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
> 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

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