Re: “Could a Quantum Computer Have Subjective Experience?”
On Sat, Jun 24, 2017 at 06:29:54PM +1000, Bruce Kellett wrote: > On 24/06/2017 5:23 pm, Russell Standish wrote: > > OK, it was possibly the case that you gave arguments earlier in the > book. But I was going on the basis of the Appendix "Derivation of > Quantum postulates". > > But the problems only begin with the assumption of a probabilistic > model. Psi(t) is the set of possibilities consistent with what is > known at time t. But how do you limit this set? At the moment, I > could go to the pub for a drink, could open a bottle of wine at > home, stroke the cat, turn on the telly, talk to my wife, etc, > etc,. The possibilities consistent with what is known at this > time is not a well defined set, or limited in any way. The everything is the set of all infinite length strings, each of which describes a universe to infinite detail. Some of these strings will describe universes compatible with our current observer moment - an infinite number even, as the information content of our OM is finite. Others will not. It is a well defined subset of the everything. > > Because you then go on to define projection operators in terms of a > sum over the members of this set of possible outcomes. That is > meaningless unless you are already assuming the the outcomes are > just possible results for a well-defined measurement, and that this > measurement process can be defined in a linear vector space. > Summation of the projection operators is defined in equation D.1 for disjoint observations a and b (ie where it is impossible to observe a and b simultaneously). Linearity is not assumed at this point. > Another problem occurs further down when you seem to have complex > numbers of observers observing an observer moment. Why you should > have more than one observer for any observer moment is a mystery yet > to be solved. It's more a measure over observer moments. In a branching multiverse, not all observer moments are equally likely, but one would expect across a branching point, measure should be conserved. Why the measure is complex, not real is more tricky. With the everything, subsets naturally induce a real valued measure. But we do know that complex measures are more general, and we need a good reason not to choose the most general. But complex measures are not the most general. I do say "more general division algebras cannot support equations of the form (D.7)", but I confess, I'm still not completely happy with that line. > But then you go on, in eq. B8 to define the inner > product in terms of the probability function. But you have merely > multiplied together two expansions in terms of projections over > possible outcomes -- assuming that there is a linear span over the > space in the process. This gives the Born rule, sure, because you > have built it into your derivation of the inner product. > By the time we get to equation D.8, we have proved that the set of observer moments is a vector space, so yes, this construction is allowed. We are entitled to define any real-valued bilinear operator on that space and call it an inner product. By using that particular inner product, you get the Born rule in the usual form. If we'd chosen another, we'd have a different expression that is equivalent to the Born rule. > > >>So you know about QM from the start, and devise a strategy to get > >>you there. One of the problems that many-worlders face in their > >>attempts to derive the Born rule from within MWI is that they cannot > >>independently justify a probabilistic model. > >Yes, but I don't start with the MWI (namely, I don't start with a > >Hilbert space and unitary equation of motion - ie Schroedinger's > >equation). I start with evolution in a generic multiverse. > > Why a multiverse? You no doubt argue for it elsewhere, but that is > not apparent in your quantum derivation. > Yes - of course. The whole book is premised on it. > And I do not understand why the most general equation for computing > psi as a function of time is a first order differential equation. > The equation could clearly be non-linear in psi -- such things have > been postulated after all, as in general relativity and GRW for > instance. > A first order differential equation needn't be linear. Linearity comes from assuming that the laws of physics don't change every time you observe something, more specifically the solutions ψ_α are also solutions. A higher order equation can be transformed into a first order equation by adding new variables - a trick commonly done in dynamical systems theory. Perhaps there's an implicit assumption that the evolution should be Markovian. I think one could make a convincing case that it should be, but perhaps that assumption needs to be made explicit. > Besides, you do not show that the operator H is the Hamiltonian and > the energy operator. You do not derive the basic commutation > relations between position and momentum operators -- a relation that > is central to the whole
Re: “Could a Quantum Computer Have Subjective Experience?”
On 24/06/2017 5:23 pm, Russell Standish wrote: On Sat, Jun 24, 2017 at 03:59:56PM +1000, Bruce Kellett wrote: Well, I have just taken a quick look. What strikes me is that the first paragraph of Appendix D defines "Observer moments psi(t) are sets of possibilities consistent with what is known at that point in time, providing variation upon which anthropic selection acts. ... We wish to determine the probability of outcome a being observed." So you assume a probabilistic model from the outcome. Why would you do that? Why not a deterministic model? I do spend over a hundred pages prior to the chapter on QM going into the reasons! But to try to signpost this, and maybe save you the effort of reading my book, the basic reason is that our 1p view must be the result of evolution - not biological evolution, per se, but anthropic evolution - the result of variation of possible futures, and anthropic selection from those possible futures to the actual result seen. Along with heredity (which in QM gives rise to unitarity), we have the three pillars of evolution as espoused by Lewontin. Consequently, the probabilistic model needs to be there right from the start to provide the variation on which anthropic selection acts. OK, it was possibly the case that you gave arguments earlier in the book. But I was going on the basis of the Appendix "Derivation of Quantum postulates". But the problems only begin with the assumption of a probabilistic model. Psi(t) is the set of possibilities consistent with what is known at time t. But how do you limit this set? At the moment, I could go to the pub for a drink, could open a bottle of wine at home, stroke the cat, turn on the telly, talk to my wife, etc, etc,. The possibilities consistent with what is known at this time is not a well defined set, or limited in any way. Because you then go on to define projection operators in terms of a sum over the members of this set of possible outcomes. That is meaningless unless you are already assuming the the outcomes are just possible results for a well-defined measurement, and that this measurement process can be defined in a linear vector space. Another problem occurs further down when you seem to have complex numbers of observers observing an observer moment. Why you should have more than one observer for any observer moment is a mystery yet to be solved. But then you go on, in eq. B8 to define the inner product in terms of the probability function. But you have merely multiplied together two expansions in terms of projections over possible outcomes -- assuming that there is a linear span over the space in the process. This gives the Born rule, sure, because you have built it into your derivation of the inner product. So you know about QM from the start, and devise a strategy to get you there. One of the problems that many-worlders face in their attempts to derive the Born rule from within MWI is that they cannot independently justify a probabilistic model. Yes, but I don't start with the MWI (namely, I don't start with a Hilbert space and unitary equation of motion - ie Schroedinger's equation). I start with evolution in a generic multiverse. Why a multiverse? You no doubt argue for it elsewhere, but that is not apparent in your quantum derivation. And I do not understand why the most general equation for computing psi as a function of time is a first order differential equation. The equation could clearly be non-linear in psi -- such things have been postulated after all, as in general relativity and GRW for instance. Besides, you do not show that the operator H is the Hamiltonian and the energy operator. You do not derive the basic commutation relations between position and momentum operators -- a relation that is central to the whole of QM. If you have a probabilistic model in 3 or more dimensions, Gleason's theorem tells you that the Born rule is the only consistent model for probabilities. My arguments go through in fewer than 3 dimensions as well, AFAIK, although that would a relatively uninteresting world - very black and white :). Which is why I suspect it is independent of Gleason. But you have to say why you want a probabilistic interpretation in the first place. Deutsch's attempts founder on the fact that he has to assume that small amplitudes have small probabilities, even to get started, so his argument is manifestly circular. Yes - I think the problem with those approaches is that they start with a Hilbert space and unitary equation of motion (ie a classic MWI), and then fail to generate the Born rule because there is no observer in their mechanics. As I said, you build a probabilistic model in at the start, so Gleason's theorem is going to get you the Born rule automatically. Or if you don't assume Gleason, you have an equivalent result by another route. Assuming a probabilistic model is a very powerful starting point.. Sure - but it is necessary.
Re: “Could a Quantum Computer Have Subjective Experience?”
On Sat, Jun 24, 2017 at 03:59:56PM +1000, Bruce Kellett wrote: > > Well, I have just taken a quick look. What strikes me is that the > first paragraph of Appendix D defines "Observer moments psi(t) are > sets of possibilities consistent with what is known at that point in > time, providing variation upon which anthropic selection acts. ... > We wish to determine the probability of outcome a being observed." > So you assume a probabilistic model from the outcome. Why would you > do that? Why not a deterministic model? I do spend over a hundred pages prior to the chapter on QM going into the reasons! But to try to signpost this, and maybe save you the effort of reading my book, the basic reason is that our 1p view must be the result of evolution - not biological evolution, per se, but anthropic evolution - the result of variation of possible futures, and anthropic selection from those possible futures to the actual result seen. Along with heredity (which in QM gives rise to unitarity), we have the three pillars of evolution as espoused by Lewontin. Consequently, the probabilistic model needs to be there right from the start to provide the variation on which anthropic selection acts. > > So you know about QM from the start, and devise a strategy to get > you there. One of the problems that many-worlders face in their > attempts to derive the Born rule from within MWI is that they cannot > independently justify a probabilistic model. Yes, but I don't start with the MWI (namely, I don't start with a Hilbert space and unitary equation of motion - ie Schroedinger's equation). I start with evolution in a generic multiverse. > If you have a > probabilistic model in 3 or more dimensions, Gleason's theorem tells > you that the Born rule is the only consistent model for > probabilities. My arguments go through in fewer than 3 dimensions as well, AFAIK, although that would a relatively uninteresting world - very black and white :). Which is why I suspect it is independent of Gleason. > But you have to say why you want a probabilistic > interpretation in the first place. Deutsch's attempts founder on the > fact that he has to assume that small amplitudes have small > probabilities, even to get started, so his argument is manifestly > circular. > Yes - I think the problem with those approaches is that they start with a Hilbert space and unitary equation of motion (ie a classic MWI), and then fail to generate the Born rule because there is no observer in their mechanics. > > As I said, you build a probabilistic model in at the start, so > Gleason's theorem is going to get you the Born rule automatically. > Or if you don't assume Gleason, you have an equivalent result by > another route. Assuming a probabilistic model is a very powerful > starting point.. Sure - but it is necessary. If evolution did not work the way it did, we could only ever be Boltzmann brains, isolated observers existing fleetingly, barely having time to consider what to have for lunch, let alone figuring out the meaning of the universe. Fortunately for us, evolution does work to generate complex worlds from simple beginnings, meaning an evolved world is overwhelming more likely to occur in the Multiverse of Everything than Boltzmann brain existences. -- Dr Russell StandishPhone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellowhpco...@hpcoders.com.au Economics, Kingston University http://www.hpcoders.com.au -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: “Could a Quantum Computer Have Subjective Experience?”
On 24/06/2017 3:02 pm, Russell Standish wrote: On Sat, Jun 24, 2017 at 01:09:41PM +1000, Bruce Kellett wrote: On 24/06/2017 11:20 am, Russell Standish wrote: The 3p is what is left after removing all personal baggage of each 1p view point. It is literally the view from nowhere (since location is just such a baggage), and cannot be conscious in itself (for exactly the reason you outline below) It is this characterization of 3p that I find misleading. If all personal baggage has been removed, how come you still talk as thought this were a third person view? I think this terminology is an unfortunate carry-over from the classical person-duplication thought experiments. The bird view would more properly be called a 0p view, since there are no 'persons' or 'person' who has this view. I have no problem with you arguing for a change in terminology, but to be clear, the term 3p has been used consistently on this list to mean roughly what I describe above for almost 2 decades. Until this discussion, it never even ocurred to me that it might be confusing - I never thought of 3p as a person. Maybe you guys should get out more? There is still another datum. Because of the reasoning used in my derivation of QM (appendix D of my book), I equate the 3p with the quantum multiverse. Of course, my derivation may well be faulty - to my knowledge, only a handful of people have dug into and critiqued the argument in its 17 years of existence, without finding any fatal flaw - however assuming its validity, then we can equate the 3p with the bird view of Tegmark's level 3 multiverse. I have not had the time or energy to delve deeply into your derivation. My experience of other attempts to 'derive' quantum mechanics is that basic quantum concepts are introduced by sleight-of-hand -- in other words, they usually beg the question. That is still quite possible in my case, of course, but I have tried my utmost to make the assumptions explicit, and give reasonable justifications for them in terms of observer properties. Brent found 1 (or maybe 2, memory's a little hazy) hidden assumptions in my first version of the argument 15 years ago, which I have since corrected. Well, I have just taken a quick look. What strikes me is that the first paragraph of Appendix D defines "Observer moments psi(t) are sets of possibilities consistent with what is known at that point in time, providing variation upon which anthropic selection acts. ... We wish to determine the probability of outcome a being observed." So you assume a probabilistic model from the outcome. Why would you do that? Why not a deterministic model? So you know about QM from the start, and devise a strategy to get you there. One of the problems that many-worlders face in their attempts to derive the Born rule from within MWI is that they cannot independently justify a probabilistic model. If you have a probabilistic model in 3 or more dimensions, Gleason's theorem tells you that the Born rule is the only consistent model for probabilities. But you have to say why you want a probabilistic interpretation in the first place. Deutsch's attempts founder on the fact that he has to assume that small amplitudes have small probabilities, even to get started, so his argument is manifestly circular. The work has passed peer review, but as you well know, that's only a minimal hurdle. It is not enough for the work to be taken seriously by the field, nor (obviously) for to actually be right. The most worrying aspect of my derivation is the requirement that the complex field is the most general measure applicable for sets of observers. Complex numbers are not the most general measure (Banach spaces are), and if we must restrict the type of measure for any reason, then why not restrict all the way to real measures (which kind of seems natural). Another open problem is what is the relationship with the Gleason theorem? The Born rule naturally falls out of my construction, so the question is whether my derivation is independent of Gleason's theorem, or just incorporates it in disguise. As I said, you build a probabilistic model in at the start, so Gleason's theorem is going to get you the Born rule automatically. Or if you don't assume Gleason, you have an equivalent result by another route. Assuming a probabilistic model is a very powerful starting point.. Bruce -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
