Re: Theory of Everything based on E8 by Garrett Lisi
rafael jimenez buendia skrev: Sorry, but I think Lisi's paper is fatally flawed. Adding altogether fermions and bosons is plain wrong. Best What is wrong with adding fermions and bosons together? Xiao-Gang Wen is working with a condensed string-net where the waves behave just like bosons (fotons) and the end of the open strings behave just like fermions (electrons). -- 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: Theory of Everything based on E8 by Garrett Lisi
[EMAIL PROTECTED] skrev: On Nov 23, 8:49 pm, Torgny Tholerus [EMAIL PROTECTED] wrote: I think that everything is reducible to physical substances and properties. And I think that all of physics is reducible to pure mathematics... You can't have it both ways. If physics was reducible to pure mathematics, then physics could not be the 'ontological base level' of reality and hence everything could not be expressed solely in terms of physical substance and properties. Besides which, mathematics and physics are dealing with quite different distinctions. It is a 'type error' it try to reduce or identity one with the other. Mathematics deals with logical properties, physics deals with spatial (geometric) properties. Although geometry is thought of as math, it is actually a branch of physics, since in addition to pure logical axioms, all geometry involves 'extra' assumptions or axioms which are actually *physical* in nature (not purely mathematical) . When I talk about "pure mathematics" I mean that kind of mathematics you have in GameOfLife. There you have "gliders" that move in the GameOfLife-universe, and these gliders interact with eachother when they meet. These gliders you can see as physical objects. These physical objects are reducible to pure mathematics, they are the consequences of the rules behind GameOfLife. -- Torgny --~--~-~--~~~---~--~~ 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: Are First Person prime?
George, you can do that indeed, but then you are particularizing things. This can be helpful from a pedagogical point of view, but the advantage of the axiomatic approach (to a knowledge theory) is that once you agree on the axioms and rules, then you agree on the consequences independently of the particular instantiation you think about. Word like machine, access, memory, world, data, are, fundamentally harder than the simple idea of knowledge the modal S4 axioms convey. Using machines, for example, could seem as a computationalist restriction, when the axioms S4 remains completely neutral, etc. Also, acceding a memory is more opinion than knowledge because we can have false memory for example. (And then what are the inference rules of your system?). S4 is a normal modal logic with natural Kripke referentials (transitive, reflexive accessibility relations). A bit more problematic is your identification of true with exist. This hangs on possible but highly debatable and complex relations between truth and reality. This is interesting per se, but imo a bit out of topics, or premature (in current thread). Perhaps we will have opportunity to debate on this, but I want make sure that what I am explaining now does not depend on those possible relations (between truth and reality). Bruno Le 24-nov.-07, à 21:23, George Levy a écrit : Bruno thank you for this elaborate reply. I would like these three statements to make use of cybernetic language, that is to be more explicit in terms of the machine or entity to which they refer. Would it be correct to rephrase the statements in the active tense, using the machine as the subject, replacing proposition p by the term data and replacing true by exist? The statements would then be: In a world W there is a machine M, data p and data q such that 1) If M has access to p (possibly in its memory), then p exists in W. 2) If M has access to p, then M has access to the access point to p. 3) If M has access to the information relating or linking p to q then if M has access to p, it also has access to q. I assumed that the term has access means in its memory... but it does not have to. I also assumed in statements 3 that the multiple uses of M refers to the same machine. I guess there may be cases where multiple machines can have access to the dame data. Same with statement 4 George Bruno Marchal wrote: Le 22-nov.-07, à 20:50, George Levy a écrit : Hi Bruno, I am reopening an old thread ( more than a year old) which I found very intriguing. It leads to some startling conclusions. Le 05-août-06, à 02:07, George Levy a écrit : Bruno Marchal wrote:I think that if you want to make the first person primitive, given that neither you nor me can really define it, you will need at least to axiomatize it in some way. Here is my question. Do you agree that a first person is a knower, and in that case, are you willing to accept the traditional axioms for knowing. That is: 1) If p is knowable then p is true; 2) If p is knowable then it is knowable that p is knowable; 3) if it is knowable that p entails q, then if p is knowable then q is knowable (+ some logical rules). Bruno, what or who do you mean by it in statements 2) and 3). The same as in it is raining. I could have written 1. and 2. like 1) knowable(p) - p 2) knowable(p) - knowable(knowable(p)) In this way we can avoid using words like it, or even like true. p is a variable, and is implicitly universally quantified over. knowable(p) - p really means that whatever is the proposition p, if it is knowable then it is true. The false is unknowable (although it could be conceivable, believable, even provable (in inconsistent theory), etc. The p in 1. 2. and 3. is really like the x in the formula (sin(x))^2 + (cos(x))^2 = 1. knowable(p) - p really means that we cannot know something false. This is coherent with the natural language use of know, which I illustrate often by remarking that we never say Alfred knew the earth is flat, but the he realized he was wrong. We say instead Alfred believed that earth is flat, but then . The axiom 1. is the incorrigibility axiom: we can know only the truth. Of course we can believe we know something until we know better. The axiom 2. is added when we want to axiomatize a notion of knowledge from the part of sufficiently introspective subject. It means that if some proposition is knowable, then the knowability of that proposition is itself knowable. It means that when the subject knows some proposition then the subject will know that he knows that proposition. The subject can know that he knows. In addition, what do you mean by is knowable, is true and entails? All the point in axiomatizing some notion, consists in giving a way to reason about that
Re: Theory of Everything based on E8 by Garrett Lisi
Le 26-nov.-07, à 04:17, [EMAIL PROTECTED] a écrit : On Nov 23, 8:49 pm, Torgny Tholerus [EMAIL PROTECTED] wrote: [EMAIL PROTECTED] skrev: As far as I tell tell, all of physics is ultimately geometry. But as we've pointed out on this list many times, a theory of physics is *not* a theory of everything, since it makes the (probably false) assumption that everything is reducible to physical substances and properties. I think that everything is reducible to physical substances and properties. And I think that all of physics is reducible to pure mathematics... You can't have it both ways. If physics was reducible to pure mathematics, then physics could not be the 'ontological base level' of reality and hence everything could not be expressed solely in terms of physical substance and properties. Are you not begging a bit the question here? Besides which, mathematics and physics are dealing with quite different distinctions. It is a 'type error' it try to reduce or identity one with the other. I don't see why. Mathematics deals with logical properties, I guess you mean mathematical properties. Since the filure of logicism, we know that math is not really related to logic in any way. It just happens that a big part of logic appears to be a branch of mathemetics, among many other branches. physics deals with spatial (geometric) properties. Although geometry is thought of as math, it is actually a branch of physics, Actually I do think so. but physics, with comp, has to be the science of what the observer can observe, and the observer is a mathematical object, and observation is a mathematical object too (with comp). since in addition to pure logical axioms, all geometry involves 'extra' assumptions or axioms which are actually *physical* in nature (not purely mathematical) . Here I disagree (so I agree with your preceding post where you agree that we agree a lot but for not always for identical reasons). Arithmetic too need extra (non logical) axioms, and it is a matter of taste (eventually) to put them in the branch of physics or math. 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 [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: Are First Person prime?
Bruno Yes I am particularizing things... But the end justifies the means. I am being positivist, trying to express these rules as a function of an observer. In any case, once the specific example is worked out, we can fall back on the general case. Your feedback about exist not really being adequate to express truth is well noted. Let me change the proposed rules to express truth as a function of an axiomatic system A existing as data either in the memory of M or as a axiomatic substrate for a simulated world W. Let's try the following: In a world W simulated according to the axiomatic data system A, there is a machine M, data p and data q such that 1) If M has access to p (possibly in its memory), then p exists in W. (exist=being simulated in W according to A ) 2) If M has access to p, then M has access to the access point to p. 3) If M has access to the information relating or linking p to q then if M has access to p, it also has access to q. Now we can make the statements reflexive ( I don't know if this is the right word) by setting data p = Machine description M. In a simulated world W following the axiomatic data system A there is a machine M=p and data q such that 1) If M has access to M then M exists in W. (reflexivity?) 2) If M has access to M, then M has access to the access point to M. (Infinite reflexivity? - description of consciousness?) 3) If M has information describing q as a consequence of M in accordance with A, then if M has access to M, it also has access to q. (This is a form of Anthropic principle) I am not sure if this is leading anywhere, but it's fun playing with it. Maybe a computer program could be written to express these staqtements. George Bruno Marchal wrote: George, you can do that indeed, but then you are particularizing things. This can be helpful from a pedagogical point of view, but the advantage of the axiomatic approach (to a knowledge theory) is that once you agree on the axioms and rules, then you agree on the consequences independently of the particular instantiation you think about. Word like machine, access, memory, world, data, are, fundamentally harder than the simple idea of knowledge the modal S4 axioms convey. Using machines, for example, could seem as a computationalist restriction, when the axioms S4 remains completely neutral, etc. Also, acceding a memory is more opinion than knowledge because we can have false memory for example. (And then what are the inference rules of your system?). S4 is a normal modal logic with natural Kripke referentials (transitive, reflexive accessibility relations). A bit more problematic is your identification of true with exist. This hangs on possible but highly debatable and complex relations between truth and reality. This is interesting per se, but imo a bit out of topics, or premature (in current thread). Perhaps we will have opportunity to debate on this, but I want make sure that what I am explaining now does not depend on those possible relations (between truth and reality). Bruno Le 24-nov.-07, à 21:23, George Levy a écrit : Bruno thank you for this elaborate reply. I would like these three statements to make use of cybernetic language, that is to be more explicit in terms of the machine or entity to which they refer. Would it be correct to rephrase the statements in the active tense, using the machine as the subject, replacing proposition p by the term data and replacing true by exist? The statements would then be: In a world W there is a machine M, data p and data q such that 1) If M has access to p (possibly in its memory), then p exists in W. 2) If M has access to p, then M has access to the access point to p. 3) If M has access to the information relating or linking p to q then if M has access to p, it also has access to q. I assumed that the term has access means in its memory... but it does not have to. I also assumed in statements 3 that the multiple uses of M refers to the same machine. I guess there may be cases where multiple machines can have access to the dame data. Same with statement 4 George Bruno Marchal wrote: Le 22-nov.-07, à 20:50, George Levy a écrit : Hi Bruno, I am reopening an old thread ( more than a year old) which I found very intriguing. It leads to some startling conclusions. Le 05-août-06, à 02:07, George Levy a écrit : Bruno Marchal wrote:I think that if you want to make the first person primitive, given that neither you nor me can really define it, you will need at least to axiomatize it in some way. Here is my question. Do you agree that a first person is a knower, and in
Re: Theory of Everything based on E8 by Garrett Lisi
Listers, (Bruno, Torgny, et al.): some (lay) remarks from another mindset (maybe I completely miss your points - perhaps even my own onesG). I go with Bruno in a lack of clear understanding what physical world may be. It can be extended into entirely mathematical ideas beside the likable assumption of it being 'geometrical ' as well as geometry 'completely physical'. I don't see these terms agreed upon as crystal clearly (maybe my ignorance). * Then again pure(?) Math, the logical entirety, is in my views different from the applied(?) math of the diverse sciences, (please note the cap vs lower case distinction, as borrowed from the late mathematician Robert Rosen) the latter applying the former's results to quantities. (I don't want to digress here into my views about the restricted (topical) aspects of those sciences, omitting the rest of the totality that, however, may have an effect of those figments derived as 'scientific quantities' within their boundaries. It may come up in a separate (different) thread). To (I think) Torgny's remark reality and hence everything could not be expressed solely in terms of physical substance and properties. I would add: also depends on a possible extension of the meaning 'physical'. * Then there is the reference to 'axioms'. These true postulates are formed AFTER a theory was thought through to maintain the validity of that theory. So I don't consider them proof, rather as a consequence for the statement it is supposed to underlie. I believe these are Bruno's (supporting?) words: Arithmetic too need extra (non logical) axioms, and it is a matter of taste (eventually) to put them in the branch of physics or math. * Please, excuse my 'out-of-context' remarks, I wanted to illustrate a different line of thoughts - also generated in a human mind. John M On Nov 26, 2007 9:54 AM, Bruno Marchal [EMAIL PROTECTED] wrote: Le 26-nov.-07, à 04:17, [EMAIL PROTECTED] a écrit : On Nov 23, 8:49 pm, Torgny Tholerus [EMAIL PROTECTED] wrote: [EMAIL PROTECTED] skrev: As far as I tell tell, all of physics is ultimately geometry. But as we've pointed out on this list many times, a theory of physics is *not* a theory of everything, since it makes the (probably false) assumption that everything is reducible to physical substances and properties. I think that everything is reducible to physical substances and properties. And I think that all of physics is reducible to pure mathematics... You can't have it both ways. If physics was reducible to pure mathematics, then physics could not be the 'ontological base level' of reality and hence everything could not be expressed solely in terms of physical substance and properties. Are you not begging a bit the question here? Besides which, mathematics and physics are dealing with quite different distinctions. It is a 'type error' it try to reduce or identity one with the other. I don't see why. Mathematics deals with logical properties, I guess you mean mathematical properties. Since the filure of logicism, we know that math is not really related to logic in any way. It just happens that a big part of logic appears to be a branch of mathemetics, among many other branches. physics deals with spatial (geometric) properties. Although geometry is thought of as math, it is actually a branch of physics, Actually I do think so. but physics, with comp, has to be the science of what the observer can observe, and the observer is a mathematical object, and observation is a mathematical object too (with comp). since in addition to pure logical axioms, all geometry involves 'extra' assumptions or axioms which are actually *physical* in nature (not purely mathematical) . Here I disagree (so I agree with your preceding post where you agree that we agree a lot but for not always for identical reasons). Arithmetic too need extra (non logical) axioms, and it is a matter of taste (eventually) to put them in the branch of physics or math. 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 [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: Theory of Everything based on E8 by Garrett Lisi
Could we have a stop to HTML-only postings please! These are hard to read. On Mon, Nov 26, 2007 at 10:51:36AM +0100, Torgny Tholerus wrote: -- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://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 [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 -~--~~~~--~~--~--~---
Several Criticisms of the Doomsday Argument
In his article, Investigations into the Doomsday Argument, Nick Bostrom introduces the Doomsday Argument with the following example: Imagine that two big urns are put in front of you, and you know that one of them contains ten balls and the other a million, but you are ignorant as to which is which. You know the balls in each urn are numbered 1, 2, 3, 4 ... etc. Now you take a ball at random from the left urn, and it is number 7. Clearly, this is a strong indication that that urn contains only ten balls. If originally the odds were fifty-fifty, a swift application of Bayes' theorem gives you the posterior probability that the left urn is the one with only ten balls. (Pposterior (L=10) = 0.90). The Use of Unnumbered Balls Let us first consider the case where the balls are not numbered. We remove a ball from the left urn, and we wonder whether it came from the urn containing ten balls or from the urn containing one million balls. The ball was chosen at random from one of the two urns. Therefore, there is a 50% probability that it came from either urn. It is important to realize that this probability is based on the number of urns, not the number of balls in each urn, which could be any number greater than zero. There is nothing here to suggest a statistical limitation on the maximum size of a group of balls. The Use of Numbered Balls Since the statistical limitation proposed by the Doomsday Argument is not apparent with unnumbered balls, it may be a consequence of numbering the balls. The balls in the ten-ball urn have been numbered according to the series of integers used to count ten objects (1, 2, 3, 4, 5, 6, 7, 8, 9, 10). The fact that each of these integers has been written on one of the balls suggests that the balls have been counted in the order indicated by the numbers. But if the balls had been counted in any of numerous other different orders, the sum would have always been the same, so the actual order used is of no significance. Furthermore, if the physical distribution of the balls in the urn had been arranged according to the series of integers written on the balls, their distribution would not be at all random. If we imagine a column of balls in each urn, ranging from 1 to 10 and from 1 to 1,000,000, the first ball selected at random from the two urns would be numbered either 10 or 1,000,000. But we know from the statement of Bostrom's example that the balls are arranged at random within the urns. Naming the Balls Uniquely If the order in which the balls were counted is not significant, and the balls have not been arranged physically in the order in which they were counted, the numbers on the balls could still be used to identify each ball uniquely, i.e., to give each ball a unique name. This idea is supported by the fact that Bostrom wonders whether the ball 7 selected at random is the ball 7 from one urn or the other. Because of the naming scheme used in the example, we could be certain that any ball with a number greater than 10 came from the million-ball urn. But the naming scheme has the flaw that it provides ambiguous names for balls 1 through 10, which are found in both urns. It is, I believe, this ambiguity in the naming of the balls that produces the statistical result mentioned by Bostrom. The very same effect could be produced by filling both urns with unnumbered white balls, except for a single unnumbered blue ball in each urn. The two blue balls would produce the same statistical effect as the two ball 7's. If all of the balls had been numbered unambiguously from 1 through 1,000,010, the statistical effect produced by Bostrom's ambiguous ball 7 would vanish. Gene Ledbetter --~--~-~--~~~---~--~~ 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: Theory of Everything based on E8 by Garrett Lisi
When I talk about pure mathematics I mean that kind of mathematics you have in GameOfLife. There you have gliders that move in the GameOfLife-universe, and these gliders interact with eachother when they meet. These gliders you can see as physical objects. These physical objects are reducible to pure mathematics, they are the consequences of the rules behind GameOfLife. -- Torgny That kind of mathematics - models of cellular automata - is the domain of the theory of computation. These are just that - models. But there is no reason for thinking that the models or mathematical rules are identical to the physical entities themselves just because these rules/models can precisely predict/explain the behaviour of the physical objects. --~--~-~--~~~---~--~~ 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: Theory of Everything based on E8 by Garrett Lisi
On Nov 27, 3:54 am, Bruno Marchal [EMAIL PROTECTED] wrote: Besides which, mathematics and physics are dealing with quite different distinctions. It is a 'type error' it try to reduce or identity one with the other. I don't see why. Physics deals with symmetries, forces and fields. Mathematics deals with data types, relations and sets/categories. The mathemtical entities are informational. The physical properties are geometric. Geometric properties cannot be derived from informational properties. Mathematics deals with logical properties, I guess you mean mathematical properties. Since the filure of logicism, we know that math is not really related to logic in any way. It just happens that a big part of logic appears to be a branch of mathemetics, among many other branches. I would classify logic as part of applied math - logic is a description of informational systems from the point of view of observers inside time and space. physics deals with spatial (geometric) properties. Although geometry is thought of as math, it is actually a branch of physics, Actually I do think so. but physics, with comp, has to be the science of what the observer can observe, and the observer is a mathematical object, and observation is a mathematical object too (with comp). since in addition to pure logical axioms, all geometry involves 'extra' assumptions or axioms which are actually *physical* in nature (not purely mathematical) . Here I disagree (so I agree with your preceding post where you agree that we agree a lot but for not always for identical reasons). Arithmetic too need extra (non logical) axioms, and it is a matter of taste (eventually) to put them in the branch of physics or math. Bruno I don't think it's a matter of taste. I think geoemtry is clearly physics, arithmetic is clearly pure math. See above. Geometry is about fields, arithmetic (in the most general sense) is about categories/sets. --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
