Re: Lobian Machine
The original source is the paper by M. H. Loeb (also written Lob or Löb) LÖB M. H., 1955, Solution of a Problem of Leon Henkin, Journal of Symbolic Logic, 20, pp. 115-118. A good introductory book is: SMULLYAN R., 1987, Forever Undecided, Alfred A. Knopf, New York. Good textbooks on Mathematical Logic usually prove the theorem of Lob, like: MENDELSON E., 1987, Introduction to Mathematical Logic, 3ème édition, Wadsworth & brooks/Cole. See also my Sane paper for more reference and an introduction to lobian machines/theories/entities: http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.htm Bruno Le 27-févr.-06, à 20:28, Jad a écrit : > Hello, > > Could you please refer me to sources of information on the "Lobian > Machine" ? > > Greets, > Jad > > 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: RE Lobian Machine
On 03/01/2006, at 1:15 PM, Russell Standish wrote: Thanks for your vote of confidence Kim, but sadly I am not attempting to write a "laypersons" guide to the subject. Stephen Hawking did that for cosmology in "Brief History of Time", which in my opinion is a heroic failure. It is very well written, and avoids the use of terminology (eg maths) unfamiliar with laypeople, but - sadly as a consequence fails to educate anyone. Well - if it's any consolation, I find "Theory of Nothing" way, way easier to grasp than BHoT which I read hungrily when it first appeared. A heroic failure indeed; I don't even find it very well written. I was unable to locate anyone at the time who could understand it either so gave up trying. Many authors have tackled the same subject matter since with a much higher degree of readability and explanatory power. Rather I'm trying put things together at a level that people on this list might understand, its a sort of least common denominator of the various disciplines involved - computer science, physics, maths, biology, cognitive science and dare I say philosophy. I picked for reference the sort of mathematical/scientific understanding I had achieved in year 11/12 of high school. This is not to say that your average year 11/12 student will be able to manage this, but I'm hoping that most of my intended audience can manage that level of logical thought, that is, that anyone interested in the topic can, with some effort perhaps, understand the material. Sad to say, I doubt that the general public will ever get it. Of course - you simply cannot and should not try to simplify it beyond a certain point. Otherwise it comes across as a bunch of hocus- pocus. That's what I like about it - you have struck the hoped-for balance between technical exposition and verbal summing-up (at least for me). Perhaps this subject can get the Hawking BHoT treatment in due course, but we're probably at least a decade or two away from that. If, as DD argues, quantum computation should be available in about a decade, should we not try to accelerate the pace of public education in this field so that the intellectual terrain is prepared a little in advance, so to speak? Unless people generally have some grasp of multiverse theory, q comp is going to appear like magic. We don't want people turning this thing into a religion, do we? On your music point, have you read "Goedel, Escher, Bach" by Hofstadter? I've just finished reading it, and wondered why I didn't read this gem 2 decades ago. It is full of musical references, so you will appreciate it. I mentioned this one to you a while back; I'm ready to re-read it now that I understand better the impact of Goedel's Incompleteness theorems (thanks mainly to the exploration of these by the very fine writers on this list). One thing is for sure, Hofstadter does approach my notion of a "musical object" spinning in its own space. I simply ask - where is this space? Probably in my head. Without necessarily talking about triangle land and blue mists of probability over Platonia a la Barbour, I have always had the firmest impression that musical statements are solid objects in some sense. That alone prompts me to seek some discussion on this point. Is music a description of a thing or is it the thing itself? Certainly no musician is able to answer that point unaided speaking from the standpoint of the "laws" of music alone - whence my bringing the notion to the rather broader field of discussion that this list allows. Probably this is simply too wayward a notion; I'm happy to be taken apart and criticised by other thinkers (I already have been, roundly) but I reject out of hand the supercilious verbal sneers about "pseudomathematical nonsense". cheers, Russ email 1: [EMAIL PROTECTED] email 2: [EMAIL PROTECTED] 9327 9492 (w) 9389 4239 (h) 0431 994 736 (m)
Re: RE Lobian Machine
On Sat, Dec 31, 2005 at 05:03:43PM +1100, Kim Jones wrote:
>
> There will come a time very soon when all of this comp stuff will
> need to be translated into terms the LAYman can understand easily.
> Russell Standish has already made the attempt. I appreciate gratly
> his attempt. Stop wanking off that mathematics is the ONLY script in
> which reality is encoded. It could well turn out to be music.
>
> Somebody (with enough musical understanding) prove me wrong
>
> Kim Jones
>
Thanks for your vote of confidence Kim, but sadly I am not attempting
to write a "laypersons" guide to the subject. Stephen Hawking did that
for cosmology in "Brief History of Time", which in my opinion is a
heroic failure. It is very well written, and avoids the use of terminology
(eg maths) unfamiliar with laypeople, but - sadly as a consequence
fails to educate anyone.
Rather I'm trying put things together at a level that people on this
list might understand, its a sort of least common denominator of the
various disciplines involved - computer science, physics, maths,
biology, cognitive science and dare I say philosophy. I picked for
reference the sort of mathematical/scientific understanding I had
achieved in year 11/12 of high school. This is not to say that your
average year 11/12 student will be able to manage this, but I'm hoping
that most of my intended audience can manage that level of logical
thought, that is, that anyone interested in the topic can, with some
effort perhaps, understand the material. Sad to say, I doubt that the
general public will ever get it.
Perhaps this subject can get the Hawking BHoT treatment in due course,
but we're probably at least a decade or two away from that.
On your music point, have you read "Goedel, Escher, Bach" by
Hofstadter? I've just finished reading it, and wondered why I didn't
read this gem 2 decades ago. It is full of musical references, so you
will appreciate it.
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 8308 3119 (mobile)
Mathematics0425 253119 (")
UNSW SYDNEY 2052 [EMAIL PROTECTED]
Australiahttp://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
pgpqzubip8Zkg.pgp
Description: PGP signature
Re: Lobian Machine
Stathis, All I have to do is to use Godel second incompleteness theorem to prove that the psychiatrist cannot be sure of his own sanity. We'll have to assume that the psychiatrist can follow a mathematical argument. And if he doesn't I'll just go to the local university math department to back me up. The psychiatrist will then be forced either to lock up the whole math department or to accept what they say. Once the psychiatrist is convinced that he may not be sane himself, it'll be a piece of cake to convince him to take antipsychotic drugs. And maybe at this point he'll really go crazy and leave me alone. :-) I bet you never had to deal with patients as wily as me. Aye, there is method in my madness! :-P George Stathis Papaioannou wrote: George Levy writes: Bruno Marchal wrote: Godel's result, known as Godel's second incompleteness theorem, is that no consistent machine can prove its own consistency: IF M is consistent then M cannot prove its consistency Bruno, After I read your email, we had a gathering of family and friends, and my head being full of the subject of this post. I wanted to test the idea of Godel's second incompleteness theorem on the average people just to see how they would respond. I found the right place in the discussion to insert the paraphrase: If I am sane, it is impossible to know for sure that I am sane. This povoked some hilarity, especially with my kids (young adults) who probably view me as some kind of nutty professor. While this statement is mathematically true, it was not considered serious by the people I was talking with. I guess that the average human has no doubt about his own sanity.(But my kids had some doubts about mine) One way to prove that you are crazy is to assert that you are sane. This means that the average human is crazy! :-) "If I am sane, it is impossible to know for sure that I am sane." Everybody believes he is sane, whether he is sane or not, and nobody can prove he is sane. In psychiatry, this is the key problem with delusions. If it were possible in general to prove one's own sanity, then deluded patients, who more often than not retain their ability to think logically, would be able to demonstrate to themselves that they were deluded. But by definition of a delusion, this is impossible. If you want to know what it is like for a psychotic patient to have forced treatment, imagine that people from the local psychiatric facility knock on your door tonight and, after interviewing you, politely explain that your belief that you are an engineer, married with adult children, own the house you are living in and the car in the driveway, and so on, is actually all a systematised delusion. All the evidence you present to show you are sane is dismissed as part of the delusion, and all the people you thought you could trust explain that they agree with the psychiatric team. You are then invited to start taking an antipsychotic drug which, over time, will rectify your deranged brain chemistry so that you come to understand that your current beliefs are delusional. If you refuse the medication, you will be taken to the psychiatric ward with the help of police, if necessary, where you will again be offered medication, perhaps in injection form if you continue to refuse tablets. Frightening, isn't it? Stathis Papaioannou _ Express yourself instantly with MSN Messenger! Download today - it's FREE! http://messenger.msn.click-url.com/go/onm00200471ave/direct/01/
Re: Lobian Machine
Stathis, Yes, it is frightening, especially since (I think) I am an "engineer, married with adult children, own the house you are living in and the car in the driveway, and so on." That is a vivid description. But even as I am being hauled away to the psychiatric ward, can I not logically cling to at least one belief? According to Wikipedia, Rene Descartes said, "But I have convinced myself that there is absolutely nothing in the world, no sky, no earth, no minds, no bodies. Does it now follow that I too do not exist? No: if I convinced myself of something [or thought anything at all] then I certainly existed. But there is a deceiver of supreme power and cunning who is deliberately and constantly deceiving me. In that case I too undoubtedly exist, if he is deceiving me; and let him deceive me as much as he can, he will never bring it about that I am nothing so long as I think that I am something. So, after considering everything very thoroughly, I must finally conclude that the proposition, I am, I exist, is necessarily true whenever it is put forward by me or conceived in my mind." (AT VII 25; CSM II 16–17) Norman ~~ "If I am sane, it is impossible to know for sure that I am sane." Everybody believes he is sane, whether he is sane or not, and nobody can prove he is sane. In psychiatry, this is the key problem with delusions. If it were possible in general to prove one's own sanity, then deluded patients, who more often than not retain their ability to think logically, would be able to demonstrate to themselves that they were deluded. But by definition of a delusion, this is impossible. If you want to know what it is like for a psychotic patient to have forced treatment, imagine that people from the local psychiatric facility knock on your door tonight and, after interviewing you, politely explain that your belief that you are an engineer, married with adult children, own the house you are living in and the car in the driveway, and so on, is actually all a systematised delusion. All the evidence you present to show you are sane is dismissed as part of the delusion, and all the people you thought you could trust explain that they agree with the psychiatric team. You are then invited to start taking an antipsychotic drug which, over time, will rectify your deranged brain chemistry so that you come to understand that your current beliefs are delusional. If you refuse the medication, you will be taken to the psychiatric ward with the help of police, if necessary, where you will again be offered medication, perhaps in injection form if you continue to refuse tablets. Frightening, isn't it? Stathis Papaioannou
Re: Lobian Machine
George Levy writes: Bruno Marchal wrote: Godel's result, known as Godel's second incompleteness theorem, is that no consistent machine can prove its own consistency: IF M is consistent then M cannot prove its consistency Bruno, After I read your email, we had a gathering of family and friends, and my head being full of the subject of this post. I wanted to test the idea of Godel's second incompleteness theorem on the average people just to see how they would respond. I found the right place in the discussion to insert the paraphrase: If I am sane, it is impossible to know for sure that I am sane. This povoked some hilarity, especially with my kids (young adults) who probably view me as some kind of nutty professor. While this statement is mathematically true, it was not considered serious by the people I was talking with. I guess that the average human has no doubt about his own sanity.(But my kids had some doubts about mine) One way to prove that you are crazy is to assert that you are sane. This means that the average human is crazy! :-) "If I am sane, it is impossible to know for sure that I am sane." Everybody believes he is sane, whether he is sane or not, and nobody can prove he is sane. In psychiatry, this is the key problem with delusions. If it were possible in general to prove one's own sanity, then deluded patients, who more often than not retain their ability to think logically, would be able to demonstrate to themselves that they were deluded. But by definition of a delusion, this is impossible. If you want to know what it is like for a psychotic patient to have forced treatment, imagine that people from the local psychiatric facility knock on your door tonight and, after interviewing you, politely explain that your belief that you are an engineer, married with adult children, own the house you are living in and the car in the driveway, and so on, is actually all a systematised delusion. All the evidence you present to show you are sane is dismissed as part of the delusion, and all the people you thought you could trust explain that they agree with the psychiatric team. You are then invited to start taking an antipsychotic drug which, over time, will rectify your deranged brain chemistry so that you come to understand that your current beliefs are delusional. If you refuse the medication, you will be taken to the psychiatric ward with the help of police, if necessary, where you will again be offered medication, perhaps in injection form if you continue to refuse tablets. Frightening, isn't it? Stathis Papaioannou _ Express yourself instantly with MSN Messenger! Download today - it's FREE! http://messenger.msn.click-url.com/go/onm00200471ave/direct/01/
Re: RE Lobian Machine
Kim, I tried to stay out of this line which produced a level of vulgarity I never experienced on a civilized list (not that it disturbs me, but it is a very low scientific argumentation IMO). Also I apologize if I mix your words with Jose's, those > and >> lines are perplexing sometimes. Hard to tell who quotes whom. * I started to play (classical) music in 1927 - mostly piano. I kept up with it while doing natural science (R&D) for ~ 50 years . As a still performing musician I try to respond to your challenge: Music does not represent 'reality', although it is part of it (as Stephen said: maybe an infinitesimal part). It happens within a different "plane" from mathematics (incl. emotional), it has allowences you would never condone in math, it has emotional motives what are disallowed in math-discipline. True, you need to have learned to 'know' music, but "understanding" it means: you are not a musicioan, rather a musical scientist. Different performers can play the same piece so differently that a mathematical-type mutual coverage is out. Physics or computer sci can catch the technicalities, not "the music". So I would not formulate into the 'total' from a minuscule part. Especially not if that part is not entirely 'part' of that so called total, which is only a model (topically etc. identified and limited). Art moves in qualia different from mathematically identified?able rationalized aspects of pour logical domains. Besides: music (as we know the western artform) is decaying to nonexistence after its 3-4 centuries in the European culture. Would you include the African drums, the Oriental 1/4-tone tunes, the "native American" hummings etc. in your term of "music"? John M --- Kim Jones <[EMAIL PROTECTED]> wrote: > So apparently those who do not scale the dizzying > heights of > metamathematics have no hope of understanding > reality? > > Try again, Jose. > > Try MUSIC > > Music is a form of mathematics which I DO > understand. I wonder how > many great mathematicians on this list have an > understanding of the > structure of that little piece of Platonia? I am > trying to see the > link between this and metamathematics. Some people > have agreed > (privately) with me that there is a link. I am not a > mathematician, > true. For that reason I make no attempt to deal with > this language > but use the musician's intuitive feeling for reality > which is highly > refined in terms of my own 1st person experience. > > There will come a time very soon when all of this > comp stuff will > need to be translated into terms the LAYman can > understand easily. > Russell Standish has already made the attempt. I > appreciate gratly > his attempt. Stop wanking off that mathematics is > the ONLY script in > which reality is encoded. It could well turn out to > be music. > > Somebody (with enough musical understanding) prove > me wrong > > Kim Jones > > > > On 31/12/2005, at 12:45 PM, Jose Ramón Brox wrote: > > > > > - Original Message - > > From: "Kim Jones" <[EMAIL PROTECTED]> > > > > > > > > That was a real bit of pure pseudomathematical > nonsense > > > > Jose Brox > >
Re: RE Lobian Machine
Stephen, thanks. To add: mathematical 'ways' (I tried to use a most generalized term) are products of our any (human, of course) logic, WE humans developed and try to squeeze ALL nature into it. Probably: disregarding what does not fit (or: whatever we - so far - did not discover of the world). We don't know how truly infinitesimal our 'perceived reality' is. Looking back into human mental development, new domains, aspects, directions emerge all the time and we have no indication that we are close to any completion of our knowledge-base. Applied math serves every level and mishap faithfully (from the Flat Earth, Newton, Relativity , QM and beyond.) Even nonquanti math cannot be trusted: it is also a tool for the human ways of thinking. Let us be happy with whatever we learned and do not make it more than what it is. Kim's: > ...I will say that without mathematical (not methamatematical) >knowledge, one cannot aspire > to understand reality (in the terms a physic understand it)< The parenthesized ending sais it all, even grammatically corrected I could paraphrase it: within the 'one plane model' of math. No qualia like "emotional" etc. no aspatial - atemporal aspects. John M --- Stephen Paul King <[EMAIL PROTECTED]> wrote: > Hello All, > > Pardon the comment, but is it not obvious to all > that Mathematics is a > realm of which faithful representations of our > Physical universe span an > infinitesimal portion? Even those of us that do not > swallow the sweet Blue > Pill of Platonia can see this. ;-) > > Onward! > > Stephen > - Original Message - > From: "Jose Ramón Brox" <[EMAIL PROTECTED]> > To: > Sent: Saturday, December 31, 2005 1:17 AM > Subject: RE Lobian Machine > > > > - Original Message - > > From: "Kim Jones" <[EMAIL PROTECTED]> > > > > > >>So apparently those who do not scale the dizzying > heights of > >>metamathematics have no hope of understanding > reality? > > > > I never said that, but you simply can't take a > theorem about a specific > > area, that is true > > within a context and take it out from that context > to try to use it "in > > reality", to > > "give" social explanations. That's what > pseudoscience do. > > > > I will say that without mathematical (not > methamatematical) knowledge, one > > cannot aspire > > to understand reality (in the terms a physic > understand it). > > > >>There will come a time very soon when all of this > comp stuff will > >>need to be translated into terms the LAYman can > understand easily. > >>Russell Standish has already made the attempt. I > appreciate gratly > >>his attempt. Stop wanking off that mathematics is > the ONLY script in > >>which reality is encoded. It could well turn out > to be music. > > > > You are thinking it the other way around - the > incorrect one. Music is a > > small, small part > > of physics, and therefore, it's represented by a > (quite simple) > > mathematical model. > > Reality is more complex than that model, and other > aspects of reality can > > be modelled by > > math different from the one used in the music > model, so the reality can't > > turn out to be > > music in that sense. > > > > Well, I'm speaking about the mechanical phenomena > of music, that are > > simple, not about the > > way our brains interpret it, that can be quite > complex and enjoyable > > (that's why we say > > it's an art). > > > > Jose > >
RE Lobian Machine
- Original Message - From: "Stephen Paul King" <[EMAIL PROTECTED]> Hello All, Pardon the comment, but is it not obvious to all that Mathematics is a realm of which faithful representations of our Physical universe span an infinitesimal portion? Even those of us that do not swallow the sweet Blue Pill of Platonia can see this. ;-) Onward! Well, I'm not sure if this is obvious or not, I'm sure it _seems_ obvious, but for me something is obvious when "a correct proof comes automatically to mind" and that's not the case for me with one of the parts: I'm quite sure there are parts of math that do not model nothing phsyical and will never do (math is not a subset of physics), but not really "sure" about the converse, if physics is a subset of math (i.e., that all physical phenomena can be mathematically modelled): I believe in it, though, the foundation of science implicitly implies to believe in it, and all the evidence we have point in that direction. But I don't manage to grasp exactly what relation has your comment with the subject discussed. I've been staying up all night, so probably it's my fault :-) Regards. Jose Brox
Re: RE Lobian Machine
Thank you Jose, for your slightly more civilised approach to my (admittedly) provocative thought about music's relation to our discussion on this list. Many people would argue (Edward de Bono as a primary example) that the whole meaning of any artistic product is the meaning that our minds bring to bear on it, whatever the author says. If that is "true" then the whole of art is a 1st person experience and cannot be reduced to anything else. I take it that we are investigating the ultimate mystery of 1st person experience (amongst other things) here. My point of view on that is surely as valid as yours since neither you nor I can appreciate (ie experience) each other's experience of anything. I feel that a little provocation from an "outsider" would actually help the discussion find new and fertile terrain - this is called lateral thinking. If you reject without some form of investigation the notion that music is encoded mathematical reality then I feel very sad for you. Many musicaians have striven to understand the link between music and mathematics. You cannot "play" a quadratic equation on your piano. Yet you can appreciate a melody by Mozart or a guitar break by Joe Satriani in JUST THE SAME WAY that you experience the elegance of a mathematical sentence. Do not physicists and mathematicians have a certain feeling for "elegance" and "symmetry" Is it not at least slightly interesting that composers and other artists strive for something like that as well? What if we are all talking the same language but simply don't have the intellectual grunt to PERCEIVE that? Notating music is a very simple problem for a computer to solve, admittedly. Composing music is a very controversial problem that people are trying to enlist the help of machines to solve at this time. UNDERSTANDING music takes a n EDUCATION in it. Just like understanding math requires a solid grounding in that discipline. Do not undedrestimate the power of the simple. There is a lot of talk on this list about complexity but I have had enough dialogues with other minds to be convinced that simplicity is a higher value in life than complexity. After all, simplicity and elegance is what physicists and philosophers are hankering after. Musicians have been dealing in that since the time of Machaut in the 15th century. Let's get together and talk seriously about this link. There is something vaguely ridiculous about playing this eternal game of trying to "prove" each other wrong. There are quite as many points of view on this issue as there are heads in the room thinking about it. There is great meaning in what you say. There is great meaning in what I say. Don't ATTACK me and I promise not to attack you. Kim Jones On 31/12/2005, at 5:17 PM, Jose Ramón Brox wrote: - Original Message - From: "Kim Jones" <[EMAIL PROTECTED]> So apparently those who do not scale the dizzying heights of metamathematics have no hope of understanding reality? I never said that, but you simply can't take a theorem about a specific area, that is true within a context and take it out from that context to try to use it "in reality", to "give" social explanations. That's what pseudoscience do. I will say that without mathematical (not methamatematical) knowledge, one cannot aspire to understand reality (in the terms a physic understand it). There will come a time very soon when all of this comp stuff will need to be translated into terms the LAYman can understand easily. Russell Standish has already made the attempt. I appreciate gratly his attempt. Stop wanking off that mathematics is the ONLY script in which reality is encoded. It could well turn out to be music. You are thinking it the other way around - the incorrect one. Music is a small, small part of physics, and therefore, it's represented by a (quite simple) mathematical model. Reality is more complex than that model, and other aspects of reality can be modelled by math different from the one used in the music model, so the reality can't turn out to be music in that sense. Well, I'm speaking about the mechanical phenomena of music, that are simple, not about the way our brains interpret it, that can be quite complex and enjoyable (that's why we say it's an art). Jose
Re: RE Lobian Machine
Hello All, Pardon the comment, but is it not obvious to all that Mathematics is a realm of which faithful representations of our Physical universe span an infinitesimal portion? Even those of us that do not swallow the sweet Blue Pill of Platonia can see this. ;-) Onward! Stephen - Original Message - From: "Jose Ramón Brox" <[EMAIL PROTECTED]> To: Sent: Saturday, December 31, 2005 1:17 AM Subject: RE Lobian Machine - Original Message - From: "Kim Jones" <[EMAIL PROTECTED]> So apparently those who do not scale the dizzying heights of metamathematics have no hope of understanding reality? I never said that, but you simply can't take a theorem about a specific area, that is true within a context and take it out from that context to try to use it "in reality", to "give" social explanations. That's what pseudoscience do. I will say that without mathematical (not methamatematical) knowledge, one cannot aspire to understand reality (in the terms a physic understand it). There will come a time very soon when all of this comp stuff will need to be translated into terms the LAYman can understand easily. Russell Standish has already made the attempt. I appreciate gratly his attempt. Stop wanking off that mathematics is the ONLY script in which reality is encoded. It could well turn out to be music. You are thinking it the other way around - the incorrect one. Music is a small, small part of physics, and therefore, it's represented by a (quite simple) mathematical model. Reality is more complex than that model, and other aspects of reality can be modelled by math different from the one used in the music model, so the reality can't turn out to be music in that sense. Well, I'm speaking about the mechanical phenomena of music, that are simple, not about the way our brains interpret it, that can be quite complex and enjoyable (that's why we say it's an art). Jose
RE Lobian Machine
- Original Message - From: "Kim Jones" <[EMAIL PROTECTED]> >So apparently those who do not scale the dizzying heights of >metamathematics have no hope of understanding reality? I never said that, but you simply can't take a theorem about a specific area, that is true within a context and take it out from that context to try to use it "in reality", to "give" social explanations. That's what pseudoscience do. I will say that without mathematical (not methamatematical) knowledge, one cannot aspire to understand reality (in the terms a physic understand it). >There will come a time very soon when all of this comp stuff will >need to be translated into terms the LAYman can understand easily. >Russell Standish has already made the attempt. I appreciate gratly >his attempt. Stop wanking off that mathematics is the ONLY script in >which reality is encoded. It could well turn out to be music. You are thinking it the other way around - the incorrect one. Music is a small, small part of physics, and therefore, it's represented by a (quite simple) mathematical model. Reality is more complex than that model, and other aspects of reality can be modelled by math different from the one used in the music model, so the reality can't turn out to be music in that sense. Well, I'm speaking about the mechanical phenomena of music, that are simple, not about the way our brains interpret it, that can be quite complex and enjoyable (that's why we say it's an art). Jose
Re: RE Lobian Machine
So apparently those who do not scale the dizzying heights of metamathematics have no hope of understanding reality? Try again, Jose. Try MUSIC Music is a form of mathematics which I DO understand. I wonder how many great mathematicians on this list have an understanding of the structure of that little piece of Platonia? I am trying to see the link between this and metamathematics. Some people have agreed (privately) with me that there is a link. I am not a mathematician, true. For that reason I make no attempt to deal with this language but use the musician's intuitive feeling for reality which is highly refined in terms of my own 1st person experience. There will come a time very soon when all of this comp stuff will need to be translated into terms the LAYman can understand easily. Russell Standish has already made the attempt. I appreciate gratly his attempt. Stop wanking off that mathematics is the ONLY script in which reality is encoded. It could well turn out to be music. Somebody (with enough musical understanding) prove me wrong Kim Jones On 31/12/2005, at 12:45 PM, Jose Ramón Brox wrote: - Original Message - From: "Kim Jones" <[EMAIL PROTECTED]> That was a real bit of pure pseudomathematical nonsense Jose Brox
RE Lobian Machine
- Original Message - From: "Kim Jones" <[EMAIL PROTECTED]> There was no attempt in it to even talk mathematics, let alone pseudomathematics. As it is my birthday I feel I have full rights to tell you to go fuck yourself, Jose. I hope you enjoy the experience as it is physically impossible for a guy's dick to reach his own arsehole - maybe you are different to the rest of us. Have a happy New Year and be careful what you say to me in future Kim Jones - Uh-oh, was that a threat? I hope you don't mind I publish your response to the group, being it related to one of it's discussions. Jose
Re: Lobian Machine
Your post gave ME the hilarity (your word): sane - I like to use: "normal" and "crazy" as "abnormal" in my central-EU distorted vocabulary - paraphrases your statement: The everage of the majority of people are abnormal, while the exceptional, the abnormal, are the normal. Which of course is counter-sense (nonsense?). We have the wrong normative? John M (not so sane) --- George Levy <[EMAIL PROTECTED]> wrote: > Bruno Marchal wrote: > > > Godel's result, known as Godel's second > incompleteness theorem, is > > that no consistent machine can prove its own > consistency: > > > > IF M is consistent then M cannot prove > its consistency > > > Bruno, > > After I read your email, we had a gathering of > family and friends, and > my head being full of the subject of this post. I > wanted to test the > idea of Godel's second incompleteness theorem on the > average people just > to see how they would respond. I found the right > place in the discussion > to insert the paraphrase: > > If I am sane, it is impossible to know for sure that > I am sane. > > This povoked some hilarity, especially with my kids > (young adults) who > probably view me as some kind of nutty professor. > While this statement > is mathematically true, it was not considered > serious by the people I > was talking with. I guess that the average human has > no doubt about his > own sanity.(But my kids had some doubts about mine) > One way to prove > that you are crazy is to assert that you are sane. > This means that the > average human is crazy! :-) > > George > > > >
RE Lobian Machine
- Original Message - From: "Kim Jones" <[EMAIL PROTECTED]> That was a real bit of pure pseudomathematical nonsense Jose Brox
Re: Lobian Machine
Le 30-déc.-05, à 07:08, rmiller a écrit : Godel was discussing sharply defined mathematical constructs, specifically, proof of N requires knowledge of non-N. As I'm sure you know, sanity is a *legal*, rather than a mathematical term. While this sort of logical fuzziness is probably in keeping with these times, I doubt if it really applies to Godel's theorem. It does not apply to Godel's theorem, but Godel's theorem applies to machines' discourse (certainly the lobian one) and if we are such machines we are invited to find plausible correspondences. ... I go now because the heat system is not working in my office. I will answer John and Kim next year ;) Happy New Year, Bruno http://iridia.ulb.ac.be/~marchal/
Re: Lobian Machine
I mainly agree. I think this is true not only for "sanity", but also for "happiness", "cleverness", and a lot of *positive* predicate. A clever person will not say "I am clever" (or will look stupid) An happy person will rarely say "I am happy" (or will look or be unhappy) (Unless special context, and nuances). Those adjectives are solution of the equation Bx -> ~x. Communicating x entails the contrary of x. So it is interesting that something as sober and crisp as Peano Arithmetic or Zermelo-Fraenkel set theory, or any sound machines, already obey that equation for any x of the shape D#. (Dt, DBf, DDt, DDDt, DDDBBf, ...), and can prove it once enough rich. Lobian machine cannot prove any sentence beginning by a diamond. Any possibility (consistency) need some sort of act of faith. Very generally, inconsistency, that is Bf, can be used to modelise Death (cf Bf can only be true in the cul-de-sac world of the Kripke multiverse) Lies (to communicate the false, 1) Error(to communicate the false, 2) Dream (to communicate the false to oneself) Madness (as you say) Dt -> DBf can then be read respectively: (reading the D by "I can"). If I am alive I can die If I am honest I can lie If I am correct I can fail If I am awake I can dream If I am sane I can be mad Bruno Le 30-déc.-05, à 05:33, George Levy a écrit : Bruno Marchal wrote: Godel's result, known as Godel's second incompleteness theorem, is that no consistent machine can prove its own consistency: IF M is consistent then M cannot prove its consistency Bruno, After I read your email, we had a gathering of family and friends, and my head being full of the subject of this post. I wanted to test the idea of Godel's second incompleteness theorem on the average people just to see how they would respond. I found the right place in the discussion to insert the paraphrase: If I am sane, it is impossible to know for sure that I am sane. This povoked some hilarity, especially with my kids (young adults) who probably view me as some kind of nutty professor. While this statement is mathematically true, it was not considered serious by the people I was talking with. I guess that the average human has no doubt about his own sanity.(But my kids had some doubts about mine) One way to prove that you are crazy is to assert that you are sane. This means that the average human is crazy! :-) George http://iridia.ulb.ac.be/~marchal/
Re: Lobian Machine
At 10:33 PM 12/29/2005, George Levy wrote: Bruno Marchal wrote: Godel's result, known as Godel's second incompleteness theorem, is that no consistent machine can prove its own consistency: IF M is consistent then M cannot prove its consistency Bruno, After I read your email, we had a gathering of family and friends, and my head being full of the subject of this post. I wanted to test the idea of Godel's second incompleteness theorem on the average people just to see how they would respond. I found the right place in the discussion to insert the paraphrase: If I am sane, it is impossible to know for sure that I am sane. This povoked some hilarity, especially with my kids (young adults) who probably view me as some kind of nutty professor. While this statement is mathematically true, it was not considered serious by the people I was talking with. I guess that the average human has no doubt about his own sanity.(But my kids had some doubts about mine) One way to prove that you are crazy is to assert that you are sane. This means that the average human is crazy! :-) George Hm. . . Godel was discussing sharply defined mathematical constructs, specifically, proof of N requires knowledge of non-N. As I'm sure you know, sanity is a *legal*, rather than a mathematical term. While this sort of logical fuzziness is probably in keeping with these times, I doubt if it really applies to Godel's theorem. RMiller
Re: Lobian Machine
George, The average human IS crazy according to comp. The smiley at the end of your sentence is unwarranted! This is a fairly undeniable ramification of what Bruno is telling us. If we *are* machines, why do we go about the place denying it? Those who have understood that computation precedes the laws of physics are the only ones who are sane (but of course I cannot prove that, being a consistent machine!) In my view this is where ART has a role in what we are discussing here. Perhaps artists (composers, painters, poets etc.) are the ones who know intuitively that we are all mad (because we don't know what we are) and who then exploit our insanity in a creative manner to remind us of this unconsciously. As Salvador Dali once said "The only difference between me and a madman is that I am not mad". But he could not prove that either. cheers, Kim Jones On 30/12/2005, at 3:33 PM, George Levy wrote: Bruno Marchal wrote: Godel's result, known as Godel's second incompleteness theorem, is that no consistent machine can prove its own consistency: IF M is consistent then M cannot prove its consistency Bruno, After I read your email, we had a gathering of family and friends, and my head being full of the subject of this post. I wanted to test the idea of Godel's second incompleteness theorem on the average people just to see how they would respond. I found the right place in the discussion to insert the paraphrase: If I am sane, it is impossible to know for sure that I am sane. This povoked some hilarity, especially with my kids (young adults) who probably view me as some kind of nutty professor. While this statement is mathematically true, it was not considered serious by the people I was talking with. I guess that the average human has no doubt about his own sanity.(But my kids had some doubts about mine) One way to prove that you are crazy is to assert that you are sane. This means that the average human is crazy! :-) George
Re: Lobian Machine
Bruno Marchal wrote: Godel's result, known as Godel's second incompleteness theorem, is that no consistent machine can prove its own consistency: IF M is consistent then M cannot prove its consistency Bruno, After I read your email, we had a gathering of family and friends, and my head being full of the subject of this post. I wanted to test the idea of Godel's second incompleteness theorem on the average people just to see how they would respond. I found the right place in the discussion to insert the paraphrase: If I am sane, it is impossible to know for sure that I am sane. This povoked some hilarity, especially with my kids (young adults) who probably view me as some kind of nutty professor. While this statement is mathematically true, it was not considered serious by the people I was talking with. I guess that the average human has no doubt about his own sanity.(But my kids had some doubts about mine) One way to prove that you are crazy is to assert that you are sane. This means that the average human is crazy! :-) George
Re: Lobian Machine
Hi Kim, Le 27-déc.-05, à 01:06, Kim Jones a écrit : for some time now you have been building up to what appears to be the core of your thesis - the "Interview with the Universal Lobian Machine". OK. I would say that there is really two cores in my thesis. The Universal Dovetailer Argument (UDA), and the interview of the Lobian Machine. - The UDA is an informal (but I think definite and rigourous) argument showing that if we believe that we are (digitalisable) machine (comp) then we should believe that the laws of physics (the laws of observable predictions) are derivable from computer science/ machine's psychology/machine theology/number theory (cf the naming issue). The whole of physics must be derivable: this includes space, time, constants, etc. The UDA does presuppose some amount of folk psychology for making sense to the expression "yes doctor", when the doctor proposes to *you* an artificial digital brain. - The interview of the lobian machine is just what logicians call "the logic of provability", or "the logic of consistency" or "the logic of arithmetical self-reference". Such an interview has begun when Godel discovered the gap between provability *by* or *in* a formal system (like PRINCIPIA MATHEMATICA, or PEANO ARITHMETICS, or ZERMELO-FRAENKEL SET THEORY, to name typical examples) and truth *about* such a formal system. I identify such "theories" with their theorem provers (all axiomatisable theory have some canonical theorem prover capable of generating all their proofs). In 1931 Godel discovered the existence of true but unprovable propositions in all such systems/machines. The most typical true but unprovable proposition (unprovable by the machine/theory) is the consistency assertion: "I am consistent". A machine or a theory is said to be consistent if the theory or the machine does not prove false proposition. That is: PA cannot prove the true proposition that PA is consistent. ZF cannot prove the true proposition asserting that ZF is consistent. Note that nobody doubt that PA is consistent. In the case of ZF this is slightly less obvious (but I will suppose so, and in any case, I will deliberately limit myself on the discourse of consistent machines). The general Godel's result, known as Godel's second incompleteness theorem, is that no consistent machine can prove its own consistency: IF M is consistent then M cannot prove its consistency [in modal logic, if you represent the "provability predicate" by a modal box B, then consistency can be written by NOT PROVABLE FALSE, or by the shorter ~Bf, with "~" put for the "not", the "B" put for the "provability" predicate, the "f" put for some falsity. With such notation, and reminding that "IF pTHEN q" is written "p -> q" by logician, Godel's second incompleteness theorem can be written: ~Bf -> ~B(~Bf), or remembering that ~Ba = D~a (NOT PROVABLE A = CONSISTENT NOT A), the second theorem by Godel can be written also with the diamond; Dt -> DBf. I guess people see that this is the formula of my "tiniest-theory-of-life-and-death". It is Kripke-semantically characterised by the "Papaioannou" multiverses.]. Now Godel showed that in each "sufficiently rich" machine/theory, the provability predicate can be defined in or by the theory/machine itself, and that such theories/machines *can* prove their own "Godel"s second incompleteness theorem". M can prove "IF M is consistent then M cannot prove its own consistency". This can be written: M can prove "IF I am consistent then I cannot prove I am consistent" But please note that "I" is a third person form of self-reference, not a first person one. The machine talk really about itself through a "scientific" description of itself. I call such "sufficiently rich" machine a LOBIAN MACHINE (Loebian, or Löbian, but "Lobian" is easier for the e-mail). The reason is that in 1955 M. Loeb (Löb) will prove a significant generalisation of Godel's theorem, and here too, it can be shown that the lobian machine can prove their own lob's theorem. In French (I mean in English) Lob's theorem says that if a lobian machine (PM, PA, or ZF for example) proves Bp -> p, for some proposition p, then soon or later the machine will prove p (if it has not been done already). This is rather weird, because it shows that (sufficiently rich) machines are "vulnerable" to some placebo effect. If you prove to such a machine that if she ever prove the existence of Santa Klaus then Santa exists, then you already have proved the existence of Santa Klaus to the machine. Much more on that can be find in my paper "the origin of the physical laws". [modally: Lob's theorem can be written B(Bp -> p) -> Bp (known as Lob's formula L). If you remember that "~A" is the same as "A -> f", and if you substitute p by f in Lob's formula, you get B(Bf -> f) -> Bf, that is B(~Bf) -> Bf, and if you remember that A -> B is equivalent with ~B -> ~A, you know t
