Re: Mathematical methods for the discrete space-time.
I have to think. I think that to retrieve a Leibniz rule in discrete mathematics, you have to introduce an operator and some non commutativity rule. This can be already found in the book by Knuth on numerical mathematics. This has been exploited by Kauffman and one of its collaborator, and they have published a book which I have ordered already two times ... without success. It is a very interesting matter. Dirac quantum relativistic wave equation can almost be retrieved form discrete analysis on complex or quaternion. It is worth investigating more. Look at Kauffman page (accessible from my url), and download his paper on discrete mathematics. There are also interesting relations with knots, and even with the way lambda calculus could be used to provide semantics for the Fourth and fifth arithmetical hypostases, but to be sure I have failed to exploit this. If this were true, the background comp physical reality would be described by a sort of number theoretical quantum topology. That would explain also the role of exceptional (and monstruous) finite simple groups. You are perhaps on a right track, but in a incredibly complex labyrinth ... to be honest ... Bruno Le 12-nov.-08, à 18:44, Torgny Tholerus a écrit : When you are going to do exact mathematical computations for the discrete space-time, then the continuous mathematics is not enough, because then you will only get an approximation of the reality. So there is a need for developing a special calculus for a discrete mathematics. One difference between continuous and discrete mathematics is the rule for how to derívate the product of two functions. In continuous mathematics the rule says: D(f*g) = f*D(g) + D(f)*g. But in the discrete mathematics the corresponding rule says: D(f*g) = f*D(g) + D(f)*g + D(f)*D(g). In discrete mathematics you have difference equations of type: x(n+2) = x(n+1) + x(1), x(0) = 0, x(1) = 1, which then will give the number sequence 0,1,1,2,3,5,8,13,21,34,55,... etc. For a general difference equation you have: Sum(a(i)*x(n+i)) = 0, plus a number of starting conditions. If you then introduce the step operator S with the effect: S(x(n)) = x(n+1), then you can express the difference equation as: Sum((a(i)*S^i)(x(n)) = 0. You will then get a polynom in S. If the roots (the eigenvalues) to this polynom are e(i), you will then get: Sum(a(i)*S^i) = Prod(S - e(i)) = 0. This will give you the equations S - e(i) = 0, or more complete: (S - e(i))(x(n)) = S(x(n)) - e(i)*x(n) = x(n+1) - e(i)*x(n) = 0, which have the solutions x(n) = x(0)*e(i)^n. The general solution to this difference equation will then be a linear combination of these solutions, such as: x(n) = Sum(k(i)*e(i)^n), where k(i) are arbitrary constants. To get the integer solutions you can then build the eigenfunctions: x(j,n) = Sum(k(i,j)*e(i)^n) = delta(j,n), for n the grade of the difference equation. With the S-operator it is then very easy to define the difference- or derivation-operator D as: D = S-1, so D(x(n)) = x(n+1) - x(n). What do you think, is this a good starting point for handling the mathematics of the discrete space-time? -- Torgny Tholerus 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 [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 -~--~~~~--~~--~--~---
Re: Mathematical methods for the discrete space-time.
Bruno Marchal skrev: I have to think. I think that to retrieve a Leibniz rule in discrete mathematics, you have to introduce an operator and some non commutativity rule. This can be already found in the book by Knuth on numerical mathematics. This has been exploited by Kauffman and one of its collaborator, and they have published a book which I have ordered already two times ... without success. It is a very interesting matter. Dirac quantum relativistic wave equation can almost be retrieved form discrete analysis on complex or quaternion. It is worth investigating more. Look at Kauffman page (accessible from my url), and download his paper on discrete mathematics. I will look closer at the Kauffman paper on Non-commutative Calculus and Discrete Physics. It seems interesting, but not quite what I am looking for. Kauffman only gets the ordinary Leibniz rule, not the extended rule I have found. What I want to know is what result you will get if you start from the axiom that *everything in universe is finite*. For this you will need a function calculus. A function is then a mapping from a (finite) set of values to this set of values. Because this value set is finite, you can then map the values on the numbers 0,1,2,3, ... , N-1. So a function calculus can be made starting from a set of values consisting of the numbers 0,1,2,3, ... , N-1, where N is a very large number, but not too large. N should be a number of the order of a googol, ie 10^100. Because the size of our universe is 10^60 Planck units, and our universe has existed for 10^60 Planck times. As the arithmetic, we can count modulo N, ie (N-1) + 1 = 0. This makes it possible for the calculus to describe our reality. A function can then be represented as an ordered set of N numbers, namely: f = [f(0), f(1), f(2), f(3), ... , f(N-1)]. This means that S(f) becomes: S(f) = [f(1), f(2), f(3), ... , f(N-1), f(0)]. The sum or the product of two functions is obtained by adding or multiplying each element, namely: f*g = [f(0)*g(0), f(1)*g(1), f(2)*g(2), ... , f(N-1)*g(N-1)]. and to apply a function f on a function g then becomes: f(g) = [f(g(0)), f(g(1)), f(g(2)), ... , f(g(N-1))]. Exercise: Show that the extended Leibniz rule in the discrete mathematics: D(f*g) = f*D(g) + D(f)*g + D(f)*D(g), is correct! -- Torgny Tholerus --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
Re: QTI euthanasia (brouillon)
2008/11/13 Kory Heath [EMAIL PROTECTED]: Second, it happens that sometimes I think the burden his on him to tell us what he means by a physical universe. I totally agree. But most people will just wave their arms and say, What do you mean? We're obviously in a physical universe. What's problematic about that? And then the burden is back on us to explain why the concept of physical existence is more problematic than it seems. Burden Tennis. Yes indeed, that's the problem. I can discuss almost any of these strange ideas (comp, many worlds, duplication thought experiments) and most people are willing to at least consider them. But tell them the world is just a dream, running on no hardware at all, and they say that's crazy. -- Stathis Papaioannou --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
Re: QTI euthanasia (brouillon)
On 13 Nov 2008, at 00:16, Kory Heath wrote: On Nov 12, 2008, at 9:33 AM, Bruno Marchal wrote: First, I have never stop to work on that and try to share the argument with people interested in the matter. True. You're tireless! (That's a complement.) Second, it happens that sometimes I think the burden his on him to tell us what he means by a physical universe. I totally agree. But most people will just wave their arms and say, What do you mean? We're obviously in a physical universe. What's problematic about that? I think there is a reason for that. Million of years of Darwinian brain washing. But we can't complain, it has also been brain-building. Note that the Greek are the first to rationally take a distance from that, and by this move created modern science including theology as the most fundamental science. But humanity was perhaps not mature enough, so when Aristotle reintroduced the idea that matter is basic, both scientist and theologian get back to it. Of course poets and mystics know better And then the burden is back on us to explain why the concept of physical existence is more problematic than it seems. Burden Tennis. This is the reason why I have developed the Movie Graph Argument (hereafter MGA). It is not a question of taste. It is a question of acknowledging use of logic and assumptions, and finding either hidden assumptions, or imprecise statements or invalid argument step(s). I see your point. But there are issues of clarity or focus, and to some extent those are a matter of taste. I'd like to read an essay (by anyone) that lays out a clear argument in favor of the position that computations don't need to be implemented in order to be conscious. Be careful with the term. The MGA is subtle and to explain it we will have to be more precise. For example here it is better to remember that only *person* are conscious. Computations are not conscious (be it soft or hard wired). I believe this argument can be made without reference to Loebian machines, first-person indeterminacy, or teleportation thought- experiments. MGA is a completely different thought experiment. It looks a bit like UDA, but it is deeply different. I hope you don't find my criticism too annoying. Not at all. But many in this list said it was obvious that the UD does not need to be run, and I remember that I thought that explaining MGA was not really necessary. Even you, right now, seem to agree that computation does not need to be implemented. This does not motivate me too much. The MGA is far more subtle than UDA, and it is a bit frustrating to explain it to people who says in advance that they already agree with the conclusion. Even Maudlin did complain to me that few people have understand its Olympia reasoning. Many confuses it with other type of criticism of comp. It's easy for me to sit on the sidelines and take potshots, while you've done a lot of actual work. And remember that I do, in fact, believe that computations don't need to be implemented in order to be conscious, so you're usually preaching to the choir with me. You see! My point is that, I can imagine Dennett reading your posts, and saying Ok, that makes sense *if* we accept that computations don't need to be implemented in order to be conscious. But I still don't see why I should believe that. Dennett, like many naturalist is not aware that the notion of matter is not obvious at all. The greeks were much more aware than all those who followed, of the mind body problem (except Descartes and Malebranche). Today people thought about the consciousness problem, when the real trouble is in defining both mind and matter and relating them. And Dennett seems not to be aware that modern physics has not progressed at all in the hard problem of matter, on the contrary, modern physics (quantum physics) makes the problem of matter even harder (which in a sense *constitutes* a progress of course). The QM many worlds saves the idea that matter is something objective, but even the many worlds does not explain what matter is, and if it is, at all. Dennett gives a good criteria of what could be an explanation of intelligence or consciousness. It has to be something relating NON- INTELLIGENT (or non-conscious) entity in such a way it explains intelligence or consciousness. This is the basic idea behind Putnam's functionalism, or even computationalism (which is the belief that functionalism is true at least at some level of description of oneself). So, why does Dennett not ask the same for an explanation of matter. Matter should be explained without any use of the word matter, and so it should be explained by relating only ... non material entities. But nobody asks for that. Why? Because we are hardwired for not doubting matter. We take for granted that matter is made of ... matter. Now, physics, if you look at it,
Re: QTI euthanasia (brouillon)
Bruno: I'd like to hear more details about MGA if you don't mind. I tried to find the detailed description with no avail. Even though I am new and still sipping through the snipits here, I feel the potential of this hypothesis. I think the all the hard problems (mind/body, subjectivity/objectivity, dualism/non-dual) are basically circular dependent, like two coupled subsystems, perhaps neither of them fundamental. How do we gain ‘the outside view’ of a closed-system if we are inside or we are the system? It’s like chess pieces being aware of their existence and searching for underneath rules by observation. I also like your ideas such as ‘self-observing ‘ideal’ machine discovers the arithmetic truth by looking inside’ (pardon my poetic distortion). How close can we look? The light is on but nobody’s home? Gordon --- On Thu, 11/13/08, Bruno Marchal [EMAIL PROTECTED] wrote: From: Bruno Marchal [EMAIL PROTECTED] Subject: Re: QTI euthanasia (brouillon) To: [EMAIL PROTECTED] Date: Thursday, November 13, 2008, 9:38 AM On 13 Nov 2008, at 00:16, Kory Heath wrote: On Nov 12, 2008, at 9:33 AM, Bruno Marchal wrote: First, I have never stop to work on that and try to share the argument with people interested in the matter. True. You're tireless! (That's a complement.) Second, it happens that sometimes I think the burden his on him to tell us what he means by a physical universe. I totally agree. But most people will just wave their arms and say, What do you mean? We're obviously in a physical universe. What's problematic about that? I think there is a reason for that. Million of years of Darwinian brain washing. But we can't complain, it has also been brain-building. Note that the Greek are the first to rationally take a distance from that, and by this move created modern science including theology as the most fundamental science. But humanity was perhaps not mature enough, so when Aristotle reintroduced the idea that matter is basic, both scientist and theologian get back to it. Of course poets and mystics know better And then the burden is back on us to explain why the concept of physical existence is more problematic than it seems. Burden Tennis. This is the reason why I have developed the Movie Graph Argument (hereafter MGA). It is not a question of taste. It is a question of acknowledging use of logic and assumptions, and finding either hidden assumptions, or imprecise statements or invalid argument step(s). I see your point. But there are issues of clarity or focus, and to some extent those are a matter of taste. I'd like to read an essay (by anyone) that lays out a clear argument in favor of the position that computations don't need to be implemented in order to be conscious. Be careful with the term. The MGA is subtle and to explain it we will have to be more precise. For example here it is better to remember that only *person* are conscious. Computations are not conscious (be it soft or hard wired). I believe this argument can be made without reference to Loebian machines, first-person indeterminacy, or teleportation thought- experiments. MGA is a completely different thought experiment. It looks a bit like UDA, but it is deeply different. I hope you don't find my criticism too annoying. Not at all. But many in this list said it was obvious that the UD does not need to be run, and I remember that I thought that explaining MGA was not really necessary. Even you, right now, seem to agree that computation does not need to be implemented. This does not motivate me too much. The MGA is far more subtle than UDA, and it is a bit frustrating to explain it to people who says in advance that they already agree with the conclusion. Even Maudlin did complain to me that few people have understand its Olympia reasoning. Many confuses it with other type of criticism of comp. It's easy for me to sit on the sidelines and take potshots, while you've done a lot of actual work. And remember that I do, in fact, believe that computations don't need to be implemented in order to be conscious, so you're usually preaching to the choir with me. You see! My point is that, I can imagine Dennett reading your posts, and saying Ok, that makes sense *if* we accept that computations don't need to be implemented in order to be conscious. But I still don't see why I should believe that. Dennett, like many naturalist is not aware that the notion of matter is not obvious at all. The greeks were much more aware than all those who followed, of the mind body problem (except Descartes and Malebranche). Today people thought about the consciousness problem, when the real trouble is in defining both mind and matter and relating them. And Dennett seems not to be aware that modern physics has not progressed at all in the hard problem of matter, on the contrary, modern physics (quantum physics)
Re: QTI euthanasia (brouillon)
On Nov 13, 2008, at 9:38 AM, Bruno Marchal wrote: Be careful with the term. The MGA is subtle and to explain it we will have to be more precise. For example here it is better to remember that only *person* are conscious. Computations are not conscious (be it soft or hard wired). Good point. What's the most concise way to say it? I believe that persons represented by unimplemented computations are conscious? Not at all. But many in this list said it was obvious that the UD does not need to be run, and I remember that I thought that explaining MGA was not really necessary. Even you, right now, seem to agree that computation does not need to be implemented. This does not motivate me too much. The MGA is far more subtle than UDA, and it is a bit frustrating to explain it to people who says in advance that they already agree with the conclusion. You're right. I do already accept the conclusion. But it's my impression that almost no one else in the world does. I suspect that there are others on this list who do, but even then, I'm not sure they represent a majority. (Should I start an informal poll? How many people on this list believe that persons represented by unimplemented computations are conscious?) My impression is that you're more interested in exploring the consequences of that conclusion after you accept it. Obviously, there's nothing wrong with focusing on the issues that interest you most. But for the world-at-large, the primary issue is *why* we should accept in the first place that persons represented by unimplemented computations are conscious. As I said earlier, I've never seen it laid out convincingly. (At least, not in the one language I can read. :) I'm aware that exploring the consequences of the conclusion can lend support to the conclusion itself. For instance, if you can show that something like quantum physics emerges from the idea that persons represented by unimplemented computations are conscious, that counts as evidence. But that's a hard road to go. Arguments involving Godel, Loebian machines, etc., go over my head, and will go over most other people's heads as well. Dennett, like many naturalist is not aware that the notion of matter is not obvious at all. For what it's worth, Dennett made some interesting comments about this somewhere. (Maybe in Dennett and His Critics, but I can't remember for sure.) He basically said that, in his capacity as a professional philosopher, he's chosen to focus on the issue of how persons represented by implemented computations can be conscious. (He didn't put it that way, but I think that's a good way of saying it.) When it comes to ontology, he's essentially a layperson. He's willing to accept the standard naturalist ontology (and the standard view of impelmentation) so that he can focus on his philosophical specialty. He even indicated that he has some private opinions about ontology, but he doesn't feel qualified enough to air those opinions in public. For all we know, he *is* aware that the notion of matter is not obvious at all. It's just not the issue he's chosen to focus on. My point is that one can read Dennett as if he were entirely agnostic about the question of whether persons represented by unimplemented computations are conscious. Almost everything he says about consciousness still makes sense without the assumption of matter, even if he himself does assume it. Now I feel guilty. There is just no presentations of the MGA in English. The MGA appears the first time in my 1988 paper, written in french. [snip] In this list, I have always suggest people to read the Maudlins paper 1989, which develops a similar argument. I don't know French, and I've never tracked down Maudlin's paper. I've only read previous threads on this list, like this one: http://groups.google.com/group/everything-list/browse_thread/thread/567c5ffde76c70a/780e5a48fb33724e?hl=enlnk=gstq=olympia#780e5a48fb33724e I don't really grasp the argument presented in that thread, so (therefore) I don't find it very convincing. Perhaps the time has come I explain the MGA on the list? Would you be interested? It seems that both you and Stathis already accept the conclusion. So ... No need to do it just on my account, but yes, I'm interested. -- Kory --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
Re: QTI euthanasia
Kory Heath wrote: Sorry for the long delay on this reply. On Nov 2, 2008, at 7:04 PM, Brent Meeker wrote: Kory Heath wrote: In this mundane sense, it's perfectly sensible for me to say, as I'm sitting here typing this email, I expect to still be sitting in this room one second from now. If I'm about to step into a teleporter that's going to obliterate me and make a perfect copy of me in a distant blue room, how can it not be sensible to ask - in that mundane, everyday sense - What do I expect to be experiencing one second from now? It's sensible to ask because in fact there is no teleporter or duplicator or simulator that can provide the continuity of experiences that is Kory. So the model in which your consciousness is a single unified thing works. But there are hypothetical cases in which it doesn't make sense, or at least its sense is somewhat arbitrary. If something like the many-worlds interpretation of quantum physics is correct, then this kind of duplication is actually happening to me all the time. But I should still be able to ask a question like, What do I expect to be experiencing one second from now?, and the answer should still be I expect to still be sitting at this computer, typing this email. If the many-worlds theory simply disallows me from making statements like that, then there's something wrong with the many- worlds theory. But if the many-worlds theory *allows* me to make statements like that, then in that same sense, I should be able to ask What am I about to experience? when I step into a duplicating machine. I think there is a misunderstanding of the MWI. Although the details haven't been worked out (and maybe they won't be, c.f. Dowker and Kent) it is generally thought that you, as a big hot macroscopic body, do not split into significantly different Korys because your interaction with the environment keeps the Kory part of the wave function continuously decohered. So in a Feynman path-integral picture, you are a very tight bundle of paths centered around the classical path. Only if some microscopic split gets amplified and affects you do you split. I doubt that it will ever be possible to build a teleporter. Lawrence Krauss wrote about the problem in The Physics of Star Trek. I'm not sure what it would mean for Bruno's argument if a teleporter were shown to be strictly impossible; after all it's just a thought experiment. On the other hand, I think it's probably not that hard to duplicate a lot of your brain function, enough to instantiate a consciousness that at least thinks it's Kory and fools Kory's friends. But would such an approximate Kory create the ambiguity in the history of Korys that is inherent in Bruno's argument? Brent --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
