On 13 Feb 2011, at 20:06, Stephen Paul King wrote:
Hi Bruno,
-----Original Message----- From: Bruno Marchal
Sent: Sunday, February 13, 2011 3:48 AM
To: [email protected]
Subject: Re: Multisolipsism
On 13 Feb 2011, at 09:23, Stephen Paul King wrote:
I am very interested in this question as it directly relates to my
questions about how interactions between multiple and separable 1-
p. I continue to be confused by this term "body problem in
computer science". Could you discuss it in some greater detail?
The body problem and the white rabbit problem are variant of the
general problem of explaining the belief in a physical universe from
numbers and computer science, without the assumption that there is a
primary physical reality (or that there is no primary physical
reality). The UD Argument is supposed to justify this in detail. (And
AUDA justifies the non boolean and quantum nature of the logic of
what
is observable by asking a 'Löbian number' her opinion on the matter
(no pun intended).
**
[SPK]
OK, sure, but that about considerations of one 'Löbian number'
communicating with another? That is what my questions are about.
DM + ~solipsism can be shown to entail the coherent multiplication of
shared computations, that is first person plural shared dreams. To
show that DM entails ~solipsism by itself, you have to solve the body
problem first. The other minds problem should be easily soluble from
the solution to the body problem, and the key notion is interaction.
But interaction is still problematical even in quantum logic, and a
fortiori in the arithmetical logic. I think you need the "degenerate"
material hypostases: the 'B^n p & D^m p' nuances. With m > n, you get
arithmetical quantum logics, and you almost get the tensor needed for
the interactions. Unfortunately those tensors don't behave so well.
Those tensors arise from a Temperley-Lieb like structure related to
the arithmetical modal projection operators (B^n p & D^m p). This, if
it works, could explain how space arise from numbers, and why the
dynamic is governed by a unitary transformation. Space seems to be
defined only by the conditions of making multi-observers interaction
possible.
Just remember that we have to extract this from arithmetical self-
reference only, in a very special particular way, so that we don't
loose the qualia in the process. Indeed the qualia, including the
quanta, are provided by the intensional variant of the Solovay G/G*
splitting.
***
[SPK]
Ok, but cannot you see that "fist person plural shared dreams" is
exactly (or close enough!) to what we see in the Many world
interpretation for each and every notion of an observer but does not
solve the question of "how is it that I experience this particular
reality and not some other"? Yes, there is a correlation between the
observer as a memory within all of the related parallel worlds such
that we do not have empty memories/ Zombie observers, but this does
not get us far enough toward answering the question. ~Solipsism
alone is necessary but not sufficient. DM + ~solipsism works but
only because the definiteness of properties (that is the key feature
of physicality) is hidden in the Yes Doctor! DM assumes all of
features of Physicalism and but throws again the word physical. One
needs to stop looking at the words and consider the properties and
features that the word refers to! What does it mean to be physical
as opposed, for example, to mental or ideal?
To bet on the Yes Doctor is to bet that there is something
definite in the sense that the outcome either is or is not a
continuance of consciousness upon digital substitution. It is the
feature of persistence of properties over time. Physicality refers
to a set of invariances under transformations such that those
transformations or dynamics exist separate and independent of any 1-
p cogitation. be it via Bp & D or whatever modality. It is the root
of the idea of Machine and is implicit in the Turing Theorem and its
variants. There must be something that is like a tape and something
that is like a read/write device for the Turing Machine to exist as
a model and the properties of being a tape and being a read/write
device must be such that they persist under the continuation from
one operation to the next.
This is not a problem. That bottom kind of invariance relies on the
"invariance" of the + and * laws of the numbers. If comp is correct,
it promise more stable foundations and invariants than anything thing
extrapolated from empirical observations.
One cannot extract change from changelessness unless one extends
Existence into a continuum of possibility and allows the further
existence of methods that can contrast one subset of that continuum
with some other, but this can only happen within finite and improper
subsets of the continuum and this the ideals that we propose to be
the case at the continuum level do not faithfully translate into the
finite filters. It is in the finite filter levels that we obtain the
persistence of properties under time translations and thus time -
the ordering of succession - emerges at that level. Time does not
and cannot exist at the level of the Continuum of Existence itself.
It is, as Russell Standish pointed out, a zero-information set. The
duality that I propose for finite filters vanishes and we obtain a
neutral monism that is neither mind (ideal) nor matter (material).
All that is OK with comp, except that the assumption of numbers is a
bit higher than zero information. You cannot get the natural numbers
from logic alone.
Quantum Mechanics has this definiteness only with the inclusion of
the vehicle of the Born Rule and is the source of the measurement
problem: How do we cross the chasm between linear superpositions of
possible properties to the definiteness of properties such that we
can have a definite set of alternative to bet upon. We cannot bet
upon superposed properties because there is no "or" between them,
the properties form a continuum that can only be cut from the outside.
The "or" comes from the first person indeterminacy, and if UDA is
correct and if the quantum description is correct, the quantum or is
comp "or" shared by populations of machines (numbers).
The answer is interaction via Pratt's proposed state transition of
Chu spaces and it is what I am investigating. My proposal is that we
drop the insistence on tensor products since they require the
equivalent of a global synchronization and consider alternatives.
The alternative that I propose is the way that time is treated as a
local variable in Hitoshi Kitada's Interpretation of QM. This makes
the variable of time in QM consistent with Relativity, but this idea
requires that we treat quantum mechanical systems as asynchronous
and non-pre-harmonized Leibnizian monads and thus require an
alternative definition of interaction which I have developed as
bisimulation via quantum pseudo-telepathy.
BTW, the empty spots between objects in a space could be defined
as "the places an event could occur but does not" such that the
entire space is an undivided whole. So on one hand a space can be
seen as a distribution of dust as the dual of a Boolean algebra, and
a complete whole object that is a single speck of dust within a
larger space, this is a non-Archimedean extension. This is just a
matter of figuring out the mereology that we are using in our
ontology. I am proposing that we use non-well founded sets and
ultrametrics as a basis for ontology and thus have self-reference
build into our logics and their duals, but we could instead take
your modal extensions and dualize them via the proper extension of
the Stone Representation Theorem. The hard part is to not impose
global flatness on our structures, we should never treat our
hypostases as all existing on the same ontological level!
As far as I can figure out what you are saying here, that might be
relevant, or not, at some stage, but might be premature in the Digital
Mechanist theory.
Bruno
http://iridia.ulb.ac.be/~marchal/
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