Re: “Markov's theorem
2012/5/20 Stephen P. King stephe...@charter.net On 5/20/2012 12:24 AM, Russell Standish wrote: On Sat, May 19, 2012 at 01:17:18PM -0400, Stephen P. King wrote: Dear Bruno, I finally found a good and accessible paperhttp://www.google.com/** url?sa=trct=jq=esrc=s**source=webcd=1sqi=2ved=** 0CEoQFjAAurl=http%3A%2F%**2Fntrs.nasa.gov%2Farchive%** 2Fnasa%2Fcasi.ntrs.nasa.gov%**2F20050243612_2005246604.pdf** ei=8NO3T9LmFu-d6AHAq_3uCgusg=**AFQjCNHMBmwAi1K7yJY3oRBnJrYRC2** H9RAsig2=yb-**YNcKWR6LNPSVy8bQquAhttp://www.google.com/url?sa=trct=jq=esrc=ssource=webcd=1sqi=2ved=0CEoQFjAAurl=http%3A%2F%2Fntrs.nasa.gov%2Farchive%2Fnasa%2Fcasi.ntrs.nasa.gov%2F20050243612_2005246604.pdfei=8NO3T9LmFu-d6AHAq_3uCgusg=AFQjCNHMBmwAi1K7yJY3oRBnJrYRC2H9RAsig2=yb-YNcKWR6LNPSVy8bQquA that discusses my bone of contention. To quote from it: A theorem proved by Markov on the non-classifiability of the 4-manifolds implies that, given some comprehensive specification for the topology of a manifold (such as its triangulation, a la Regge calculus, or instructions for constructing it via cutting and gluing simpler spaces) _there exists no general algorithm to decide whether the manifold is homeomorphic to some other manifold _ [l]. The impossibility of classifying the 4-manifolds is a well-known topological result, the proof of which, however, may not be well known in the physics community. It is potentially a result of profound physical implications, as the universe certainly appears to be a manifold of at least four dimensions. Funnily enough, I remember from the dim-distant undergraduate days, that the classifiability of 3 and 4-manifolds were open problems. 1 2-manifolds had known classifications (2-manifolds are classified by the number of holes (aka genus), for instance). Manifolds of dimension higher than 4 are known to be unclassifiable. So a result that 4-manifolds are unclassifiable would be a significant topological result. What's suspicious is the claim that this was proved in 1960. Also suspicious in light of the Wikipedia entry claiming the problem is still open: http://en.wikipedia.org/wiki/**4-manifoldhttp://en.wikipedia.org/wiki/4-manifold Hi Russell, Could you be a bit more exact? The paper that I linked and quoted was considering classification in terms of general algorithms. This is a rather narrow case, no? I am not discussing the Poincare conjecture... Conversely, as for the 3-manifold problem, this looks it might have been solved by Perelman's work that also solved the more famous Poincare conjecture in 2003. If there's anybody about that more knowledgeable on these matters, please comment. Perelman solved the 3-d case of the Poincare conjecture AFAIK. I am pointing out something different, a bit more subtle. I remember there was something peculiar about 4-dimensional space that wasn't true of any other dimension - unfortunately, the sands of time have erased the details from my memory. But I remember people were speculating that it was a possible reason for why we lived in 4D space-time. Yes, the possibility that dovetailing via general algorithm is not possible for 4-manifolds. This is important because if our perceived physical world has a structure that cannot be defined by a general algorithm then some other explanation is necessary. Bruno is trying to convince us that our experiences of a physical world is nothing more than the shared dreams of numbers. I believe that this is false, numbers cannot form a primitive ontological basis from which our experiences of our universe and its physics obtains. In Bruno's theory, the physical world is not computed by an algorithm, the physical world is the limit of all computations going throught your current state... what is computable is your current state, an infinity of computations goes through it. So I don't see the problem here, the UD is not an algorithm which computes the physical world 4D or whatever. Quentin It is my opinion that we live in a 4D space-time because of this non-computable feature. It cannot be specified in advance, thus we actually have to go through the process of computing finite approximations to the general problem of 4-manifold classification. This problem and the one of QM (of finding boolean Satisfiable lattices of Abelian von Neuman subalgebras or equivalent) are both places where physics is not reducible to a pre-existing string of numbers. My discussion of Leibniz' Monadology and its flawed idea of pre-established harmony was an attempt to show how this problem has shown up in philosophy many years ago and we are only now finding solutions to it. -- Onward! Stephen Nature, to be commanded, must be obeyed. ~ Francis Bacon -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group,
Re: “Markov's theorem
Stephen, I have a more general question. I am not a mathematician and I do not quite understand the relationship between mathematics and the world that surround me. It seems to me that your writing implies that there is the intimate connections between mathematics and the Universe. Could you please express your viewpoint in more detail on why findings in mathematics could influence our understanding of the world? From a viewpoint of a not-mathematician this looks a bit like a numerology. Evgenii -- 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 everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: “Markov's theorem
On 5/20/2012 9:39 AM, Evgenii Rudnyi wrote: Stephen, I have a more general question. I am not a mathematician and I do not quite understand the relationship between mathematics and the world that surround me. Dear Evgenii, I am just a person with insatiable curiosity and the strange ability/curse of dyslexia. I consider myself a student of philosophy. I think of mathematics as a more precise form of language and that it is, like all other languages, a representation of experience in the collective sense. Some people believe that there is a one-to-one and onto relationship between mathematics and the totality of what exists. I do not have sufficient information for form an opinion yet. It seems to me that your writing implies that there is the intimate connections between mathematics and the Universe. Well, our ability to understand representations, mathematical or purely linguistic, argues strongly for some kind of intimate relationship between representations and the Universe (which is to me a word representing the totality of what exists). Could you please express your viewpoint in more detail on why findings in mathematics could influence our understanding of the world? From a viewpoint of a not-mathematician this looks a bit like a numerology. We use mathematics to reason and argue about the world because that is all we have. We cannot communicate with each other without the ability to represent. These are good questions! Evgenii -- Onward! Stephen Nature, to be commanded, must be obeyed. ~ Francis Bacon -- 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 everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: “Markov's theorem
On 20 May 2012, at 19:03, Stephen P. King wrote: On 5/20/2012 9:39 AM, Evgenii Rudnyi wrote: Stephen, I have a more general question. I am not a mathematician and I do not quite understand the relationship between mathematics and the world that surround me. Dear Evgenii, I am just a person with insatiable curiosity and the strange ability/curse of dyslexia. I consider myself a student of philosophy. I think of mathematics as a more precise form of language and that it is, like all other languages, a representation of experience in the collective sense. Some people believe that there is a one-to-one and onto relationship between mathematics and the totality of what exists. I do not have sufficient information for form an opinion yet. Nor me. But with comp, we know that there are no such correspondence. Now, using axiomatic, or semi-axiomatic, like mathematicians, in any field, makes possible to progress, even when disagreeing on the interpretations on the terms. It seems to me that your writing implies that there is the intimate connections between mathematics and the Universe. Well, our ability to understand representations, mathematical or purely linguistic, argues strongly for some kind of intimate relationship between representations and the Universe (which is to me a word representing the totality of what exists). OK. Could you please express your viewpoint in more detail on why findings in mathematics could influence our understanding of the world? From a viewpoint of a not-mathematician this looks a bit like a numerology. We use mathematics to reason and argue about the world because that is all we have. We cannot communicate with each other without the ability to represent. And the ability to point, too. Bruno These are good questions! Evgenii -- Onward! Stephen Nature, to be commanded, must be obeyed. ~ Francis Bacon -- 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 everything-list+unsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/everything-list?hl=en . 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 everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: “Markov's theorem
On Sat, May 19, 2012 at 01:17:18PM -0400, Stephen P. King wrote: Dear Bruno, I finally found a good and accessible paper http://www.google.com/url?sa=trct=jq=esrc=ssource=webcd=1sqi=2ved=0CEoQFjAAurl=http%3A%2F%2Fntrs.nasa.gov%2Farchive%2Fnasa%2Fcasi.ntrs.nasa.gov%2F20050243612_2005246604.pdfei=8NO3T9LmFu-d6AHAq_3uCgusg=AFQjCNHMBmwAi1K7yJY3oRBnJrYRC2H9RAsig2=yb-YNcKWR6LNPSVy8bQquA that discusses my bone of contention. To quote from it: A theorem proved by Markov on the non-classifiability of the 4-manifolds implies that, given some comprehensive specification for the topology of a manifold (such as its triangulation, a la Regge calculus, or instructions for constructing it via cutting and gluing simpler spaces) _there exists no general algorithm to decide whether the manifold is homeomorphic to some other manifold _ [l]. The impossibility of classifying the 4-manifolds is a well-known topological result, the proof of which, however, may not be well known in the physics community. It is potentially a result of profound physical implications, as the universe certainly appears to be a manifold of at least four dimensions. Funnily enough, I remember from the dim-distant undergraduate days, that the classifiability of 3 and 4-manifolds were open problems. 1 2-manifolds had known classifications (2-manifolds are classified by the number of holes (aka genus), for instance). Manifolds of dimension higher than 4 are known to be unclassifiable. So a result that 4-manifolds are unclassifiable would be a significant topological result. What's suspicious is the claim that this was proved in 1960. Also suspicious in light of the Wikipedia entry claiming the problem is still open: http://en.wikipedia.org/wiki/4-manifold Conversely, as for the 3-manifold problem, this looks it might have been solved by Perelman's work that also solved the more famous Poincare conjecture in 2003. If there's anybody about that more knowledgeable on these matters, please comment. I remember there was something peculiar about 4-dimensional space that wasn't true of any other dimension - unfortunately, the sands of time have erased the details from my memory. But I remember people were speculating that it was a possible reason for why we lived in 4D space-time. -- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au -- 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 everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: “Markov's theorem
On 5/20/2012 12:24 AM, Russell Standish wrote: On Sat, May 19, 2012 at 01:17:18PM -0400, Stephen P. King wrote: Dear Bruno, I finally found a good and accessible paperhttp://www.google.com/url?sa=trct=jq=esrc=ssource=webcd=1sqi=2ved=0CEoQFjAAurl=http%3A%2F%2Fntrs.nasa.gov%2Farchive%2Fnasa%2Fcasi.ntrs.nasa.gov%2F20050243612_2005246604.pdfei=8NO3T9LmFu-d6AHAq_3uCgusg=AFQjCNHMBmwAi1K7yJY3oRBnJrYRC2H9RAsig2=yb-YNcKWR6LNPSVy8bQquA that discusses my bone of contention. To quote from it: A theorem proved by Markov on the non-classifiability of the 4-manifolds implies that, given some comprehensive specification for the topology of a manifold (such as its triangulation, a la Regge calculus, or instructions for constructing it via cutting and gluing simpler spaces) _there exists no general algorithm to decide whether the manifold is homeomorphic to some other manifold _ [l]. The impossibility of classifying the 4-manifolds is a well-known topological result, the proof of which, however, may not be well known in the physics community. It is potentially a result of profound physical implications, as the universe certainly appears to be a manifold of at least four dimensions. Funnily enough, I remember from the dim-distant undergraduate days, that the classifiability of 3 and 4-manifolds were open problems. 1 2-manifolds had known classifications (2-manifolds are classified by the number of holes (aka genus), for instance). Manifolds of dimension higher than 4 are known to be unclassifiable. So a result that 4-manifolds are unclassifiable would be a significant topological result. What's suspicious is the claim that this was proved in 1960. Also suspicious in light of the Wikipedia entry claiming the problem is still open: http://en.wikipedia.org/wiki/4-manifold Hi Russell, Could you be a bit more exact? The paper that I linked and quoted was considering classification in terms of general algorithms. This is a rather narrow case, no? I am not discussing the Poincare conjecture... Conversely, as for the 3-manifold problem, this looks it might have been solved by Perelman's work that also solved the more famous Poincare conjecture in 2003. If there's anybody about that more knowledgeable on these matters, please comment. Perelman solved the 3-d case of the Poincare conjecture AFAIK. I am pointing out something different, a bit more subtle. I remember there was something peculiar about 4-dimensional space that wasn't true of any other dimension - unfortunately, the sands of time have erased the details from my memory. But I remember people were speculating that it was a possible reason for why we lived in 4D space-time. Yes, the possibility that dovetailing via general algorithm is not possible for 4-manifolds. This is important because if our perceived physical world has a structure that cannot be defined by a general algorithm then some other explanation is necessary. Bruno is trying to convince us that our experiences of a physical world is nothing more than the shared dreams of numbers. I believe that this is false, numbers cannot form a primitive ontological basis from which our experiences of our universe and its physics obtains. It is my opinion that we live in a 4D space-time because of this non-computable feature. It cannot be specified in advance, thus we actually have to go through the process of computing finite approximations to the general problem of 4-manifold classification. This problem and the one of QM (of finding boolean Satisfiable lattices of Abelian von Neuman subalgebras or equivalent) are both places where physics is not reducible to a pre-existing string of numbers. My discussion of Leibniz' Monadology and its flawed idea of pre-established harmony was an attempt to show how this problem has shown up in philosophy many years ago and we are only now finding solutions to it. -- Onward! Stephen Nature, to be commanded, must be obeyed. ~ Francis Bacon -- 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 everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: “Markov's theorem
On 5/18/2012 10:19 PM, Stephen P. King wrote: Hi Bruno and Russell, This is one of the reasons I am skeptical of Bruno's immaterialism: http://www.mathnet.ru/php/archive.phtml?wshow=paperjrnid=impaperid=471option_lang=eng Markov's theorem and algorithmically non-recognizable combinatorial manifolds M. A. Shtan'ko http://www.mathnet.ru/php/person.phtml?option_lang=engpersonid=8892 *Abstract:* We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial -dimensional manifold for every . We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all . We use Borisov's group [8] with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem. -- Did you read the paper? Can you provide a translation? Brent -- 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 everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. image/pngimage/pngimage/png
Re: “Markov's theorem
Stephen, I presented an argument. Whatever you read, if it casts a doubt on the validity of the argument, you have to use what you read to find the invalid step. If not, you act like so many papers pretending that cannabis is a dangerous, but which are only speculation on plausible danger, not proof. A proof, both in math and in applied math in some theoretical framework does not depend on any further research, by construction. If you doubt about immaterialism, by reading on Markow (say), then you might find a way to use Markov against computationalism, or you must make precise which step in the reasoning you are doubting and why, and this without doing interpretation or using philosophy. If not, you confuse science and philosophy, which is easy when the scientific method tackle a problem easily randed in philosophy, or at the intersection of philosophy and science. Now, I don't see why the work you mention has anything to do with the immaterialism derived from comp. You might elaborate a lot. Bruno On 19 May 2012, at 07:19, Stephen P. King wrote: Hi Bruno and Russell, This is one of the reasons I am skeptical of Bruno's immaterialism: http://www.mathnet.ru/php/archive.phtml?wshow=paperjrnid=impaperid=471option_lang=eng Markov's theorem and algorithmically non-recognizable combinatorial manifolds M. A. Shtan'ko Abstract: We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial 006E.png-dimensional manifold for every 006E.png2265.png0034.png. We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all 006E.png2265.png0034.png. We use Borisov's group [8] with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem. -- Onward! Stephen Nature, to be commanded, must be obeyed. ~ Francis Bacon -- 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 everything-list+unsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/everything-list?hl=en . 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 everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: “Markov's theorem
On 5/19/2012 3:02 AM, meekerdb wrote: On 5/18/2012 10:19 PM, Stephen P. King wrote: Hi Bruno and Russell, This is one of the reasons I am skeptical of Bruno's immaterialism: http://www.mathnet.ru/php/archive.phtml?wshow=paperjrnid=impaperid=471option_lang=eng Markov's theorem and algorithmically non-recognizable combinatorial manifolds M. A. Shtan'ko http://www.mathnet.ru/php/person.phtml?option_lang=engpersonid=8892 *Abstract:* We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial -dimensional manifold for every . We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all . We use Borisov's group [8] with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem. -- Did you read the paper? Can you provide a translation? Brent -- My apologies. The full English version is behind a pay-wall http://iopscience.iop.org/1064-5632/68/1/A08. I have read of Markov's theorem on this previously but I cannot find my reference for it atm. -- Onward! Stephen Nature, to be commanded, must be obeyed. ~ Francis Bacon -- 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 everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. image/pngimage/pngimage/png
Re: “Markov's theorem
On 5/19/2012 12:34 PM, Stephen P. King wrote: On 5/19/2012 3:02 AM, meekerdb wrote: On 5/18/2012 10:19 PM, Stephen P. King wrote: Hi Bruno and Russell, This is one of the reasons I am skeptical of Bruno's immaterialism: http://www.mathnet.ru/php/archive.phtml?wshow=paperjrnid=impaperid=471option_lang=eng Markov's theorem and algorithmically non-recognizable combinatorial manifolds M. A. Shtan'ko http://www.mathnet.ru/php/person.phtml?option_lang=engpersonid=8892 *Abstract:* We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial -dimensional manifold for every . We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all . We use Borisov's group [8] with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem. -- Did you read the paper? Can you provide a translation? Brent -- My apologies. The full English version is behind a pay-wall http://iopscience.iop.org/1064-5632/68/1/A08. I have read of Markov's theorem on this previously but I cannot find my reference for it atm. An accessible paper in postscript format that discusses the theorem is found here: www.math.toronto.edu/nabutovsky/gravity2005.ps I will write up more on this in my reply to Bruno. -- Onward! Stephen Nature, to be commanded, must be obeyed. ~ Francis Bacon -- 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 everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- Onward! Stephen Nature, to be commanded, must be obeyed. ~ Francis Bacon -- 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 everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. image/pngimage/pngimage/png
Re: “Markov's theorem
On 5/19/2012 4:06 AM, Bruno Marchal wrote: Stephen, I presented an argument. Whatever you read, if it casts a doubt on the validity of the argument, you have to use what you read to find the invalid step. If not, you act like so many papers pretending that cannabis is a dangerous, but which are only speculation on plausible danger, not proof. A proof, both in math and in applied math in some theoretical framework does not depend on any further research, by construction. If you doubt about immaterialism, by reading on Markow (say), then you might find a way to use Markov against computationalism, or you must make precise which step in the reasoning you are doubting and why, and this without doing interpretation or using philosophy. If not, you confuse science and philosophy, which is easy when the scientific method tackle a problem easily randed in philosophy, or at the intersection of philosophy and science. Now, I don't see why the work you mention has anything to do with the immaterialism derived from comp. You might elaborate a lot. Bruno Dear Bruno, I finally found a good and accessible paper http://www.google.com/url?sa=trct=jq=esrc=ssource=webcd=1sqi=2ved=0CEoQFjAAurl=http%3A%2F%2Fntrs.nasa.gov%2Farchive%2Fnasa%2Fcasi.ntrs.nasa.gov%2F20050243612_2005246604.pdfei=8NO3T9LmFu-d6AHAq_3uCgusg=AFQjCNHMBmwAi1K7yJY3oRBnJrYRC2H9RAsig2=yb-YNcKWR6LNPSVy8bQquA that discusses my bone of contention. To quote from it: A theorem proved by Markov on the non-classifiability of the 4-manifolds implies that, given some comprehensive specification for the topology of a manifold (such as its triangulation, a la Regge calculus, or instructions for constructing it via cutting and gluing simpler spaces) _there exists no general algorithm to decide whether the manifold is homeomorphic to some other manifold _ [l]. The impossibility of classifying the 4-manifolds is a well-known topological result, the proof of which, however, may not be well known in the physics community. It is potentially a result of profound physical implications, as the universe certainly appears to be a manifold of at least four dimensions. The reference to the proof by Markov is: Markov A. A. 1960 Proceedings of the International Congress of Mathematicians, Edinburgh 1958 (edited by J. Todd Cambridge University Press, Cambridge) p 300 The point of this is that if the relation between a pair of 4-manifolds is not related by a general algorithm, how then is it coherent to say that our observed physical universe is the result of general algorithms? -- Onward! Stephen Nature, to be commanded, must be obeyed. ~ Francis Bacon -- 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 everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: “Markov's theorem
On 19 May 2012, at 19:17, Stephen P. King wrote: On 5/19/2012 4:06 AM, Bruno Marchal wrote: Stephen, I presented an argument. Whatever you read, if it casts a doubt on the validity of the argument, you have to use what youread to find the invalid step. If not, you act like so many papers pretending that cannabis is a dangerous, but which are only speculation on plausible danger, not proof. A proof, both in math and in applied math in some theoretical framework does not depend on any further research, by construction. If you doubt about immaterialism, by reading on Markow (say), then you might find a way to use Markov against computationalism, or you must make precise which step in the reasoning you are doubting and why, and this without doing interpretation or using philosophy. If not, you confuse science and philosophy, which is easy when the scientific method tackle a problem easily randed in philosophy, or at the intersection of philosophy and science. Now, I don't see why the work you mention has anything to do with the immaterialism derived from comp. You might elaborate a lot. Bruno Dear Bruno, I finally found a good and accessible paper that discusses my bone of contention. To quote from it: A theorem proved by Markov on the non-classifiability of the 4-manifolds implies that, given some comprehensive specification for the topology of a manifold (such as its triangulation, a la Regge calculus, or instructions for constructing it via cutting and gluing simpler spaces) there exists no general algorithm to decide whether the manifold is homeomorphic to some other manifold [l]. The impossibility of classifying the 4-manifolds is a well-known topological result, the proof of which, however, may not be well known in the physics community. It is potentially a result of profound physical implications, as the universe certainly appears to be a manifold of at least four dimensions. The reference to the proof by Markov is: Markov A. A. 1960 Proceedings of the International Congress of Mathematicians, Edinburgh 1958 (edited by J. Todd Cambridge University Press, Cambridge) p 300 The point of this is that if the relation between a pair of 4- manifolds is not related by a general algorithm, how then is it coherent to say that our observed physical universe is the result of general algorithms? But comp explained why it has to be like that. The observable universe cannot be the result of general algorithm, given that it results from a first person plural indeterminacy on infinite set of possible computations. By computation I mean a set of states together with an universal number relating them. The only thing proved by Markov here is that the homeomorphism relation is not Turing decidable. It suggests that 4-manifold + homeomorphism is Turing universal (as proved for braids). Any intensional identity, for any Turing complete system is as well not Turing decidable. There is no general algorithm saying that two programs compute the same functions, or even run the same computation. It is a well known result for logicians. You don't give a clue what it has to do with immateriality. To be franc, I doubt that there is any. 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 everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: “Markov's theorem
On 5/19/2012 2:11 PM, Bruno Marchal wrote: On 19 May 2012, at 19:17, Stephen P. King wrote: On 5/19/2012 4:06 AM, Bruno Marchal wrote: Stephen, I presented an argument. Whatever you read, if it casts a doubt on the validity of the argument, you have to use what you read to find the invalid step. If not, you act like so many papers pretending that cannabis is a dangerous, but which are only speculation on plausible danger, not proof. A proof, both in math and in applied math in some theoretical framework does not depend on any further research, by construction. If you doubt about immaterialism, by reading on Markow (say), then you might find a way to use Markov against computationalism, or you must make precise which step in the reasoning you are doubting and why, and this without doing interpretation or using philosophy. If not, you confuse science and philosophy, which is easy when the scientific method tackle a problem easily randed in philosophy, or at the intersection of philosophy and science. Now, I don't see why the work you mention has anything to do with the immaterialism derived from comp. You might elaborate a lot. Bruno Dear Bruno, I finally found a good and accessible paper http://www.google.com/url?sa=trct=jq=esrc=ssource=webcd=1sqi=2ved=0CEoQFjAAurl=http%3A%2F%2Fntrs.nasa.gov%2Farchive%2Fnasa%2Fcasi.ntrs.nasa.gov%2F20050243612_2005246604.pdfei=8NO3T9LmFu-d6AHAq_3uCgusg=AFQjCNHMBmwAi1K7yJY3oRBnJrYRC2H9RAsig2=yb-YNcKWR6LNPSVy8bQquA that discusses my bone of contention. To quote from it: A theorem proved by Markov on the non-classifiability of the 4-manifolds implies that, given some comprehensive specification for the topology of a manifold (such as its triangulation, a la Regge calculus, or instructions for constructing it via cutting and gluing simpler spaces) _there exists no general algorithm to decide whether the manifold is homeomorphic to some other manifold _ [l]. The impossibility of classifying the 4-manifolds is a well-known topological result, the proof of which, however, may not be well known in the physics community. It is potentially a result of profound physical implications, as the universe certainly appears to be a manifold of at least four dimensions. The reference to the proof by Markov is: Markov A. A. 1960 Proceedings of the International Congress of Mathematicians, Edinburgh 1958 (edited by J. Todd Cambridge University Press, Cambridge) p 300 The point of this is that if the relation between a pair of 4-manifolds is not related by a general algorithm, how then is it coherent to say that our observed physical universe is the result of general algorithms? But comp explained why it has to be like that. The observable universe cannot be the result of general algorithm, given that it results from a first person plural indeterminacy on infinite set of possible computations. Hi Bruno, Can you not see that I am claiming that your notion of an infinite set of possible computations is incoherent if the immaterialism derived from comp is such that computations have content and consequences in a way that is separate from the physical implementations of those computations. By computation I mean a set of states together with an universal number relating them. States of what? Is there a referent, an object, that is the referent of the word states here? How are the states distinguished from each other? You claim that this computation has immaterial existence in the sense that is is separable and independent of the physical word(s). You claim that the physical world are not primitive ontologically. I agree with this claim, but I do not agree that the universal numbers have a primitive existence either. We cannot put numbers, or any other entity, at a lower ontological level than the physical world. The only thing proved by Markov here is that the homeomorphism relation is not Turing decidable. It suggests that 4-manifold + homeomorphism is Turing universal (as proved for braids). Any intensional identity, for any Turing complete system is as well not Turing decidable. There is no general algorithm saying that two programs compute the same functions, or even run the same computation. Therefore we know that there does not exist a means to generate a Pre-established Harmony nor can we imagine coherently that the universe we observe is just some kind of pre-existing structure that our mind is somehow running in. This implies to me that we have to think of the universe we observer to be something like the result of an ongoing and maybe even eternal process. It is a well known result for logicians. You don't give a clue what it has to do with immateriality. To be franc, I doubt that there is any. Immateriality, just as in Ideal monism, is a bankrupt ontology. It is incoherent
“Markov's theorem
Hi Bruno and Russell, This is one of the reasons I am skeptical of Bruno's immaterialism: http://www.mathnet.ru/php/archive.phtml?wshow=paperjrnid=impaperid=471option_lang=eng Markov's theorem and algorithmically non-recognizable combinatorial manifolds M. A. Shtan'ko http://www.mathnet.ru/php/person.phtml?option_lang=engpersonid=8892 *Abstract:* We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial -dimensional manifold for every . We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all . We use Borisov's group [8] with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem. -- Onward! Stephen Nature, to be commanded, must be obeyed. ~ Francis Bacon -- 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 everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. inline: 006E.pnginline: 2265.pnginline: 0034.png
