Re: Observer Moment = Sigma1-Sentences
On Wed, Aug 01, 2007 at 11:31:51AM +0200, Bruno Marchal wrote:
> >
> > No, I mean all information known by the observer (including, but not
> > exclusively information know by the observer about erself).
>
>
> OK, but then adding "about the universe" is confusing at this stage.
> You interpret the quantum state as describing knowledge. (And then I am
> not sure I follow what you mean by quantum state: you are supposing the
> quantum hyp. here, aren't you (or perhaps your linearity hyp. only?
> Again where would that linearity come from?).
>
Sorry, I realised I hadn't responded to this before. Things have got
away from me, including recovering from a harddisk crash.
I am using universe somewhat colloquially here, to help intuition. But
sometime it doesn't help.
What we have are observer moments, which somehow contain all
knowledge, or are circumscribed by all knowledge that an observer has
at an instant of time.
The use of the word "universe" was meant to make some connection back
to discussions of "many universes", or "many worlds", but to be
precise we are just talking about observer moments which are in a
sense primitive.
>
> >
> >>
> >>
> >>> this led me to identify the observer moment
> >>> and the quantum state vector.
> >>
> >>
> >> ... and the partial relative quantum state vector corresponding to the
> >> observer. OK, but at this stage this would be cheating. We can not yet
> >> explain why the quantum histories wins over the comp/number relations.
> >>
> >
> > Well I have my own reasons, considering knowledge acquisition as an
> > evolutionary process. But I disagree about it being cheating, because
> > I don't a priori assume quantum states are elements of a Hilbert
> > space. That is a derived property.
>
>
> So, how do you define quantum state?
>
I don't define quantum state. I use the word state as a synonym of
observer moment, again as a means of contact with quantum
terminology. I make the statement "identify observer moment with
quantum state" as a shorthand for the following argument.
Assume that the state (or observer moment) undergoes evolution (I'm
refraining from qualifiying this with Darwinian) in that:
1) subsequent OMs (obviously a successor relationship is a
prerequisite here - something I call the TIME postulate) are
related closely to the previous OM, ie they inherit.
2) There is variation between successor OMs - ie the "many worlds"
idea.
3) That a particular successor OM x_i of OM y is what is observed
("anthropically selected"), with a probability P(x_i|y). The
probability function P(x|y) satisfies the Kolmogorov probability
axioms. This also implies that OMs must satisy set axioms. I also
call this third assumption the "PROJECTION postulate".
There is a final assumption. The initial OMs are drawn from the set of
all OMs according to some sort of measure, which happens to be complex. Since
measures can be more general than complex measures, I'm not entirely
sure why the measure should be restricted to being complex.
And that is it. From this idea (that OMs evolve), the following three
postulates of QM follow by a mechanistic proof
1. States are elements of a Hilbert space over a complex field
2. States evolve unitarily (ie according to a Schroedinger equation)
i\hbar d\psi/dt = H\psi
between measurements
3. The probability function P(x_i|y) satisfies the Born rule
P(x_i|y) = ||^2 /
Now some people have complained about how one can derive quantum
probabilities from the Kolmogorov axioms. It seems
counterintuitive. But this part is the most rigorous. The argument has
been put for the last seven years, and a number of very smart people
have looked at it without finding a flaw. Of course that doesn't mean
there isn't a flaw, but it would have to be quite subtle.
>
> >
> >>
> >>
> >>> This is not incompatible with with your
> >>> notion of the OM being a Sigma1 sentence, but it places severe
> >>> restrictions on the form of the quantum state vector.
> >>
> >>
> >> The OM are the Sigma1 sentences, when they are considered as third
> >> person constructs.
> >
> > Third person is that which is accessible to all observers.
>
>
> ? (This correspond more to the first person plural notion as I have
> defined it in most of my papers: observers appeared in the fourth and
> fifth hypostases, and perhaps already a part of it appears in the third
> one; but there are no observer in the second or first hypostases).
>
> cf:
> 1 p (truth, 0-person)
> 2 Bp (provable, 3-person)
> 3 Bp & p (knowable, 1-person)
> 4 Bp & Dp (observable, measurable; 1-plural-person)
> 5 Bp & Dp & p (sensationalisable, feelable, personally
> observable/measurable, 1 person again)
>
Thinking about it, I'm not sure our x-person terminology is completely
compatible. And it comes down to the problems I've had even in
understanding (or grokking, more to the point) the Theatetus
definition of knowledge. I can understand it from a purely
intellectual
Re: Rép : Observer Moment = Sigma1-Sentences
Bruno Marchal wrote: > > Question to David, and others who could be interested: is the notion > of enumerable and non enumerable set clear? Can you explain why the set > of functions from N to N is not enumerable? > > > Let us go slow and deep so that everybody can understand, once and for > all. OK? Hello Bruno ! I am a freshman to this list and it seems to me that some kind of a 'course' is going to happen. I checked a couple of last messages and it looks interesting. Please, would you mind to repeat what is approximately the starting point of your explanations and where do you aim? Hopefully, I'll be able to follow. Best regards, Mirek --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Observer Moment = Sigma1-Sentences
On 11/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote: > That the 'comp reality' is founded on the number realm, is almost > trivial. What is not trivial at all, and this is what the UDA shows, is > that, once you say "yes" to the digital doctor, for some level of > substitution, then your immateriality (somehow like the quantum > superpositions) is contagious on your most probable neighborhoods. So > that physics has to be shown to emerge statistically from the "measure" > on the UD accessible relative states. This perhaps needs to be explained more slowly. What - exactly - do you mean by "immateriality", and "contagious on your most probable neighbourhoods"? Also, precisely what do you intend to be included in - or excluded from - the notion of 'physics' in this context? Is it to be equated with what is observable, and if so, how and by whom? > To be sure, it is needed, > however, for the understanding that with comp, we *have to* derive the > physics from "intensional numbers prevailing discourses". With comp, > postulating a physical world cannot be used as an explanation relating > mind and appearance of matter (memory-stable observations). > It is not that (aristotelian primary )substance does not exist, but > that such primary substance is provably (with the comp hyp) void of > explanation power. It strikes me, reading the above, that it might be a good idea to find a way to limit ourselves - at this deliberately elementary stage - to an agreed set of terms with which to designate each of your key ideas, for example with respect to physics deriving from "intensional number prevailing discourses". Perhaps what we need is not so much grandmother-version, but a kindergarten-level introduction to the key terms and concepts, which we can then use slowly and clearly to build up the argument. At each stage, perhaps you could refer to the appropriate points in the UDA, or other key papers, that could then be consulted for comparison and further elucidation. Would this work? > The best book is without > doubt the one by Cutland: > > CUTLAND N. J., 1980, Computability An introduction to recursive > function theory, > Cambridge University Press. Thanks > OK. I will begin by saying two words on the language we will use when > discussing with the machine. I can already explain the difference > between the layman (or grandmother) and the logician. This is not just > for you (I guess you know what I will say) but for those who just > abandon logic for reason of notation. > > The main difference is that where a layman says "Alfred is serious", > the logician says serious(Alfred). > > Where the layman will say there is a ferocious dog, a logician will say > that it exists something such that that something is a dog and is > ferocious. Because of laziness he will write Ex(dog(x) & ferocious(x)). > For saying that all dogs are ferocious, he will say that for all dogs > (i.e. choose any thing that is a dog) that things will be ferocious: > and he will write Ax (dog(x) -> ferocious(x)). > > Of course, there is perhaps no effective test to see if a dog is > ferocious or not, perhaps the notion is not well defined, but we have > to live with things like that: even in the pure realm of numbers we > will encounter some unexpected (I guess) complexity. Thanks, this is useful. > By the way, David, do you know what is called "classical propositional > calculus", the truth table method? Do you need some refreshing? > Some refreshing is in Smullyan's FU, but I can do it, or focus on some > difficulty (classical propositional calculus is not so simple indeed, > even if simpler than most other logics). I can always use wikipedia - which I've looked at - or other sources online, but anything you would also be prepared to do here would be most helpful. David > > Le 10-août-07, à 22:32, David Nyman a écrit : > > > > > On 10/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote: > > > >> OK. Have you seen that this is going to made physics a branch of > >> "intensional number theory", by which I mean number theory from the > >> points of view of number ... ? > > > > Insofar as we accept that the foundation of 'comp reality' is the > > number realm, comp physics must indeed be a branch of this (e.g. as > > per my previous example of 'digital digestion'). > > > That the 'comp reality' is founded on the number realm, is almost > trivial. What is not trivial at all, and this is what the UDA shows, is > that, once you say "yes" to the digital doctor, for some level of > substitution, then your immateriality (somehow like the quantum > superpositions) is contagious on your most probable neighborhoods. So > that physics has to be shown to emerge statistically from the "measure" > on the UD accessible relative states. Withouth this, the arithmetical > interview would not lead to making comp testable. > This reasoning shows really the incompleteness of Everett's work: once > you accept the observer can be locally described by its digi
Re: Rép : Observer Moment = Sigma1-Sentences
On 13/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote: > Question to David, and others who could be interested: is the notion > of enumerable and non enumerable set clear? Can you explain why the set > of functions from N to N is not enumerable? Do please remind us. "Off the top of my head", do you mean, by non-enumerable, arbitrary extensibility by the generation of new members via diagonalisation? > Do you people know the difference between ordinal and cardinal (I know > some knows 'course). Yes > I don't think Church thesis can be grasped > conceptually without the understanding that the class of programmable > functions is closed for the diagonalization procedure. Please explain 'programmable functions' and 'closed for the diagonalisation procedure'. > Do everyone > (interested) know how to prove the non enumerability of the subset of N > by diagonalization? Which subset do you mean? I've encountered the diagonalisation/enumerability argument, assuming it's the one I referred to above. > Let us go slow and deep so that everybody can understand, once and for > all. OK? Definitely OK. David > > > Le 13-août-07, à 13:29, Kim Jones a écrit : > > > where he appears to serve the option of being machine or some other > > order of being. I must confess that I still don't understand the > > ontology of angels as opposed to machines but I'm sure his reply > > contains the reason > > > Don't worry, I will try to explain. > > > Question to David, and others who could be interested: is the notion > of enumerable and non enumerable set clear? Can you explain why the set > of functions from N to N is not enumerable? > > Just say no, and I go back to Cantor, the one who discussed with the > pope about the question of naming infinities (!), and indeed the one > who will discover (or invent) the varieties of infinities. > > Do you people know the difference between ordinal and cardinal (I know > some knows 'course). I don't think Church thesis can be grasped > conceptually without the understanding that the class of programmable > functions is closed for the diagonalization procedure. Do everyone > (interested) know how to prove the non enumerability of the subset of N > by diagonalization? > > Let us go slow and deep so that everybody can understand, once and for > all. OK? > > > Bruno > > > http://iridia.ulb.ac.be/~marchal/ > > > > > --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
SV: Rép : Observer Moment = Sigma1-Sentences
-Ursprungligt meddelande- Från: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] För Bruno Marchal Skickat: den 13 augusti 2007 16:36 Till: [EMAIL PROTECTED] Ämne: Re: Rép : Observer Moment = Sigma1-Sentences >I don't think Church thesis can be grasped >conceptually without the understanding that the class of programmable >functions is closed for the diagonalization procedure. This is something I never grasped but would love to understand. LN --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Rép : Observer Moment = Sigma1-Sentences
Le 13-août-07, à 13:29, Kim Jones a écrit : > where he appears to serve the option of being machine or some other > order of being. I must confess that I still don't understand the > ontology of angels as opposed to machines but I'm sure his reply > contains the reason Don't worry, I will try to explain. Question to David, and others who could be interested: is the notion of enumerable and non enumerable set clear? Can you explain why the set of functions from N to N is not enumerable? Just say no, and I go back to Cantor, the one who discussed with the pope about the question of naming infinities (!), and indeed the one who will discover (or invent) the varieties of infinities. Do you people know the difference between ordinal and cardinal (I know some knows 'course). I don't think Church thesis can be grasped conceptually without the understanding that the class of programmable functions is closed for the diagonalization procedure. Do everyone (interested) know how to prove the non enumerability of the subset of N by diagonalization? Let us go slow and deep so that everybody can understand, once and for all. OK? Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Rép : Observer Moment = Sigma1-Sentences
Just to clarify - my question to Bruno was serious. He has mentioned angels before. I thank him for his considered response which I am still studying. The part of his post which prompted my question was: Also, if we are machine (or just lobian), we can indeed contemplate the consistency of *little part* of math, but certainly not the consistency of the whole of math, still less the consistency of the whole of creation. where he appears to serve the option of being machine or some other order of being. I must confess that I still don't understand the ontology of angels as opposed to machines but I'm sure his reply contains the reason regards, Kim On 13/08/2007, at 2:00 AM, John Mikes wrote: > Dear Bruno, > did your scientific emotion just trapped you into showing that your > theoretical setup makes no sense? > Angels have NO rational meaning, they are phantsms of a (fairy?) > tale and if your math-formulation can be applied to a (really) > meaningless phantasy-object, the credibility of it suffers. > How can your formalism be applied to something nonexistent? What > does it say about the 'real' value of it? > > I read Kim's question as a joke, you took it seriously with some > (imagined) meaning you had in mind. Faith? > Please, do not tell me that your theories are as well applicable to > faith-items! Next time sopmebody will calculate the enthalpy of the > resurrection. > > John > > On 8/9/07, Bruno Marchal <[EMAIL PROTECTED]> wrote: > > > Le 09-août-07, à 11:22, Kim Jones a écrit : > > > > > What is "lobian" apart from la machine, Bruno? Are you referring to > > "angels" here? > > > > Aren't angels machines too? > > > Angels are not machine. Unless you extend the meaning of machine > 'course, but Angels' provability extend the provability of any > turing-emulable machine. Sometimes people use the term "supermachine" > for what I call angel, but mathematically, in principle, angels have > nothing to do with machine. Angels can prove any sentence having the > shape AxP(x) with P(x) decidable. (AxP(x) = For all x P(x)). Universal > machine are Sigma_1 complete. Angels are PI_1 complete. A sigma_1 > sentence asserts something like "It exists a number having such or > such > verifiable (decidable) property". PI_1 sentences asserts something > like > "all numbers have such or such verifiable (decidable) property". > The most famous PI_1 sentences is the *machine* consistency statement: > it is indeed equivalent with: all number have the (verifiable) > property > of not being the Godel number (or any arithmetical encoding) of a > proof > of f. > (f = any arithmetical contradiction, like (1+1=2 & ~(1+1=2)). > Angels can be shown to be lobian. They obey G and G*, and G and G* > describe completely their propositional provability logic. > (btw, I call "god" any non turing emulable entity obeying G and G*, > but > for which G and G* are not complete (you need more axioms to > characterize their provability power; and I call supergods, entities > extending vastly the gods. > All that is really the subject matter of recursion theory, alias > computability theory (which should have been called, like someone said > in Siena, the theory of un-computability). recursion theory is really > the science of Angels and Gods, well before being the science of > Machines. But (and this is a consequence of incompleteness), you > cannot > seriously study machines without studying angels too For example > the quantifies version of G* (the first order modal logic of > provability, the one I note qG*) can be shown to be a superangel: > it is > P1-complete *in* Arithmetical Truth (making bigger than the > "unnameable > God of the machine). This means that the divine intellect, or the > Plato's "NOUS" is bigger, in some sense than "God" (Plotinus' ONE). > Plato would have appreciate, and perhaps Plotinus too because he wants > the ONE to be simple , but yes the divine intellect is much more > powerful than the "God" (accepting the arithmetical interpretation of > the hypostases: see my Plotinus papert). > > I will certainly come back on all definitions. But roughly speaking, a > machine is (Turing)-universal (Sigma_1 complete) if it proves all true > Sigma_1 sentences. A machine is lobian if not only the machine proves > all true Sigma_1 sentences, but actually proves, for each Sigma_1 > sentence, that if that sentence is true then she can prove it. Put in > another way, a machine is universal if, for any Sigma_1 sentence S, it > is true that S->BS (B = beweisbar, provable). A machine is lobian if > she proves, for any Sigma_1 sentence S, S->BS. For a universal machine > (talking a bit of classical logic) S->BS is true about the machine. > For > a lobian machine S->BS is not only true, but provable (again with S > representing Sigma_1 sentence). > > But all this is a theorem. My "abstract" definition of lobianity is: > any entity proving B(Bp->p)->Bp where B is her provabi
SV: Rép : Observer Moment = Sigma1-Sentences
Le 12-août-07, à 18:00, John Mikes a écrit : >Please, do not tell me that your theories are as well applicable to faith-items! Next time sopmebody will calculate the enthalpy of the resurrection. Frank Tipler calculated the probability of the resurrection in his last book "The Physics of Christianity" as follows: "This probability is 10 raised to the power of -100. We must then raise this enormously small number to a power equal to the number of atoms in a human body, something like 10 raised to the power of 29". --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Rép : Observer Moment = Sigma1-Sentences
Dear John, Le 12-août-07, à 18:00, John Mikes a écrit : > Dear Bruno, > did your scientific emotion just trapped you into showing that your > theoretical setup makes no sense? > Angels have NO rational meaning, they are phantsms of a (fairy?)tale > and if your math-formulation can be applied to a (really) meaningless > phantasy-object, the credibility of it suffers. > How can your formalism be applied to something nonexistent? What does > it say about the 'real' value of it? I think you have missed the posts where I defined Angels, Gods, Supergods, etc. By definition they refer to lobian entities which are NOT emulable by Turing Machines. They exists mathematically. They are the main object study of a branch of mathematical logic known as recursion theory or computability theory (which could be called uncomputability theory aswell). A detailed example of a very powerful, yet lobian, "angel" is given in Boolos 93, and called "Analysis + Omega-rule", and I have often refer to it by calling it Anomega. Perhaps later I will explain that the full (first order modal logical system) which I use to interpret Plotinus "divine intellect" is really an angel too, actually more powerful than the unnameable "god" (the plotinus' ONE) of the machine. > > I read Kim's question as a joke, you took it seriously with some > (imagined) meaning you had in mind. Faith? I remind you that we have already talk a lot about the necessity of some "faith" from the part of lobian entities (machine or not). The machine cannot prove its own consistency, but can bet on it, and use that bet in many different ways. > Please, do not tell me that your theories are as well applicable to > faith-items! Next time sopmebody will calculate the enthalpy of the > resurrection. Don't worry. each term I am using have been well defined. By "Angel" I just mean those lobian entities which are not machines. I did already, in 2000, in this list called G* the "guardian angel" of the machine, because it knows a lot about the machine that the machine cannot know or prove about itself. Now, with the arithmetical interpretation of Plotinus, I have to use those terms in a bit more systematic ways. The G/G* type of theology works for (ideally correct) machine, but also on many self-referentially correct entities which are NOT machine. OK? Best, Bruno > > John > > On 8/9/07, Bruno Marchal <[EMAIL PROTECTED]> wrote: >> >> Le 09-août-07, à 11:22, Kim Jones a écrit : >> >> > >> > What is "lobian" apart from la machine, Bruno? Are you referring to >> > "angels" here? >> > >> > Aren't angels machines too? >> >> >> Angels are not machine. Unless you extend the meaning of machine >> 'course, but Angels' provability extend the provability of any >> turing-emulable machine. Sometimes people use the term "supermachine" >> for what I call angel, but mathematically, in principle, angels have >> nothing to do with machine. Angels can prove any sentence having the >> shape AxP(x) with P(x) decidable. (AxP(x) = For all x P(x)). Universal >> machine are Sigma_1 complete. Angels are PI_1 complete. A sigma_1 >> sentence asserts something like "It exists a number having such or >> such >> verifiable (decidable) property". PI_1 sentences asserts something >> like >> "all numbers have such or such verifiable (decidable) property". >> The most famous PI_1 sentences is the *machine* consistency statement: >> it is indeed equivalent with: all number have the (verifiable) >> property >> of not being the Godel number (or any arithmetical encoding) of a >> proof >> of f. >> (f = any arithmetical contradiction, like (1+1=2 & ~(1+1=2)). >> Angels can be shown to be lobian. They obey G and G*, and G and G* >> describe completely their propositional provability logic. >> (btw, I call "god" any non turing emulable entity obeying G and G*, >> but >> for which G and G* are not complete (you need more axioms to >> characterize their provability power; and I call supergods, entities >> extending vastly the gods. >> All that is really the subject matter of recursion theory, alias >> computability theory (which should have been called, like someone said >> in Siena, the theory of un-computability). recursion theory is really >> the science of Angels and Gods, well before being the science of >> Machines. But (and this is a consequence of incompleteness), you >> cannot >> seriously study machines without studying angels too For example >> the quantifies version of G* (the first order modal logic of >> provability, the one I note qG*) can be shown to be a superangel: it >> is >> P1-complete *in* Arithmetical Truth (making bigger than the >> "unnameable >> God of the machine). This means that the divine intellect, or the >> Plato's "NOUS" is bigger, in some sense than "God" (Plotinus' ONE). >> Plato would have appreciate, and perhaps Plotinus too because he wants >> the ONE to be simple , but yes the divine intellect is much more >>
