Hi Bruno,
Interleaving...
From: Bruno Marchal
Sent: Sunday, October 10, 2010 11:16 AM
To: [email protected]
Subject: Re: A paper for your Comments
Hi Stephen,
The discussion has evolved enough now from my original topic as to
require that I restate my thesis and add some new ideas in a new post with a
new subject line, given some new understanding of your ideas. I greatly
appreciate your patience and comments as I have learned a great deal from it. I
believe that we agree on sufficient points to move forward so that I will leave
you comments below stand as a reference for the future. Right now I have one
question: Are you familiar with Jaakko Hintikka's idea of game semantics for
Logic in which (crudely put) on thinks of a proof is related to the existence
of a winning strategy in a 2-person game.
What is your opinion of such, if any?
For examples please see:
http://plato.stanford.edu/entries/logic-games/
http://www.csc.villanova.edu/~japaridz/CL/gsoll.html
http://en.wikipedia.org/wiki/Game_semantics
[BM] That is very interesting, but with respect to the question I am
interested in, this is a question of implementation. The point of mechanism is
that the internal views does not depend on the choice of the initial system.
[SPK]
My idea is that the "top-down" instantiation of proofs from Arithmetic
Realism's P.o.V. is reflected in a "bottom-up" way by an infinite number of
interactions between many. This sets up a natural symmetry of sorts between the
ONE and the MANY, where the "internal views" are within the MANY. There would
be no unique "initial system" in the objective sense for the same reason that
there can be no first implementation in the objective sense. This has the
implication for physical systems that there is no origin for time and space in
an objective sense. The Perfect Cosmological Principle that the Universe is
homogenous and isotropic in space and time would obtain for an average
"observer"; thus a finite space and duration of the world would obtain for any
instance. This would solve the initial conditions problem in physics.
**
I ask this because it seems that one of the key points of divergence in
our discussion is related to my use of ideas that are implicit in game semantic
based logics.
[BM] All digital parallelism can be emulated by digital sequences. In the
mind-body problem parallelism is a red herring, because IF it plays some role
for the measure problem, THEN it will be justified by the extraction of space
and time. Of course in concrete 3D-time applications, parallelism is without
doubt of upmost importance.
[SPK]
I agree and this goes straight to the root of the idea that I am
exploring. This is why I am looking at the duality between Boolean algebras
(and their generalizations) and disconnected/scattered spaces that we see in
the Stone Representation theorem. Minds would be instances of the former and
Bodies would be instances of the latter. The trick is to see how the evolution
of these works; this is what Pratt has figured out (in basic terms).
Additionally, your repeated notion that if "any empirical difference between
this arithmetical physics and the empirical physics, would refute, not
Plotinus, but the present arithmetical interpretation" requires a means to
connect or analytically continue into physical theory; "concrete 3D-time
applications" are instances of the latter. By the way, the passages that I
quoted previously from Stephen Wolfram where relating to that physical side and
speak to limits on the content of individual Mechanisms; those are what I am
considering in the bisimulation model of interactions.
I am not advocating physicalism except as one side of a duality. I am
against the idea that the physical (or the logical) is "all that exists" and
the proof of sorts that I point to is the epiphenomena problem that both
physical monism and mental/ideal monism have. Of course we need a neutral
common ground to absorb both into but that is taken into account in terms of
"in the limit of where all differences vanish". Forgive me here as I am
sacrificing clarity for brevity.
**
Additionally there is resent work that seems to strongly support my crazy
idea of how we might solve the measurement problem in QM (which is my main
motivation).
[BM] So you do assume QM, even QM + collapse apparently. I don't assume
anything in physics, given that the results is that physics is derivable from
arithmetic, and *has to be derived* from arithmetic if we want obtain the
qualia, and not just the quanta.
[SPK]
Yes, because I am coming from the opposite direction from you! I
assume QM but not "collapse" per say as the metaphysical assumptions in
"collapse" go against the Perfect Cosmological Principle. We see this in the
preferred reference frame that any objective collapse model generates. What we
need, I believe, is a model where we obtain what appears as a Collapse from a
1st person P.o.V. but is more like the Everett-Dewitt idea from the outside 3rd
person view all the while understanding that there is no special "observer"
that could perceive the latter except as an abstract notion.
**
Please see: http://pages.stern.nyu.edu/~abranden/icig-05-27-08.pdf This is
very much related to the work of Jean-Yves Girard in his "Geometry of
Interaction".
[BM] ? (The relation is either trivial, or is not obvious for me. Very
technical paper(s). You should stick a bit more on the idea(s) instead of
mentioning so much papers which seems to me both a bit 1004-like with respect
to the topic).
[SPK]
That paper discusses the notion of correlations in games which is another
way of looking at bisimulations between Mechanisms. From the abstract:
"Correlations arise naturally in non-cooperative games, e.g., in the
equivalence between undominated
and optimal strategies in games with more than two players. But the
non-cooperative assumption
is that players do not coordinate their strategy choices, so where do these
correlations come from?
The epistemic view of games gives an answer. Under this view, the players’
hierarchies of beliefs
(beliefs, beliefs about beliefs, . . . ) about the strategies played in the
game are part of the description
of a game. This gives a source of correlation: A player believes other
players’ strategy choices are
correlated, because he believes their hierarchies of beliefs are correlated.
We refer to this kind of
correlation as “intrinsic,” since it comes from variables—viz., the
hierarchies of beliefs—that are part
of the game. We compare the intrinsic route with the “extrinsic” route taken
by Aumann [2, 1974],
which adds signals to the original game."
I hoped that you might get an intuition of what I am trying to work out
by reading this paper... It seems to me that the notion of Belief that
Brandenburger et al are using would be related to your B as in Bp&p. In my idea
this manifests as simulations of simulations, etc.
**
By the way, almost all of Girard's papers are inaccessible to me as I am
not in a university. I know of his work from my study of Pratt's papers.
Take a look here:
http://iml.univ-mrs.fr/~girard/Articles.html
from Girard's web page:
http://iml.univ-mrs.fr/~girard/
Best,
Bruno
[SPK]
Thanks for pointing me to that, now I have 2X reasons to learn to read
French. :P I am still thinking on how to write up the interaction idea. It
takes me time to translate pictures in my head to words on the screen.
Kindest regards,
Stephen
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