I got a bounce (" ----- The following addresses had permanent fatal errors ----- "|flist everything-list" (expanded from: <[EMAIL PROTECTED]>)

so I'm trying to send this a second time: Begin forwarded message: > From: Tim May <[EMAIL PROTECTED]> > Date: Mon Jul 08, 2002 12:17:27 PM US/Pacific > To: [EMAIL PROTECTED] > Subject: Re: being inside a universe > > > On Monday, July 8, 2002, at 10:39 AM, Bruno Marchal wrote: >> Mmh... Most people here have a good understanding of the "many"-idea, >> by which >> I mean have realised that the idea of a unique universe is far more >> speculative >> that O universe or many universe. I will not insist. >> Perhaps you could read the very interesting paper by Louis Crane, >> which is quite >> convincing on the importance of category theory in frames of quantum >> gravity+ >> observers, and which use cleverly Everett relative states. He even >> concludes that >> his proposal can be seen as an attempt to fuse the many worlds with >> general >> relativity. It is a paper by Crane entitled "categorical physics". He >> gives >> the TEX source somewhere on the net. (If you don't find it I can >> eventually >> send you a photocopy). > > Thanks, but I can no doubt find it at UC Santa Cruz. I have most of his > later papers already printed out, from the xxx.lanl.gov archive site, > and his papers will refer to his earlier papers that may not be on the > arXive site. > > Crane is one of the Sultans of Spin, as Egan dubs them, along with > Rovelli, Sen, Ashtekar, Smolin, Baez, Markopoulou, Susskind, etc. > > I have to admit that I'm more prosaic in my approach...the quantum > gravity and MWI stuff is interesting to think about, to speculate > about, but my focus is a bit closer. And I'm still learning this new > language (category, topos theory). > > >> One day I will talk you about the work of Yetter on >> models for non commutative linear logic. Yetter is at a relevent >> crossroad of >> logic and physics imo. (Then I guess you heard about Crane, Kauffman >> Yetter >> papers?) > > I have the Crane-Yetter paper " On the Classical Limit of the Balanced > State Sum," but I haven't read it yet. From glancing at it, it didn't > seem to be cosmic. I'll look at it more closely. > > Is it related to the noncommutative geometry work of A. Connes? > > >> About linguistic use of Kripke, most of them, imo, use technical >> approach >> of language to explain problems ... away. Beware sophisticated tricks >> for >> putting interesting (but hard) problems under the rug. > > My main interest in Kripke is his discussion of "possible worlds," > which is a kind of superset of the MWI/Tegmark view. (Supersets can be > nebulous, and I am not claiming the MWI/Tegmark stuff is some trivial > subset of a larger theory.) > > We constantly make plans and think about futures in terms of these > possible worlds. David Lewis gives an example in one of his many papers > on possible worlds (plurality of worlds). A cat being chased by a dog, > for example. The cat imagines one possible world in which he has gotten > safely away, another possible world in which the dog's jaws have gotten > him. It seems likely that reasoning about possible worlds is much more > innate than, say, reasoning using formal syllogistic logic! > > I believe, in fact, that the conventional semantic networks of AI, > exemplified by some large knowledge engineering efforts like Doug > Lenat's CYC project, may need to be scrapped in favor of networks > embodying the morphisms, functors, and functors of functors of category > theory. This is not _directly_ linked to MWI and Tegmark, of course, > but it has some partial links. > >> >>> Personally, I'm not (yet) "taking seriously" either the David Lewis >>> "plurality of worlds" or Max Tegmark "everything" or Greg Egan "all >>> topologies model" ideas. At least not yet. I need to learn a lot more >>> of the language first. >> >> I am more problem driven, and even "mind-body" problem driven. I gave >> an >> argument in this list (argument on which my phd thesis is based) that >> IF we are machine then physics is utimately reducible to machine's >> psychology. The laws >> of physics emerge from some collection of sharable "dreams" by >> machines, where >> a dream is basically a computation seen from first person point of >> view. >> And first person notion are captured by 1) memory, 2) S4 modal logic, >> 3) toposes >> (but only in my technical notes for the 3). >> I hope you will continue to read my posts now that I confess that I am >> not >> sure physics is the *fundamental* way to get a TOE. > > As you can see, I also don't treat physics as necessarily the sine qua > non for all knowledge. > > However, "TOE" is pretty much a term of art referring to a theory which > unifies the worlds of quantum mechanics (and follow-ons like QCD, > supersymmetry, and our theories at the microscopic level) with the > world(s) of special and general relativity. Some say "Theory of > Everything" was intended as a partial joke. Certainly if a TOE were to > be finalized tomorrow it would not have much to do with mind-body, AI, > and other cognitive or computer science problems. > > (The "Everything" of Tegmark is yet another use of "everything," closer > to the "possible worlds" usage.) > > I don't know what the physics is going to turn out to be. But I > believe, perhaps due to my current enthusiasm, that the mathematical > formalism for a lot of these TOE/Tegmark/Possible Worlds discussions is > topos theory. (I'm hardly the first to see this, pace the work in the > 60s and 70s mentioned in many places.) > >> Still, my favorite theory >> is quantum mechanics, so much that I want to provide serious >> foundation for it. > > Tegmark and Wheeler, in their paper on the history of QM, refer to > "shut up and calculate!" Meaning, stop worrying about the deep > weirdnesses and just use the formalism to calculate. Nothing in QM, > QED, or QCD really requires any particular "interpretation" for the > formalism to work. QED is accurate to something like 22-23 decimal > places. > > Cameron, in a book on "Sets, Logic, and Category Theory," tells a funny > story of a large castle with a deep basement marked "Foundations." The > spiders live down in the foundations, spinning webs of set theory and > logic, quantum mechanics, whatever is foundational. Once a year the > residents upstairs send down a cleaning crew to clean out the cobwebs. > The spiders cower in the corners, fearful that destroying their > carefully-spun webs will bring down the entire castle. > > The fact is, there are very, very few "unexplained phenomena." We are > in a much, much different situation than 60-100 years ago, when many > easily-observed phenomena like emission lines in spectra, like the > stability of the hydrogen atom, like the decay of radioactive > materials, like how the sun works, had no explanation. This has all > changed, and now it takes pushing way out at the extremes of size and > energy to find unexplained phenomena. > > (By "explanation" I mean predictive and consistent theories. Some might > argue that we don't "understand" the double slit experiment, or the > delayed choice experiment, or the deep meaning of > Einstein-Podolsky-Rosen and all the other weirdnesses of QM. But we > know how to calculate everything, and all interpretations of QM give > the same results.) > > It is true that we have mounting evidence that a unification of gravity > (relativity) and quantum (all flavors) theories may be needed. Hence > the work on strings, loops, knots, spin foams, and other such stuff. > >>> Hugh Everett, I assume you mean. Yes, indeed. I have the book edited >>> by Bryce DeWitt and Neill Graham, "The Many-Worlds Interpretation of >>> Quantum Mechanics," 1973. I think this is how many in the physics >>> community encountered MWI, through DeWitt's late 60s, early 70s >>> re-analysis. >> >> >> Yes. Note that Everett just abandons the wave collapse postulate. The >> "many- >> world" expression came latter (through DeWitt I think, indeed). I mean >> what >> Everett proposed is a new theory, not a new interpretation of a theory. > > I disagree. I don't think Everett's idea that evolutions proceed > unitarily, that is, without any collapse, is a new theory. It's an > interpretation, like collapse (Copenhagen), like Cramer > (transactional), etc. > > It leads to no predictions which can be tested to show a difference > with the other interpretations. > > (Yeah, I know there are possible "leftovers from early universes" which > might show the MWI interpretation to be the correct theory. Or some > might argue that the building of a quantum computer able to perform > lots of computations in short amounts of time means, pace Deutsch, that > parallel worlds "must" then exist. Or we might we get signals from some > parallel reality, a la James Hogan's "Paths to Otherwhere," 1996. But > as it stand right now, MWI gives no different predictions from > Copenhagen.) >> > >> Even before, Hartle makes the same derivation as Graham, about the >> same time. >> Consistent histories are good ways to tackle QM basic problem >> seriously. I have >> appreciated the work of Savvidou, a student of Isham. Savvidou's >> thesis is available >> on Los Alamos archive. You have been lucky having Hartle as >> intructors :) > > Well, I was a junior in college taking a graduate-level class which I > really wasn't adequately prepared for. And most of the class was grunge > about calculating tensors, event horizons, Killing vectors, and other > grunge out of a preprint Xerox of Misner, Thorne, and Wheeler. > > (I now study things in a completely different way. And I am now less > impatient and more willing to study foundational (in the sense of > basics) material. I wish, for example, I'd spent a year studying > algebra and topology instead of taking Hartle's relativity class. But, > wishing for alternate pasts is silly.) > >>> >>> Sounds intriguing. I'm currently less-focused on the role of human >>> (or machine) observers. >> >> >> Ah, but if you search for a TOE, you will never get rid of the human, >> or machine or >> whatever sort of observers .... >> And honestly TOPOSES are objective approach toward the subject and its >> horizon. >> I disagree with Smolin use of topos for dismissing the "other" worlds. >> That is >> just a modern reinstantiation of the solipsistic move. What exist is >> what I feel? >> I am much more platonist than that! ('course Smolin book is very nice, >> but I don't >> follow him on that point). > > I'm not sure what you mean by this. I don't recall Smolin spending much > time talking about MWI or "other" worlds, let alone using topos theory > to justify any dismissal of these other worlds. >> > >> Everett clearly proposed a new *formulation* of QM. Just SWE (+ math >> decor). >> The collapse of the wave packet has never been succesfully explained. >> It introduces >> a cut subject/object which has never been succesfully defined. To use >> TOPOS against >> Everett formulation is like using an electronical microscope to >> sharpen a flint. > > Here's how I think the formulation using time-varying sets (closely > identified with toposes, a la Isham) makes sense: > > * at some point in time, a point is not known to be either inside or > outside a region inside a set. (Can't draw pictures here, but think of > a set A and a subset B contained in A. Then ask whether a point P is > inside B or not.) > > * at some later time, for whatever reason, point P is determined or > measured to be inside B. > > * all honest measurements or observers or instruments or minds will > continue to perceive P to be inside of B. > > (or outside of B, as the case may be) > > Think of P being the cat and "inside" B being "alive" and "outside" of > B being "dead." > > Now in a Boolean system (logic/algebra), P is either inside B or not > inside B. Law of the excluded middle and all that. But we know from > delayed choice experiments (photons in an interferometer) that P is not > either in B or not in B...it is in fact in a "mixed state" (to use the > language of the Copenhagen interpretation). > > Our common sense logic goes like this: "Whether we can see inside the > box, the cat actually is either alive or dead at any given time. God, > for example, knows. Someone with the power to look inside the box would > know." This is the Boolean or Aristotelian logic that "Point P is > either contained in set B or not contained in set B." > > Common sense? Not necessarily. > > Moving on. Once a measurement is made (and there is nothing mystical > about the measurement being a mind, or a machine of some complexity), > the logic _does_ become Boolean. At least, we have never a case where > honest observers will disagree on the outcome. (At least in our track > of the multiverse...) > > What kind of structure can allow non-Boolean logic (Heyting logic) up > to some point of measurement and then Boolean logic afterward? > > The logic of time-varying sets...the logic of a topos. (Where the set > inclusion is generalized to "subobject classifier.") > > Isham's streaming video I mentioned makes this fairly clear. > > This still doesn't "explain" why/when/how this transition (aka > collapse) occurs, but the naturalness of the topos point of view is > "comforting." If we lived at the quantum level, we'd probably see > Heyting logic as the norm. It would be "weird" to imagine that > time-varying sets are not the norm. Indeed, since I see time-varying > sets all around me, I view the Boolean point of view as the weird > situation! > >> >>> I just wish mathematicians would do more of what John Baez in his >>> papers: show the reader the motivations. >> >> >> Gosh...I wish too. But for some mathematicians, transparent >> motivations are just >> forbidden, alas! >> >> >> Bruno >> >> PS >> 1) Another nice book on toposes for logically minded reader is the >> book >> by J.L. BELL "Toposes and Local Set Theories" (Oxford Science >> Publications, >> Clarendon Press 1988). It is the same Bell who wrote an important paper >> on "a new approach of quantum logic" which plays some role in my work >> (ref in the >> thesis). It is not the J.S. BELL of BELL's inequality. > > This is another of the books I have looked at in the library but have > been unable to buy. I'm hoping that Johnstone merges all this work done > by others into his massive forthcoming set. > > --Tim May > (.sig for Everything list background) > Corralitos, CA. Born in 1951. Retired from Intel in 1986. > Current main interest: category and topos theory, math, quantum > reality, cosmology. > Background: physics, Intel, crypto, Cypherpunks > >