On Friday, October 4, 2002, at 09:13 AM, Bruno Marchal wrote:
> At 9:36 -0700 1/10/2002, Tim May wrote:
>
>> MWI looks, then, like just another variant of "modal realism." To
>> wit, there IS a universe in which unicorns exist, and another in
>> which Germany won the Second World War, but these universes are
>> forever and completely out of touch with us.
>
> Not quite due to possible interferences. We do have empirical evidences
> for those "worlds" imo. (if only the two slits + Bell or better GHZ)
While I find Deutsch fairly persuasive, the verdict is of course not
yet in whether MWI is the correct interpretation. The double slit
results had a "traditional" wave mechanics interpretation 75 years ago
("wave-particle duality"), and this remains a viable interpretation
even today. (I'm not talking about popularity, either on this list or
in the overall community, just "technical viability.")
However, I take your point that full Lewis-Stalnaker-D. Lewis modal
realism is "more disjoint" than the "less disjoint" (initial
interference of branching worlds) MWI. In terms of topology, one might
say full modal realism is the discrete (perhaps Zariski) topology,
while MWI has more notions of closeness, overlap, etc. (I think this
could be worked out, but I haven't.)
Certainly after a time interval where decoherence occurs, the
interaction between macroscopically different worlds is essentially
zero.
So, I will amend my earlier statement to read: "After the very early,
entangled period, MWI looks, then, like just another variant of "modal
realism." To wit, there IS a universe in which unicorns exist, and
another in which Germany won the Second World War, but these universes
are forever and completely out of touch with us."
And since the time of entanglement/coherence is small for most systems,
most worlds in MWI are as "far apart" as modal realism worlds are.
(Digression: I wonder what kind of work has been done on _evolution_ in
topology, e.g., the transition of systems from "overlapping open sets"
to the "discrete" topology? Looks like nucleation and growth out of a
continuous medium, or formation of tree structures, perhaps.)
>
> A very natural generalisation (!). Just replace the hom Sets by hom
> Categories.
> In which you can again replace the hom sets by hom categories ....
> What is intriguing is the existence of coherence conditions making
> those
> constructions apparently very genuine for many stuff from quantum
> field theories.
Baez (IIRC) has an anecdote about talking with a noted quantum field
theorist at a conference. The theorist was highly skeptical of
"generalized abstract nonsense" (i.e., category theory). Baez told him
about some of the developments and the theorist went off to sleep on
it. The next morning he buttonholed Baez and said "Braided monoidal
categories are really cool" (I'm paraphrasing from memory).
>
> I have used the smullyan trees for the G and Co. theorem provers. The
> tableaux
> structure reflects in some way the Kripke structure. Posets appears
> with
> S4-like modal logic.
> You should study Gentzen presentation of logic which are naturally
> related
> to categories. An indigest but brilliant introduction to many
> (intuitionnist)
> logics is the North-Holland logic book by Szabo: Algebra of proofs.
> To bad he miss the braided monoidal categories ... For a categorician,
> knots
> theory is a branch of logic.
I haven't gotten to knots yet, except for a look a few years ago at the
Vaughan Jones stuff on classifications of knots (more related to string
theory, which I did a little bit of reading on).
Gentzen is referred to, of course, in the books on logic I'm reading,
but I'm still absorbing the more basic stuff.
>> "Possible worlds," something I only encountered in any form (besides
>> Borges, Everett, parallel universes sorts of references) in the past
>> several years, is my real touchstone.
>>
>> And, more mundanely, I think it applies to cryptography and money. I
>> had a meeting/party at my house a few weeks ago with about 50 people
>> in attendance (gulp!). We had a series of very short presentations. I
>> gave a very rushed 10-minute introduction to intuitionistic logic,
>> mainly focused on my "time as a poset, a lattice" example, citing the
>> natural way in which "not-not A" is not necessarily the same as A. If
>> the past of an event is A, then not-A is its future. But the
>> not-future is larger than the original past, as "incomparable" (in
>> the poset/trichotomy sense) events influence the future. Or, put in
>> relatitivity/cosmology terms, which many people are more familiar
>> with, ironically, events outside the light cone of the present figure
>> into the future. So the natural causal structure of spacetime is
>> intuitionistic, a Brouwerian lattice.
>
>
> Very plausible. But be careful of the solipsist move here.
> Unless I miss something, like a universal first person may be, I really
> don't know.
I'm not following you here.
If you're commenting on my "it applies to cryptography and money," we
can talk about it further (though it gets away from the focus of the
Everything list, except in the interesting mathematics and logic).
If you're referring to the cosmological points, my argument is just my
own reinterpretation of points made by Smolin, Markopoulou, Sorkin, and
others. Time is the most natural ordering we have, and the time of
non-absolute spacetime is a natural partial ordering (because some
events are incomparable, are not in order relative to each other). This
is a point made by Goldblatt and (apparently) many years earlier by
Arthur Prior (whose books I have not yet seen...an updated reprint of
one of his classics is coming in November, and I expect to read it
then).
> I think---with comp---
> that those brouwerian lattices emerge from the non distributive
> structures
> which rises from the coherent glueing of all little pieces of
> consistent (in a
> logical sense) histories.
Sounds interesting, but I'm not getting a clear mental picture of it.
Could you provide a natural transformation from your internal picture
to one I might be able to form?
>> Enough for this digression. But MWI, belief, possible worlds,
>> alternate forms of logic, knowledge, category theory, toposes, and
>> more are all deeply "intertwingled," as Ted Nelson would say. It's
>> all math. Good stuff.
>
>
> Yes. And the intertwingling grows up the deeper is the fundamental
> question, isn't it?
>
It's certainly my focus. Great stuff.
--Tim
