On 09/08/07, Bruno Marchal <marchal.domain.name.hidden> wrote:
> I hope you will not mind if I ask you "stupid" question, like "Do you
> know what mathematicians mean by "function?".
> Sometimes I realize that some people does not grasp what I say because
> they just miss some elementary vocabulary, or they have a problem with
> the notation.
> Of course anyone can ask any questions. Math is something easy (the
> easiest of all sciences) but if you miss a definition then it *looks*
> difficult.
Thank you for asking, it's very important to ensure full understanding
at all points. My maths are indeed a bit rusty, but fortunately
resources are easily available as needed to refresh the memory. Would
you be happy with the wikipedia treatment of 'function'?
http://en.wikipedia.org/wiki/Mathematical_function
> OK. But for this I need to be sure you grasp well the UD argument, at
> least the seven first step. The steps will always refer to the 8-steps
> presentation of the summary PDF Slides available here:
> http://iridia.ulb.ac.be/~marchal/publications/
> SANE2004MARCHALAbstract.html
How can I best demonstrate this to your satisfaction? I accept the
validity of the demonstration in the UDA (which I believe that I'd
already intuited as a consequence of the 'solipsism of the One') that
the first person or reflexive OM must be indeterminate with respect to
its third person manifestations. However, I also wanted to ask
whether it was important in this context to define in detail the
content and informational limits of a given OM (e.g. its temporal
scope or 'duration')?
> Well, the UDA can already be seen as a 'grandmother' way of making this
> intuitive. What you have to understand is the turing-universality of
> addition and multiplication, in the first order logic framework. I will
> explain this in all detail, but I have to begin with Church thesis. I
> propose we try to organize ourself through a well defined sequence of
> posts, which we can from time to time transform into a pdf, so that we
> can refer to the pages of that pdf, instead of post messages with
> fragile addresses. OK?
OK indeed.
> Peter was putting too much philosophical weight to the notion of
> existence. Recall that the "ontic base of reality" will just be te
> numbers, and that when I say a number exist, I mean it in the usual
> sense of elementary high school arithmetic. The key point is that a
> machine which can prove all the true sigma1-sentence is turing
> universal. this is already well explained in Torkel Franzen's book (in
> his first appendix). Again, don't worry I will explain.
Do I need Franzen's book too?
> Now, to
> eliminate redundancy in the explanations, I insist we organize ourself.
> I have already explain many of those things, but never in a way so that
> I can easily refer to the (too many) posts. All right?
Alright!
> The idea is really this: if you are in front of a running (and thus
> never stopping UD), the seven steps shows that, taking comp seriously,
> to make any 100% prediction, you have to take into account all the
> reconstitutions of yourself (which exist by the comp hyp) and their
> continuations.
OK, again in terms of 'the One', since all the 'reconstitutions'
exist, they must all indeed play a role in the 'account' (which can be
synonymous with narrative or story).
> By the first person indeterminacy, your future will be determined by
> the most probable comp histories going through your actual state.
By 'probable' you refer to the elusive measure?
> The problem then will consist in defining what is a "probable comp
> history". This is a very difficult problem: for example, when can we
> say that two computations are equivalent, etc.
i.e. from the third person pov?
> The trick I have done is to abandon the idea of searching directly a
> measure on the computations, and, instead, to isolate the mathematical
> structure for the "certain-propositions" by using the self-referential
> logics.
IOW you adopt the view from the inside out? I would like to
understand this securely. It seems to me that you're saying that
focusing on self-reference relies on the intrinsic self-location of
first person 'pages' within the 'Library of Babel' of the UD's output.
Given this, how do such pages then 'cohere' into 'narratives through
time'?
> The first person will feel herself restricted 'in time' indeed.
> Somehow, she creates subjective time/consciousness. But from the ontic
> view, with the "block-all-computations" (alias UD*) there is no time.
> From the material (first person plural view) pov, it is an open problem
> if there is an "objective time".
I think we may have to come back later to this question of subjective
time. But for now I rely on you to set the agenda of our more
structured modus operandi.
David
>
>
> Le 08-août-07, à 15:26, David Nyman a écrit :
>
> >
> > On 30/07/07, Bruno Marchal <marchal.domain.name.hidden> wrote:
> >
> >> Meanwhile I would suggest you read the book by David
> >> Albert: "Quantum Mechanics and Experience"
> >
> > OK, I've ordered it.
>
>
> Good.
>
>
>
>
> >
> >> I can compare only the "logic of probability/credibility one" of
> >> nature
> >> (more or less quantum logic) and the logic of "probability/credibility
> >> one" extracts from the discourse of the self-observing machine. It
> >> *is*
> >> technical. It cannot be a starting point, I think.
> >> In my opinion, the starting point is Church thesis. Once you are back,
> >> tell me and I can do that.
> >
> > OK
>
>
> I hope you will not mind if I ask you "stupid" question, like "Do you
> know what mathematicians mean by "function?".
> Sometimes I realize that some people does not grasp what I say because
> they just miss some elementary vocabulary, or they have a problem with
> the notation.
> Of course anyone can ask any questions. Math is something easy (the
> easiest of all sciences) but if you miss a definition then it *looks*
> difficult.
>
>
>
>
>
> >
> >>> The following may not be
> >>> relevant in this context, but I'm particularly interested in
> >>> something
> >>> you said elsewhere ('simulation argument') about how comp can relate
> >>> OMs (and presumably the multiverse structures associated with them)
> >>> geometrically 'through time'.
> >>
> >>
> >> If this is not relevant in this context, I ask what is relevant ... ?
> >
> > I was referring only to its relevance as a a starting point. However,
> > it appears that you think it is.
>
> OK, it is important, but cannot be used as a starting point. We will
> get it soon after Church thesis.
>
>
>
> >
> >> Now, as I said some days ago, I think that a way to link more
> >> formally my work and the everything discussion can consist in defining
> >> a notion of basic atomic third person observer moment.
> >
> > It would help me if you would define the content of this fundamental
> > OM concept rather specifically for the purpose of this discussion.
>
>
> OK. But for this I need to be sure you grasp well the UD argument, at
> least the seven first step. The steps will always refer to the 8-steps
> presentation of the summary PDF Slides available here:
> http://iridia.ulb.ac.be/~marchal/publications/
> SANE2004MARCHALAbstract.html
>
>
>
>
> >
> >> The UDA, plus
> >> Church thesis + a theorem proved in Boolos and Jeffrey (but see also
> >> and better perhaps just Franzen's appendix A) makes it possible to
> >> define the comp third person OMs by the Sigma1 sentences of
> >> arithmetical language. Those have the shape ExF(x) with F(x)
> >> decidable.
> >> For example ExPrime(x) (a prime number exists), Ex(x = code of
> >> triple(a,b,c) and machine a gives c on argument b),
> >
> > Is there a 'grandmotherly' way of making it intuitively compelling
> > what makes it possible for the OM to be defined thus?
>
>
>
> Well, the UDA can already be seen as a 'grandmother' way of making this
> intuitive. What you have to understand is the turing-universality of
> addition and multiplication, in the first order logic framework. I will
> explain this in all detail, but I have to begin with Church thesis. I
> propose we try to organize ourself through a well defined sequence of
> posts, which we can from time to time transform into a pdf, so that we
> can refer to the pages of that pdf, instead of post messages with
> fragile addresses. OK?
>
>
>
>
>
> > In your various
> > debates with Peter, I guess I've picked up essentially that such truth
> > statements stand here for 'existence'. Yes?
>
> Peter was putting too much philosophical weight to the notion of
> existence. Recall that the "ontic base of reality" will just be te
> numbers, and that when I say a number exist, I mean it in the usual
> sense of elementary high school arithmetic. The key point is that a
> machine which can prove all the true sigma1-sentence is turing
> universal. this is already well explained in Torkel Franzen's book (in
> his first appendix). Again, don't worry I will explain. Now, to
> eliminate redundancy in the explanations, I insist we organize ourself.
> I have already explain many of those things, but never in a way so that
> I can easily refer to the (too many) posts. All right?
>
>
> >
> >> ... This last
> >> example show that the notion of Sigma1 sentences is rather rich and
> >> encompasses full computability. So the very restricted notion of
> >> Sigma1-proof (restricted from the point of view of provability) is
> >> already absolutely universal with respect to computability. A machine
> >> is universal iff the machine is Sigma1 complete, i.e. is capable of
> >> proving all true Sigma1 sentences.
> >
> > Could you expand more slowly on the particular importance of 'full
> > computability' here. Sorry if I'm being slow, but I want to make sure
> > I get the intuitions as you intend them.
>
>
> I will perhaps begin by that important question. Never apologize for
> being slow. It is a symptom that you try to understand the real thing.
> It is normal to be slow.
>
>
>
> >
> >> Such a machine codes automatically
> >> a Universal Dovetailer: to be a UD accessible state is Sigma1.
> >> So the measure we are searching can be put on the set of Sigma1
> >> sentences. Intuitively, from UDA, the weight for each Sigma1 sentences
> >> should be given by the "number" of proof going trough those sentences
> >> (including the many infinite proofs of some false sigma1 sentences).
> >> Now we can search for some equivalence relation on those proofs, but
> >> this is known to be very hard, and that is why I prefer to interview
> >> the universal lobian machine directly, and content myself with the
> >> corresponding logic of "certainty".
> >
> > Is a more 'grandmotherly' form of all this possible to begin with?
> > I'm remembering the idea of the roadmap, in terms of which the
> > destination, and the journey towards it, could first be set out in
> > more general terms, in order to make the problems and their possible
> > solutions as intuitively compelling as possible at the outset. It
> > seems to me often that I get the general drift, and some of the main
> > ideas, but there's still some confusion as to the whole picture.
> > Could there be a sort of master 'storybook' version - a narrative of
> > the key points into which the emerging formal detail could be fitted?
>
>
> The idea is really this: if you are in front of a running (and thus
> never stopping UD), the seven steps shows that, taking comp seriously,
> to make any 100% prediction, you have to take into account all the
> reconstitutions of yourself (which exist by the comp hyp) and their
> continuations.
> By the first person indeterminacy, your future will be determined by
> the most probable comp histories going through your actual state.
> The problem then will consist in defining what is a "probable comp
> history". This is a very difficult problem: for example, when can we
> say that two computations are equivalent, etc.
> The trick I have done is to abandon the idea of searching directly a
> measure on the computations, and, instead, to isolate the mathematical
> structure for the "certain-propositions" by using the self-referential
> logics.
>
>
>
> >
> >> Yes and No.
> >> Yes for two reasons: 1) if we assume comp, the UDA shows we have to
> >> recover knowledge from infinities of computations in the UD* (the
> >> "block" universal dovetailing. And FOR does presuppose comp. 2) in
> >> the
> >> arithmetization of the UDA, the notion of knowledge coherent with the
> >> UD thought experience is just given by the older definition of
> >> knowledge as true justified opinion (in platonism, but also in a lot
> >> of
> >> east and west rational account of mystical experiences). It is a gift
> >> that we arrive formally here at temporal-like logic of evolving first
> >> person knowledge.
> >
> > Do you mean that first person knowledge by definition can emerge only
> > in an 'evolutionary' way -
>
>
> No, from a third person view.
> Yes, from a first person view.
>
>
>
> > i.e. that it must necessarily be restricted
> > 'in time', as opposed to some all-encompassing atemporal form (e.g.
> > the 'knowledge' of the One, if it had a pov)?
>
> The first person will feel herself restricted 'in time' indeed.
> Somehow, she creates subjective time/consciousness. But from the ontic
> view, with the "block-all-computations" (alias UD*) there is no time.
> From the material (first person plural view) pov, it is an open problem
> if there is an "objective time".
>
> Bruno
>
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
> >
>
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Received on Fri Aug 10 2007 - 08:26:37 PDT