On 27 Nov 2012, at 11:55, Roger Clough wrote:
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.
Hmm... You are too quick here. I can see the idea though, but to
answer this precisely would be long, and premature.
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.
I think that the monads might be just the number, but seen relatively
to some universal number, and so they are programs. the supreme monads
is then played by the universal number. You need a universal system to
start, and arithmetic is handy for that, conceptually.
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.
The fleshy brain is associate with infinities of computations. It
includes all the different computations going thorugh your mind state,
but that you cannot distinguish from you 1p view. There is an infinity
of such computations in arithmetic.
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.
I reason from comp, and then look how make sense of what we can
observe. here you are too fuzzy, and probably have not yet see that
"fleshy" is an emergent pattern in the dream of the numbers, not
something existing in some primitive reality. That's the point of
reasoning assuming comp.
Bruno
[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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