Re: Cosmology and Boltzmann brains
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/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Cosmology and Boltzmann brains
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 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Cosmology and Boltzmann brains
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 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Cosmology and Boltzmann brains
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 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Cosmology and Boltzmann brains
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/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Cosmology and Boltzmann brains
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 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Cosmology and Boltzmann brains
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 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Cosmology and Boltzmann brains
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. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Cosmology and Boltzmann brains
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
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 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Cosmology and Boltzmann brains
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. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Cosmology and Boltzmann brains
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). -- Stathis Papaioannou --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Cosmology and Boltzmann brains
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
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. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Cosmology and Boltzmann brains
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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Cosmology and Boltzmann brains
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: http://golem.ph.utexas.edu/category/2008/06/urban_myths_in_contemporary_co.html#c017260 The fact that an observer selected at random from the pool of all observers would be more likely to be class 2 under theory A is irrelevant; nobody has to “select us at random” before we’re allowed to make an observation. And here: http://golem.ph.utexas.edu/category/2008/06/urban_myths_in_contemporary_co.html#c017310 There is one aspect of the BB argument that is independent of these issues, though; rather than debating whether far-future life will be “freakish” or “Darwinian”, if we accept an infinite or extremely long future in which observers of any kind are present – so long as they can make observations that show them that they are not living in the early universe – then “typicality” is not a matter of being a Boltzmann brain or a Darwinian brain, but simply whether you are living in the early universe or the later universe. The way the BB fans use probability, they would then argue that the universe is very unlikely to have this very long extended future, because then a “typical” observer would live in the far future … making us “atypical” because we live in the early universe. I guess that’s really just a variant of the infamous Doomsday argument, applied to the universe as a whole: the universe is unlikely to last very long, otherwise it would be “unlikely” for us to find ourselves so near the beginning. That’s where I think they’re simply misusing probability: we are not a random selection of observers taken from the entire history of the universe. That is what I think is the real problem with DA arguments: it is a decision strategy; but OM's are not playing games ;-); they do reasoning; and while this strategy would assure that most OM's are correct, it is not very satisfactory for the current OM - it only gains knowledge about optimal strategy, but not of it's _concrete_ situation. That is why I think RSSA is better than ASSA. But RSSA is still not satisfactory. Hmm; this whole continuation of experience business is the whole mystery anyway IMHO. 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 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Cosmology and Boltzmann brains
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 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Cosmology and Boltzmann brains
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 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
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.
--
A/Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics
UNSW SYDNEY 2052 [EMAIL PROTECTED]
Australiahttp://www.hpcoders.com.au
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