Re: Theory of Everything based on E8 by Garrett Lisi
Le 30-nov.-07, à 20:00, Torgny Tholerus a écrit : Here I am an ultrafinitist. I believe that the universe is strictly finite. The space and time are discrete. And the space today have a limit. But the time might be without limit, that I don't know. Then you are physicalist before being ultrafinitist. Now ultrafinitism implies comp (OK?, 'course comp does not imply ultrafinitism!) But I have already argued that comp implies the falsity of physicalism (UDA), so? BTW, you often quote wiki or other standard definition of math concept. But few are justifiable in the ultrafinitist realm, so many of your statements seems contradictory to me. 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
Le 30-nov.-07, à 20:21, Torgny Tholerus a écrit : Why can't our universe be modelled by a cellular automata? By UDA, this is just a priori impossible. What *is* still possible, is that you can modelize the emergence of the appearance of a universe by modelling, with a cellular automata, a couple observer + a quantum cellular automata, or by modelling all possible observers through universal dovetaling. Normally the appearance of the quantum will be generated as well. If you are a machine, the physical universe (the sharable third person pov) is not describable in term of working machine. Unless you are the whole universe yourself, which I doubt. If, you are the whole universe, and if you (the universe) exist, and if comp is false and ultrafinitism true, then you are right. But then, about the mind body problem, you are reintroducing the material bullet making even impossible to really addressed the question. Imo: it would be a regression. This comment assumes a good understanding of the seven first steps of the UDA. Our universe is very complicated, but why can't it be modelled by a very complicated automata? Because, by assuming comp, the (physical) universe has to emerge non locally from an infinity of infinite computations. An automata where you have models for protons and electrons and photons and all other elementary particles, that obey the same laws as the particles in our universe? Of course I talk here on exact emulation. FAPP, you can simulate electron and photon. About reality, I am not even sure there are photons and electrons, we have non local (in our local histories/branches) wavy interacting fields. Note that Newton's law, taken seriously enough, are also not turing emulable, like almost everything in naïve 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
Le Thursday 29 November 2007 19:28:05 Torgny Tholerus, vous avez écrit : Quentin Anciaux skrev: Le Thursday 29 November 2007 18:52:36 Torgny Tholerus, vous avez écrit : Quentin Anciaux skrev: What is the production rules of the noset R ? How do you define the set R? http://en.wikipedia.org/wiki/Construction_of_real_numbers Choose your method... The most important part of that definition is: 4. The order ? is /complete/ in the following sense: every non-empty subset of *R* bounded above http://en.wikipedia.org/wiki/Upper_bound has a least upper bound http://en.wikipedia.org/wiki/Least_upper_bound. This definition can be translated to: If you have a production rule that produces rational numbers that are bounded above, then this production rule is producing a real number. This is the production rule for real numbers. And how this render the *set R* ]-infinity,infinity[ finite/limited or even the set N [0,infinity[ ? If as you say you have elements/events/... after the last element/event/... it is totally contradictory and meaning less to call it last... If I take it as a demonstration by absurd, then you've just demonstrated that there exists no last element/event/... How can you avoid this contradiction ? Regards, Quentin Anciaux -- All those moments will be lost in time, like tears in the rain. --~--~-~--~~~---~--~~ 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
Bruno Marchal skrev: Le 29-nov.-07, à 17:22, Torgny Tholerus a écrit : There is a difference between unlimited and infinite. Unlimited just says that it has no limit, but everything is still finite. If you add something to a finite set, then the new set will always be finite. It is not possible to create an infinite set. Come on! Now you talk like a finitist, who accepts the idea of potential infinity (like Kronecker, Brouwer and the intuitionnist) and who rejects only the so called actual infinities, like ordinal and cardinal numbers (or sets). Yes, I am more like a finitist than an ultrafinitist in this respect. I accept that something can be without limit. But I don't want to use the word potential infinity, because infinity is a meaningless word for me. At the ontic level, (or ontological, I mean the minimum we have to bet on at the third person pov), comp is mainly finitist. Judson Webb put comp (he calls it mechanism) in Finitism. But that is no more ultrafinitism. With finitism: every object of the universe is finite, but the universe itself is infinite (potentially or actually). With ultrafinitism, every object is finite AND the universe itself is finite too. Here I am an ultrafinitist. I believe that the universe is strictly finite. The space and time are discrete. And the space today have a limit. But the time might be without limit, that I don't know. Jesse wrote: My instinct would be to say that a well-defined criterion is one that, given any mathematical object, will give you a clear answer as to whether the object fits the criterion or not. And obviously this one doesn't, because it's impossible to decide where R fits it or not! But I'm not sure if this is the right answer, since my notion of well-defined criteria is just supposed to be an alternate way of conceptualizing the notion of a set, and I don't actually know why the set of all sets that are not members of themselves is not considered to be a valid set in ZFC set theory. Frege and Cantor did indeed define or identify sets with their defining properties. This leads to the Russell's contradiction. (I think Frege has abandoned his work in despair after that). One solution (among many other one) to save Cantor's work from that paradox consists in formalizing set theory, which means using belongness as an undefined symbol obeying some axioms. Just two examples of an axiom of ZF (or its brother ZFC = ZF + axiom of choice): is the extensionality axiom: AxAyAz ((x b z - y b z) - x = y) b is for belongs. It says that two sets are equal if they have the same elements. AxEy(z included-in x - z b y) with z included-in x is a macro for Ar(r b z - r b x). This is the power set axiom, saying that the set of all subsets of some set is also a set). For me belongness is not a problem, because everything is finite. For me the axiom of choice always is true, because you can always do a chioce in a finite world. Paradoxes a-la Russell are evacuated by restricting Jesse's well-defined criteria by 1) first order formula (in the set language, that is with b as unique relational symbols (+ equality) ... like the axioms just above. 2) but such first order formula have to be applied only to an already defined set. This 2) rule is a very important restriction, and it is just this that my type theory is about. When you construct new things, those things can only be constructed from things that are already defined. So when you construct the set of all sets, then that new set will not be included in the new set. For example, you can defined the set of x such that x is in y and has such property P(x). With P defined by a set formula, and y an already defined set. Also, ZFC has the foundation axiom which forbids a set to belong to itself. This is a natural consequence of my type theory. When you construct a set, that set can never belong to itself, because that set is not defined before it is constructed. In particular the informal collection of all sets which does not belongs to themselves is the universe itself, which cannot be a set (its power set would be bigger than the universe!). Yes, the set of all sets which does not belongs to themselves is the universe itself. But this is not a problem for me, because you can always extend the universe by creating new objects. So you can create the power set, and the power set will then be bigger than the universe. But this power set will not be part of the universe. -- 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
Re: Theory of Everything based on E8 by Garrett Lisi
[EMAIL PROTECTED] skrev: On Nov 28, 9:56 pm, Torgny Tholerus [EMAIL PROTECTED] wrote: You only need models of cellular automata. If you have a model and rules for that model, then one event will follow after another event, according to the rules. And after that event will follow another more event, and so on unlimited. The events will follow after eachother even if you will not have any implementation of this model. Any physics is not needed. You don't need any geometric properties. In this model you may have a person called Torgny writing a message on a google group, and that event may be followed by a person called Marc writing a reply to this message. And you don't need any implementation of that model. A whole lot of unproven assumptions in there. For starters, we don't even know that the physical world can be modelled solely in terms of cellular automata at all. Why can't our universe be modelled by a cellular automata? Our universe is very complicated, but why can't it be modelled by a very complicated automata? An automata where you have models for protons and electrons and photons and all other elementary particles, that obey the same laws as the particles in our universe? Digital physics just seems to be the latest 'trendy' thing, but actual evidence is thin on the ground. Mathematics is much richer than just discrete math. Discrete math deals only with finite collections, and as such is just a special case of algebra. Isn't it enough with this special case? You can do a lot with finite collections. There is not any need for anything more. Algebraic relations extend beyond computational models. Finally, the introduction of complex analysis, infinite sets and category theory extends mathematics even further, beyond even algebraic relations. So you see that cellular automata are only a small part of mathematics as a whole. There is no reason for thinking for that space is discrete and in fact physics as it stands deals in continuous differential equations, not cellular automata. The reason why physics deals in continuous differential equations is that they are a very good approximation to a world where the distance between the space points and the time points are very, very small. And if you read a book in Quantum Field Theory, they often start from a discrete model, and then take the limit when the distances go to zero. Further, the essential point I was making is that an informational model of something is not neccesserily the same as the thing itself. An informational model of a person called Marc would capture only my mind, not my body. The information has to be super-imposed upon the physical, or embodied in the physical world. If the model models every atom in your body, then that model will describe your body. That model will describe how the atoms in your body react with eachother, and they will describe all your actions. -- 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: Theory of Everything based on E8 by Garrett Lisi
Date: Fri, 30 Nov 2007 09:00:17 +0100 From: [EMAIL PROTECTED] To: [EMAIL PROTECTED] Subject: Re: Theory of Everything based on E8 by Garrett Lisi Jesse Mazer skrev: Date: Thu, 29 Nov 2007 19:55:20 +0100 From: [EMAIL PROTECTED] As soon as you say the set of ALL numbers, then you are forced to define the word ALL here. And for every definition, you are forced to introduce a limit. It is not possible to define the word ALL without introducing a limit. (Or making an illegal circular definition...) Why can't you say If it can be generated by the production rule/fits the criterion, then it's a member of the set? I haven't used the word all there, and I don't see any circularity either. What do you mean by a well-defined criterion? Is this a well-defined criterion? : The set R is defined by: (x belongs to R) if and only if (x does not belong to x). If it fits the criterion (x does not belong to x), then it's a member of the set R. Then we ask the question: Is R a member of the set R?. How shall we use the criterion to answer that question? If we substitute R for x in the criterion, we will get: (R belongs to R) if and only if (R does not belong to R)... What is wrong with this? My instinct would be to say that a well-defined criterion is one that, given any mathematical object, will give you a clear answer as to whether the object fits the criterion or not. And obviously this one doesn't, because it's impossible to decide where R fits it or not! But I'm not sure if this is the right answer, since my notion of well-defined criteria is just supposed to be an alternate way of conceptualizing the notion of a set, and I don't actually know why the set of all sets that are not members of themselves is not considered to be a valid set in ZFC set theory. Jesse --~--~-~--~~~---~--~~ 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
Jesse Mazer skrev: Date: Thu, 29 Nov 2007 19:55:20 +0100 From: [EMAIL PROTECTED] As soon as you say the set of ALL numbers, then you are forced to define the word ALL here. And for every definition, you are forced to introduce a limit. It is not possible to define the word ALL without introducing a limit. (Or making an illegal circular definition...) Why can't you say If it can be generated by the production rule/fits the criterion, then it's a member of the set? I haven't used the word all there, and I don't see any circularity either. What do you mean by a well-defined criterion? Is this a well-defined criterion? : The set R is defined by: (x belongs to R) if and only if (x does not belong to x). If it fits the criterion (x does not belong to x), then it's a member of the set R. Then we ask the question: Is R a member of the set R?. How shall we use the criterion to answer that question? If we substitute R for x in the criterion, we will get: (R belongs to R) if and only if (R does not belong to R)... What is wrong with this? -- 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: Theory of Everything based on E8 by Garrett Lisi
Quentin Anciaux skrev: Hi, Le Wednesday 28 November 2007 09:56:17 Torgny Tholerus, vous avez écrit : You only need models of cellular automata. If you have a model and rules for that model, then one event will follow after another event, according to the rules. And after that event will follow another more event, and so on unlimited. The events will follow after eachother even if you will not have any implementation of this model. Any physics is not needed. You don't need any geometric properties. Sure, but you can't be ultrafinitist and saying things like And after that event will follow another more event, and so on unlimited. There is a difference between unlimited and infinite. Unlimited just says that it has no limit, but everything is still finite. If you add something to a finite set, then the new set will always be finite. It is not possible to create an infinite set. So it is OK to use the word unlimited. But it is not OK to use the word infinite. Is this clear? Another important word is the word all. You can talk about all events. But in that case the number of events will be finite, and you can then talk about the last event. But you can't deduce any contradiction from that, because that is forbidden by the type theory. And there will be more events after the last event, because the number of events is unlimited. As soon as you use the word all, you will introduce a limit - all up to this limit. And you must then think of only doing conclusions that are legal according to type theory. So the best thing is to avoid the word all (and all synonyms of that word). -- 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: Theory of Everything based on E8 by Garrett Lisi
Le Thursday 29 November 2007 17:22:59 Torgny Tholerus, vous avez écrit : Quentin Anciaux skrev: Hi, Le Wednesday 28 November 2007 09:56:17 Torgny Tholerus, vous avez écrit : You only need models of cellular automata. If you have a model and rules for that model, then one event will follow after another event, according to the rules. And after that event will follow another more event, and so on unlimited. The events will follow after eachother even if you will not have any implementation of this model. Any physics is not needed. You don't need any geometric properties. Sure, but you can't be ultrafinitist and saying things like And after that event will follow another more event, and so on unlimited. There is a difference between unlimited and infinite. Unlimited just says that it has no limit, but everything is still finite. If you add something to a finite set, then the new set will always be finite. It is not possible to create an infinite set. I'm sorry I don't get it... The set N as an infinite numbers of elements still every element in the set is finite. Maybe it is an english subtility that I'm not aware of... but in french I don't see a clear difference between infini and illimité. So it is OK to use the word unlimited. But it is not OK to use the word infinite. Is this clear? No, I don't see how a set which have not limit get a finite number of elements. Another important word is the word all. You can talk about all events. But in that case the number of events will be finite, and you can then talk about the last event. But you can't deduce any contradiction from that, because that is forbidden by the type theory. And there will be more events after the last event, because the number of events is unlimited. If there are events after the last one, how can the last one be the last ? As soon as you use the word all, you will introduce a limit - all up to this limit. And you must then think of only doing conclusions that are legal according to type theory. o_O... could you explain what is type theory ? So the best thing is to avoid the word all (and all synonyms of that word). like everything ? Regards, Quentin Anciaux -- All those moments will be lost in time, like tears in the rain. --~--~-~--~~~---~--~~ 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
Quentin Anciaux skrev: Le Thursday 29 November 2007 17:22:59 Torgny Tholerus, vous avez écrit : There is a difference between unlimited and infinite. Unlimited just says that it has no limit, but everything is still finite. If you add something to a finite set, then the new set will always be finite. It is not possible to create an infinite set. I'm sorry I don't get it... The set N as an infinite numbers of elements still every element in the set is finite. Maybe it is an english subtility that I'm not aware of... but in french I don't see a clear difference between infini and illimité. As soon as you talk about the set N, then you are making a closure and making that set finite. The only possible way to talk about something without limit, such as natural numbers, is to give a production rule, so that you can produce as many of that type of objects as you want. If you have a natural number n, then you can produce a new number n+1, that is the successor of n. So it is OK to use the word unlimited. But it is not OK to use the word infinite. Is this clear? No, I don't see how a set which have not limit get a finite number of elements. It is not possible for a set to have no limit. As soon as you construct a set, then that set will always have a limit. Either you have to accept that the set N is finite, or you must stop talking about the set N. It is enough to have a production rule for natural numbers. Another important word is the word all. You can talk about all events. But in that case the number of events will be finite, and you can then talk about the last event. But you can't deduce any contradiction from that, because that is forbidden by the type theory. And there will be more events after the last event, because the number of events is unlimited. If there are events after the last one, how can the last one be the last ? The last event is the last event in the set of all events. But because you have a production rule for the events, it is always possible to produce new events after the last event. But these events do not belong to the set of all events. As soon as you use the word all, you will introduce a limit - all up to this limit. And you must then think of only doing conclusions that are legal according to type theory. o_O... could you explain what is type theory ? Type theory is one of the solutions of Russel's paradox. You have a hierarchy of types. Type theory says that the all quantifiers only can span objects of the same type (or lower types). When you create new objects, such that the set of all sets that do not belong to themselves, then you will get an object of a higher type, so that you can not say anything about if this set belongs to itself or not. The same thing with the set of all sets. You can not say anything about if it belongs to itself. So the best thing is to avoid the word all (and all synonyms of that word). like everything ? Yes... :-) -- 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: Theory of Everything based on E8 by Garrett Lisi
Le Thursday 29 November 2007 18:25:54 Torgny Tholerus, vous avez écrit : Quentin Anciaux skrev: Le Thursday 29 November 2007 17:22:59 Torgny Tholerus, vous avez écrit : There is a difference between unlimited and infinite. Unlimited just says that it has no limit, but everything is still finite. If you add something to a finite set, then the new set will always be finite. It is not possible to create an infinite set. I'm sorry I don't get it... The set N as an infinite numbers of elements still every element in the set is finite. Maybe it is an english subtility that I'm not aware of... but in french I don't see a clear difference between infini and illimité. As soon as you talk about the set N, then you are making a closure and making that set finite. Ok then the set R is also finite ? The only possible way to talk about something without limit, such as natural numbers, is to give a production rule, so that you can produce as many of that type of objects as you want. If you have a natural number n, then you can produce a new number n+1, that is the successor of n. What is the production rules of the noset R ? So it is OK to use the word unlimited. But it is not OK to use the word infinite. Is this clear? No, I don't see how a set which have not limit get a finite number of elements. It is not possible for a set to have no limit. As soon as you construct a set, then that set will always have a limit. I don't get it. Either you have to accept that the set N is finite, or you must stop talking about the set N. It is enough to have a production rule for natural numbers. I don't accept and/or don't understand. Another important word is the word all. You can talk about all events. But in that case the number of events will be finite, and you can then talk about the last event. But you can't deduce any contradiction from that, because that is forbidden by the type theory. And there will be more events after the last event, because the number of events is unlimited. If there are events after the last one, how can the last one be the last ? The last event is the last event in the set of all events. But because you have a production rule for the events, it is always possible to produce new events after the last event. But these events do not belong to the set of all events. There exists no last element in the set N. As soon as you use the word all, you will introduce a limit - all up to this limit. And you must then think of only doing conclusions that are legal according to type theory. o_O... could you explain what is type theory ? Type theory is one of the solutions of Russel's paradox. You have a hierarchy of types. Type theory says that the all quantifiers only can span objects of the same type (or lower types). When you create new objects, such that the set of all sets that do not belong to themselves, then you will get an object of a higher type, so that you can not say anything about if this set belongs to itself or not. The same thing with the set of all sets. You can not say anything about if it belongs to itself. So the best thing is to avoid the word all (and all synonyms of that word). like everything ? Yes... :-) What you are saying seems like to me So the best thing is to avoid words at all (and any languages)... Regards, Quentin Anciaux -- All those moments will be lost in time, like tears in the rain. --~--~-~--~~~---~--~~ 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
Quentin Anciaux skrev: Le Thursday 29 November 2007 18:25:54 Torgny Tholerus, vous avez écrit : As soon as you talk about the set N, then you are making a closure and making that set finite. Ok then the set R is also finite ? Yes. The only possible way to talk about something without limit, such as natural numbers, is to give a production rule, so that you can produce as many of that type of objects as you want. If you have a natural number n, then you can produce a new number n+1, that is the successor of n. What is the production rules of the noset R ? How do you define the set R? -- 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: Theory of Everything based on E8 by Garrett Lisi
Le Thursday 29 November 2007 18:52:36 Torgny Tholerus, vous avez écrit : Quentin Anciaux skrev: Le Thursday 29 November 2007 18:25:54 Torgny Tholerus, vous avez écrit : As soon as you talk about the set N, then you are making a closure and making that set finite. Ok then the set R is also finite ? Yes. o_O The only possible way to talk about something without limit, such as natural numbers, is to give a production rule, so that you can produce as many of that type of objects as you want. If you have a natural number n, then you can produce a new number n+1, that is the successor of n. What is the production rules of the noset R ? How do you define the set R? http://en.wikipedia.org/wiki/Construction_of_real_numbers Choose your method... Regards, Quentin Anciaux -- All those moments will be lost in time, like tears in the rain. --~--~-~--~~~---~--~~ 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
Date: Thu, 29 Nov 2007 18:25:54 +0100 From: [EMAIL PROTECTED] To: [EMAIL PROTECTED] Subject: Re: Theory of Everything based on E8 by Garrett Lisi Quentin Anciaux skrev: Le Thursday 29 November 2007 17:22:59 Torgny Tholerus, vous avez écrit : There is a difference between unlimited and infinite. Unlimited just says that it has no limit, but everything is still finite. If you add something to a finite set, then the new set will always be finite. It is not possible to create an infinite set. I'm sorry I don't get it... The set N as an infinite numbers of elements still every element in the set is finite. Maybe it is an english subtility that I'm not aware of... but in french I don't see a clear difference between infini and illimité. As soon as you talk about the set N, then you are making a closure and making that set finite. Why is that? How do you define the word set? The only possible way to talk about something without limit, such as natural numbers, is to give a production rule, so that you can produce as many of that type of objects as you want. If you have a natural number n, then you can produce a new number n+1, that is the successor of n. Why can't I say the set of all numbers which can be generated by that production ruler? It almost makes sense to say a set is *nothing more* than a criterion for deciding whether something is a member of not, although you would need to refine this definition to deal with problems like Russell's set of all sets that are not members of themselves (which could be translated as the criterion, 'any criterion which does not match its own criterion'--I suppose the problem is that this criterion is not sufficiently well-defined to decide whether it matches its own criterion or not). So it is OK to use the word unlimited. But it is not OK to use the word infinite. Is this clear? No, I don't see how a set which have not limit get a finite number of elements. It is not possible for a set to have no limit. As soon as you construct a set, then that set will always have a limit. Is there something intrinsic to your concept of the word set that makes this true? Is your concept of a set fundamentally different than my concept of well-defined criteria for deciding if any given object is a member or not? Jesse --~--~-~--~~~---~--~~ 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
Quentin Anciaux skrev: Le Thursday 29 November 2007 18:52:36 Torgny Tholerus, vous avez écrit : Quentin Anciaux skrev: What is the production rules of the noset R ? How do you define the set R? http://en.wikipedia.org/wiki/Construction_of_real_numbers Choose your method... The most important part of that definition is: 4. The order ? is /complete/ in the following sense: every non-empty subset of *R* bounded above http://en.wikipedia.org/wiki/Upper_bound has a least upper bound http://en.wikipedia.org/wiki/Least_upper_bound. This definition can be translated to: If you have a production rule that produces rational numbers that are bounded above, then this production rule is producing a real number. This is the production rule for real numbers. -- 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: Theory of Everything based on E8 by Garrett Lisi
Jesse Mazer skrev: From: [EMAIL PROTECTED] As soon as you talk about the set N, then you are making a closure and making that set finite. Why is that? How do you define the word set? The only possible way to talk about something without limit, such as natural numbers, is to give a production rule, so that you can produce as many of that type of objects as you want. If you have a natural number n, then you can produce a new number n+1, that is the successor of n. Why can't I say the set of all numbers which can be generated by that production ruler? As soon as you say the set of ALL numbers, then you are forced to define the word ALL here. And for every definition, you are forced to introduce a limit. It is not possible to define the word ALL without introducing a limit. (Or making an illegal circular definition...) It almost makes sense to say a set is *nothing more* than a criterion for deciding whether something is a member of not, although you would need to refine this definition to deal with problems like Russell's set of all sets that are not members of themselves (which could be translated as the criterion, 'any criterion which does not match its own criterion'--I suppose the problem is that this criterion is not sufficiently well-defined to decide whether it matches its own criterion or not). A well-defined criterion is the same as what I call a production rule. So you can use that, as long as the criterion is well-defined. (What does the criterion, that decides if an object n is a natural number, look like?) It is not possible for a set to have no limit. As soon as you construct a set, then that set will always have a limit. Is there something intrinsic to your concept of the word set that makes this true? Is your concept of a set fundamentally different than my concept of well-defined criteria for deciding if any given object is a member or not? Yes, the definition of the word all is intrinsic in the concept of the word set. -- 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: Theory of Everything based on E8 by Garrett Lisi
Date: Thu, 29 Nov 2007 19:55:20 +0100 From: [EMAIL PROTECTED] To: [EMAIL PROTECTED] Subject: Re: Theory of Everything based on E8 by Garrett Lisi Jesse Mazer skrev: From: [EMAIL PROTECTED] As soon as you talk about the set N, then you are making a closure and making that set finite. Why is that? How do you define the word set? The only possible way to talk about something without limit, such as natural numbers, is to give a production rule, so that you can produce as many of that type of objects as you want. If you have a natural number n, then you can produce a new number n+1, that is the successor of n. Why can't I say the set of all numbers which can be generated by that production ruler? As soon as you say the set of ALL numbers, then you are forced to define the word ALL here. And for every definition, you are forced to introduce a limit. It is not possible to define the word ALL without introducing a limit. (Or making an illegal circular definition...) Why can't you say If it can be generated by the production rule/fits the criterion, then it's a member of the set? I haven't used the word all there, and I don't see any circularity either. It almost makes sense to say a set is *nothing more* than a criterion for deciding whether something is a member of not, although you would need to refine this definition to deal with problems like Russell's set of all sets that are not members of themselves (which could be translated as the criterion, 'any criterion which does not match its own criterion'--I suppose the problem is that this criterion is not sufficiently well-defined to decide whether it matches its own criterion or not). A well-defined criterion is the same as what I call a production rule. So you can use that, as long as the criterion is well-defined. (What does the criterion, that decides if an object n is a natural number, look like?) I would just define the criterion recursively by saying 1 is a natural number, and given a natural number n, n+1 is also a natural number. Jesse --~--~-~--~~~---~--~~ 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
Marc, please, allow me to write in plain language - not using those fancy words of these threads. Some time ago when the discussion was in commonsensically more understandable vocabulary, I questioned something similar to Günther, as pertaining to numbers - the alleged generators of 'everything' (physical, quality, ideation, process, you name it). As Bruno then said: the positive integers do that - if applied in sufficiently long expressions. (please, Bruno, correct this to a bottom-low simplification) - I did not follow that and was promised some more explanatory text in not so technical language. The discussion over the past some weeks is even more technical for me. Is not the distinction relevant what I hold, that there are two kinds of 'number'-usage: the (pure, theoretical Math and the in sciences - (quantity related) - applied math - that uses the formalism (the results, even logics) of 'Math' to exercise 'math'? (Cap vs lower m) Geometry seems to be in between() and symmetry can be both, I think. I am no physicist AND no mathematician, (not even a logician), so I pretend to keep an objective eye on things in which I am not prejudiced by knowledge. (G). John M On Nov 27, 2007 11:40 PM, [EMAIL PROTECTED] wrote: On Nov 28, 1:18 am, Günther Greindl [EMAIL PROTECTED] wrote: Dear Marc, Physics deals with symmetries, forces and fields. Mathematics deals with data types, relations and sets/categories. I'm no physicist, so please correct me but IMHO: Symmetries = relations Forces - could they not be seen as certain invariances, thus also relating to symmetries? Fields - the aggregate of forces on all spacetime points - do not see why this should not be mathematical relation? The mathemtical entities are informational. The physical properties are geometric. Geometric properties cannot be derived from informational properties. Why not? Do you have a counterexample? Regards, Günther Don't get me wrong. I don't doubt that all physical things can be *described* by mathematics. But this alone does not establish that physical things *are* mathematical. As I understand it, for the examples you've given, what happens is that based on emprical observation, certain primatives of geometry and symmetry are *attached to* (connected with) mathematical relations, numbers etc which successfully *describe/predict* these physical properties. But it does not follow from this, that the mathematical relations/numbers *are* the geometric properties/symmetrics. In order to show that the physical properties *are* the mathematical properties (and not just described by or connected to the physical properties), it has to be shown how geometric/physical properties emerge from/are logically derived from sets/categories/numbers alone. --~--~-~--~~~---~--~~ 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: 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 only need models of cellular automata. If you have a model and rules for that model, then one event will follow after another event, according to the rules. And after that event will follow another more event, and so on unlimited. The events will follow after eachother even if you will not have any implementation of this model. Any physics is not needed. You don't need any geometric properties. In this model you may have a person called Torgny writing a message on a google group, and that event may be followed by a person called Marc writing a reply to this message. And you don't need any implementation of that model. -- 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: Theory of Everything based on E8 by Garrett Lisi
Hi, Le Wednesday 28 November 2007 09:56:17 Torgny Tholerus, vous avez écrit : [EMAIL PROTECTED] skrev: 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 only need models of cellular automata. If you have a model and rules for that model, then one event will follow after another event, according to the rules. And after that event will follow another more event, and so on unlimited. The events will follow after eachother even if you will not have any implementation of this model. Any physics is not needed. You don't need any geometric properties. In this model you may have a person called Torgny writing a message on a google group, and that event may be followed by a person called Marc writing a reply to this message. And you don't need any implementation of that model. Sure, but you can't be ultrafinitist and saying things like And after that event will follow another more event, and so on unlimited. Also why do you limit yourself to one computational model ? Turing Machine, Lambda calcul, cellular automata are all equivalents. Regards, Quentin Anciaux -- All those moments will be lost in time, like tears in the rain. --~--~-~--~~~---~--~~ 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
Le 28-nov.-07, à 05:48, [EMAIL PROTECTED] a écrit : On Nov 28, 3:16 am, Bruno Marchal [EMAIL PROTECTED] wrote: Le 27-nov.-07, à 05:47, [EMAIL PROTECTED] a écrit : Geometric properties cannot be derived from informational properties. I don't see why. Above all, this would make the computationalist wrong, or at least some step in the UDA wrong (but then which one?). I'll find the flaw in UDA in due course ;) Thanks. I recall that there is an argument (UDA) showing that if comp is true, then not only geometry, but physics, has to be derived exclusively from numbers and from what numbers can prove (and know, and observe, and bet, ...) about themselves, that is from both extensional and intensional number theory. The UDA shows *why* physics *has to* be derived from numbers (assuming CT + yes doctor). The Lobian interview explains (or should explain, if you have not yet grasp the point) *how* to do that. Bruno If the UDA is sound that would certainly refute what I'm claiming yes. I want to see how physics (which as far I'm concerned *is* geometry - at least I think pure physics=geometry) emerges *purely* from theories of sets/numbers/categories. OK. Note that UDA says only why, not how. how is given by the lobian interview, and gives only the propositional physics (as part of the propositional theology). I base my claims on ontological considerations (5 years of deep thought about ontology), which lead me to strongly suspect the irreducible property dualism between physical and mathematical properties. Thus I'm highly skeptical of UDA but have yet to property study it. Lacking resources to do proper study here at the moment :-( We are in the same boat ... 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
Le 28-nov.-07, à 09:56, Torgny Tholerus a écrit : [EMAIL PROTECTED] skrev: 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 only need models of cellular automata. If you have a model and rules for that model, then one event will follow after another event, according to the rules. And after that event will follow another more event, and so on unlimited. The events will follow after eachother even if you will not have any implementation of this model. Any physics is not needed. You don't need any geometric properties. In this model you may have a person called Torgny writing a message on a google group, and that event may be followed by a person called Marc writing a reply to this message. And you don't need any implementation of that model. OK. Do you agree now that the real Torgny, by which I mean you from your first person point of view, cannot known if it belongs to a state generated by automata 345 or automata 6756, or automata 6756690003121, or automata 65656700234676611084899 , and so one ... Do you agree we have to take into account this first person indeterminacy when making a first person prediction? 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
Bruno Marchal skrev: Le 28-nov.-07, à 09:56, Torgny Tholerus a écrit : You only need models of cellular automata. If you have a model and rules for that model, then one event will follow after another event, according to the rules. And after that event will follow another more event, and so on unlimited. The events will follow after eachother even if you will not have any implementation of this model. Any physics is not needed. You don't need any geometric properties. In this model you may have a person called Torgny writing a message on a google group, and that event may be followed by a person called Marc writing a reply to this message. And you don't need any implementation of that model. OK. Do you agree now that the real Torgny, by which I mean you from your first person point of view, cannot known if it belongs to a state generated by automata 345 or automata 6756, or automata 6756690003121, or automata 65656700234676611084899 , and so one ... Do you agree we have to take into account this first person indeterminacy when making a first person prediction? I agree that the real Torgny belongs to exactly one of those automata, but I don't know which one. So I can not tell what will happen to the real Torgny in the future. I can not do any prediction. If we call the automata that the real Torgny belongs to, for automata X, then I can look at automata X from the outside, and I will then see that all that the real Torgny will do in the future is completely determined. There is no indeterminacy in automata X. -- 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: Theory of Everything based on E8 by Garrett Lisi
On Nov 28, 9:56 pm, Torgny Tholerus [EMAIL PROTECTED] wrote: You only need models of cellular automata. If you have a model and rules for that model, then one event will follow after another event, according to the rules. And after that event will follow another more event, and so on unlimited. The events will follow after eachother even if you will not have any implementation of this model. Any physics is not needed. You don't need any geometric properties. In this model you may have a person called Torgny writing a message on a google group, and that event may be followed by a person called Marc writing a reply to this message. And you don't need any implementation of that model. -- Torgny A whole lot of unproven assumptions in there. For starters, we don't even know that the physical world can be modelled solely in terms of cellular automata at all. Digital physics just seems to be the latest 'trendy' thing, but actual evidence is thin on the ground. Mathematics is much richer than just discrete math. Discrete math deals only with finite collections, and as such is just a special case of algebra. Algebraic relations extend beyond computational models. Finally, the introduction of complex analysis, infinite sets and category theory extends mathematics even further, beyond even algebraic relations. So you see that cellular automata are only a small part of mathematics as a whole. There is no reason for thinking for that space is discrete and in fact physics as it stands deals in continuous differential equations, not cellular automata. Further, the essential point I was making is that an informational model of something is not neccesserily the same as the thing itself. An informational model of a person called Marc would capture only my mind, not my body. The information has to be super-imposed upon the physical, or embodied in the physical world. --~--~-~--~~~---~--~~ 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
Dear Marc, Physics deals with symmetries, forces and fields. Mathematics deals with data types, relations and sets/categories. I'm no physicist, so please correct me but IMHO: Symmetries = relations Forces - could they not be seen as certain invariances, thus also relating to symmetries? Fields - the aggregate of forces on all spacetime points - do not see why this should not be mathematical relation? The mathemtical entities are informational. The physical properties are geometric. Geometric properties cannot be derived from informational properties. Why not? Do you have a counterexample? Regards, Günther -- Günther Greindl Department of Philosophy of Science University of Vienna [EMAIL PROTECTED] http://www.univie.ac.at/Wissenschaftstheorie/ Blog: http://dao.complexitystudies.org/ Site: http://www.complexitystudies.org --~--~-~--~~~---~--~~ 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
Le 27-nov.-07, à 05:47, [EMAIL PROTECTED] a écrit : Geometric properties cannot be derived from informational properties. I don't see why. Above all, this would make the computationalist wrong, or at least some step in the UDA wrong (but then which one?). I recall that there is an argument (UDA) showing that if comp is true, then not only geometry, but physics, has to be derived exclusively from numbers and from what numbers can prove (and know, and observe, and bet, ...) about themselves, that is from both extensional and intensional number theory. The UDA shows *why* physics *has to* be derived from numbers (assuming CT + yes doctor). The Lobian interview explains (or should explain, if you have not yet grasp the point) *how* to do that. Bruno 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. 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
On Nov 28, 1:18 am, Günther Greindl [EMAIL PROTECTED] wrote: Dear Marc, Physics deals with symmetries, forces and fields. Mathematics deals with data types, relations and sets/categories. I'm no physicist, so please correct me but IMHO: Symmetries = relations Forces - could they not be seen as certain invariances, thus also relating to symmetries? Fields - the aggregate of forces on all spacetime points - do not see why this should not be mathematical relation? The mathemtical entities are informational. The physical properties are geometric. Geometric properties cannot be derived from informational properties. Why not? Do you have a counterexample? Regards, Günther Don't get me wrong. I don't doubt that all physical things can be *described* by mathematics. But this alone does not establish that physical things *are* mathematical. As I understand it, for the examples you've given, what happens is that based on emprical observation, certain primatives of geometry and symmetry are *attached to* (connected with) mathematical relations, numbers etc which successfully *describe/predict* these physical properties. But it does not follow from this, that the mathematical relations/numbers *are* the geometric properties/symmetrics. In order to show that the physical properties *are* the mathematical properties (and not just described by or connected to the physical properties), it has to be shown how geometric/physical properties emerge from/are logically derived from sets/categories/numbers alone. --~--~-~--~~~---~--~~ 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 28, 3:16 am, Bruno Marchal [EMAIL PROTECTED] wrote: Le 27-nov.-07, à 05:47, [EMAIL PROTECTED] a écrit : Geometric properties cannot be derived from informational properties. I don't see why. Above all, this would make the computationalist wrong, or at least some step in the UDA wrong (but then which one?). I'll find the flaw in UDA in due course ;) I recall that there is an argument (UDA) showing that if comp is true, then not only geometry, but physics, has to be derived exclusively from numbers and from what numbers can prove (and know, and observe, and bet, ...) about themselves, that is from both extensional and intensional number theory. The UDA shows *why* physics *has to* be derived from numbers (assuming CT + yes doctor). The Lobian interview explains (or should explain, if you have not yet grasp the point) *how* to do that. Bruno If the UDA is sound that would certainly refute what I'm claiming yes. I want to see how physics (which as far I'm concerned *is* geometry - at least I think pure physics=geometry) emerges *purely* from theories of sets/numbers/categories. I base my claims on ontological considerations (5 years of deep thought about ontology), which lead me to strongly suspect the irreducible property dualism between physical and mathematical properties. Thus I'm highly skeptical of UDA but have yet to property study it. Lacking resources to do proper study here at the moment :-( Time will tell. --~--~-~--~~~---~--~~ 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
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: 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: 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 -~--~~~~--~~--~--~---
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 -~--~~~~--~~--~--~---
Re: Theory of Everything based on E8 by Garrett Lisi
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. 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) . --~--~-~--~~~---~--~~ 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
Sorry, but I think Lisi's paper is fatally flawed. Adding altogether fermions and bosons is plain wrong. Best Date: Thu, 22 Nov 2007 18:30:03 -0800 Subject: Re: Theory of Everything based on E8 by Garrett Lisi From: [EMAIL PROTECTED] To: [EMAIL PROTECTED] On Nov 23, 1:10 am, Bruno Marchal [EMAIL PROTECTED] wrote: Now such work raises the remark, which I don't really want to develop now, which is that qualifiying TOE a theory explaining only forces and particles or field, is implicit physicalism, and we know (by UDA) that this is incompatible with comp. Yes indeed Bruno. 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. Thus we both are in agreement on this, but for different reasons (you because, you think math is the ultimate basis of everything aka COMP, me, because of my property dualism, aka the need for a triple-aspect explanation of physical/teleological/ mathematical properties as the basis for everything). We keep telling mainstream scients, but mainstream scients are not listening to us. *sigh*. Yet I bet Lisi is quite close to the sort of physics derivable by machine's or number's introspection. Actually, getting physics from so few symmetries is a bit weird (I have to study the paper in detail). With comp, we have to explain the symmetries *and* the geometry, and the quantum logic, from the numbers and their possible stable discourses ... If not, it is not a theory of everything, but just a classification, a bit like the Mendeleev table classifies atoms without really explaining. But Lisi's theory seems beautiful indeed ... BrunoThere's too many people mucking around with physics - I do wish more people were working on computer science. Physics is the most advanced of our sciences, but computer science lags behind. It just seems to be an unfortunate historical accident that physical theories developed first and then lots of social status got attached to theoretical physics (stemming from the glorification of Newton in Europe). As a result, physics has advanced well ahead of comp-sci, and there's lots of money and status attached to physics breakthroughs. But comp- sci is actually far more important to us in practical sense - artificial general intelligence would be way way more valuable than any fundamental physics breakthrough. We would have had real AGI long ago if there was the same money and glory for comp-sci as there is for physics *sigh*. _ Tecnología, moda, motor, viajes,…suscríbete a nuestros boletines para estar a la última http://newsletters.msn.com/hm/maintenanceeses.asp?L=ESC=ESP=WCMaintenanceBrand=WLRU=http%3a%2f%2fmail.live.com --~--~-~--~~~---~--~~ 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
Le 21-nov.-07, à 19:54, George Levy a écrit : A theory of everyting is sweeping the Physics community. The theory by Garrett Lisi is explained in this Wiki entry. A simulation of E8 can be found a the New Scientist. The Wiki entry on E8 is also interesting. Thanks, very interesting indeed. Note that the original paper is accessible from the New Scientist entry. Not so easy to read (need of differential geometry, simple groups, etc. Quite close to the idea of the importance of 24 which I mention periodically ... :) Now such work raises the remark, which I don't really want to develop now, which is that qualifiying TOE a theory explaining only forces and particles or field, is implicit physicalism, and we know (by UDA) that this is incompatible with comp. Yet I bet Lisi is quite close to the sort of physics derivable by machine's or number's introspection. Actually, getting physics from so few symmetries is a bit weird (I have to study the paper in detail). With comp, we have to explain the symmetries *and* the geometry, and the quantum logic, from the numbers and their possible stable discourses ... If not, it is not a theory of everything, but just a classification, a bit like the Mendeleev table classifies atoms without really explaining. But Lisi's theory seems beautiful indeed ... 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
On Nov 23, 1:10 am, Bruno Marchal [EMAIL PROTECTED] wrote: Now such work raises the remark, which I don't really want to develop now, which is that qualifiying TOE a theory explaining only forces and particles or field, is implicit physicalism, and we know (by UDA) that this is incompatible with comp. Yes indeed Bruno. 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. Thus we both are in agreement on this, but for different reasons (you because, you think math is the ultimate basis of everything aka COMP, me, because of my property dualism, aka the need for a triple-aspect explanation of physical/teleological/ mathematical properties as the basis for everything). We keep telling mainstream scients, but mainstream scients are not listening to us. *sigh*. Yet I bet Lisi is quite close to the sort of physics derivable by machine's or number's introspection. Actually, getting physics from so few symmetries is a bit weird (I have to study the paper in detail). With comp, we have to explain the symmetries *and* the geometry, and the quantum logic, from the numbers and their possible stable discourses ... If not, it is not a theory of everything, but just a classification, a bit like the Mendeleev table classifies atoms without really explaining. But Lisi's theory seems beautiful indeed ... Bruno There's too many people mucking around with physics - I do wish more people were working on computer science. Physics is the most advanced of our sciences, but computer science lags behind. It just seems to be an unfortunate historical accident that physical theories developed first and then lots of social status got attached to theoretical physics (stemming from the glorification of Newton in Europe). As a result, physics has advanced well ahead of comp-sci, and there's lots of money and status attached to physics breakthroughs. But comp- sci is actually far more important to us in practical sense - artificial general intelligence would be way way more valuable than any fundamental physics breakthrough. We would have had real AGI long ago if there was the same money and glory for comp-sci as there is for physics *sigh*. --~--~-~--~~~---~--~~ 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: 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... I have now read Garrett Lisis paper. It was interesting, but it is still to early to say if it is important. There is a lot of symmetries in the elementary particles, and there is a lot of symmetries in the E8 Lie group. So it is not any suprise that they both can be mapped on each other. Lisi has mapped 222 elementary particles on the 242 elements of E8, and he has predicted that the rest of the 20 elements correspond to 20 yet to be discovered elementary particles. If it is true, then Lisi will have the Nobel price. If it is not, then we will have to look for another TOE. But it is possible that we will never find any TOE. Because there is 10^500 different possiblities for our universe, and all of these 10^500 universes exist in the same way. By experiments we will have to decide which of those that is our universe, but we will never reach the correct answer, the number of experiments needed will be too many. -- 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 -~--~~~~--~~--~--~---
