Hi Bruno Marchal
I am not a mathematician, my background is in physical science (metallurgy)
and of laboratory results therein. So I have a problem keeping up. But I
think I can say this:
Ultimately, IMHO any math or mental abstractions based on the fleshly brain
have to be also true for the fleshly brain. The problem is perhaps
that the fleshly brain is in <>, the abstractions in []. I suppose that
logically
one could use <>[]p.
I don't know how one could do this, so to begin with, one could keep
operating as usual, by assuming that comp and monads both apply to all
brain activity.
And in addition, IMHO if you want to also use Leibniz's monads, these must also
be associated to appropriate parts of the fleshly brain. A simple form
of this would be to at first use a functional account of the brain, and the
tripartite brain
model (bdi, or belief, desire, intention). Later on, there can be more than one
of each
type according to what neuroscience tells us. Magnetic resonance imaging
could be used to label each functionally different brain area of b,d, and i.
So you have a Venn diagram of three circles with the fleshly brain as the
central circle with some overlap on either side with comp and monadology.
[Roger Clough], [rclo...@verizon.net]
11/27/2012
"Forever is a long time, especially near the end." -Woody Allen
----- Receiving the following content -----
From: Bruno Marchal
Receiver: everything-list
Time: 2012-11-23, 11:54:57
Subject: Re: Nothing happens in the Universe of the Everett Interpretation
On 22 Nov 2012, at 18:38, Stephen P. King wrote:
How exactly does the comparison occur?
By comparing the logic of the observable inferred from observation (the quantum
logic based on the algebra of the observable/linear positive operators) and the
logic obtained from the arithmetical quantization, which exists already.
How does the comparison occur? I will not ask what or who is involved, only
how. What means exists to compare and contrast a pair of logics?
The logic exists, because, by UDA, when translated in arithmetic, makes a
relative physical certainty into a true Sigma_1 sentence, which has to be
provable, and consistent. So the observability with measure one is given by []p
= Bp & Dt & p, with p arithmetical sigma_1 (this is coherent with the way the
physical reality has to be redefined through UDA). Then the quantum logic is
given by the quantization []<>p, thanks to the law p -> []<>p, and this makes
possible to reverse the Goldblatt modal translation of quantum logic into
arithmetic.
Comparison is used in the everyday sense. Just look if we get the quantum
propositions, new one, different one, etc.
Comp seems to necessitate all possible physical worlds in an equiprobable way.
?
Does not comp require all possible 1p to exist?
Comp makes all possible 1p existing in arithmetic, from the possible
arithmetical pov.
There is a deep problem with notions of priors as it seems that we cannot
escape from the problem of subjectivity as we see in the (so-called) anthropic
principle: each observer will necessarily find itself in a world what has laws
compatible with its existence. It seems to me that the observational act itself
is a breaking of the perfect symmetry of equiprobability of possible worlds.
?
But this claim implies violence to the idea of a 3p.
I found at http://higgo.com/qti/Mallah.htm an exchange between Mallah and
Standish that seems to illustrate this problem:
"Russell Standish: The predictions can easily depend of the 'picture' but must
be consistent with each other. Let me give a simple example: In one picture,
observer A decides to measure the spin of an electron in the x direction. In
the other, observer B decides to measure the spin of the electron in the y
direction. Observer A will see the spin of the electron aligned with x axis,
and Observer B will see it aligned with the y axis. Both observations are
correct in the first person picture of that observer. A "person" with the third
person perspective, sees observers A and B as inhabiting separate `worlds' of a
multiverse, each with appropriate measure that can be computed from Quantum
Mechanics.
Jacques Mallah: On the contrary, this is a textbook example of the way I said
it works. The theory predicts some measure distribution of observers; an
individual observer sees an observation drawn from that distribution. There are
no different sets of predictions for different pictures, just the measure
distribution and the sample from it.
Russell Standish: It sounds to me like you don't think the prediction changes
according to what the observer chooses to observe? An electron cannot have its
spin aligned with the x axis and the y axis at the same time. Once the
experimenter has chosen which direction to measure the spin, the history of
that particular is observer is constrained by that fact, and the predictions of
QM altered accordingly. This is true both in MWI and the Copenhagen
interpretation, and is the "spooky" nature of QM. I used to think that QM gave
predictions in terms of distributions, and that because one didn't see isolated
particles, rather ensembles of such particles, I didn't see a problem. The
properties of an ensemble are well defined. However, the ability of
experimenters to isolate a single particle, such as a photon, or an atom, means
we have to take this "spookiness" seriously."
The idea of a 3p cannot be applied consistently to the notion of a 'person'
or observer if one is considering the 1p of observers in separate 'worlds' of a
multiverse unless, for example, A and B have observables that mutually commute
and thus have some chance of being mutually consistent and capable of being
integrated into a single narrative. I think that this problem is being
overlooked because the problem of Satisfiability is being ignored.
?
I hope that we can agree that there is at least an illusion of a physical world
that 'we' - you, me, Russell, .... can consider... Is it necessarily
inconsistent with comp?
? ? ?
Not at all. The whole point of UDA is in explaining why the physical reality is
unavoidable for the dreaming numbers, and how it emerges from + and * (in the
"number base"). It is indeed a first person plural product, with the persons
being all L bian machines, etc.
I am coming at the idea of a 'physical reality' as an emergent structure
and not some pre-defined ordering.
Good.
Comp gives the complete algorithm to extract bodies and physical laws, making
comp testable, even if that is technically difficult,
I claim that it is not even technically difficult; it is impossible for the
simple reason that there does not exist a unique Boolean algebra for all
possible 1p.
? (I agree such BA does not exist, but this is exactly what we need to find a
measure theorem à-la Gleason). We need a sufficiently good quantum logic, and
up to now the comp quantum logic fits rather well.
Gleason's theorem is interesting:
http://en.wikipedia.org/wiki/Gleason%27s_theorem
"For a Hilbert space of dimension 3 or greater, the only possible measure of
the probability of the state associated with a particular linear subspace a of
the Hilbert space will have the form Tr(µ(a) W), the trace of the operator
product of the projection operator µ(a) and the density matrix W for the
system."
We sidestep the problem of how we define the transition from pure states to
density matrices. Andrew's discussion might be seen as addressing this...
OK.
Why? Because it cannot be proven to be satisfiable(aka globally
self-consistent) by any finite sequence of algorithms. Completeness and
consistency for such cannot be assumed a priori.
?
Do you ever address the question of satisfiability?
Which satisfiability? I use it all the time. p->p is satisfiable by all
interpretation, and this is used all the time. I do not use the complexity of
satisfiability, as if this needed to be used, it has to be justified by the
modal logic extracted from self-reference.
but up to now, it fits remarkably, and that would not have been the case
without QM. That would not have the case if "p->[]<>p" was not a theorem of the
Z1* logics (matter).
Your reasoning is correct only because you are assuming the impossible to
be true a priori: that there exists a solution to the Satisfiability problem
It exists. "Satisfability" is non tractable, not insoluble. The first persons
don't care "waiting exponential time" by the invariance of first person
experience on delays.
Of course, but an infinite BA requires eternity (infinitely many steps) to
solve its satisfiability problem.
But no machine ever need to do that (and can't). The BA might be infinite, but
not the proposition, unless you are using infinitary logic, which does not play
a big role in comp up to now.
I am not claiming non-solubility; I am pointing out that the computation of
satisfiability must run to obtain a solution,
The 1p depends on truth, not on proof.
otherwise it is false to claim that the solution is accessible.
The UD does "prove", or arithemtic proves, all the true sigma_1 sentences,
which is enough for the computations to be emulated. then the 1p are
distirubuted non constructively on that, independently of the complexity of the
proofs. Without this, no measure problem.
And with no measure problem, you lost the reduction of physics to computer
science.
It is a profound mistake to claim that the existence of the largest prime
number defines the exact sequence of numerals that would enumerate that prime
number.
You need to decide in which base you write it, and then it is defined. But we
don't need this.
Similarly, the mere possibility of satisfiability of a BA
Satisfiability concerns sentences, not BA.
cannot be used to argue about the particular distribution of propositions of
the BA.
You are considering first persons in the eternal and ideal case, but that
does not connect omniscient machines to finite human brains.
The connection is explained by the UDA.
This is the challenge to Plato and Parmenides, how do we bridge between the
Realm of Truth and the world of appearances?
By the realtion between machines' belief and reality. With comp, today, we can
use the work of Tarski and others.
We could make claims forever but showing a proof requires physical effort.
And time, money, if not a sense of public relation. But that is relevant at
some meta-meta-level.
There are no shortcuts to knowledge. You seem to be OK with the idea that
knowledge can obtain 'for free'.
Free of physics, yes. Free of math? No. You need to postulate enough to get
Turing universality.
Perhaps I am mistaken, but it seems that you are assuming the impossible to be
real.
I don't. Unless you come back with the idea that 1+1=2 requires a physical
world, or thing like that.
*and* that it is accessible for any finitely expressible logical structure.
It is accessible, but then I don't see at all the relevance of this.
Please explain how it is accessible.
You were using the term. I am the one asking the question here.
Bruno
http://iridia.ulb.ac.be/~marchal/
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