific theory.  Occams razor is a vague desiderata. You can justify 
 almost anything by choosing your definition of complex, e.g.  theists 
 say, God did it. is the simplest possible theory.
 
 no you can't:
 http://www.overcomingbias.com/2007/09/occams-razor.html
 
 most relevant quote from the above post:
 
 This lets us see clearly the problem with using The lady down the 
 street is a witch; she did it to explain the pattern in the sequence 
 0101010101.  If you're sending a message to a friend, trying to 
 describe the sequence you observed, you would have to say:  The lady 
 down the street is a witch; she made the sequence come out 0101010101. 
   Your accusation of witchcraft wouldn't let you shorten the rest of the 
 message; you would still have to describe, in full detail, the data 
 which her witchery caused.
 
 Witchcraft may fit our observations in the sense of qualitatively 
 permitting them; but this is because witchcraft permits everything, like 
 saying Phlogiston!  So, even after you say witch, you still have to 
 describe all the observed data in full detail.  You have not compressed 
 the total length of the message describing your observations by 
 transmitting the message about witchcraft; you have simply added a 
 useless prologue, increasing the total length.
 
 The real sneakiness was concealed in the word it of A witch did it. 
   A witch did what?
 
 QUOTE END
 
 same goes for god did it
 
 Cheers,
 Günther
 

That's a computer scientist's idea of explanation, a definite description. 
  In fact you can use an ostensive definition, That., while pointing and 
no description is needed.  The witch did it. is a casual explanation, not 
a description, and a casual explanation is often the kind needed since it 
tells you something you can do to change That, e.g. kill the witch.

But I agree that the problem with God or The Witch as a theory is that they 
can explain anything and so fail to explain at all.

Brent

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Re: Cosmology and Boltzmann brains

2008-06-17 Thread Bruno Marchal

Hi  Greg,


 Thanks very much, everyone, for an interesting discussion, and thanks
 for your patience towards someone who hasn't read your previous
 debates on these issues.


You are welcome Greg.



 I hope to find time to follow up all the links people gave.  Russell,
 that link to the Everything Wiki currently gives a 403.


Don't hesitate to ask any question or make any remark  if interested.

Best,

Bruno


http://iridia.ulb.ac.be/~marchal/




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Re: Cosmology and Boltzmann brains

2008-06-17 Thread Brent Meeker

Russell Standish wrote:
 On Sun, Jun 15, 2008 at 01:40:09AM -0700, Greg Egan wrote:
...
 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?
 We reject those claims because they flow from theories that we reason
 should have led to observable consequences in the past (e.g. theories
 of interventionist deities).  So what we have are prior probabilities
 that strongly disfavour those crackpot theories -- and given equal
 crackpot ratings, their predictions about the future are irrelevant.
 If crackpot A tells me that the world will end in 2012, and crackpot B
 tells me that the world will end in 20,012, then all else being equal
 I will (in 2008) give them both *equal* low credence.

 
 I was actually thinking more of theories like the law of gravity will
 be suspended on the 25th of July, 2012, but otherwise everything else
 is the same. Obviously it makes the same retrodictions as our usual
 scientific theories (doing so by definition). The reason it is
 rejected is because of the arbitrary nature of the date makes it a
 more complex theory (in the Occam's razor sense).

And it is not POVI.

Brent Meeker


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Re: Cosmology and Boltzmann brains

2008-06-16 Thread Russell Standish

Sorry about that. It seems one needs the stuff after the domain - try

http://everythingwiki.gcn.cx/wiki/index.php?title=Main_Page

Cheers

On Sun, Jun 15, 2008 at 07:34:39PM -0700, Greg Egan wrote:
 
 Thanks very much, everyone, for an interesting discussion, and thanks
 for your patience towards someone who hasn't read your previous
 debates on these issues.
 
 I hope to find time to follow up all the links people gave.  Russell,
 that link to the Everything Wiki currently gives a 403.
 
-- 


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


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Re: Cosmology and Boltzmann brains

2008-06-15 Thread Greg Egan

On Jun 15, 1:27 pm, Russell Standish [EMAIL PROTECTED] wrote:
 What sparked our/my interest is that you seemed to have
 interesting argument against the use of anthropic reasoning.

I'm certainly not arguing against *all* anthropic reasoning; every
argument needs to be examined on a case by case basis.

 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.

This is where reasoning about conventional cosmology departs from
reasoning about all-universe models.  In the latter context, it might
make sense to consider myself, right now as comprising a vast number
of instances who have identical current experiences, but whose next
experience will be different for different instances.  I might then
concern myself with adopting a strategy that will benefit a majority
of my instances, and which can exploit the fact that those instances,
in their totality, obey some distribution.  In that context, there
certainly is a distribution of observers to be sampled from.

But in conventional cosmology, although observers of this form are a
possibility, they're not a given.  If I really am living, solely, on
one particular planet at one particular time, then I have never
sampled the distribution of all observers in the history of the
universe, and nothing about my experience can tell me anything about
that distribution (beyond the fact that I, and my fellow humans,
belong to it).

 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.

I probably haven't made my point very clearly here.  What I'm arguing
against is what you wrote previously:

 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?

Why is your height and weight drawn from a certain distribution?  It's
because you've been exposed to certain statistical influences on those
attributes, and those influences are influences that you have in
common with a certain subset of the human population.  But it would be
absurd to say that *your* height and weight is drawn from the
distribution of heights and weights of all living creatures in the
history of the universe.  Equally, it would be absurd to say that your
observer class has been drawn from the distribution of all observers
in the history of the universe.

  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?

We reject those claims because they flow from theories that we reason
should have led to observable consequences in the past (e.g. theories
of interventionist deities).  So what we have are prior probabilities
that strongly disfavour those crackpot theories -- and given equal
crackpot ratings, their predictions about the future are irrelevant.
If crackpot A tells me that the world will end in 2012, and crackpot B
tells me that the world will end in 20,012, then all else being equal
I will (in 2008) give them both *equal* low credence.

And given two (non-crackpot) cosmological theories with equal
grounding in modern physics and which imply no observable differences
up to the present epoch, but wildly different consequences in the very
far future, we *cannot* use those far-future consequences to
discriminate between them.  Specifically, we cannot use differences in
the numbers of future observers in various classes that the different
theories predict, in order to favour one theory over another, here and
now.
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Re: Cosmology and Boltzmann brains

2008-06-15 Thread Bruno Marchal

Hi Greg,


On 15 Jun 2008, at 10:40, Greg Egan wrote:


 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?

 Why is your height and weight drawn from a certain distribution?  It's
 because you've been exposed to certain statistical influences on those
 attributes, and those influences are influences that you have in
 common with a certain subset of the human population.  But it would be
 absurd to say that *your* height and weight is drawn from the
 distribution of heights and weights of all living creatures in the
 history of the universe.  Equally, it would be absurd to say that your
 observer class has been drawn from the distribution of all observers
 in the history of the universe.





I agree, and I think one half of the everything-list participants  
agree on this (cf our Relative versus Absolute Self-Sample Assumption  
debates). The probabilities are relatively conditioned on the brain/ 
body states  *histories*, and things are not so different from  
Feynman integral formulation of QM.
Now, the question is why *quantum* histories. My point is that if we  
assume we are turing-emulable, then the probabilities have to be  
derived from a sum on *all* computations. Not just the quantum one.  
This means we can test the computationalist theory by comparing the  
sum on all quantum histories/computations (with its weird probability/ 
amplitude relation) and the sum on all histories/computations.
At first sight the comp theory is false because it leads to many more  
white rabbits than the quantum, but by taking into account constraints  
related to incompleteness phenomena and logic of self-references,  
there are (rather technical alas) evidences that the third person  
white rabbits go away too.
It remains abnormally too much first person white rabbits, and I am a  
bit stuck on that. QM, and physics in general, per se, does not even  
address those first person purely qualia rabbits (although Galileo,  
Einstein, Boscovitch, Everett, .Wheeler, Rossler, ... can be seen as a  
sequences of physicists converging to that.
Assuming we are turing emulable, we have to radicalize Everett. We  
have to justify why, in appearance, the QM computations wins in the  
observable game. All the pieces of the puzzle are there.

Greg, I have read and appreciate very much your Permutation City  
novel, but to be honest, I see you still believe physics study what  
there is. This seems to prevent you to follow your own logical line.  
See my Sane04 paper for an argument (in english) showing that IF we  
are turing emulable, THEN the observable is just what emerges from all  
possible local merging and differentiations of computational histories  
(= as seen as first person point of view, probably plural first  
person. Merging works through amnesia, and I don't explicitly tackle  
merging in my publications).

In Laws without Laws, or It from bits John Archibald Wheeler got  
that point: the physical laws emerges on something non-physical.  
Assuming we are digital machine, that non-physical stuff has not to be  
more than the additive and multiplicative properties of natural  
numbers. Poetically: what we take for being the physical reality is in  
fact the border of the ignorance of self-introspecting universal  
machine/number (us). That Ignorance is *very* big, and productive,  
almost alive when seen from inside. And mathematically tractable by  
computer science/recursion theory.
To sum up in a Soccer way: Plato 1, Aristotle 0.  (I don't pretend the  
match is over!)

But I think a lot that QM confirms already the comp hypothesis, and  
the non-materiality of matter.
To sum up in a Kronecker's way: God creates the natural numbers, all  
the rest are web of coherent (and less coherent) dreams by natural  
numbers.
I think I have an argument showing that the comp hyp reduces the mind- 
body problem into a pure body problem. The problem now is that most  
physicist takes bodies from granted, and this prevents the  
understanding of the argument. But that is religion.
(For example, Vic Stenger in his God, the failed hypothesis  
identifies material with natural, and immaterial with supernatural,  
making math and logic, what? parapsychology? Theology perhaps. At  
least physicists like Penrose, Wheeler, Deutch, Tegmark are aware of  
the mathematical reality. Only logicians seems to be aware of (and  
familiar with) the intricacy of digital self-reference. It is pity  
that the gap between logicians, physicists and philosopher of mind/ 
theologian remain so wide.  At more than one level, I'm afraid. I am  
quite opposed to creationism and any authoritative bible-god  
crackpot theology, but many scientists aggravate the hiatus by being a  
bit dogmatic on matter like if we would have solved the mind-body  
problem. My modest work, and our discussions here, just points toward  
a 

Re: Cosmology and Boltzmann brains

2008-06-15 Thread Russell Standish

On Sun, Jun 15, 2008 at 01:40:09AM -0700, Greg Egan wrote:
 
  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?
 
 Why is your height and weight drawn from a certain distribution?  It's
 because you've been exposed to certain statistical influences on those
 attributes, and those influences are influences that you have in
 common with a certain subset of the human population. 

Of course. That was my point about it not being an actual sampling process.

 But it would be
 absurd to say that *your* height and weight is drawn from the
 distribution of heights and weights of all living creatures in the
 history of the universe.  Equally, it would be absurd to say that your
 observer class has been drawn from the distribution of all observers
 in the history of the universe.
 

It is absurd to say we're drawn from a distribution over all living
creatures. But it is not absurd to say we're drawn from a
distribution over all conscious things. That is the essence of
anthropic reasoning. It seems we're destined to disagree on this.

  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?
 
 We reject those claims because they flow from theories that we reason
 should have led to observable consequences in the past (e.g. theories
 of interventionist deities).  So what we have are prior probabilities
 that strongly disfavour those crackpot theories -- and given equal
 crackpot ratings, their predictions about the future are irrelevant.
 If crackpot A tells me that the world will end in 2012, and crackpot B
 tells me that the world will end in 20,012, then all else being equal
 I will (in 2008) give them both *equal* low credence.
 

I was actually thinking more of theories like the law of gravity will
be suspended on the 25th of July, 2012, but otherwise everything else
is the same. Obviously it makes the same retrodictions as our usual
scientific theories (doing so by definition). The reason it is
rejected is because of the arbitrary nature of the date makes it a
more complex theory (in the Occam's razor sense).

 And given two (non-crackpot) cosmological theories with equal
 grounding in modern physics and which imply no observable differences
 up to the present epoch, but wildly different consequences in the very
 far future, we *cannot* use those far-future consequences to
 discriminate between them.  Specifically, we cannot use differences in
 the numbers of future observers in various classes that the different
 theories predict, in order to favour one theory over another, here and
 now.

Actually, I think this statement follows as a consequence of the RSSA
which Bruno mentioned earlier, in as far as we're discussing the
future of our universe (rather than all possible universes).

There is some discussion in my book Theory of Nothing about the RSSA
versus its main competitor the ASSA. Also
http://everythingwiki.gcn.cx/.

Cheers

--


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


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Re: Cosmology and Boltzmann brains

2008-06-15 Thread Greg Egan

Thanks very much, everyone, for an interesting discussion, and thanks
for your patience towards someone who hasn't read your previous
debates on these issues.

I hope to find time to follow up all the links people gave.  Russell,
that link to the Everything Wiki currently gives a 403.
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Re: Cosmology and Boltzmann brains

2008-06-14 Thread Colin Hales
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 
experience.*

*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.

regards,

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 

Re: Cosmology and Boltzmann brains

2008-06-14 Thread Stathis Papaioannou
2008/6/14 Greg Egan [EMAIL PROTECTED]:

 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).

There is also the argument that the appearance of having a clear
Darwinian history is not necessarily evidence that we are not
Boltzmann brains. This is because the problem of what sort of
observers would be generated by Boltzmann brains reduces to the
problem of what sort of observers would be generated by the ensemble
of all possible observer moments, or all possible computations. How
such an ensemble might give rise to the orderly world we observe has
been one of the main topics of discussion on this list over the years
(eg. see Russel's paper here:
http://www.journaloftheoretics.com/Links/Papers/ockham.pdf).



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Stathis Papaioannou

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Re: Cosmology and Boltzmann brains

2008-06-14 Thread Russell Standish

Hi Greg, and welcome to the list. Your ears must be burning - you have
often been talked about here, always in a good light!

On Fri, Jun 13, 2008 at 09:28:07PM -0700, 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.

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?

Of course, in reality, there may be no well defined meaning to terms
like p(2|A), particularly if, as I suspect, observer moments satisfy a
complex valued measure. However, in this toy problem you presented,
the terms are well defined.

 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.

 (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.
 

H does not discriminate, but 2 (I am of class 2) does. And all the
result does is give a preference to theory A rather than B, assuming
no prior preference (eg Occams razor). 

 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.
 

That is largely what we do with applications of Occams razor. We
choose the simpler theory on the basis that it is more likely to
continue being right when tested with future observations.

 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

I would agree that this subject is marred by too many
unknowns. However on the issue of the likelihood of having found
ourselves being a Bolztmann brain, it is no different IMHO to that of
finding oneself in a White Rabbit universe (or Harry Potter
universe - as discussed in some other forums). Whilst there are an

Re: Cosmology and Boltzmann brains

2008-06-14 Thread Greg Egan

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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Re: Cosmology and Boltzmann brains

2008-06-13 Thread Greg Egan

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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Re: Cosmology and Boltzmann brains

2008-06-12 Thread Stathis Papaioannou
2008/6/13 Günther Greindl [EMAIL PROTECTED]:

 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

Is the ensemble of observer moments generated by the postulated BB's
different from the ensemble of all possible observer moments?



-- 
Stathis Papaioannou

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Re: Cosmology and Boltzmann brains

2008-06-12 Thread Russell Standish

On Fri, Jun 13, 2008 at 10:28:28AM +1000, Stathis Papaioannou wrote:
 
 Is the ensemble of observer moments generated by the postulated BB's
 different from the ensemble of all possible observer moments?
 

I don't see how it could be different. AFAICT BBs are nothing other
than the infamous white rabbit. Still I'm trying to digest Greg Egan's
objections to the DA - not sure that I understand yet, but it has the
flavour of a debate I had with someone else a couple of years ago on
a-void (not sure, maybe Jonathan Colvin, but probably someone else).

Cheers

-- 


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


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Re: Cosmology and Boltzmann brains

2008-06-12 Thread Russell Standish

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. 

-- 


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


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