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), 
> parallel
> histories or parallel universes cannot communicate, they can only
> interfere(*). The same happens with comp. Probability measures are 
> global
> and depends on the whole collection of relative computational 
> histories, but
> this does not allow the transfer of one bit from one computation to
> another.

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 
stuff.

--Tim May

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