The Mathematico-Cognition Reality Theory (MCRT) Ver 6.0
An update to some of my earlier horribly crude metaphysics ideas. This
latest version of my theory of metaphysics is at last *starting* to
converge on an academic quality philosophy paper. I think it's OK to
post so long as I keep all postings under 4 000 words or so.
I make very clear my alternative mathematical philosophy to that of
ordinary Platonism and at the end make a clear radical suggestion for
the explanation of Qualia. My key postulate is that not all
mathematical truths are fixed -i.e pure Platonism is false - this idea
will certainly not please Bruno! ;) I've talked before about the
possibility that there may be more than one kind of 'time' - now I make
very clear what I meant by that.
Mathematico-Cognition: Towards a Universal Ontology
By Marc Geddes
Version 6
This version: 7th Sep, 2006
Auckland, New Zealand
Abstract:
'The skeleton out-line for a new metaphysics is presented. The
argument against reductive materialism is based on Mathematical
Platonism. The theory presented is a variant of Many-Aspect Monism, or
'Fundamental Property Pluralism'. The framework is aiming to be
universal in scope - a logical scaffolding capable of integrating all
general classes of knowledge under a single explanatory umbrella. It
is proposed that reality manifests itself as 3 different fundamental
knowledge domains - Physical, Volitional and Mathematical/Cognitive.
It is proposed that each domain has associated with it its own
definition of 'causality'. The radical new idea proposed is that
mathematical entities are not static, but can change their state by
moving through 'mathematical time'in 'configuration space'.
Reality itself is postulated to have a two-level structure reflecting
the difference between objects (concrete things with definite locations
in physical space and time) and classes (abstract things which are
universal in scope).
Mathematico-Cognition: Towards a Universal Ontology
Mathematical Platonism
Mathematical Platonism is the idea that mathematical concepts have
objective reality. The basic position is that human mathematicians are
engaged in *discovery* of mathematical facts that exist *out there* in
reality. Mathematical facts are not created by humans, but are things
which exist external to human society and are discovered. Mathematical
entities are patterns, or abstractions derived from concrete facts.
Mathematical Platonism is the idea that these abstractions have a real
existence external to the human mind.
Since mathematical Platonism is central to the theory presented here,
an over-view of the arguments in favor of Platonism will first be
given.
First, why should we believe in the objective existence of mathematical
entities? Surely, some will argue, mathematical entities are really
just abstract fictions (or invented languages) we use for describing
what are really material processes. This position is known as
nominalism.
However, there's an argument known as *The argument from
Indispensability*. Certain mathematical theories (for instance
analysis) are indispensable for modern physics. Physics uses
quantifiers which range over domains that include mathematical entities
not in space and time. Thus, the argument goes; since we have to accept
our best scientific theories of the world, we should accept that the
entities referred to in our theories really exist.
Now one could try to remove the references to mathematical entities in
scientific theories. For instance the philosopher Hartry Field (1980)
has proposed this - he suggested trying to remove talk of real numbers
in Newton's theory of gravity and replacing numbers with space-time
points and regions. But if one tries to do this, one finds that the
theories become enormously unwieldy - mathematical entities such as
numbers are just so *useful* in science. If there are entities in our
theories which it is very useful to refer to, this provides some
pragmatic grounds for believing in their existence. The argument at
work here is Occam's razor: in science the general rule of thumb is
that simple explanations are favored over more complex ones. Since in
science references to mathematical entities simplify scientific
theories, the simplest explanation is that these mathematical entities
really exist.
The physicist David Deutsch in his book 'The Fabric Of Reality', uses
the principle to establish 'Criterion for reality'. The idea is that we
should regard as real those postulated entities which, if we tried to
replace them with something else would complicate our explanations.
Deutsch's principle was this:
'If according to the simplest explanation, an entity is complex and
autonomous, then that entity is real.' ('The Fabric Of Reality', Pg 91)
As Detusch points out, mathematical entities do appear to match the
criteria for reality: 'Abstract entities that are complex and
autonomous exist objectively and are part of the fabric of reality.
There exist logically necessary truths about these entities, and
Re: computationalism and supervenience
Russel Standish writes: Or my point that in a Multiverse, counterfactuals are instantiated anyway. Physical supervenience and computationalism are not incompatible in a multiverse, where physical means the observed properties of things like electrons and so on. I'd think that in the context of a multiverse, physical supervenience would say that whether consciousness is instantiated would depend only on physical conditions here, at this point in the multiverse, and would not depend on conditions elsewhere. It would be a sort of locality condition for the multiverse. In that case it seems you still have a problem because even if counterfactuals are tested elsewhere in the multiverse, whether they are handled correctly will not be visible locally. So you'd still have a contradiction, with supervenience saying that consciousness depends only on local physical conditions, while computationalism would say that consciousness depends on the results of counterfactual tests done in other branches or worlds of the multiverse. Hal Finney --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: computationalism and supervenience
On Wed, Sep 06, 2006 at 12:25:10AM -0700, Hal Finney wrote: I'd think that in the context of a multiverse, physical supervenience would say that whether consciousness is instantiated would depend only on physical conditions here, at this point in the multiverse, and would not depend on conditions elsewhere. It would be a sort of locality condition for the multiverse. Why do you say this? Surely physical supervenience is simply supervenience on some physical object. Physical objects are spread across the multiverse, and are capable of reacting to all counterfactuals presented to it. Inside views are local - but the whole shebang must be spread across the Multiverse. Cheers -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: computationalism and supervenience
Le 05-sept.-06, à 00:00, 1Z a écrit : However, comp may not be the same as computationalism. In that case there should be an error in the Universal Dovetailer Argument. 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 everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
RE: computationalism and supervenience
Peter Jones writes: Stathis Papaioannou wrote: Peter Jones writes: [Stathis Papaioannou] If every computation is implemented everywhere anyway, this is equivalent to the situation where every computation exists as a platonic object, or every computation exists implemented on some computer or brain in a material multiverse. This gives rise to the issues of quantum immortality and the white rabbit problem, as discussed at great length in the past on this list. One way to discredit all this foolishness is to abandon computationalism... [Brent Meeker] I don't see how assuming consciousness is non-computational solves any of these conundrums about every object implementing every possible computation. It would mean that every object implementing every possible computation doesn't imply that every object is conscious. Of course, one can also deny that conclusion be regading computation as structural rather than semantic. You don't have to go as far as saying that *computation* is structural rather than semantic. You only need to say that *consciousness* is structural, and hence non-computational. That's what some cognitive scientists have done, eg. Penrose, Searle, Maudlin. Personally, I don't see why there is such a disdain for the idea that every computation is implemented, including every conscious computation. The idea is still consistent with all the empirical facts, since we can only interact with a special subset of computations, implemented on conventional computers and brains. Occam's razor, It is an unncessary complication. No, it's simpler. You would otherwise have to come up with an explanation as to why only particular conscious computations are implemented, and it is that which would make the theory more complicated than it needs to be. Statthis Papaioannou _ Be one of the first to try Windows Live Mail. http://ideas.live.com/programpage.aspx?versionId=5d21c51a-b161-4314-9b0e-4911fb2b2e6d --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
RE: computationalism and supervenience
Peter Jones writes: But if implementing a particular computation depends on an observer, or a dicitonary, or somesuch, it is not the case that everything implements every computation unless it can be shown that evey dictionary somehow exists as well. The computation provides its own observer if it is conscious, by definition. But providing its own observer, if computationalism is true, must be a computational property, ie. a property possesed only by particular programmes. However, if any system can be interpreted as running every programme, everysystems has the self-observation property, if interpretedt he right way. IOW, one you introduce interpretation-dependence, you can't get away from it. That's right: if there is at least one physical system, then every computation is implemented, although we can only interact with them at our level if they are implemented on a conventional brain or computer, which means we have the means to interpret them at hand. The non-conscious computations are there in the trivial sense that a block of marble contains every possible statue of a given size. All the computations are merely potential, in the absence of interpreters and dictionaries, whether conscious or not. The conscious computations, on the other hand, are there and self-aware Not really. They are just possibilities. even though we cannot interact with them, just as all the statues in a block of marble would be conscious if statues were conscious and being embedded in marble did not render them unconscious. But that gets to the heart of the paradox. You are suggesting that conscious computations are still conscious even thought hey don't exst and are mere possiiblities! That is surely a /reductio/ of one of your premisses A non-conscious computation cannot be *useful* without the manual/interpretation, and in this sense could be called just a potential computation, but a conscious computation is still *conscious* even if no-one else is able to figure this out or interact with it. If a working brain in a vat were sealed in a box and sent into space, it could still be dreaming away even after the whole human race and all their information on brain function are destroyed in a supernova explosion. As far as any alien is concerned who comes across it, the brain might be completely inscrutable, but that would not make the slightest difference to its conscious experience. then it can be seen as implementing more than one computation simultaneously during the given interval. AFAICS that is only true in terms of dictionaries. Right: without the dictionary, it's not very interesting or relevant to *us*. If we were to actually map a random physical process onto an arbitrary computation of interest, that would be at least as much work as building and programming a conventional computer to carry out the computation. However, doing the mapping does not make a difference to the *system* (assuming we aren't going to use it to interact with it). If we say that under a certain interpretation - here it is, printed out on paper - the system is implementing a conscious computation, it would still be implementing that computation if we had never determined and printed out the interpretation. The problem remains that the system's own self awareness, or lack thereof, is not observer-relative. something has to give. Self-awareness is observer-relative with the observer being oneself. Where is the difficulty? Stathis Papaioannou _ Be one of the first to try Windows Live Mail. http://ideas.live.com/programpage.aspx?versionId=5d21c51a-b161-4314-9b0e-4911fb2b2e6d --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
RE: computationalism and supervenience
Peter Jones writes: Stathis Papaioannou wrote: Under one mapping, the physical system implements a program which thinks, I am now experiencing my first second of life. Under a different mapping, it implements a program which thinks, I am now experiencing my second second of life. And who is doing all the interpreting ? Who is doing the interpreting for your conscious experience? Stathis Papaioannou _ Be one of the first to try Windows Live Mail. http://ideas.live.com/programpage.aspx?versionId=5d21c51a-b161-4314-9b0e-4911fb2b2e6d --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Rép: ROADMAP (well, not yet really...
Le 04-sept.-06, à 16:12, 1Z a écrit : Bruno Marchal wrote: Le 04-sept.-06, à 02:56, 1Z a écrit : Why should a belief in other minds (which I do not directly experience) be more reasonable thant a belief in unexperienced primary matter ? It's a question of consistency. Attributing mind to others explains many things. And the project of expaling things with matter has been going strong for many centuries. But if you know the literature in philosophy of mind you know that the notion of matter has never been successful. It has ease the progress in *quantitative physics, but only by paying the price of hiding the fundamental mind/body question. Of course the fundamental questions has been appropriated by the fake-authoritative religion people. And as I have said often, if you look at the literature in physics, primary matter never play an explicit role. It just help to interpret formula without jeopardizing common sense. There are rich (albeit vague) theories about those other mind (treated in Psychology (cf jealousy, shame, fear, ...) and Theology (does other minds go to paradise?). Although I have no direct experience of other minds I have many indirect evidences. Yes, that;s the problem. What stands between your mind and other minds is your body and other bodies. Yes. But we can believe in bodies without attributing to them primary matters. Unexperienced primary matter? I have not even indirect experiences, No experience of time and change ? Sure. So what? Time and change can be explained by the third hypostase which appears naturally when you define the first person in terms of the provability logics. and with comp and/or the quantum I can not even ascribe a simple meaning to the concept. Quantum mechanics is a theory *of* matter. Yes. But it is even less a theory of primary matter than Newtonian physics, where we can still imagine matter is composed of real atomos (non splitable entities). 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 everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: computationalism and supervenience
Le 04-sept.-06, à 16:57, David Nyman a écrit : Bruno Marchal wrote: Either those *specific* physical activities are turing emulable, and we are back to 1) and 2), or they are not, and then comp is false. Recall we assume comp. I don't follow. I thought Maudlin is proposing a physical machine running the consciousness program, not a turing-emulated one. Are you saying that if we assume comp, the 'physical activity level' of a correctly substituted emulation is posited as equivalent to that of a 'real' machine (i.e. there is in fact no meaningful distinction)? Once Maudlin proposes a physical machine running a (consciousness) program, obviously he assumes its turing emulability. Then the reasoning shows that comp makes it very hard to attribute the consciousness to the physical activity corresponding to that physical emulation. Anything a physical computer can compute is turing emulable, 'course. In this case AFAICS the substitution level would need to be below that of 'registers' etc, which are insufficiently constrained aspects of machine architecture. We would have zombie. Why not. Once comp is false ... Why talk of zombies? A zombie is a being that is supposedly conceivable (though not to me) as being 'unconscious' despite apparently possessing the structural/ behavioural prerequisites of consciousness. I was referring to the issue that, if the characteristics of consciousness are indeed correlated with specific physical activities, then aspects of consciousness would necessarily *co-vary* with physical instantiation. To avoid this, comp would need to adopt a substitution level that preserved the invariance of whatever 'physical activities' were deemed relevant to consciousness (as I suggest above). OK. That follows from the comp hyp. OK in this situation. But comp makes impossible to distinguish the experience of driving a car, and the experience of driving a virtual car in a virtual environment, done at the right level of substitution (or below). Then the movie-graph or Maudlin's Olympia shows that machines cannot even distinguish a physical virtual environment and a purely arithmetical virtual environment. So this is all about the level of substitution. Exactly. Well, as I've suggested, I think the level would have to be at or below that at which machine architecture differences become indistinguishable. Well. I am not sure where are you in the reasoning. Both me and Maudlin presuppose some material background before arriving at a epistemological contradiction. Comp predict that if we look at ourself or at our neighborhood at a level below our substitution level then we should find the trace of the parallel computation existing in platonia. That is why physics is redefined through comp as the study of a relative measure on an infinite set of computation quotientized by an non-distinguishability relation, which is then so hard to define than I isolate it indirectly through the lobian interview. So I don't believe that arguments involving registers etc. can be correct, because it becomes hard to argue coherently that the necessary invariances are preserved at this level. We might debate atom-by-atom, or circuit-by-circuit, or does the doctor have some more general principle to resolve this? No. Comp explicitly forbid any rule there. That's why a comp-honest doctor should always tell his patient that a digital brain/body substitution is proposed at the patient risk and peril. If you read the literature by the neurosurgeon you will see most of them bet the level is high (neuronal). Imo it is at least biochemical, if not quantum (just above Heizenberg indetermincay). BTW I think I see now that most of our original disagreements were language based. If comp is in essence an objective idealist model, in effect it begins from the assumption that 'objective idealist reality' exists 'in the sense that I exist' (although of course not constrained solipsistically to my 1st-person pov). That is all I have ever sought in terms of '1st-person primacy'. Perhaps. let us proceed. I think you will see the nuance which should be added here at the right moment. If I try to explain now, there is 99% of chance that it will look purely terminological. And perhaps it is. let us come back on this latter. 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 everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: computationalism and supervenience
Le 06-sept.-06, à 10:48, Russell Standish a écrit : On Wed, Sep 06, 2006 at 12:25:10AM -0700, Hal Finney wrote: I'd think that in the context of a multiverse, physical supervenience would say that whether consciousness is instantiated would depend only on physical conditions here, at this point in the multiverse, and would not depend on conditions elsewhere. It would be a sort of locality condition for the multiverse. Why do you say this? Surely physical supervenience is simply supervenience on some physical object. Physical objects are spread across the multiverse, and are capable of reacting to all counterfactuals presented to it. I agree with Hal Finney objection. A simpler one is that if the physics needed is of the type MW or quantum (without collapse), then IF this is relevant for solving the maudlin's paradox then a quantum physical system should NOT been turing emulable. Put in another way: suppose that a quantum system is conscious, and that comp is correct. Then a classical computer emulation of the quantum system should be conscious, but for this one only the classical counterfactual can play a role, and Maudlin's paradox will reappear at that level. In your preceding posts, Russel says: I think what you're trying to say is move Maudlin's construction one level up. The computer (eg Klara) actually emulates a Multiverse, and Olympia is some kind of recording of the Multiverse. This is not clear. The many Klaras are just inactive computers during PI, which should be activated in case of counterfactuals. They are inactive in the normal parallel world too. But in this case I would say that Olympia and Klara are actually identical, and linking the two is not of much conceptual value. ? I also have difficulty in saying that a Multiverse is conscious when some interior views of the Multiverse experience conscious states Comp implies two things: - The multiverse is not a priori conscious (unless you are the multiverse, it means the substitution level is as low as possible). (As Plotinus realized this is the major problem with Aristotle: the consciousness of the big One). - The observable (multi)-universe is not a priori computable (the physics is given by an 1-indeterminacy average on an infinity of computations). t is the fallacy of assuming that a collection of things is always more (complex) than the individual things themselves. I agree, both with comp and the quantum, although the notion of subsystem is rather complex in those settings. Multiverses are rather simple things - about the simplicity of Schroedinger's equation, and hardly what I'd call conscious. We agree. Normal: it is the basic assumption of the everything-list, above comp... But I think we are headed in the direction of whether computable Multiverses really satisfy what we mean by computationalism. If someone copies the entirety of reality, do I still survive in a folk psychology sense. I am still confused on this point. How could you not survive that? 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 everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: computationalism and supervenience
Le 05-sept.-06, à 15:38, 1Z a écrit : The conscious computations, on the other hand, are there and self-aware Not really. They are just possibilities. even though we cannot interact with them, just as all the statues in a block of marble would be conscious if statues were conscious and being embedded in marble did not render them unconscious. But that gets to the heart of the paradox. You are suggesting that conscious computations are still conscious even thought hey don't exst and are mere possiiblities! That is surely a /reductio/ of one of your premisses The everything-lister, with or without comp, takes as natural the idea that all possibilities exist, and that actuality is just a possibility viewed from that possibility. It is known by some philosopher as the indexical approach of actuality. Very common for the explanation of time (cf Saunders, Deutsch, Einstein, ...), it can be used for all sort of actuality, not just the indexical nowness but also hereness, etc. 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 everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Universal Numbers (was: computationalism and supervenience
Le 05-sept.-06, à 19:59, 1Z a écrit : Stathis Papaioannou wrote: Under one mapping, the physical system implements a program which thinks, I am now experiencing my first second of life. Under a different mapping, it implements a program which thinks, I am now experiencing my second second of life. And who is doing all the interpreting ? The program itself. And who interprets the program? The universal numbers (= +/- the godel numbers of the universal machines). (Note: from the program first person pov, it is the most *probable* universal numbers which will count). And who interprets the universal numbers? I can show that if you believe in the independent truth of even a tiny recursively enumerable subset of the set of the true arithmetical propositions, then you should understand that that tiny part of Arithmetic does, or better, cannot not do the interpretation of the universal numbers. Incompleteness follows, and self-referentially correct universal numbers cannot not gamble on many form of self-indeterminateness (p, Bp, Bp p, Bp ~B~p, Bp ~B~p p, ...): the n-person point of views (similar to Plotinus' hypostases, I have discovered since). Comp restricts the interpretation of p on true Sigma1 sentences (the arithmetical version of turing-equivalence). B is the arithmetical Godel-Lob predicate of provability. With the comp (sigma1) restriction, it is exactly the same arithmetical sentences which are true (p), provable (Bp), known (Bp p), observed (Bp ~B~p), feeled (Bp ~B~p p), but incompleteness (the G* \minus G gap) makes it impossible for any self-referentially correct universal number to either prove, know, observe, or feel that equivalence, but only to bet on it for some self survival purpose, or not. Realities could emerge from (extensional) arithmetical truth through its unavoidable many internal angle or (intensional, modal) variant. Strictly speaking one for each universal numbers. It is striking that they all obeys similar laws with respect to their self-referential abilities: B is an indexical(*). (*) But still a third person one bearing on a third person! But the fact that B is an indexical does explain a basic relationship which first person based TOE like George, David, ... I think. 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 everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: ROADMAP (SHORT)
Bruno Marchal wrote: Le 16-août-06, à 18:36, Tom Caylor a écrit : I noticed that you slipped in infinity (infinite collection of computations) into your roadmap (even the short roadmap). In the technical posts, if I remember right, you said that at some point we were leaving the constructionist realm. But are you really talking about infinity? It is easy to slip into invoking infinity and get away with it without being noticed. I think this is because we are used to it in mathematics. In fact, I want to point out that David Nyman skipped over it, perhaps a case in point. But then you brought it up again here with aleph_zero, and 2^aleph_zero, so it seems you are really serious about it. I thought that infinities and singularities are things that physicists have dedicated their lives to trying to purge from the system (so far unsuccessfully ?) in order to approach a true theory of everything. Here you are invoking it from the start. No wonder you talk about faith. Even in the realm of pure mathematics, there are those of course who think it is invalid to invoke infinity. Not to try to complicate things, but I'm trying to make a point about how serious a matter this is. Have you heard about the feasible numbers of V. Sazanov, as discussed on the FOM (Foundations Of Mathematics) list? Why couldn't we just have 2^N instantiations or computations, where N is a very large number? I would say infinity is all what mathematics is about. Take any theorem in arithmetic, like any number is the sum of four square, or there is no pair of number having a ratio which squared gives two, etc. And I am not talking about analysis, or the use of complex analysis in number theory (cf zeta), or category theory (which relies on very high infinite) without posing any conceptual problem (no more than elsewhere). When you say infinity is what math is all about, I think this is the same thing as I mean when I say that invariance is what math is all about. But in actuality we find only local invariance, because of our finiteness. You have said a similar thing recently about comp. But here you seem to be talking about induction, concluding something about *all* numbers. Why is this needed in comp? Is not your argument based on Robinson's Q without induction? Even constructivist and intuitionist accept infinity, although sometimes under the form of potential infinity (which is all we need for G and G* and all third person point of view, but is not enough for having mathematical semantics, and then the first person (by UDA) is really linked to an actual infinity. But those, since axiomatic set theory does no more pose any interpretative problem. True, I heard about some ultrafinitist would would like to avoid infinity, but until now, they do have conceptual problem (like the fact that they need notion of fuzzy high numbers to avoid the fact that for each number has a successor. Imo, this is just philosophical play having no relation with both theory and practice in math. The UDA is not precise enough for me, maybe because I'm a mathematician? I'm waiting for the interview, via the roadmap. UDA is a problem for mathematicians, sometimes indeed. The reason is that although it is a proof, it is not a mathematical proof. And some mathematician have a problem with non mathematical proof. But UDA *is* the complete proof. I have already explain on this list (years ago) that although informal, it is rigorous. The first version of it were much more complex and technical, and it has taken years to suppress eventually any non strictly needed difficulties. I have even coined an expression the 1004 fallacy (alluding to Lewis Carroll), to describe argument using unnecessary rigor or abnormally precise term with respect to the reasoning. So please, don't hesitate to tell me what is not precise enough for you. Just recall UDA is not part of math. It is part of cognitive science and physics, and computer science. The lobian interview does not add one atom of rigor to the UDA, albeit it adds constructive features so as to make possible an explicit derivation of the physical laws (and more because it attached the quanta to extended qualia). Now I extract only the logic of the certain propositions and I show that it has already it has a strong quantum perfume, enough to get an arithmetical quantum logic, and then the rest gives mathematical conjectures. (One has been recently solved by a young mathematician). Bruno http://iridia.ulb.ac.be/~marchal/ What is the non-mathematical part of UDA? The part that uses Church Thesis? When I hear non-mathematical I hear non-rigor. Define rigor that is non-mathematical. I guess if you do then you've been mathematical about it. I don't understand. Tom --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List
Re: computationalism and supervenience
Bruno Marchal wrote: Le 05-sept.-06, à 15:38, 1Z a écrit : The conscious computations, on the other hand, are there and self-aware Not really. They are just possibilities. even though we cannot interact with them, just as all the statues in a block of marble would be conscious if statues were conscious and being embedded in marble did not render them unconscious. But that gets to the heart of the paradox. You are suggesting that conscious computations are still conscious even thought hey don't exst and are mere possiiblities! That is surely a /reductio/ of one of your premisses The everything-lister, with or without comp, takes as natural the idea that all possibilities exist, and that actuality is just a possibility viewed from that possibility. Of course it is not natural, or we would not have two separate words for possible and actual. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: computationalism and supervenience
On Wed, Sep 06, 2006 at 01:44:35PM -0700, Hal Finney wrote: Russell Standish writes: Why do you say this? Surely physical supervenience is simply supervenience on some physical object. Physical objects are spread across the multiverse, and are capable of reacting to all counterfactuals presented to it. Inside views are local - but the whole shebang must be spread across the Multiverse. I suppose it depends on your definitions. As I suggested, supervenience in a single world model means that consciousness depends on local physical activity, and not on causally unconnected events. In a multiverse, actions in parallel worlds are causally unconnected to actions here. It seems rather odd to say that the supervenience thesis says that whether my computer is conscious depends on what is happening in some remote parallel universe. I also think there are problems with this notion that objects are spread across the multiverse, and in particular that all counterfactuals are tested. It's not clear to me that we can unambiguously define the counterpart to this particular object in an arbitrary multiverse. For very near or similar multiverses it may seem unproblematic, while for extremely far or different multiverses there will obviously be no counterparts. There would probably be a gray area in the middle in which an object was related to one in our universe but perhaps not exactly the same. This exposes a difficulty with the notion that all counterfactuals are tested. In the first place, many thought experiments aim to refrain from testing counterfactuals - Maudlin's is of this nature. Something has to go seriously wrong with Maudlin's scenario for counterfactuals to be tested. In the second place, many counterfactuals may be bizarre and unlikely, so that the circumstances under which they are tested may require extremely strange events. These situations would suggest that such counterfactuals will only be tested in relatively remote parts of the multiverse, parts quite different from our own. And then we have to ask, is it really the same machine that is being tested? And by same here, I think we mean more than just designed the same or isomorphic - we mean that it has some kind of shared identity, that in some sense this *is* the machine we see in our universe, just exposed to different inputs. Given the problems I mentioned with this notion of identity across the multiverse, it's not clear that this concept makes sense. Hal Finney Take an object, say this coffee cup that is sitting on my desk in front of me. It was created a few years ago in some vitreous furnace in a factory. Ever since then, it has been a part of all those universes that share the history of this coffee cup's creation (except of course those in which the cup has been destroyed). Sure there will be borderline cases - eg the cup smashed, but strangely retaining the form of the cup and so on, but I would argue that these borderline cases are of small measure relative to the universes in which the cup exists or doesn't exist in an unproblematic way. This satisfies your shared identity requirement. It is more than simply being isomorphic - it has shared history. All counterfactuals *compatible with* that coffee cup's existence will be experienced by the coffee cup. All physical objects have this identity property across the Multiverse (not covering the Multiverse, but occupying a non-zero measure slice of it). We had this debate recently about whether persons could have this identity property or not - with me being somewhat underwhelmed by David Parfitt's arguments on this subject, but the situation is quite clear with physical objects. With physical supervenience, it is possible for the same person to supervene on multiple physical objects. What is disallowed is multiple persons to supervene on the same physical object. -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED]
RE: computationalism and supervenience
Peter Jones writes: Bruno Marchal wrote: Le 05-sept.-06, à 15:38, 1Z a écrit : The conscious computations, on the other hand, are there and self-aware Not really. They are just possibilities. even though we cannot interact with them, just as all the statues in a block of marble would be conscious if statues were conscious and being embedded in marble did not render them unconscious. But that gets to the heart of the paradox. You are suggesting that conscious computations are still conscious even thought hey don't exst and are mere possiiblities! That is surely a /reductio/ of one of your premisses The everything-lister, with or without comp, takes as natural the idea that all possibilities exist, and that actuality is just a possibility viewed from that possibility. Of course it is not natural, or we would not have two separate words for possible and actual. Where does the idea that conscious computations might only be potentially conscious come from? If it isn't actually conscious, then it isn't a conscious computation. It so happens that all the conscious beings of which we are aware in nature interact with their environment most of the time, but even if such interaction is necessary for consciousness, you could make the inputs part of a larger system, which is then inputless. Stathis Papaioannou _ Be one of the first to try Windows Live Mail. http://ideas.live.com/programpage.aspx?versionId=5d21c51a-b161-4314-9b0e-4911fb2b2e6d --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: computationalism and supervenience
On Wed, Sep 06, 2006 at 12:25:53PM +0200, Bruno Marchal wrote:
Le 06-sept.-06, à 10:48, Russell Standish a écrit :
On Wed, Sep 06, 2006 at 12:25:10AM -0700, Hal Finney wrote:
I'd think that in the context of a multiverse, physical supervenience
would say that whether consciousness is instantiated would depend only
on physical conditions here, at this point in the multiverse, and
would
not depend on conditions elsewhere. It would be a sort of locality
condition for the multiverse.
Why do you say this? Surely physical supervenience is simply
supervenience on some physical object. Physical objects are spread
across the multiverse, and are capable of reacting to all
counterfactuals presented to it.
I agree with Hal Finney objection. A simpler one is that if the
physics needed is of the type MW or quantum (without collapse), then IF
this is relevant for solving the maudlin's paradox then a quantum
physical system should NOT been turing emulable.
Put in another way: suppose that a quantum system is conscious, and
that comp is correct. Then a classical computer emulation of the
quantum system should be conscious, but for this one only the classical
counterfactual can play a role, and Maudlin's paradox will reappear at
that level.
This simplest way of addressing this is to use your dovetailer instead
of quantum multiverses, which tends to confuse people, and get
associated with quantum mysticism. The dovetailer is obviously
computable, but not the internal trace of one of its branches. (A
point you have frequently made).
In fact lets go one further and write a program that prints out all
combinations of 10^{30} bits in Library of Babel style. This is more
than enough information to encode all possible histories of neuronal
activity of a human brain, so most of us would bet this level of
substitution would satisfy yes doctor.
So does this mean that the entire library of babel is conscious, or
the dovetailer program (which is about 5 lines of Fortran) is
conscious? To me it is an emphatic no! Does it mean that one of the
10^{30} length bitstrings is conscious? Again I also say no. The only
possible conscious thing is the subcollection of bitstrings that
corresponds to the actions of a program emulating a person under all
possible inputs. It will have complexity substantially less than
10^{30}, but substantially greater than the 5 line dovetailer.
But I think we are headed in the direction of whether computable
Multiverses really satisfy what we mean by computationalism. If
someone copies the entirety of reality, do I still survive in a folk
psychology sense. I am still confused on this point.
How could you not survive that?
Bruno
If I have inoperable brain cancer in reality A, and someone duplicates
reality A to reality B, then unfortunately I still have inoperable brain
cancer in reality B.
Maybe I'm being too literal...
I can also never experience your famous Washinton-Moscow teleportation
excercise - in reality B I am still stuck in Brussels.
--
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RE: computationalism and supervenience
Russell Standish writes: With physical supervenience, it is possible for the same person to supervene on multiple physical objects. What is disallowed is multiple persons to supervene on the same physical object. That is what is usually understood, but there is no logical reason why the relationship between the physical and the mental cannot be one-many, in much the same way as a written message can have several meanings depending on its interpretation. Whatever physical supervenience is, it isn't like the usual causal relationships between objects. Stathis Papaioannou _ Be one of the first to try Windows Live Mail. http://ideas.live.com/programpage.aspx?versionId=5d21c51a-b161-4314-9b0e-4911fb2b2e6d --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
RE: computationalism and supervenience
Russell Standish writes:
In fact lets go one further and write a program that prints out all
combinations of 10^{30} bits in Library of Babel style. This is more
than enough information to encode all possible histories of neuronal
activity of a human brain, so most of us would bet this level of
substitution would satisfy yes doctor.
So does this mean that the entire library of babel is conscious, or
the dovetailer program (which is about 5 lines of Fortran) is
conscious? To me it is an emphatic no! Does it mean that one of the
10^{30} length bitstrings is conscious? Again I also say no. The only
possible conscious thing is the subcollection of bitstrings that
corresponds to the actions of a program emulating a person under all
possible inputs. It will have complexity substantially less than
10^{30}, but substantially greater than the 5 line dovetailer.
Why do you disagree that one of the bitstrings is conscious? It seems to
me that the subcollection of bitstrings that corresponds to the actions of
a program emulating a person under all possible inputs is a collection of
multiple individually conscious entities, each of which would be just as
conscious if all the others were wiped out.
Stathis Papaioannou
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Re: computationalism and supervenience
On Thu, Sep 07, 2006 at 11:19:47AM +1000, Stathis Papaioannou wrote:
Russell Standish writes:
In fact lets go one further and write a program that prints out all
combinations of 10^{30} bits in Library of Babel style. This is more
than enough information to encode all possible histories of neuronal
activity of a human brain, so most of us would bet this level of
substitution would satisfy yes doctor.
So does this mean that the entire library of babel is conscious, or
the dovetailer program (which is about 5 lines of Fortran) is
conscious? To me it is an emphatic no! Does it mean that one of the
10^{30} length bitstrings is conscious? Again I also say no. The only
possible conscious thing is the subcollection of bitstrings that
corresponds to the actions of a program emulating a person under all
possible inputs. It will have complexity substantially less than
10^{30}, but substantially greater than the 5 line dovetailer.
Why do you disagree that one of the bitstrings is conscious? It seems to
me that the subcollection of bitstrings that corresponds to the actions of
a program emulating a person under all possible inputs is a collection of
multiple individually conscious entities, each of which would be just as
conscious if all the others were wiped out.
Stathis Papaioannou
It is simply the absurdity of a recording being conscious. I know we
are on opposite sides of that fence. The question is whether you can
see a difference between one and the other.
To recap - there are three things being talked about here:
1) The set of all strings, which can be generated by a dovetailer or
similar simple program
2) A single string capturing the trace of a conscious observer in a
single history, which whilst enormously complex itself, can be
played back by a trivial program, or by Maudlin's construction a
counterfactual handling device in which only the trivial playback
device is active.
3) A set of strings corresponding to the trace of a conscious observer
over all possible histories. This can only be generated by a
program equivalent to the original observer, however I suppose it
can be stored (since it is still finite) on a vastly longer tape
(2^{complexity observer=10^15 (say)} bits) and played back using a
dovetailer. In fact one way of doing this might be to use a
2^{10^30} length tape, and mark a 1 for all those traces generated
by the original observer, and 0 for those that are not. Then the
dovetailer can do a simple search on this immense tape to see
whether a particular branch appears as a prefix to the binary
expansion of any of the conscious traces. Then one can do a
Maudlin-type argument. However, even this construction will fail in
the presence of subjective immortality (eg QTI or
COMP-immortality).
So the question is 1), 2) or 3) conscious. I would argue only 3) is,
particularly with immortality. I'll leave this thread for now - I have
some more ideas based on physicality being phenomenal, which rules out
a Maudlin-like construction of the 1) (and possibly 3) case.
Cheers
--
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is of type application/pgp-signature. Don't worry, it is not a
virus. It is an electronic signature, that may be used to verify this
email came from me if you have PGP or GPG installed. Otherwise, you
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Mathematics
UNSW SYDNEY 2052 [EMAIL PROTECTED]
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Re: computationalism and supervenience
Stathis Papaioannou wrote: Brent Meeker writes: If every computation is implemented everywhere anyway, this is equivalent to the situation where every computation exists as a platonic object, or every computation exists implemented on some computer or brain in a material multiverse. But if implementing a particular computation depends on an observer, or a dicitonary, or somesuch, it is not the case that everything implements every computation unless it can be shown that evey dictionary somehow exists as well. The computation provides its own observer if it is conscious, by definition. I'm always suspicious of things that are true by definition. How exactly does an observer provide meaning or whatever it is that makes a computation? And how does consciousness fulfill this function. I, in my conscious thoughts, certainly don't observe the computation that my brain performs. In fact my thoughts seem to spring from nowhere more or less spontaneously in coherent trains or as prompted by perceptions. Let's not try to define consciousness at all, but agree that we know what it is from personal experience. Computationalism is the theory that consciousness arises as a result of computer activity: that our brains are just complex computers, and in the manner of computers, could be emulated by another computer, so that computer would experience consciousness in the same way we do. (This theory may be completely wrong, and perhaps consciousness is due to a substance secreted by a special group of neurons or some other such non-computational process, but let's leave that possibility aside for now). What we mean by one computer emulating another is that there is an isomorphism between the activity of two physical computers, so that there is a mapping function definable from the states of computer A to the states of computer B. If this mapping function is fully specified we can use it practically, for example to run Windows on an x86 processor emulated on a Power PC processor running Mac OS. If you look at the Power PC processor and the x86 processor running side by side it would be extremely difficult to see them doing the same computation, but according to the mapping function inherent in the emulation program, they are, and they still would be a thousand years from now even if the human race is extinct. In a similar fashion, there is an isomorphism between a computer and any other physical system, even if the mapping function is unknown and extremely complicated. I don't see how there can be an isomorphism between any two systems. Without some structural constraint that seems to throw away the iso part and simply leave a morphism. That's not very interesting for non-conscious computations, because they are only useful or meaningful if they can be observed or interact with their environment. However, a conscious computation is interesting all on its own. It might have a fuller life if it can interact with other minds, but its meaning is not contingent on other minds the way a non-conscious computation's is. Empirically, all of the meaning seems to be referred to things outside the computation. So if the conscious computation thinks of the word chair it doesn't provide any meaning unless there is a chair - outside the computation. So it is not clear to me that meaning can be supplied from the inside in this way. I think this is where Bruno talks about the required level of substitution and allows that the level may be the brain at a neural level PLUS all the outside world. So that within this simulation the simulated brain is conscious *relative* to the rest of the simulated world. I know this because I am conscious, however difficult it may be to actually define that term. But do you know you would be conscious if you could not interact with the world? That seems doubtful to me. Of course you can close your eyes, stop your ears, etc and still experience consciousness - for a while - but perhaps not indefinitely and maybe not even very long. The conclusion I therefore draw from computationalism is that every possible conscious computation is implemented necessarily if any physical process exists. That would seem to require mappings that are not isomorphisms. This seems to me very close to saying that every conscious computation is implemented necessarily in Platonia, as the physical reality seems hardly relevant. It seems to me to be very close to a reductio ad absurdum. Brent Meeker --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list
Re: computationalism and supervenience
Stathis Papaioannou wrote: Peter Jones writes: But if implementing a particular computation depends on an observer, or a dicitonary, or somesuch, it is not the case that everything implements every computation unless it can be shown that evey dictionary somehow exists as well. The computation provides its own observer if it is conscious, by definition. But providing its own observer, if computationalism is true, must be a computational property, ie. a property possesed only by particular programmes. However, if any system can be interpreted as running every programme, everysystems has the self-observation property, if interpretedt he right way. IOW, one you introduce interpretation-dependence, you can't get away from it. That's right: if there is at least one physical system, then every computation is implemented, although we can only interact with them at our level if they are implemented on a conventional brain or computer, which means we have the means to interpret them at hand. The non-conscious computations are there in the trivial sense that a block of marble contains every possible statue of a given size. All the computations are merely potential, in the absence of interpreters and dictionaries, whether conscious or not. The conscious computations, on the other hand, are there and self-aware Not really. They are just possibilities. even though we cannot interact with them, just as all the statues in a block of marble would be conscious if statues were conscious and being embedded in marble did not render them unconscious. But that gets to the heart of the paradox. You are suggesting that conscious computations are still conscious even thought hey don't exst and are mere possiiblities! That is surely a /reductio/ of one of your premisses A non-conscious computation cannot be *useful* without the manual/interpretation, and in this sense could be called just a potential computation, but a conscious computation is still *conscious* even if no-one else is able to figure this out or interact with it. If a working brain in a vat were sealed in a box and sent into space, it could still be dreaming away even after the whole human race and all their information on brain function are destroyed in a supernova explosion. As far as any alien is concerned who comes across it, the brain might be completely inscrutable, but that would not make the slightest difference to its conscious experience. Suppose the aliens re-implanted the brain in a human body so they could interact with it. They ask it what is was dreaming all those years? I think the answer might be, Years? What years? It was just a few seconds ago I was in the hospital for an appendectomy. What happened? And who are you guys? then it can be seen as implementing more than one computation simultaneously during the given interval. AFAICS that is only true in terms of dictionaries. Right: without the dictionary, it's not very interesting or relevant to *us*. If we were to actually map a random physical process onto an arbitrary computation of interest, that would be at least as much work as building and programming a conventional computer to carry out the computation. However, doing the mapping does not make a difference to the *system* (assuming we aren't going to use it to interact with it). If we say that under a certain interpretation - here it is, printed out on paper - the system is implementing a conscious computation, it would still be implementing that computation if we had never determined and printed out the interpretation. And if you added the random values of the physical process as an appendix in the manual, would the manual itself then be a computation (the record problem)? If so how would you tell if it were a conscious computation? The problem remains that the system's own self awareness, or lack thereof, is not observer-relative. something has to give. Self-awareness is observer-relative with the observer being oneself. Where is the difficulty? Self-awareness is awareness of some specific aspect of a construct called myself. It is not strictly reflexive awareness of the being aware of being aware... So in the abstract computation it is just this part of a computation having some relation we identify as awareness relative to some other part of the computation. I think it is a matter of constructing a narrative for memory in which I is just another player. Brent Meeker --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: The Mathematico-Cognition Reality Theory (MCRT) Ver 6.0
[EMAIL PROTECTED] wrote: ... Different levels of Causality Brain processes are enacting things which are *mathematical* in nature - 'algorithms' (See 'Functionalism').Mathematical entities are abstracted patterns. But abstracted patterns themselves (like 'algorithms') don't exist directly inside physical causal networks, only particular instances of them do. This is clear by pointing to the fact that many different brains could enact the *same* computation (algorithm) - the philosophical term is that the algorithm is 'multiply realizable'.So the particular physical processes in the brain can't be *identical* to the mathematical entity (the algorithm) itself. But is it true that different brains can implement the same algorithm? It seems it is only true because we abstract a certain algorithm from it's various representation, e.g. as written on paper. Every actual realization, in brains or computer or on paper is actually slightly different at a microscopic level at least. We call it the same algorithm because we're abstracting a common functionality or purpose. It was an argument similar to this that led to the demise of the original 'Identity Theory' of mind (a theory which attempted to identity mental states with physical processes). Again, the trouble is that many different brain states could be associated with the *same* algorithm (or have the same mental states) which shows that physical processes cannot be identified with mathematical entities in any simple way. But this only shows that mathematical objects exist in the sense that chair exists; as a abstraction from chairs. So chair isn't identical with any particular chair. The weaker 'Token Identity' theories concede this, but still attempt to equate mental states with physical processes. Couldn't one simply say that there's some general high-level properties of physical matter which can be equated with the algorithm, and hence dispense with ghostly mathematical entities? The reason one can't really say this boils down to Occam's razor and inference to the best explanation again. Attempting to replace the concept of 'algorithm' with some high level properties of physical matter is results in descriptions that are enormously complex and unwieldy. But you can look at it the other way around. The algorithm is already the general high-level property that is common to all the brains and computers implementing. The Mathematico-Cognition Ontology This looks more like botany than ontology. Brent Meeker --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
