Dear Wei and Bruno,
If I may interject. Interleaving.
----- Original Message -----
From: "Wei Dai" <weidai.domain.name.hidden>
To: "Bruno Marchal" <marchal.domain.name.hidden>
Cc: <everything-list.domain.name.hidden>
Sent: Friday, July 12, 2002 11:06 PM
Subject: Re: being inside a universe
> On Fri, Jul 12, 2002 at 06:47:46PM +0200, Bruno Marchal wrote:
> > OK I will try to read Joyce's book asap. In general I am quite skeptic
> > about the use of the notion of "causality". I have also no understanding
> > of your posts in which you argue about a relationship between the search
> > of a TOE and decision theory.
>
> See my recent reply to Hal. Basically they are related through the concept
> of probabilities (if the TOE makes use of probabilities).
>
> > >I'm aware of *a* mind-body problem. I'm not sure if it's the same one
you
> > >have in mind. The one I have in mind is this: how do I derive a
> > >probability distribution for the (absolute) SSA from a third-person
> > >description of the multiverse?
> >
> > The mind-body problem I am talking about is the one formulated by
Descartes
> > (but also by Hindu philosophers before J.C). It is really the problem
> > of linking private (first person) sensations and third person
communicable
> > phenomena. How a grey brain produces sensation of color, as someone put
it.
>
> Could you state the problem more formally? Also, you asked me whether I
> was aware of the mind-body problem. What did my answer tell you?
>
> > Those I have encapsulated in the label "comp". Precisely it consists in
> > 1)accepting a minimal amount of arithmetical realism, i.e. the truth of
> > elementary statements of arithmetic does not depend of me or us ...
>
> I agree with (1).
[SPK]
As do I. ;-)
>
> > 2) the Church Thesis (also called the Church Turing Thesis, or the
> > Post Law, etc.)
> > i.e. all universal machine are equivalent with respect to their
simulation
> > abilities (making abstraction of the duration of those simulation).
>
> I don't think that is settled yet. We may be able to build machines that
> are more powerful than Turing machines. I don't think we should rule it
> out at this point.
>
[SPK]
Could I offer this paper as a possible elaboration of your thought, Wei, :
http://arxiv.org/abs/quant-ph/0112087
Quantum Physics, abstract
quant-ph/0112087
From: Cristian S. Calude <c.calude.domain.name.hidden>
Date (v1): Sat, 15 Dec 2001 22:27:53 GMT (38kb)
Date (revised v2): Mon, 7 Jan 2002 09:30:45 GMT (38kb)
Date (revised v3): Fri, 1 Mar 2002 20:30:43 GMT (42kb)
Coins, Quantum Measurements, and Turing's Barrier
Authors: Cristian S. Calude, Boris Pavlov
Comments: 23 pages to appear in "Quantum Information Processing"
Is there any hope for quantum computing to challenge the Turing barrier,
i.e. to solve an undecidable problem, to compute an uncomputable function?
According to Feynman's '82 argument, the answer is {\it negative}. This
paper re-opens the case: we will discuss solutions to a few simple problems
which suggest that {\it quantum computing is {\it theoretically} capable of
computing uncomputable functions}. In this paper a mathematical quantum
``device" (with sensitivity $\varepsilon$) is constructed to solve the
Halting Problem. The ``device" works on a randomly chosen test-vector for
$T$ units of time. If the ``device" produces a click, then the program
halts. If it does not produce a click, then either the program does not halt
or the test-vector has been chosen from an {\it undistinguishable set of
vectors} ${\IF}_{\varepsilon, T}$. The last case is not dangerous as our
main result proves: {\it the Wiener measure of} ${\IF}_{\varepsilon, T}$
{\it constructively tends to zero when} $T$ {\it tends to infinity}. The
``device", working in time $T$, appropriately computed, will determine
with a pre-established precision whether an arbitrary program halts or not.
{\it Building the ``halting machine" is mathematically possible.}
***
> > 3) The existence of a level of description of my body (whatever it
> > is) such that
> > my first person experience remains invariant through a functional
substitution
> > made at that level.
>
> Can you state this more formally? Specificly how do you define "functional
> substitution"?
>
> > (Note that the Arithmetical uda makes it possible to eliminate the "3)"
above).
>
> I guess I'll have to wait for your English paper to understand how.
>
[SPK]
I am waiting for it too, Bruno! ;-) This may be where you migh answer my
"physical resources" question. ;-)
> > I was referring to the second incompleteness theorem by Godel: a
consistent
> > machine cannot prove its own consistency. This means that if you add the
> > inconsistency as a new axiom the machine will not derive a
contradiction,
> > (because if the machine derive a contradiction from her inconsistency,
she
> > will prove its consistency by reductio ad absurdo). So a consistent
machine
> > will not be inconsistent when she asserts its own inconsistency.
>
> But in second order logic, if you add a new axiom to a consistent theory
> stating that it's inconsistent, the theory is no longer satisfiable (i.e.,
> it no longer has a model, even though it's still consistent), right? In
> first order logic, the theory would still be satisfiable but that just
> indicates that the semantics of first order logic is flawed. BTW remind me
> what's the relevance of this again?
>
> > Of course I restrict us and the machines I interview to sound logics.
Why
> > should I interview unsound machines? It would be like an historian
working on
> > a biography of Napoleon, and interviewing a mad guy in an asylum
pretending
> > to be Napoleon. I limit my interview to sound machine for the same
reason
> > I would stop reading papers by someone if I realize
> > he is using (systematically) a theory which is unsound.
> > Except for clinical case I have never find someone using unsound
> > basic theories.
>
> Ok, I guess I thought your restriction to sound machines was a substantial
> ones, but perhaps its not. However I still am not sure what point you're
> making by making this restriction explicit.
>
> > >I don't have to explain how I "keep being in the same computation"
because
> > >I don't know or claim that. I'm not sure that's even a meaningful
> > >sentence.
> >
> > It seems to me you claim it in your next sentence, here:
> >
> > >All I do claim is that for any given computation, if I am in
> > >that computation, I care about the future version of me in that
> > >computation, and I can causally affect its future (and only its
future).
> > >In other words, the causal influence of my actions stay in the same
> > >computation.
> >
> > The whole point of the uda thought experiment consists in showing that
> > expressions like "I am in that computation" are not well defined. The
uda shows
> > also that we have a lot of futures ("future, btw, is a first person
construct:
> > there is no notion of future in any "block-reality" approach).
>
> To me, future is a concept linked with causality, because causes always
> occur before effects. In any "block-reality" approach that takes causality
> into account, it would have to be littered with arrows indicating causal
> relationships, and those arrows would differentiate between past and
> future.
>
[SPK]
Has anyone considered how they are doing to show that GR - with all the
strange metrics it allows, such as wormholes - is derived from Comp?
Causality may just be an "emergent property" of some kind. ;-)
> Certainly in a computation there is a natural concept of past and future
> that is not a first person construct, and the causal relationship between
> one state of a computation and the next one should be quite clear.
>
[SPK]
This is not so clearly defined when one consideres issues related to
computational concurrency! There are many computational situations where the
order in which events/states occur is not easily representable as some
algorithmic chaining. Also, there are computational complexity issues, like
what does UDA have to say about the P = NP question, Bruno?
> > The fact that "I can causally affect its future" is not clear at all,
> > and any clearer version should be justified.
>
> Read Joyce's book, it should clarify and justify it for you. If not come
> back and we'll talk about it.
>
> > Let me give you a simple example.
> > Suppose you decide to drink a cup of coffee.
> > You will prepare that cup of coffee hoping this will causally affect
"its
> > (yours!) future, in a way such that you make the first person experience
> > of drinking that cup of coffee.
>
> Ok.
>
> > But the UD, because he is shallow, will generate an infinite number of
> > computations in which you will experience drinking a cup of tea (if
> > not a white rabbit), and this although you have the same experience
> > of the past which include
> > your preparing that cup of coffee).
>
> You can just ignore those universes because their algorithmic
> complexities are very high (and therefore their measures are very low).
>
[SPK]
Is there a clear definition of this "measure" available?
> > The "invariance lemma" prevents "easy" use of (Kolmogorov or
> > Chaitin) complexity
> > notion for dismissing those abnormal stories.
>
> Why? I just did it. Are you saying each copy of you in any universe counts
> equally regardless of how small the measure of the universe is? If that is
> what you mean by "invariance lemma" then I certainly don't agree with you.
>
> > The comp indeterminacy hints to transform that problem into a search
> > of a measure,
> > and into showing that relatively abnormal consistent
> > extension/stories are rare.
> > This is not unlike the Feynman integration on path in quantum mechanics.
>
> I do not see the necessity of it.
[SPK]
Could you elaborate on this, Bruno?
Kindest regards,
Stephen
Received on Fri Jul 12 2002 - 21:08:04 PDT