Provable vs Computable
jue...@idsia.ch
Which are the logically possible universes? Max Tegmark mentioned
a somewhat vaguely defined set of ``self-consistent mathematical
structures,'' implying provability of some sort. The postings of Bruno
Marchal and George Levy and Hal Ruhl also focus on what's provable and
what's not.
Is provability really relevant? Philosophers and physicists find
it sexy for its Goedelian limits. But what does this have to do with
the set of possible universes?
I believe the provability discussion distracts a bit from the
real issue. If we limit ourselves to universes corresponding to
traditionally provable theorems then we will miss out on many formally
and constructively describable universes that are computable in the
limit yet in a certain sense soaked with unprovable aspects.
Example: a never ending universe history h is computed by a finite
nonhalting program p. To simulate randomness and noise etc, p invokes a
short pseudorandom generator subroutine q which also never halts. The
n-th pseudorandom event of history h is based on q's n-th output bit
q(n) which is initialized by 0 and set to 1 as soon as the n-th element
of an ordered list of all possible program prefixes halts. Whenever q
modifies some q(n) that was already used in the previous computation of
h, p appropriately recomputes h since the n-th pseudorandom event.
Such a virtual reality or universe is perfectly well-defined. At some
point each history prefix will remain stable forever. Even if we know p
and q, however, in general we will never know for sure whether some q(n)
that is still zero won't flip to 1 at some point, because of Goedel etc.
So this universe features lots of unprovable aspects.
But why should this lack of provability matter? It does not do any harm.
Note also that observers evolving within the universe may write
books about all kinds of unprovable things; they may also write down
inconsistent axioms; etc. All of this is computable though, since the
entire universe history is. So again, why should provability matter?
Juergen Schmidhuber http://www.idsia.ch/~juergen/toesv2/
scerir
> Which are the logically possible universes? Max Tegmark mentioned
> a somewhat vaguely defined set of "self-consistent mathematical
> Marchal and George Levy and Hal Ruhl also focus on what's provable
> and what's not.
> Is provability really relevant? Philosophers and physicists find
> it sexy for its Goedelian limits. But what does this have to do with
> the set of possible universes?
Many people think that if a formal statement is neither provable nor
refutable, then it should be considered neither true, nor false.
But it is not that way that we - normally - use the term "true".
Somebody wrote: "Suppose that I have a steel safe that nobody
knows the combination to. If I tell you that the safe contains 100
dollars - and it really does contain 100 dollars - then I'm telling the
truth, whether or not anyone can prove it. And if it doesn't contain 100
dollars, then I'm telling a falsehood, whether or not anyone can prove it."
(A multi-valued logics can deal with statements that are either definitely
true or definitely false, but whose actual truth value may, or may not,
be known, or even be knowable.).
- scerir
jamikes
> Juergen Schmidhuber wrote:
> > Which are the logically possible universes? Max Tegmark mentioned
> > a somewhat vaguely defined set of "self-consistent mathematical
> > structures'' implying provability of some sort. The postings of Bruno
> > Marchal and George Levy and Hal Ruhl also focus on what's provable
> > and what's not.
> > Is provability really relevant? Philosophers and physicists find
> > it sexy for its Goedelian limits. But what does this have to do with
> > the set of possible universes?
scerir writes an enjoyable version on the last part of the quote.
Let me address the first part about "possible universes". Of course Juergen
was
cautious and included "logically" in his phrase.
"Logically" most likely refers to human (on this list: even mathematical)
logic.
Do we really think that human (math) logic is the restrictive principle for
nature?
What we see (what we want to see?) seems to point to that, but do we see'em
all?
Isn't "possible" what we don't see or understgand or realize?
Didn't our horizon (logic, math) increase over some time? Are we at the end?
In considering plenitude/multiverse, does it make sense to select part of it
(maybe a small, unimportant segment only)?
Even if we cannot develop "knowledge" about the rest, we should not deny its
"possibility" of existence. The farthest from this list would be a closed
mind!
John Mikes
Hal Ruhl
I am not so much interested in provability as I am in whether or not the
"noise" in a universes history is pseudorandom or random and forging an .
George Levy
jue...@idsia.ch wrote:
> Example: a never ending universe history h is computed by a finite
> nonhalting program p. To simulate randomness and noise etc, p invokes a
> short pseudorandom generator subroutine q which also never halts. The
> n-th pseudorandom event of history h is based on q's n-th output bit
> q(n) which is initialized by 0 and set to 1 as soon as the n-th element
> of an ordered list of all possible program prefixes halts. Whenever q
> modifies some q(n) that was already used in the previous computation of
> h, p appropriately recomputes h since the n-th pseudorandom event.
>
> Such a virtual reality or universe is perfectly well-defined.
Such a universe would violate Bell' inequality theorem. Quantum randomness
cannot be simulated by hidden variables. We have to move beyond
realism......to get a model of objective reality we must first develop a
model of consciousness.
George
Saibal Mitra
I disagree. Hidden variables are indeed excluded, but that doesn't mean that
deterministic models proposed by Jürgen or 't Hooft are in conflict with
Bell's theorem. In the case of the model proposed by 't Hooft, you have a
universe that is very chaotic. Quantum mechanics arises in a statistical
description of the theory. Particles such as electrons, photons etc. don't
describe the degrees of freedom of the original deterministic theory, but
rather they arise only in the statistical description of this theory. In
other words: Mach was right in not believing that atoms exist.
In the case of the two slits experiment,
a hidden variable theory would tell you through what particular slit an
elecron travelled, and this is not possible. Okay, but does the electron
exist in the first place? I think not. The electron is just a mathematical
tool that allows you to calculate probabilities and is unphysical, just like
virtual particles and ghosts in Feynman diagrams. Why believe in electrons,
but not in the Fadeev-Popov ghost?
Saibal
Marchal
>Which are the logically possible universes? Max Tegmark mentioned
>a somewhat vaguely defined set of ``self-consistent mathematical
>structures,'' implying provability of some sort. The postings of Bruno
>Marchal and George Levy and Hal Ruhl also focus on what's provable and
>what's not.
You know that Hal Ruhl doesn't distinguish computability and provability,
so
it is open for me if his approach is nearer your's or mine.
The difference relies more between averaging on the (local) set
of consistent extensions defined in the whole UD*, or finding a priori
defining universes probabilities, or Universal prior.
I communicate with the sound lobian machine because I agree (in
arithmetic)
with the laws of exclude middle, and all classical logic.
Provable plays the role of thoroughly verifiable "scientific"
communication. (BTW *you* were the guy asking for formalisation!). Now
we are working at the metalevel (as George aptly remarks) and we will
interview the machine on its self-reference abilities. Recall the goal
consists in translating UDA in a language interpretable by a sound UTM.
And UDA is a self-referential thought experiment.
It will happen that the incompleteness phenomenon will force us to
take into account the nuance between []p and ([]p & p) and
([]p & <>p) in the discourse of the machine. They will correspond to
provable p,
knowable p, probability(p)=1.
Knowable will give rise to intuitionist logic and probability 1 will give
quantum logic.
Probability(p) 1 will really be no more that 1) there is consistent
extension,
2) p is true in all those consistent extension. (Only in an ideal frame
we have []p -> <>p, remember that in the cul-de-sac world []p is always
true).
>Is provability really relevant? Philosophers and physicists find
>it sexy for its Goedelian limits. But what does this have to do with
>the set of possible universes?
Wait and see. Remember I told George we have not yet really
beging the proof. The hard and tiedous thing is to arithmetise
the provability predicate.
I will define knowledge and "observable" (in the UDA sense)
*in* the language of the machine and I will show that the observable
propositions obeys some quantum logic. I will only consider the case
observable with a probability one. This will give a concrete
purely arithmetical interpretation of a quantum logic.
The probabilities are taken on the set of relative consistent
(UD accessible) extensions, and by consistent I just mean "-[]-"
with [] Goedel's provability predicate. (so you can guess the
role of provability).
The UD will be translated in the form of the set of
all (true) \Sigma_1 sentences.
>Is provability really relevant? Philosophers and physicists find
>it sexy for its Goedelian limits. But what does this have to do with
>the set of possible universes?
It has to do with the origin of the belief in universe(s) once
we bet we do survive digital substitution.
>I believe the provability discussion distracts a bit from the
>real issue. If we limit ourselves to universes corresponding to
>traditionally provable theorems then we will miss out on many formally
>and constructively describable universes that are computable in the
>limit yet in a certain sense soaked with unprovable aspects.
Actually, provability is just a step in my derivation (and we have still
not begin to discusse it! nor to define it). We have just seen some
modal logic which have a priori nothing to do with provability.
You are still anticipating.
It is a good thing you are open to unprovable aspects, and it makes
weirder you are not open to uncomputable aspects. (Although I know
provability is relative and computability is absolute (Church's Thesis)
Do you really believe than one of us limit "universes" to sets of provable
theorems. I am myself just defining the local *discourse* of a
machine-scientist.
>Such a virtual reality or universe is perfectly well-defined. At some
>point each history prefix will remain stable forever. Even if we know p
>and q, however, in general we will never know for sure whether some q(n)
>that is still zero won't flip to 1 at some point, because of Goedel etc.
>So this universe features lots of unprovable aspects.
I have no problem with that. As you should know from our earlier
discussion. Remember that the big role in my work comes from
(G* minus G), which
is a logic of the *unprovable* statements. G ang G* will be defined
formally soon, but you can also consult Solovay 1976 or Boolos ...
By logic here I mean a well defined set (of formulas) logically
closed for modus ponens.
>Note also that observers evolving within the universe ...
The UDA shows that such an expression has no meaning.
The movie graph (or Maudlin's Olympia) illustrates how non trivial
the "mind-body" problem is with comp.
I am aware there is something very hard to swallow here.
But it is a consequence of comp.
> ...may write
>books about all kinds of unprovable things; they may also write down
>inconsistent axioms; etc. All of this is computable though, since the
>entire universe history is. So again, why should provability matter?
It matters for the same reason which makes you proving theorems
in your papers. Proving is just a polite way to communicate
third person propositions.
You believe that we are modelising universes with proofs, when
we are just interviewing sound machines on their possible extension
in UD*.
If we are sound machines, it is natural to be interested in what those
sound machines can prove about themselves, what they can know about
themselves, what part of themselves they can observe, and on which
computational consistent extensions they can bet, etc.
All the term in the preceding sentence will be formally defined and
tranlated in arithmetic (the language of a sound UTM I will use).
The conclusion will be independent of the language chosen.
Bruno
Marchal
>Juergen Schmidhuber wrote:
>> Which are the logically possible universes? Max Tegmark mentioned
>> a somewhat vaguely defined set of "self-consistent mathematical
>> structures'' implying provability of some sort. The postings of Bruno
>> Marchal and George Levy and Hal Ruhl also focus on what's provable
>> and what's not.
>> Is provability really relevant? Philosophers and physicists find
>> it sexy for its Goedelian limits. But what does this have to do with
>> the set of possible universes?
>
>Many people think that if a formal statement is neither provable nor
>refutable, then it should be considered neither true, nor false.
>But it is not that way that we - normally - use the term "true".
>Somebody wrote: "Suppose that I have a steel safe that nobody
>knows the combination to. If I tell you that the safe contains 100
>dollars - and it really does contain 100 dollars - then I'm telling the
>truth, whether or not anyone can prove it. And if it doesn't contain 100
>dollars, then I'm telling a falsehood, whether or not anyone can prove it."
>(A multi-valued logics can deal with statements that are either definitely
>true or definitely false, but whose actual truth value may, or may not,
>be known, or even be knowable.).
That is basicaly the difference between classical logic
with gap between proof and truth, and intuitionistic
logic, or constructive logic, which equivote truth and provability.
And that is something which will be translated in the language of
the machine ... It is part of the proof I explain currently.
I have begin the explanations of logic with classical logics.
But other logics are fundamental in the derivation (mainly
intuitionist and quantum logics).
Bruno
scerir
> cannot be simulated by hidden variables. We have to move beyond
> realism......to get a model of objective reality we must first develop a
> model of consciousness.
The picture seems even more fuzzy. There are, also, classical dynamical
systems, and classical fields, violating Bell's inequality. And we can
realize quantum entanglement ... by classical computers (experiment done).
And, above all, can we use (as Bell did) the classical probability theory in
the quantum domain?
- scerir
----------
quant-ph/0007019
Non-locality and quantum theory: new experimental evidence
Luigi Accardi, Massimo Regoli
Starting from the late 60's many experiments have been performed to verify
the violation Bell's inequality by Einstein-Podolsky-Rosen (EPR) type
correlations. The idea of these experiments being that: (i) Bell's
inequality is a consequence of locality, hence its experimental violation is
an indication of non locality; (ii) this violation is a typical quantum
phenomenon because any classical system making local choices (either
deterministic or random) will produce correlations satisfying this
inequality. Both statements (i) and (ii) have been criticized by quantum
probability on theoretical grounds (not discussed in the present paper) and
the experiment discussed below has been devised to support these theoretical
arguments. We emphasize that the goal of our experiment is not to reproduce
classically the EPR correlations but to prove that there exist perfectly
local classical dynamical systems violating Bell's inequality.
----------
quant-ph/0007005
Locality and Bell's inequality
Luigi Accardi, Massimo Regoli
We prove that the locality condition is irrelevant to Bell in equality. We
check that the real origin of the Bell's inequality is the assumption of
applicability of classical (Kolmogorovian) probability theory to quantum
mechanics. We describe the chameleon effect which allows to construct an
experiment realizing a local, realistic, classical, deterministic and
macroscopic violation of the Bell inequalities.
----------
quant-ph/9606019
A Proposed Experiment Showing that Classical Fields Can Violate Bell's
Inequalities
Patrick Suppes (Stanford University, USA), J. Acacio de Barros (Federal
University at Juiz de Fora, Brazil), Adonai S. Sant'Anna (Federal University
at Parana, Brazil)
We show one can use classical fields to modify a quantum optics experiment
so that Bell's inequalities will be violated. This happens with continuous
random variables that are local, but we need to use the correlation matrix
to prove there can be no joint probability distribution of the observables.
----------
quant-ph/0007044
The Violation of Bell Inequalities in the Macroworld
Diederik Aerts, Sven Aerts, Jan Broekaert, Liane Gabora
We show that Bell inequalities can be violated in the macroscopic world. The
macroworld violation is illustrated using an example involving connected
vessels of water. We show that whether the violation of inequalities occurs
in the microworld or in the macroworld, it is the identification of
nonidentical events that plays a crucial role. Specifically, we prove that
if nonidentical events are consistently differentiated, Bell-type Pitowsky
inequalities are no longer violated, even for Bohm's example of two
entangled spin 1/2 quantum particles. We show how Bell inequalities can be
violated in cognition, specifically in the relationship between abstract
concepts and specific instances of these concepts. This supports the
hypothesis that genuine quantum structure exists in the mind. We introduce a
model where the amount of nonlocality and the degree of quantum uncertainty
are parameterized, and demonstrate that increasing nonlocality increases the
degree of violation, while increasing quantum uncertainty decreases the
degree of violation.
----------
Hal Ruhl
I am not so much interested in provability as I am in whether or not the
"noise" in a universe's evolution is pseudorandom or random and forging an
Everything that was as free of information [selection] as possible. I try
to use incompleteness in various forms to show that as far as an individual
universe is concerned the noise comes from outside that universe.
I believe that many proposals on this list are more in agreement than we
might at first glance think. Below I use the approach of producing numbers
using the null set to try to demonstrate this.
Using the symbol * to represent the null set and {} to represent sets with
elements:
horizontal
the
on this
page isomorphically
isomorphic
linked
anisomorphic links string
* <
::: > * = 0
{*} =
1
{*,{*}} =
10
{*,{*},{*,{*}}} =
11
: :
:
: :
:
=
11001110111...0110
||
active
and inactive
page
"vertical" isomorphic
links
to this string
:
:
=
11100110111...0011
||
active
and inactive
page
"vertical" isomorphic
links
to this string
:
:
etc.
The page horizontal isomorphic links on the right hand side are the usual
ones.
The page vertical isomorphic links are the ones I have used in my
model. Each of these vertical isomorphic links [there can be more than one
per string] uses a portion of the string to which it links to define its
self contained FAS. The rest of the string determines the associated state
of the vertical isomorphism. The current state of a vertical isomorphism
is the active link for that isomorphism. All inactive links are either
past or future states of isomorphisms. The self contained FAS of a
particular vertical isomorphism determines which links are acceptable
immediate successor states of that isomorphism. Depending on the nature of
the FAS there could be more than one acceptable immediate successor state
for that isomorphism.
The symbol "< ::: >" indicates that the isomorphism tree structure - "The
Everything" - vanishes upon occasion and the anisomorphic null set - "The
Nothing" - resumes. This is the E/N alternation. Neither the anisomorphic
null set nor the isomorphism tree since they both contain no information
can internally address the unavoidable question of their own
durability. This bilateral incompleteness drives the E/N
alternation. The alternation since it destroys any record of the previous
mix of active/inactive vertical isomorphic links causes a new random
active/inactive mix each time the isomorphism tree resumes. This avoids a
"selected" structure to The Everything.
In order for a vertical isomorphic link to transfer to another string both
the current link and an acceptable successor link must be simultaneously
active. The transfer inactivates the prior link. Vertical isomorphic
links driven active or inactive by the E/N alternation absent an active
acceptable successor is simply in stasis. For a transfer to take place
both the current and acceptable successor link must be simultaneously
active. It is the transfer that is an "event" to an isomorphism.
Are UD's or other such string generating machines vertical isomorphic
links? I think so if I understand them correctly. Simply concatenate all
the output strings of a UD so that successor vertical link shifts are just
based on very localized regions of the overall string.
I also think this process is similar to "observer moments" if "observer
moment" means active links.
Since the null set just "is" then the process may satisfy the idea that the
Everything just "is".
It is the isomorphic tree that undergoes change.
Now I see nothing wrong with FAS that have a "do not care" content to their
rules determining acceptable successor links.
My goal is to try to show that universes [vertical isomorphic links] that
can support SAS have at least some "do not care" content in the rules. To
do this I turn to Chaitin and explore the viability of deterministic
cascades. By deterministic I mean each state has only one possible prior
and one possible successor - the computational exercise is by definition
elegant. However, the complexity of the strings to which such sequences
form isomorphic links must relentlessly increase . This produces a
conflict between the idea of cascade and the idea of a limit on the
complexity of the string that the finite self contained FAS can determine
is acceptable using only elegant programs.
This conflict is resolved by an injection of complexity into the FAS from
"outside".
It is also reasonable that some of these FAS are subject to the
incompleteness of Godel.
So it is just Chaitin and Godel that interest me as far as "proof" is
concerned.
Other than the above I really can not find a simple thing in your post
below with which I disagree.
Yours
Hal
At 5/4/01, you wrote:
>Which are the logically possible universes? Max Tegmark mentioned
>a somewhat vaguely defined set of ``self-consistent mathematical
>structures,'' implying provability of some sort. The postings of Bruno
>Marchal and George Levy and Hal Ruhl also focus on what's provable and
>what's not.
>
>Is provability really relevant? Philosophers and physicists find
>it sexy for its Goedelian limits. But what does this have to do with
>the set of possible universes?
>
>I believe the provability discussion distracts a bit from the
>real issue. If we limit ourselves to universes corresponding to
>traditionally provable theorems then we will miss out on many formally
>and constructively describable universes that are computable in the
>limit yet in a certain sense soaked with unprovable aspects.
>
>Example: a never ending universe history h is computed by a finite
>nonhalting program p. To simulate randomness and noise etc, p invokes a
>short pseudorandom generator subroutine q which also never halts. The
>n-th pseudorandom event of history h is based on q's n-th output bit
>q(n) which is initialized by 0 and set to 1 as soon as the n-th element
>of an ordered list of all possible program prefixes halts. Whenever q
>modifies some q(n) that was already used in the previous computation of
>h, p appropriately recomputes h since the n-th pseudorandom event.
>
>Such a virtual reality or universe is perfectly well-defined. At some
>point each history prefix will remain stable forever. Even if we know p
>and q, however, in general we will never know for sure whether some q(n)
>that is still zero won't flip to 1 at some point, because of Goedel etc.
>So this universe features lots of unprovable aspects.
>
>But why should this lack of provability matter? It does not do any harm.
>
>Note also that observers evolving within the universe may write
>books about all kinds of unprovable things; they may also write down
>inconsistent axioms; etc. All of this is computable though, since the
>entire universe history is. So again, why should provability matter?
>
>Juergen Schmidhuber http://www.idsia.ch/~juergen/toesv2/
Hal Ruhl
At , you wrote:
>Juergen Schmidhuber wrote
>
> >Which are the logically possible universes? Max Tegmark mentioned
> >a somewhat vaguely defined set of ``self-consistent mathematical
> >structures,'' implying provability of some sort. The postings of Bruno
> >Marchal and George Levy and Hal Ruhl also focus on what's provable and
> >what's not.
>
>You know that Hal Ruhl doesn't distinguish computability and provability,
>so
>it is open for me if his approach is nearer your's or mine.
Awhile ago I did identify computability and provability, but now see
provability as a subset of the computable. But is computable enough and
computable where [inside/outside a particular universe considerations]?
I place myself nearer your work Bruno and also that of Russell
Standish. This is particularly due to my stand that true random noise is
inherent in each universe within the Everything.
This does not mean that I consider the isomorphic tree I described in
another post to contain randomly generated strings [the horizontal
isomorphisms will be a list of all strings] but rather that isomorphic
links to these strings necessarily IMO have some random nature in the
determination of acceptable successor links - the evolution of the
active/inactive mix I described.
Also IMO the logics we may find in our universe derive from this foundation
not the reverse. If one looks at the frequency of events versus event size
in the "large" event region we find that some experiments in our universe
produce slopes close to but slightly higher than -1. The field
observations I have seen produce somewhat higher valued slopes going
towards -2. A slope of -1 would as I see it indicate a deterministic
cascade. However, one must also examine the "small" event part of the
spectrum. Here a slope of +1 IMO indicates a deterministic cascade but the
two ends of the spectrum need not be symmetric.
Our logic IMO is in the "large" event part of the spectrum and a thought
experiment as well [not even a "lab" let alone the "field"] and therefore
likely to be almost deterministic in our universe. IMO the incompleteness
types we have discovered do not have a large impact on our everyday use of
our reasoning methods.
Yours
Hal
Hal Ruhl
My little isomorphism tree did not transmit very well.
The second column heading should read: "horizontal on this page isomorphic
links"
The third should read: "the isomorphically linked string"
All the binary strings should be under the third column.
Yours
Hal
:
etc.
Yours
Hal
At 5/4/01, you wrote:
>Which are the logically possible universes? Max Tegmark mentioned
>a somewhat vaguely defined set of ``self-consistent mathematical
>structures,'' implying provability of some sort. The postings of Bruno
>Marchal and George Levy and Hal Ruhl also focus on what's provable and
>what's not.
>
Marchal
>This is particularly due to my stand that true random noise is
>inherent in each universe within the Everything.
Remember that true random noise appear in the UDA because we don't know
in which computation ("universe") we belong. So random noise does
not need to be added. It is something we cannot avoid from our first
person point of view of embedded observer.
It is the point where Schmidhuber disagrees so much. We will come back
on this question soon. Well, I hope, because for teachers may and june are
terrible :-(.
Bruno
Hal Ruhl
At , you wrote:
>Hal Ruhl wrote:
>
> >This is particularly due to my stand that true random noise is
> >inherent in each universe within the Everything.
>
>Remember that true random noise appear in the UDA because we don't know
>in which computation ("universe") we belong. So random noise does
>not need to be added. It is something we cannot avoid from our first
>person point of view of embedded observer.
>It is the point where Schmidhuber disagrees so much. We will come back
>on this question soon.
My position is a bit different - I think - in that I do not see observers
as essential to the presence of true random noise in a universe. The UD,
IMO - after a concatenation of its output strings into one long one that is
then altered at the knit points in some pattern - is within itself a single
valued elegant cascade. This would hold even if the activity around the
knit points is spread out along a region of the string as in Juergen's
model [If I have it right]. It is one out of an infinite number of similar
cascades that form a sub set within the more general isomorphism tree I
described.
My position is that all these attempted single valued elegant cascades run
into the complexity limit imposed by Chaitin's incompleteness in such a way
as to be unable to halt absent contradiction. The contradiction can only
be cured by an increase in complexity of the FAS governing the
cascade. The added information can only come from outside the
cascade. Not from outside the isomorphism tree.
If I have it right your approach is that the UD has an inherent true random
noise content if some of its sub strings define universes sufficiently rich
in logic to be subject to other incompleteness mechanisms especially if
observers are present. Actually I think you may be saying that the entire
UD is rich enough in any manifestation to necessarily posses this
characteristic. With this I would agree if a minimum possible complexity
UD can be shown to meet the threshold of these incompleteness mechanisms.
If you rely on the scanner transporter duplicator for this demonstration I
consider it to be the same as my E/N alternation.
However, in my approach the UD [all of them] are a small part of the
Everything.
> Well, I hope, because for teachers may and june are
>terrible :-(.
Perhaps this will allow me a chance to catch up with your logic posts.
Yours
Hal
jamikes
"George Levy" <GL...@Quantics.net> wrote
Saturday, May 05, 2001 :
(SNIP Jurgen's remark about "such a universe" whatever, my remark is not
topical, rather principle:)
> Such a universe would violate Bell' inequality theorem. Quantum randomness
> cannot be simulated by hidden variables. We have to move beyond
> realism......to get a model of objective reality we must first develop a
> model of consciousness.
>
> George
Can you restrict a universe according to its compliance with or violation of
a theory, no matter how ingenious, or vice versa? Are WE the creators who
has to perform according to some rules/circumstances of human logic or
computability?
John Mikes
>
George Levy
jamikes wrote:
I am not restricting anything. I am only saying that Juergens has to choose
between violating Bell's inequality theorem and all that this implies, or not
and all that this implies. My stand is that we shouldn't.
George
Hal Ruhl
I do not see how the aspect of Juergen's approach he cited at the
initiation of this part of the thread causes a dilemma re Bell's
inequality. As I understand it the history h is not THE history until the
applicable portion of h stops changing. But p and q are both non
halting. No part of h may settle in a finite time. So what? The generator
q" is not "in" h. The fact that p may recompute virtually any amount of h
depending on what happens to q(n) is not a non locality "in" h but rather a
substitution of a new h for the old h. The old h is no longer relevant.
However, p itself being global seems to me to allow the violation of Bell's
inequality in its universe. My "formal" system has the same feature as
does a UD IMO. As far as I know the violation of Bell's inequality was
already well established in our universe.
Hal
Brent Meeker
in) by the anthropic principle. But if the anthropic principle is to
meant to include all intelligent beings, then some theory will be
necessary to say in what respects the universe could differ and still
produce intelligent beings.
Have you read Tegmark's paper, quant-ph/9907009v2 10 Nov 1999, which
shows that entangled quantum probabilities are not necessary for
consciousness - only ordinary randomness.
Brent Meeker
"As far as the laws of mathematics refer to reality, they are not
certain, and as far as they are certain, they do not refer to reality."
-- Albert Einstein
Regards
jamikes
hard-to-follow as was my question. You wrote:
> I am not restricting anything. I am only saying that Juergens has to
choose
> between violating Bell's inequality theorem and all that this implies, or
not
> and all that this implies. My stand is that we shouldn't.
> George
>
So ;let me rephrase the question:
is your stand that if an imaginary universe would violate eg. Bell's
theorem, it should be excluded from consideration as a possibility,
- or -
we should rather conclude that Bell's theorem (or any other fundemntal
"human" rule) has a limited validity and does not cover every possible
universe?
John
George Levy
I have to leave on a week long trip.... I'll reply to your posts when I return.
George
George Levy
Let me first reply to John and Hal because it is the shortest reply. Let's go back to the original Juergens' post
jue...@idsia.ch wrote:
> Example: a never ending universe history h is computed by a finite
> nonhalting program p. To simulate randomness and noise etc, p invokes
a
> short pseudorandom generator subroutine q which also never halts.
The
> n-th pseudorandom event of history h is based on q's n-th output
bit
> q(n) which is initialized by 0 and set to 1 as soon as the n-th element
> of an ordered list of all possible program prefixes halts.
Whenever q
> modifies some q(n) that was already used in the previous computation
of
> h, p appropriately recomputes h since the n-th pseudorandom event.
>
> Such a virtual reality or universe is perfectly well-defined.
I replied:
>Such a universe would violate Bell' inequality theorem. Quantum randomness
>cannot be simulated by hidden variables. We have to move beyond
>realism......to get a model of objective reality we must first develop
a
>model of consciousness.
A purely mechanical model no matter how complicated, including random variables, cannot replicate the results generated by Quantum mechanics + probability theory. This is exactly what Bell's inequality implies. In fact Bell proved his inequality using Quantum theory and probability.
Therefore, Juergens' erector (fr: meccano) set approach using pseudo-random generators, would definitely violate Bell's inequality theorem, and would not be phenomenally or experimentally equivalent to quantum mechanics. Some of his (our) choices are:
1) Quantum mechanics + probability -> Bell's inequality and give up on a mechanical hidden variable, on pseudo random generators, and more generally, on realism.
2) Something else of power equivalent to Quantum mechanics in describing nature....Good Luck!!! I do not believe the route to this solution is the erector set technique. Many a 19th and early 20th century physicist has broken a tooth on that bone!
George
jue...@idsia.ch
> A purely mechanical model no matter how complicated, including random
> variables, cannot replicate the results generated by Quantum mechanics +
> probability theory. This is exactly what Bell's inequality implies. In
> fact Bell proved his inequality using Quantum theory and probability.
> generators, would definitely violate Bell's inequality theorem, and would
> not be phenomenally or experimentally equivalent to quantum mechanics.
I do not agree, of course. Since you keep insisting on this, I suggest
you clearly write down all implicit assumptions and why exactly you
believe Bell's inequality is not compatible with pseudorandomness and
algorithmic TOEs.
http://www.idsia.ch/~juergen/everything/html.html
http://www.idsia.ch/~juergen/toesv2/