On Thu, Aug 31, 2017 at 12:28:26PM +1000, Bruce Kellett wrote: > On 29/08/2017 3:17 pm, Russell Standish wrote: > >I attach a brief PDF of what I have so far. It shows how observer > >moments, modelled as sets of bitstrings classified by looking at a > >finite number of bits naturally map to vectors in a complex vector > >space. There are some lemmas, proofs and conjectures (theorems I > >haven't managed to prove yet, but think are plausible). > > I have had a look through your notes.I am not sure that I fully > understand the direction you are heading in, but I have one or two > comments to make at this stage.
Good. I'm glad you're casting a critical eye over it. Sorry for taking a while to respond - my son was struck by a car on Friday night. Fortunately, he survived with just a few grazes and bruises, and what with the car having to be towed away with a cracked windscreen, he can say in this case of car vs man, the car came off second best. Nevertheless, it was a harrowing Friday night... > > You say: "A conscious observer of these strings will only examine a > finite number of bits prior to making a decision on the meaning." > This strikes me a tending to be a little dualist -- there is no-one > examining any strings; some string or other corresponds to the > actual observer (moment), so it is not "observed", it is the actual > OM. The whole point of the the bitstrings is that they are interpreted by something we call an observer. In the usual Comp Sci setup, there is a reference universal Turing machine, but when talking about everything theories, there can be no such thing - it must always be relative to an observer. Note that this doesn't rule out that it is the bitstrings, or some part of the bitstrings that is the observer, so that what is happening is self-observation, so one cannot claim this must be dualist. > Secondly, you take this string to be a fixed, finite length > prefix, followed by an infinite string of "don't care" bits. I don't > see that you can take the OM to be the leading section of the string > -- it could occur anywhere, and there might be an essentially > infinite string of lead-in "don't care" bits. Of course, not all of the finite length prefix needs to be fixed. "Don't care" bits may be scattered throughout, including the initial sequence of bits. However, what I dispute is that there can be an infinite string of "don't care" bits, unless one is talking about the Everything/Nothing itself. No Turing machine can skip an infinite number of bits from the start of it's tape. > But I don't think that > this is necessarily a problem for your analysis. The assumption that > the OM is a finite section of the string might be a bit strong -- > why could it not be an infinite sub-section of the infinite string? > The problem with infinite bit strings describing OMs might be that > indexing becomes problematic. > One can build up an infinite section by taking an infinite union of these atomic OMs. Whilst each observer only observes a finite number of bits before halting and experiencing a particular OM, there is no limit to the number of bits that can be read before experiencing any given OM. If you consider all identical copies of an OM, there may well be an infinite number of bits involved. > The main difficulty I see is that you are simply analysing some > properties of sets of strings. I do not see any way that you can > characterize these strings as OMs. You start by picking out the set > of strings containing an OM, but I do not see how you can ensure > that manipulations of these strings necessarily leads to other > possible OMs. What makes a string an OM -- other thanthe fact that > that is how you select the string in the first place. Changing it in > any way has not been shown to lead to some other OM. I don't see > that an OM can match a number of different prefixes -- after all, > the "prefix" is the OM! Exactly the same way that a given program implemented in Fortran and also in Lisp is the same program, regardlessof the fact that a different sequence of bits is involved. > Of course, the same prefix might have any > number of following "don't care" bits, so an OM is a union of atomic > OMs, as you say. > > I also don't really like the idea that the outcome of a measurement > can be modelled via set intersection. The usual, canonical idea of a measurement is that it further constrains the set of possible world you might exist in. If your world is described by set A, and we make a measurement that implies your world can be found in set B, then we would normally infer that our world is in A∩B. The insight, as it were, is how to deal with the situation where the measure provides some conflicting information - in that case we end up with less information than we had before, and the resultant world is more like A∪B, or somewhere in between. > OM A plus measurement outcome > B is not necessarily the intersection of A and B. B is a measurement > outcome, not necessarily an OM in itself. The OM representing A > observing some measurement outcome B is surely some new OM, and it > is not clear to me how it is to be related to either A or B without > making some pretty strong assumptions. Yes, or course it is a new OM. Abstracting away the measurement process, and considering only the information provided by the measurement, the information either adds to what we already know (in which case the resultant subset describing our knowledge is reduced by an intersection), or it contradicts what we know, which case we must take a union. An intermediate case might be where some part of the measurement results adds to what we know, and another part contradicts, but we can simplify things by considering just those measurements that result in 1 bit of information, so that only intersections and unions are relevant. Re the direction this is headed, the idea is still the derivation of the usual QM axioms from this notion of partitioning the set of all infinite length strings. What this current work shores up is the generation of a complex field Banach space (later Hilbert space with appropriate inner product). The difficulty on the previous work was requiring a complex measure for observers to be drawn from (and your quite valid observation that a linear combination of observer moments is not necessarily an OM). This all proved to be unnecessary - the complex field comes about from the requirement that only the everything/nothing object maps to the zero of the vector space, and we considering all unions of the atomic OMs, without requiring that they all be valid OMs - which is just as valid as in regular QM, where not all vectors of the Hilbert space correspond to valid physical scenarios. Note there is an actual measure on the sets of strings, which should be related somehow to the Born rule. I agree with you that the current approach in my appendix is too arbitrary, it depends too much on the initial partition chosen. It may be that the partitioning doesn't matter, and that approach in the appendix can be resurrected, or it may be that Gleason comes to help, but I'm expecting that the Born rule should be related to the set measure ultimately. Cheers -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow hpco...@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.
