On Tuesday, October 1, 2002, at 06:37 AM, Bruno Marchal wrote:
> At 12:26 -0700 30/09/2002, Tim May wrote:
>> If the alternate universes implied by the mainstream MWI (as opposed
>> to variants like consistent histories) are "actual" in some sense,
>> with even the slightest chance of communication between universes,
>> then why have we not seen solid evidence of such communication?
> I am not sure I understand why you oppose the "mainstream MWI" and the
> consistent histories (although many does that, I don't know why).
> In all case, if QM is right (independently of any interpretation),
> histories or parallel universes cannot communicate, they can only
> interfere(*). The same happens with comp. Probability measures are
> and depends on the whole collection of relative computational
> histories, but
> this does not allow the transfer of one bit from one computation to
I of course was not claiming such communication (or travel, whatever)
would be easy. Just doing a thought experiment settting some very rough
bounds on how impossible the communication or travel would be.
One of the conclusions of "How come they're not here?" is that, in
fact, such communication or travel is essentially impossible (else
they'd _be_ here).
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.
> BTW, Tim, I am discovering n-categories. Quite interesting. John Baez
> has written good papers on that, like his categorification paper.
> Have you read those stuff. Could be useful for the search of coherence
> condition in "many world/observer" realities ...
I've been reading Baez for a while. An excellent teacher. I hear he's
working on a book on n-categories. And Baez and my namesake, J. Peter
May--unrelated to me, are leading a consortium to research n-categories
more deeply. I confess that I have only vague ideas what they
are....sort of generalizations of natural transformations, I sense.
(I'm still studying categories at a more basic level, having "jumped
ahead" to other areas, as is my wont.)
His "From Categories to Feynman Diagrams" (co-authored with James
Dolan) and several of his related papers are good introductions.
Chris Isham is also very good on drawing the connections between
conventional quantum mechanics (i.e., stuff in the lab, not necessarily
quantum gravity or quantum cosmology) and category/topos theory. (In
particular, the collapse of the wave function and measurement looks
like a subobject classifier, or, put another way, the usual transition
from "neither true nor false" in a Heyting algebra to the "one or the
other" we _always_ see once there is any chance to
observe/measure/decide. That is, Heyting --> Boolean is what the
mystery of QM centers around.
(I am intrigued to find that Jeffrey Bub, in his "Interpreting the
Quantum World," 1997, makes central use of possible worlds, lattices,
and such. While he does not explicitly mention Heyting algebras, the
connection is close, and is implicit in the math. Had I encountered
this approach when I was studying QM, I might have pursued it as a
career. Instead, I was bored out of my mind solving partial
differential equations for wave functions inside boxes. Ugh.)
I'm reading Graham Priest's "An Introduction to Non-Classical Logic,"
2001, which covers various modal logics, conditional logics,
intuitionist logic, many-valued logics, and more ("first degree
entailment," "relevant logic," etc.).
The tableaux approach is new to me. They look like the trees of
Smullyan, and hence like semilattices. (I'm also reading Davey and
Priestley's "Introduction to Lattices and Order," along with parts of
Birkhoff's classic, and the lattice/poset approach continues to appeal
to me greatly. It's a vantage point which makes all of this
heretofore-boring-to-me logic stuff look terribly interesting. I'm
viewing most programs/trees/refinements/tableaux as branching worlds,
as possible worlds (a la Kripke), to be further branched or discarded.
Hence my focus on MWI and "Everything" remains more on the mathematics.
(I just ordered my own copy of Goldblatt's "Mathematics of Modality.")
"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.
Anyway, I managed to spend a couple of minutes relating this to the
world of finite knowledge about such things as "money." This is related
to belief, trust, reputation, and suchlike.
Afterwards, a senior member of a leading crypto company came up to me
and said he'd done work in mathematical logic in school. He said he's
been waiting for ten years for crypto to turn into mathematical logic,
that the focus on number theory has been a kind of diversion.
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