Re: Cantor's Diagonal
Hi Barry, Le 18-déc.-07, à 18:52, Barry Brent a écrit : Bruno-- Ahh, my amateur status is nakedly exposed. I'm going to expose my confusion even further now. That is the courageous attitude of the authentic scientists. I like amateur because they have less prejudices, they have inner motivations, and rarely follow authoritative arguments. Never heard of a universal language. I thought I was familiar with Church's thesis, but apparently no. As I said a while ago, coming back from an international meeting on computability (in Siena, where my Plotinus' paper has been accepted), I got the feeling that few people really grasp Church Thesis, including some experts. My Brussels thesis has been criticized for being too much pedagogical on Church thesis, but each time people try to debunk my work, soon enough I realize they have a problem with Godel or Church, never (yet) with my contribution. The worst is that most people *feel* at ease with CT but apparently are not. I take as an honor to explain this too you, I *do* appreciate your work in Number Theory, as far as I understand it. Possible links could emerge. (You make me discover also the nice paper on prime percolation by Vardi: I love percolation. Not just because I am an amateur of good coffe, but because exact percolation problem have led to the Temperley Lieb algebra/category; which makes links between knot theory, combinators/lambda-calculus, quantum computations, and eventually number theory, if not the number 24 itself). I thought it was the claim that two or three or four concepts (including recursive function and computable function) were extensionally equivalent. I have heard of the lambda calculus, but I don't know what it is, or what its connection is with Church's thesis. I have a rough guess, based on what you're saying. I'm surprised. I imagine that the claim of existence of a universal language must be made in the context of a theory of languages? Never heard of that theory. This happens because the expression theory of languages is used in the context of non universal languages, like in the Chomsky hierarchy of languages for example. Universal languages and machines appears in what is called computability theory or recursion theory. Well, if I imagine such a theory, it must involve both syntax and semantics, yes? Semantics connects a language to a world, right? (The experts are cringing, I'm sure) Can one language encompass all possible worlds? Can't we imagine worlds, the structures of which are so dissonant, that their languages could never be consistently subsumed under some single larger (universal) language? (More cringing, no doubt) Or, is it that when we restrict the worlds in question to some suitable realm--say, numbers-- all these things work out? (Cringes redoubled!) I can imagine other ways out. Maybe we're concerned with just one world, suitably described. Maybe structural inconsistencies of possible worlds are no more an impediment to being expressible in one language than logical inconsistencies? (But how do we know?) We have to distinguish logic and computability. In logic we will have language in which sentences are to be interpreted in some world/model. But in computability we can go very far by just interpreting them in some procedural way. The expressions in computer language are really basic instruction like in the coffee-bar machine. Eventually we can describe them all in term of NAND gates, delay and electrical current. A computing language is then universal if all computable functions (from N to N, or from finite things coded in N to finite things coded in N) can be computed by following a finite set of instructions in the language. What about cardinality? From your remarks, I imagine that the number of elementary symbols in any language, including the universal language, is supposed to be finite, Yes. so that the set of algorithms is countable? Yes. And so are the computable functions. If there are lots of worlds and languages, I wonder how people make that work. Because all the languages or machines which have been invented for computing (computable) functions from N to N, have been shown equivalent, and that the closure of the set of computable functions by those machines, for the (transcendental) diagonalization procedure, give a powerful argument that those language/machine are universal. Careful: they are universal with respect to the class of computable functions. They are not universal with respect to the propositions they can express or prove. A universal language/machine is not a theory. Most universal language don't even have a way to assert propositions, just some sort of commands (cf the coffee-bar instructions as example). Is such a language going to be adequate for expressing propositions about all possible worlds? How do we know? In computing, well ... like in Number theory,
Re: Cantor's Diagonal
Excellent, Bruno, Thanks! Barry On Dec 19, 2007, at 7:57 AM, Bruno Marchal wrote: Hi Barry, Le 18-déc.-07, à 18:52, Barry Brent a écrit : Bruno-- Ahh, my amateur status is nakedly exposed. I'm going to expose my confusion even further now. That is the courageous attitude of the authentic scientists. I like amateur because they have less prejudices, they have inner motivations, and rarely follow authoritative arguments. Never heard of a universal language. I thought I was familiar with Church's thesis, but apparently no. As I said a while ago, coming back from an international meeting on computability (in Siena, where my Plotinus' paper has been accepted), I got the feeling that few people really grasp Church Thesis, including some experts. My Brussels thesis has been criticized for being too much pedagogical on Church thesis, but each time people try to debunk my work, soon enough I realize they have a problem with Godel or Church, never (yet) with my contribution. The worst is that most people *feel* at ease with CT but apparently are not. I take as an honor to explain this too you, I *do* appreciate your work in Number Theory, as far as I understand it. Possible links could emerge. (You make me discover also the nice paper on prime percolation by Vardi: I love percolation. Not just because I am an amateur of good coffe, but because exact percolation problem have led to the Temperley Lieb algebra/category; which makes links between knot theory, combinators/lambda-calculus, quantum computations, and eventually number theory, if not the number 24 itself). I thought it was the claim that two or three or four concepts (including recursive function and computable function) were extensionally equivalent. I have heard of the lambda calculus, but I don't know what it is, or what its connection is with Church's thesis. I have a rough guess, based on what you're saying. I'm surprised. I imagine that the claim of existence of a universal language must be made in the context of a theory of languages? Never heard of that theory. This happens because the expression theory of languages is used in the context of non universal languages, like in the Chomsky hierarchy of languages for example. Universal languages and machines appears in what is called computability theory or recursion theory. Well, if I imagine such a theory, it must involve both syntax and semantics, yes? Semantics connects a language to a world, right? (The experts are cringing, I'm sure) Can one language encompass all possible worlds? Can't we imagine worlds, the structures of which are so dissonant, that their languages could never be consistently subsumed under some single larger (universal) language? (More cringing, no doubt) Or, is it that when we restrict the worlds in question to some suitable realm--say, numbers-- all these things work out? (Cringes redoubled!) I can imagine other ways out. Maybe we're concerned with just one world, suitably described. Maybe structural inconsistencies of possible worlds are no more an impediment to being expressible in one language than logical inconsistencies? (But how do we know?) We have to distinguish logic and computability. In logic we will have language in which sentences are to be interpreted in some world/model. But in computability we can go very far by just interpreting them in some procedural way. The expressions in computer language are really basic instruction like in the coffee-bar machine. Eventually we can describe them all in term of NAND gates, delay and electrical current. A computing language is then universal if all computable functions (from N to N, or from finite things coded in N to finite things coded in N) can be computed by following a finite set of instructions in the language. What about cardinality? From your remarks, I imagine that the number of elementary symbols in any language, including the universal language, is supposed to be finite, Yes. so that the set of algorithms is countable? Yes. And so are the computable functions. If there are lots of worlds and languages, I wonder how people make that work. Because all the languages or machines which have been invented for computing (computable) functions from N to N, have been shown equivalent, and that the closure of the set of computable functions by those machines, for the (transcendental) diagonalization procedure, give a powerful argument that those language/machine are universal. Careful: they are universal with respect to the class of computable functions. They are not universal with respect to the propositions they can express or prove. A universal language/machine is not a theory. Most universal language don't even have a way to assert propositions, just some sort of commands (cf the coffee-bar instructions as example).
James Higgo and Four Reasons Why You Don't Exist
Hi everyone, This is my first post to this group. I find so many of the posts so fascinating, but I am still immersing myself in the discussion, so forgive the somewhat trivial direction of the present post. I found a website memorializing James Higgo's thoughts on quantum physics, quantum immortality, etc. From what I understand, he was a prolific contributor to this group right up until is tragic and untimely death (in this universe, at least) in 2001. The page http://www.higgo.com/ quantum/fourreasons.htm offers an intriguing 'synopsis' of a book called Four Reasons Why You Don't Exist, including word counts for each chapter. My question is: What is the status of this book? How much of it did Higgo complete? Has it been published? A few searches in some obvious and unobvious places did not uncover to me the existence of this book. Was it a work in progress, and who was handling the details? Any information that anyone might have about this would be greatly appreciated. Cheers Dan --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
