At 14:03 -0700 21/08/2002, Tim May wrote:

>Many thanks for remembering my current main interest, but I still 
>have a long, long way to go before I can understand your logic 
>points. (I have several "advanced" books on logic, but mainly for 
>inspiration and direction. Have recently picked up more introductory 
>books by Tarski, Boolos, Smullyan, etc. My focus is more on the 
>lattice/Heyting algebra side, so a lot of logic has not yet been 
>needed.)


BM:
The difficulty is Godel incompleteness theorem. I thought that
books like Nagel & Newman's "GODEL'S PROOF, or Hofstadter's "Godel, 
Escher Bach" would popularize Godel's proof, but since I have defended
my thesis I realize Godel's result have not yet been really
understood even by most mathematicians.
No problem with your concentration on the lattice/Heyting algebra.
French speakers say "tous les chemins menent a Rome" (all the
roads lead to Rome) !


At 14:03 -0700 21/08/2002, Tim May wrote:
>Yes, but the conventional logic point of view has not proved to be 
>especially useful for understanding mind and AI, as I'm sure you 
>know very well.


BM:
Mmmh... I am not sure about that. This is also a question of fashion.
There is also a conflict between more theoretically oriented long term
project and then doing money quickly in private business.
I would be more cautious about those matter. Also, a lot of things in
traditional practical computer science were developed first in symbolic
AI. In fact I do not believe in a net separation between computer
science, artificial intelligence, artificial life, control theory, etc.


At 14:03 -0700 21/08/2002, Tim May wrote:
>So while I think the IL/Brouwer/Heyting/topos stuff will 
>_eventually_ be of use in epistemology and ontology aspects of AI, 
>I'm not expecting quick progress.


BM:
We will see. In geological time progress is explosive!


At 14:03 -0700 21/08/2002, Tim May wrote:
>As for mind-body issues, I've never understood what the big deal is.


BM:
On this point we differ a lot. I cannot imagine a more fundamental
issue. But with psychology we are still at pre-galilean time. Mind
is still a religious taboo, especially for religious materialist,
who are usually not aware their thought on the matter are religious.

>[...]


>At 14:03 -0700 21/08/2002, Tim May wrote:
>>BM: And it is not at all an exaggeration to say my work is an attempt
>>to explain QUBITS from BITS. Actually I show more and less:
>
>TM: This interests me a lot more than dealing with the mind-body 
>problem...perhaps because I only think about things I can "sort of" 
>grasp. The problem of mind is just too large a problem at this time, 
>I think.


BM:
Have you try to understand the UDA? Have you read Hofstadter and
Dennett's "Mind's I" ? With the comp hyp we have all the piece of
the puzzle. The qubits/bits relation I made was just an opportunist
rephrasing. But perhaps I should see it as a not too bad pedagogical
tool. I don't know.

>  [...]

At 14:03 -0700 21/08/2002, Tim May wrote:
>BTW, the most exciting recent thread for me was the one about the 
>"reversability of time" arguements, raised initially by Wei Dai and 
>then argued by Hal Finney. Writing the "Professor Ludwig" piece, in 
>which an 1860 Prof. Ludwig (Boltzmann, obviously) predicts that the 
>simplest time-reversed pocket of the universe means telescopes will 
>likely see nothing but chaos outside the local region, helped me to 
>clarify my thinking on anthropic arguments. And motivated me to 
>finish reading Huw Price's book.


BM:
All that is indeed very interesting indeed. (A little premature
from my angle of approach though). As the question of space, which
is much more mysterious for me than time. My approach leads quickly
to subjective time (through S4Grz), but subjective space is quite
more difficult. It is there that non-topos categories, and probably
braided monoidal categories should introduce themselves.


At 14:03 -0700 21/08/2002, Tim May wrote:
>This is the real blessing of mailing lists like this one! I may now 
>be motivated to understand the kinds of logic you discuss if only to 
>try to refute you! (no offense intended)


BM:
Please try. It would be an honor to be refuted :-)
Until now some people have pretended having find a flaw, but nothing
serious has been shown. Serious critics are necessary for improvements though.

OK Tim I will finish the "Yetter" post this afternoon or tomorrow,
may be trying to be a little less technical. But the technics are
much more simple than the concepts. Old preliminary versions of my
work did not use modal logic at all, but was done directly in term
of godel numbers. The modal technics and the Solovay results has made
possible to shorten considerably the presentation of my result,
making things truly far simpler. It's not important if you don't
understand at once the technics. Give time to time ;)

-Bruno


PS In the meantime I let you meditate, just for fun, on the following
paragraph by Yetter in the introduction of his "functorial knot theory":

  <<Another feature of these recent developments is the difference
between the role categories and functors have usually played
since their discovery and the role they now play in quantum topology.
Rather than serving a foundational role, as a clean way of encoding
"natural" constructions of one kind of mathematical object from
another, categories in quantum topology stand as algebraic objects
in their own right. This difference has not always been generally
understood, even by quite brilliant mathematicians working in related
areas, as the following personal anecdote involving the late Moshé
Flato illustrates. One evening at a joint Summer Research Conference
in the early 1990's Nicholai Reshetikhin and I button-holed Flato,
and explained at length Shum's Coherence theorem and the role of
categories in "quantum knot invariants". Flato was persistently
dismissive of categories as a "mere language". I retired for the
evening, leaving Reshetikhin and Flato to the discussion. At the
next morning's session, Flato tapped me on the shoulder, and giving
a thumbs-up sign, whispered, "Hey! Vive les categories! These new
ones, the braided monoidal ones.">>

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