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
>
>
