Re: Russell's book + UD*/strings
Le 26-sept.-06, à 16:03, Russell Standish a écrit : I would say also that interpretations could be inconsistent, ? ? ? I guess you are using the word interpretation in some non standard way. It would help us, and you, if you could work on a glossary. but perhaps there is not much difference between interpretation and theory. Would you say There is a red flower is a theory, or merely an interpretation of an image? It could be a theory, ... then if you interpret the word red by the adjective green with its usual meaning, and the word flower by inhabitant of the planet mars, then the interpretation of there is a red flower is a correct theory with respect to realities where there are green inhabitant on Mars, and incorrect in the realities where there are no green inhabitant on Mars. In that sense there is a red flower can be seen as a theory. I assume here that there is is borrowed from a classical logic in the background. If it were possible to view the entire Nothing, ? it would be an inconsistent interpretation. However it is not so possible, and indeed it may be true that it is impossible to have an inconsistent interpretation (I do not assert this however). I think it would be helpful to use the standard meaning of those term, or at least, to define them precisely if you use them in some other sense. Indeed - however we do have a difference in emphasis. Yours is towards more formal models, but with obscure modeling relations, My emphasis is on machine which are formal by construction, and the obscure modeling relation are old and new theorems in mathematical logic. It is just applied mathematics. The modelling relations are strange and mysterious, but this is just because Godel and Lob theorems are somehow themselves strange and mysterious. But is this 1-3 distinction implicit within your statement of COMP? I'm not sure that it is. I think it is, and the following quote makes me thing you believe this too, at least in the quantum framework, when you say: Collapse is conceived of as a physical process, and as such is problematic. Nonphysical collapse is just the 1 POV of the Multiverse. That's all I'm talking about. It is not new, it underlies all of Chapter 2 of my book, and also of Why Occams Razor. Perhaps I'm guilty of assuming it without explicitly stating it, but by way of challenge can you give me a piece of knowledge that doesn't come in the form of a string? Knowledge comes from third person finite strings, with a measure determined by *some* infinite strings (the non halting immaterial computations) generating them. It is certainly hard, given we live on the opposite sides of a digital world - a record of a telephone conversation we have will be a a string of bits, as will any emails we use, any my book left my hands in the form of a string of bits and so on. OK, but that are finite strings conceived and manipulated (by your computer and your brain with some high level comp assumption) as numbers. Most test editor manipulate a structure of finite strings together with a concatenation or substitution structure. Again this is infinitely richer that your set of all infinite strings. I use the usual one (excluded middle), and I don't use any infinity axiom that I'm aware of. Now I am very confused. I thought you were assuming infinite strings. A glossary would really help, I am not sure you are not changing the meaning of your term from paragraph to paragraph. Yes - I appreciate the ontological difference. I would say that only Nothing exists (in ontological meaning). Strings and sets of strings only exist in the same sense that the number 1 exists. This contradict the definition of Nothing you gave us. I could elaborate a lot about the vagueness of the notion of finding something in the UD* (the infinite complete running of the UD). I could ask finding by who?, from inside? from the terrestrial (verifiable) view or the divine one (true but non verifiable)?, from which x-person point of view? Etc. Given that the UD cannot not dovetail on all the reals, there is a sense in saying all the infinite strings are generated, but this gives a noisy background first person machine have to live with. The UD is not equivalent with all infinite strings, the UD* is a static given of all computations. Those computations can be represented by very peculiar finite and infinite strings together with a non trivial structure inherited from computer science/number theory. About the only difference I see is that the measure might be different... And that *is* the key issue, I think. I more or less always assumed this. Either COMP is more specialised (you can derive some my postulates from COMP, and others are compatible with it), or COMP is the only way of deriving these same postulates, or COMP in some way contradicts these postulates. As you admit yourself there is a lot of work to get enough precision in
Re: Russell's book + UD*/strings
On Fri, Sep 29, 2006 at 11:46:20AM +0200, Bruno Marchal wrote: Le 26-sept.-06, à 16:03, Russell Standish a écrit : I would say also that interpretations could be inconsistent, ? ? ? I guess you are using the word interpretation in some non standard way. It would help us, and you, if you could work on a glossary. Interpretation of something means meaning an observer attaches to something. Is this nonstandard? I wouldn't have thought so. Indeed - however we do have a difference in emphasis. Yours is towards more formal models, but with obscure modeling relations, My emphasis is on machine which are formal by construction, and the obscure modeling relation are old and new theorems in mathematical logic. It is just applied mathematics. The modelling relations are strange and mysterious, but this is just because Godel and Lob theorems are somehow themselves strange and mysterious. But so are your postulates, for example the Theatetus notion of knowledge is far from obvious. I can follow the logic as a formal system, but I struggle to make sense of it (interpret it). But is this 1-3 distinction implicit within your statement of COMP? I'm not sure that it is. I think it is, and the following quote makes me thing you believe this too, at least in the quantum framework, when you say: Collapse is conceived of as a physical process, and as such is problematic. Nonphysical collapse is just the 1 POV of the Multiverse. That's all I'm talking about. But I have an explicit 1-3 distinction in the format of my PROJECTION postulate, and that quoted statement is taken in that context. Obviously I have no objection to the 1-3 distinction, but I failed to see how it follows explicitly from AR+CT+YD, or even from I am a machine (in the Turing sense). It is not new, it underlies all of Chapter 2 of my book, and also of Why Occams Razor. Perhaps I'm guilty of assuming it without explicitly stating it, but by way of challenge can you give me a piece of knowledge that doesn't come in the form of a string? Knowledge comes from third person finite strings, with a measure determined by *some* infinite strings (the non halting immaterial computations) generating them. But finite strings are just sets of infinite strings. It is certainly hard, given we live on the opposite sides of a digital world - a record of a telephone conversation we have will be a a string of bits, as will any emails we use, any my book left my hands in the form of a string of bits and so on. OK, but that are finite strings conceived and manipulated (by your computer and your brain with some high level comp assumption) as numbers. Most test editor manipulate a structure of finite strings together with a concatenation or substitution structure. Again this is infinitely richer that your set of all infinite strings. No - sets have subsets, and all finite strings can be found as a subset of the set of all infinite strings. I use the usual one (excluded middle), and I don't use any infinity axiom that I'm aware of. Now I am very confused. I thought you were assuming infinite strings. A glossary would really help, I am not sure you are not changing the meaning of your term from paragraph to paragraph. You introduced the term infinity axiom. If by a infinity axiom you mean the existence of infinite strings, or the existence of infinite sets, then yes I have an infinity axiom. Yes - I appreciate the ontological difference. I would say that only Nothing exists (in ontological meaning). Strings and sets of strings only exist in the same sense that the number 1 exists. This contradict the definition of Nothing you gave us. The set of all strings is a model of the Nothing (or equivalently the Everything). It is meant to be the ultimate model, capturing all that is possible to know about it. About the only difference I see is that the measure might be different... And that *is* the key issue, I think. I more or less always assumed this. Either COMP is more specialised (you can derive some my postulates from COMP, and others are compatible with it), or COMP is the only way of deriving these same postulates, or COMP in some way contradicts these postulates. As you admit yourself there is a lot of work to get enough precision in your approach to compare it with the consequence of the computationalist hypothesis. As I do have a lot of work to compare the comp-physics with the experimental physics. Yes - in that respect, my work ties more closely to physics. However, there is a distinct difference between my string ensemble and Schmidhuber's speed prior one, particularly with respect to randomness. Sometimes I define strong comp by saying yes to the doctor, and weak comp by accpetoing your child marry someone who has say yes to the doctor. Surely you have an opinion on that, no? To be quite frank,
Russell's book + UD*/strings
Hi Russell, I got your book. Congratulation for that very nice introduction to the subject and to your ideas. It is a very gentle and lovely book. Probably because you are to kind to your audience, it seems to me you have sacrifice perhaps a bit of rigor. I am still not sure about your most basic assumption, but I see we share a big amount of the philosophy. I am already glad you did take into account 1/5 of my earlier remarks, I wish you at least five next editions ;-). To be honest I don't think you really get the comp idea, and it is a good think your work does not really rely on it. Now I will not hide the pleasure I have when seeing the 8 hypostases (even the sixteen one!) sum up through their modal logic in table 71 page 129. I will neither repeat my olds comments nor make new one, but hope our future discussion will give opportunities to clarify the possible misunderstandings and relationship between our approaches. I let you know that I will be very busy from now until end of october, so that I will be more slow for the comments' replies (or more grave for the spelling mistakes if that is possible). == Russell wrote On Sun, Sep 24, 2006 at 03:23:44PM +0200, Bruno Marchal wrote: Le 23-sept.-06, ˆ 07:01, Russell Standish a Žcrit : Anything provable by a finite set of axioms is necessarily a finite string of symbols, and can be found as a subset of my Nothing. You told us that your Nothing contains all strings. So it contains all formula as theorems. But a theory which contains all formulas as theorems is inconsistent. I am afraid you confuse some object level (the strings) and theory-level (the theorems about the strings). Actually, I was wondering if you were making this confusion, owing to the ontological status you give mathematical statements. The Nothing, if interpreted in its entirety, This can make sense only if you tell us how to interpret a string or how you interpret the Nothing, I mean formally. From this I infer that your nothing is an informal theory of infinite strings. Also I give only ontological status to object in the scope of an arithmetical existential statement. For example I do believe in the existence of prime numbers. must be inconsistent, of course. Only a theory can be inconsistent. But I don't see a theory. Our reasoning about it need not be, and certainly I would be grateful for anyone pointing out inconsistencies in my writing. That is why I would insist to be as clear as possible so that the inconsistencies are more easy to find. Perhaps the exchange is unfair because I react as a professional logician, and you try to convey something informally. But I think that at some point, in our difficult subject, we need to be entirely clear on what we assume or not especially if you are using formal objects, like strings. I'm not that informal. What I talk about are mathematical objects, and one can use mathematical reasoning. The formal/informal distinguo has nothing to do with the mathematical/non-mathematical distinguo. Nor with rigorous/non-rigorous. 100 % of mathematics, including mathematical logic is informal. Now, logicians studied formal theories or machines because it is what they are studying. But they prove things about formal systems in an informal way like any scientist. In some context formal and informal are relative. Of course a description of a formal system looks formal, but we reason *about* those formal systems. Now, if your strings are all there is, I wait for an explanation of what those strings does formally, but I am not asking to formalize your reasoning in your string-language, unless for illustrative purpose in case you want to illustrate how a string interprets something. Like we can explain how a brain or more simply how a turing machine can interpret some data. To be sure, given that your strings are infinite I have no clue how the strings can interpret things. I should note that the PROJECTION postulate is implicit in your UDA when you come to speak of the 1-3 distinction. I don't think it can be derived explicitly from the three legs of COMP. I'm afraid your are confusing the UDA, which is an informal (but rigorous) argument showing that IF I am digitalisable machine, then physics or the laws of Nature emerge and are derivable from number theory, and the translation of UDA in arithmetic, alias the interview of a universal chatty machine. The UDA is a reductio ad absurdo. It assumes explicitly consciousness (or folk psychology or grandma psychology as I use those terms in the SANE paper) and a primitive physical universe. With this, the 1-3 distinction follows from the fact that if am copied at the correct level, the two copies cannot know the existence of each other and their personal discourse will differentiate. This is an illusion of projection like the wave packet *reduction* is an illusion
Re: Russell's book + UD*/strings
On Tue, Sep 26, 2006 at 04:10:32PM +0200, Bruno Marchal wrote: Hi Russell, I got your book. Congratulation for that very nice introduction to the subject and to your ideas. It is a very gentle and lovely book. Probably because you are to kind to your audience, it seems to me you have sacrifice perhaps a bit of rigor. I am still not sure about your most basic assumption, but I see we share a big amount of the philosophy. I am already glad you did take into account 1/5 of my earlier remarks, I wish you at least five next editions ;-). That's a bit like the old chinese curse - I wish you live in interesting times! To be honest I don't think you really get the comp idea, and it is a good think your work does not really rely on it. It is true that my work is an independent line of work, but probably related. I am interested in the connections, however. Now I will not hide the pleasure I have when seeing the 8 hypostases (even the sixteen one!) sum up through their modal logic in table 71 page 129. I will neither repeat my olds comments nor make new one, but hope our future discussion will give opportunities to clarify the possible misunderstandings and relationship between our approaches. Indeed. I let you know that I will be very busy from now until end of october, so that I will be more slow for the comments' replies (or more grave for the spelling mistakes if that is possible). == This can make sense only if you tell us how to interpret a string or how you interpret the Nothing, I mean formally. Interpretation is by an observer. Formally, the observer is a map from a string to an integer. To understand why the observer is such a formal object requires informal modelling talk, obviously. From this I infer that your nothing is an informal theory of infinite strings. It is a mixture of both. The formal part is not so interesting, but necessary to get some interesting conclusions. Also I give only ontological status to object in the scope of an arithmetical existential statement. For example I do believe in the existence of prime numbers. Whereas I think the whole notion of existence is highly dubious. :) must be inconsistent, of course. Only a theory can be inconsistent. But I don't see a theory. I would say also that interpretations could be inconsistent, but perhaps there is not much difference between interpretation and theory. Would you say There is a red flower is a theory, or merely an interpretation of an image? If it were possible to view the entire Nothing, it would be an inconsistent interpretation. However it is not so possible, and indeed it may be true that it is impossible to have an inconsistent interpretation (I do not assert this however). Our reasoning about it need not be, and certainly I would be grateful for anyone pointing out inconsistencies in my writing. That is why I would insist to be as clear as possible so that the inconsistencies are more easy to find. Indeed - however we do have a difference in emphasis. Yours is towards more formal models, but with obscure modeling relations, whereas I prefer to spend more effort on the modeling relation than with the formal content (the formal content of my ideas are small, no doubt why you are disappointed!) In that respect, I am more the physicist, and you the mathematician. :) Perhaps the exchange is unfair because I react as a professional logician, and you try to convey something informally. But I think that at some point, in our difficult subject, we need to be entirely clear on what we assume or not especially if you are using formal objects, like strings. I'm not that informal. What I talk about are mathematical objects, and one can use mathematical reasoning. The formal/informal distinguo has nothing to do with the mathematical/non-mathematical distinguo. Nor with rigorous/non-rigorous. 100 % of mathematics, including mathematical logic is informal. Now, logicians studied formal theories or machines because it is what they are studying. But they prove things about formal systems in an informal way like any scientist. Well, yes - we probably are using the word formal differently then. For me, a formal system is a mathematical system with the modelling relation thrown away. Triangles without trangular shaped paddocks for example. In some context formal and informal are relative. Of course a description of a formal system looks formal, but we reason *about* those formal systems. Now, if your strings are all there is, I wait for an explanation of what those strings does formally, but I am not asking to formalize your reasoning in your string-language, unless for illustrative purpose in case you want to illustrate how a string interprets something. Like we can explain how a brain or more simply how a turing machine can interpret some data.
