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From: Tim May <tcmay.domain.name.hidden>

Date: Mon, 8 Jul 2002 13:27:49 -0700

I got a bounce (" ----- The following addresses had permanent fatal

errors -----

"|flist everything-list"

(expanded from: <everything-list.domain.name.hidden>)

so I'm trying to send this a second time:

Begin forwarded message:

*> From: Tim May <tcmay.domain.name.hidden>
*

*> Date: Mon Jul 08, 2002 12:17:27 PM US/Pacific
*

*> To: everything-list.domain.name.hidden
*

*> 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
*

*>
*

*>
*

Received on Mon Jul 08 2002 - 13:35:37 PDT

Date: Mon, 8 Jul 2002 13:27:49 -0700

I got a bounce (" ----- The following addresses had permanent fatal

errors -----

"|flist everything-list"

(expanded from: <everything-list.domain.name.hidden>)

so I'm trying to send this a second time:

Begin forwarded message:

Received on Mon Jul 08 2002 - 13:35:37 PDT

*
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