Re: Numbers
Le Samedi 18 Mars 2006 01:58, [EMAIL PROTECTED] a écrit : Ground them operationally, then. Real things have real properties and unreal things don't. Real properties can be observed empirically. Primeness then is not a real property. I have to ask you one more time, but I'll reverse the question, what does it means for an object not to be real (hence being abstract) ? it is not a joke, I want to know. All your explanations till now are tautologies and in themself have no explanatory power at all. Quentin --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Numbers
Le Samedi 18 Mars 2006 01:58, [EMAIL PROTECTED] a écrit : Ground them operationally, then. Real things have real properties and unreal things don't. Real properties can be observed empirically. Primeness then is not a real property. I'll take another stupid example to try to explain my question... Considering materialist view, what does it means to have existed ? So I'm living right now, I'd say I exists, one day I'll die and in a materialist view I'll not exists anymore, will not ever have conscious state. What remains of my existance is in the memory of people who knew me, when they'll die, It'll be in the memory of people who have been taugh that I existed... then they'll die too, and one day humanity will disappear, earth will disappear, any trace that humanity has ever existed will disappear, when this time come what will render me more real as Tintin (the Hergé comics hero)... I have existed but nothing could tell it (even me as at that time I'll not be anymore), so what does it means to have existed at all ? Quentin --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Numbers
[EMAIL PROTECTED] wrote: Georges Quénot wrote: [EMAIL PROTECTED] wrote: Since I don't adopt the premise that everything is mathematical, I would like to clarify just that point. I understood that you do not adopt it (and whatever your reasons I have to respect the fact). By the way I am not sure I really :-) adopt it either. But can you make a difference between adopting it and being able to consider that it might make sense (whether it is true or not) and conduct (or follow) reflections in a context in which it would be conjectured as true? I don't think Mathematical Monism makes sense OK. Just consider that it does make sense to some people. (to be precise it is either incoherent, in asserting that only some mathematical objects exist, or inconsistent with observation in asserting that they all do).. I do not see how it can be inconsistent with observation. [...] Maps are isomorphic to territories, but are not territories. Well. Territories *are* maps. Just a very specific type of map but maps anyway. err...no they are not. You can't grow potatoes in a map of a farm. Identity is just an isomorphism among possibly many others. All identity relations are isomorphisms as well. Not all isomporhisms are identity relations. The territory can be the map and indeed vice versa. You can't fold up the farm and put it in your pocket. You're right. I can't. Georges. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Numbers
Georges Quénot wrote: [EMAIL PROTECTED] wrote: Georges Quénot wrote: [EMAIL PROTECTED] wrote: Since I don't adopt the premise that everything is mathematical, I would like to clarify just that point. I understood that you do not adopt it (and whatever your reasons I have to respect the fact). By the way I am not sure I really :-) adopt it either. But can you make a difference between adopting it and being able to consider that it might make sense (whether it is true or not) and conduct (or follow) reflections in a context in which it would be conjectured as true? I don't think Mathematical Monism makes sense OK. Just consider that it does make sense to some people. (to be precise it is either incoherent, in asserting that only some mathematical objects exist, or inconsistent with observation in asserting that they all do).. I do not see how it can be inconsistent with observation. If every mathematical structure exists , then mathematical structures consisting of a counterpart of me plus a Harry Potter universe exist. Yet this is not observed. Of course that might be coincidence. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Numbers
Quentin Anciaux wrote: Le Samedi 18 Mars 2006 01:58, [EMAIL PROTECTED] a écrit : Ground them operationally, then. Real things have real properties and unreal things don't. Real properties can be observed empirically. Primeness then is not a real property. I have to ask you one more time, but I'll reverse the question, what does it means for an object not to be real (hence being abstract) ? it means it is not an object at all. it is not a joke, I want to know. All your explanations till now are tautologies what is tautologous about: Real properties can be observed empirically i.e. unreal ones cannot. and in themself have no explanatory power at all. Quentin Quentin Anciaux wrote: Le Samedi 18 Mars 2006 01:58, [EMAIL PROTECTED] a écrit : Ground them operationally, then. Real things have real properties and unreal things don't. Real properties can be observed empirically. Primeness then is not a real property. I'll take another stupid example to try to explain my question... Considering materialist view, what does it means to have existed ? So I'm living right now, I'd say I exists, one day I'll die and in a materialist view I'll not exists anymore, will not ever have conscious state. What remains of my existance is in the memory of people who knew me, when they'll die, It'll be in the memory of people who have been taugh that I existed... then they'll die too, and one day humanity will disappear, earth will disappear, any trace that humanity has ever existed will disappear, when this time come what will render me more real as Tintin (the Hergé comics hero)... I have existed but nothing could tell it (even me as at that time I'll not be anymore), so what does it means to have existed at all ? The question is what it means to exist now. You, now, are real. What connects with you causally is also real. Quentin --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Numbers
[EMAIL PROTECTED] wrote: Georges Quénot wrote: [EMAIL PROTECTED] wrote: Georges Quénot wrote: [EMAIL PROTECTED] wrote: Since I don't adopt the premise that everything is mathematical, I would like to clarify just that point. I understood that you do not adopt it (and whatever your reasons I have to respect the fact). By the way I am not sure I really :-) adopt it either. But can you make a difference between adopting it and being able to consider that it might make sense (whether it is true or not) and conduct (or follow) reflections in a context in which it would be conjectured as true? I don't think Mathematical Monism makes sense OK. Just consider that it does make sense to some people. (to be precise it is either incoherent, in asserting that only some mathematical objects exist, or inconsistent with observation in asserting that they all do).. I do not see how it can be inconsistent with observation. If every mathematical structure exists , then mathematical structures consisting of a counterpart of me plus a Harry Potter universe exist. Yet this is not observed. Of course that might be coincidence. I see at least three possibilities: 1. It is not so sure that there actually exist sets of equations of which a Harry Potter universe includes a counterpart of you. 2. There may well exist a Harry Potter universe that includes a counterpart of you but it is not causaly related to our universe (too far for instance) and this is why we cannot observe it. 3. You actually are in a Harry Potter universe but it just happened that you are not a sorcerer and you must know that in Harry Potter universes, non sorcerers are prevented fromm observing magical events. Georges. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Numbers
Georges Quénot wrote: [EMAIL PROTECTED] wrote: Georges Quénot wrote: [EMAIL PROTECTED] wrote: Georges Quenot wrote: That [The universe] has real existence, as opposed to the other mathematical objects which are only abstract. is what I called a dualist view. Dualism says there are two really existing realms or substances. Saying the physical realm is concrete and real and the mathematical realm is abstract and unreal is not dualism. This *splits* things into realness and abstractedness. No abstract objects aren't real things at all. Well... I am not sure I should insist. I do not want to force you to believe or consider something you are not willing to believe or consider. The question is not whether they are real things or not. It is whether they are things or not. They are not. The King of France is not a person. Once they are things, you have to decide how many types of things there must be. You might well feel otherwise but, for me, *they are not nothing*. Just tell me: do you consider natural numbers as something, as nothing, as something that would neither be something nor nothing, or as anything else (please explain)? I consider them as concepts , as the intentional objects of neural activity. Of course intentional objects are not real things -- things are not brought into existence by thinking about them. Please answer without considering whether they are real or not, just whether thet are something, nothing, ... *Then* we can discuss *which type of* thing (or whatever) they might be. There is only one kind of existing thing, ie real, physical things. You should clarify: do you mean existing, real or physical? Which is which and on which ground which is a specific of (or identical to) which? How do you define any of them? It think they all mean the same as each other, i.e. causally connected to me. It postulates material substance yes, but only material substance. Hence it is monism, not dualism. No, this is material substance besides abstract objetcs. Not if abstract objects do not really exist at all. You do split things between material and immaterial. I do not split existing things. just as classical dualism postulates a spiritual substance as well as a material substance. Yes and you do oppose material (real) things to immaterial (abstract) ones. I oppose existence to non-existence. However, existence is not sub-divided into two realms. (and just as once vitalism postulated a living substance). Last but not least: you are unable to explain what you mean bt real except by a tautology or via a reference to common sense that no longer appears to be consensual. I am not sure what you mean by non-consensual. Everyone believes that sticks and stones and what they had for breakfast are real. Not everyone believe that and that is not a joke. But the main point is that not everybody gives the same meaning to real. I guarantee you that there are people (including me) that do not feel things as you do in this matters (not to say that something must be wrong either way, only that several distinct and incompatible views actually coexist). Even people who think numbers are real do not think they are real in the same sense as their breakfast. Both view seem to have their champions here. I guesse that when saying This has to be saying simply that the multiverse IS a mathematical object. Tom ([EMAIL PROTECTED]) defends the monist view as obvious and the only one making sense while when saying [The universe] has real existence, as opposed to the other mathematical objects which are only abstract. Well, I've never seen a mathematical object. Have you ever seen the number 3? Have you ever seen a single photon? Or even an electron? They can be detected by apropriate instrumentation. This might be more complicated. Looking at them can significantly change them. They are still causally conneceted to me, and I to them They might also be an abstraction. Why ? Why should two-way causality imply anstractness ? They can hardly be objects in the common sense of the word. Why ? all you are saying is that they kick back. Do you descend from the ape by your father or by your mother? :-) You may find the monist idea crazy or a nonsense but it does not (completely) appear as such to everybody. The Devil is in the details. I await mathematical-monist accounts of consciousness, causality and time. Don't be so impatient. Mankind has been awaiting for thousands of years an account of how living beings can have appeared in an inert world and though the account is now about a century and a half old it still did not make it to a significant portion of mankind (if not the majority). Switching to a maths-only ontology does not necessarily make that any easier. I am also awaiting for a physical-monist account of how consciousness can arise in living beings.
Re: Numbers
Brent Meeker wrote: [EMAIL PROTECTED] wrote: Georges Quénot wrote: [EMAIL PROTECTED] wrote: Quentin Anciaux wrote: What properties of the multiverse would render only one mathematical object real and others abstract... A non-mathematical property. Hence mathematics alone is not sufficient to explain the world. QED. This has to be a non-mathematical property because it is contingent, and all mathematical truth is necessary. It is necessairly true *given the axioms*. Suppose there is an axiom that picks out some worlds as real. An axiom that follows necessarily from other axioms, or a contingent, optional axiom ? Picks out some worlds as real ..from what ? --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Numbers
Georges Quénot wrote: 1. It is not so sure that there actually exist sets of equations of which a Harry Potter universe includes a counterpart of you. I meant: 1. It is not so sure that there actually exist sets of equations of which a Harry Potter universe including a counterpart of you would be a solution. Georges. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Numbers
[EMAIL PROTECTED] wrote: Georges Quénot wrote: [EMAIL PROTECTED] wrote: Georges Quénot wrote: [EMAIL PROTECTED] wrote: Georges Quenot wrote: That [The universe] has real existence, as opposed to the other mathematical objects which are only abstract. is what I called a dualist view. Dualism says there are two really existing realms or substances. Saying the physical realm is concrete and real and the mathematical realm is abstract and unreal is not dualism. This *splits* things into realness and abstractedness. No abstract objects aren't real things at all. Well... I am not sure I should insist. I do not want to force you to believe or consider something you are not willing to believe or consider. The question is not whether they are real things or not. It is whether they are things or not. [...] Thanks for your answers. Georges. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Numbers
Le 17-mars-06, à 16:32, [EMAIL PROTECTED] a écrit : I don't agree. I think you slip from minds can be implemented on more than one kind of hardware to minds do not need any kind of hardware. I slip? Where ? I take care of precisely not doing that, mainly through UDA *plus* the movie graph argument for eliminating any use of Occam razor. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Numbers
Le 15-mars-06, à 17:51, Georges Quenot a écrit : *If* comp is true. I am not sure of that. Me too. But it is the theory I am studying. Also comp provides some neat etalon philosophy to compare with other theories. The advantage of comp (which I recall includes Church thesis) is that, at least, many fundamental questions can be addressed. Which one for instance (that is not addressed in the view of the universe/multiverse as a mathematical object)? The relation between first and third person concepts. Comp allows (at least) and actually necessitates the use of theoretical computer science(s). It is a mine of interesting results. My work exploits many of them for the translation of the UD Argument in the language of the universal machine. Actually it is one of them, Godel's theorem, which convinces me of the possibility of the enterprise. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Solipsism (was: Numbers)
Le 17-mars-06, à 20:27, Hal Finney a écrit : John M writes: 1. do we have a REAL argument against solipsism? Let me express how solipsism can be analyzed in the model where physical reality is part of mathematical reality. Let us adopt Bruno's UDA perspective: the Universal Dovetailer (UD) is an abstract machine that runs all possible computer programs. In this way it creates all possible universes, and more... it creates all possible information objects: all of mathematics, logic, all written texts, everything. In particular it creates the information patterns of conscious entities like you and me. Let us assume that this in fact represents the reality of the multiverse, that what we perceive and experience is all caused by the operation of the UD, when it creates information patterns that correspond to those experienes. I know that many people here reject this hypothesis, but let us follow it forward to see what it can say about solipsism. The first thing to notice is that within the UD, each person exists more than once. There are many programs that include a particular information pattern in their output, in fact an infinite number of programs. Some of those programs will look much like the kind of model a physicist might construct for a theory of everything. It would include the physical laws and initial conditions that define our universe. Running that program forward would create the entire history of our universe, including the experiences of all of its inhabitants. However there are other kinds of programs that would also create the patterns of our conscious experiences. Some might do it purely by random chance: they might produce enormous outputs and somewhere buried in there will be the pattern that corresponds to a portion of our experience. Others would include bizarre universes such as one inhabited by aliens who create computer simulations of other kinds of beings, and who have created us. Yet another example would be a universe composed only of one person, with all that is outside of him being supplied by the computer program, perhaps from some kind of table of sensory impressions, so that only he is real within that universe. Solipsism is the doctrine that only I exist, that everything else is an illusion. In the context of the platonic multiverse, it would correspond to that last case: a portion of the UD program where only the one person is in his universe, and nothing else in the universe is real. So this raises the question: given that I exist multiple times within the UD structure, and given that in some of them the universe I see around me is real and in some of them it is an illusion, which is the reality for me? In which one do I actually exist? I believe Bruno argues, and I agree, that this is a meaningless question. You exist in all of them. There is no single instance of your information pattern which is really you. Your consciousness spans all of the places in the UD where it is instantiated. However, there is a related question which is relevant: what will happen next? If some of your consciousness is in the real universe, and some of it is in universes where you are an alien simulation, some in a universe where it is a random fluctuation, and some in a universe where you are all there is, how can you make a prediction about the future? In the random universe you would expect to disintegrate into chaos. In the aliens, they might open up the simulation and start talking to you. In the solipsism case, various bizarre things might happen. And in the plain vanilla universe, you would expect things to go along pretty much as you remember them. Here is where I may depart from Bruno, although I am not sure. OK. I argue that you can in fact set up a probability distribution over all of the places in the UD where your mind exists, and it is based roughly on the size of the part of the UD program that creates that information pattern. I will take the time to come back on this. I have a problem with this which is not entirely unrelated to our perennial ASSA/RSSA debate. Another problem is related with the fact that from the first person point of view it is hard to distinguish big and little programs, and their way of recurring hyper-redundantly. Recall that the UD in effect runs all programs at once. But some programs are shorter than others. I use the notion of algorithmic complexity and the associated measure, which is called the Universal Distribution (an unfortunate collision of the UD acronym). Basically this says that the measure of the output of a given UD program of n bits is 1/2^n. Yes. And it is even a machine independent notion (modulo some constant). But big programs cannot be dismissed so easily, I will try to find a short explanation for why I think saying yes to the doctor makes, for the first person point of view,
Re: Numbers
Quentin Anciaux wrote: Le Samedi 18 Mars 2006 01:58, [EMAIL PROTECTED] a écrit : Ground them operationally, then. Real things have real properties and unreal things don't. Real properties can be observed empirically. Primeness then is not a real property. I have to ask you one more time, but I'll reverse the question, what does it means for an object not to be real (hence being abstract) ? it is not a joke, I want to know. I will insert my grain of salt in a very active thread In my opinion, reality is relative, more precisely, the perception of reality depends on the level of implementation or the level of illusion. Here I use the term implementation to refer to third person perception and illusion to refer to first person perception. For example, a simulated character perceives simulated objects as real. He has the illusion that they are real. Similarly we perceive our world to be real. It kicks back. We have the illusion that our world is real. Is it? It all depends how you look at it. One could say that our consciousness is emergent by the bootstrapping of reflexive illusions: our world is an illusion that allows us to have the illusion that we exist. (I am not sure but it may be that my term "illusion" has the same meaning as the term "dream" that Bruno very often uses as in "we are dreaming machines." ) Thus, in my opinion, there is no absolute reality. All we have is the implementation/illusion of reality at our level of implementation/illusion. George Levy --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Numbers
Georges Quénot wrote: Georges Quénot wrote: 1. It is not so sure that there actually exist sets of equations of which a Harry Potter universe includes a counterpart of you. I meant: 1. It is not so sure that there actually exist sets of equations of which a Harry Potter universe including a counterpart of you would be a solution. Georges. 1) Any configuration of matterial bodies can be represented as a some very long number 2) Any number is the solution to some sufficiently complicated polynomial --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Numbers
George Levy wrote: Quentin Anciaux wrote: Le Samedi 18 Mars 2006 01:58, [EMAIL PROTECTED] a écrit : Ground them operationally, then. Real things have real properties and unreal things don't. Real properties can be observed empirically. Primeness then is not a real property. I have to ask you one more time, but I'll reverse the question, what does it means for an object not to be real (hence being abstract) ? it is not a joke, I want to know. I will insert my grain of salt in a very active thread In my opinion, reality is relative, more precisely, the perception of reality depends on the level of implementation or the level of illusion. Here I use the term implementation to refer to third person perception and illusion to refer to first person perception. For example, a simulated character perceives simulated objects as real. He has the illusion that they are real. Yes but he is simulated by something real (or simulated by something simulated by something real). Similarly we perceive our world to be real. It kicks back. We have the illusion that our world is real. Is it? that's the simplest explanation. It all depends how you look at it. One could say that our consciousness is emergent by the bootstrapping of reflexive illusions: our world is an illusion that allows us to have the illusion that we exist. Although the illusions we are familiar with do not work on a bootstrapping basis, --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Territories and maps
On Fri, Mar 17, 2006 at 04:55:37PM -0800, [EMAIL PROTECTED] wrote: [...] Maps are isomorphic to territories, but are not territories. Well. Territories *are* maps. Just a very specific type of map but maps anyway. err...no they are not. You can't grow potatoes in a map of a farm. If the map is sufficiently detailed it contains a full simulation down to the chemistry level of the soil, then most people would say that you can grow (simulated) potatoes on the map. Identity is just an isomorphism among possibly many others. All identity relations are isomorphisms as well. Not all isomporhisms are identity relations. The territory can be the map and indeed vice versa. You can't fold up the farm and put it in your pocket. I can't fold up the atlas that sits on my bookshelf and fit it in my pocket either. Yet the atlas is undeniably a map, and undeniably less detailed than the sorts of maps that might be confused with territory. Bruno's commentary is still valid. Ad hominem arguments like these are simply laughable. -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Numbers
[EMAIL PROTECTED] wrote: Georges Quénot wrote: 1. It is not so sure that there actually exist sets of equations of which a Harry Potter universe including a counterpart of you would be a solution. 1) Any configuration of material bodies can be represented as a some very long number Unlike some others I did not introduce representations. One cannot represent any configuration of material bodies by a number with an infinite precision however long the number. As some mentioned also, you would need a (de)coding scheme. My 2. and 3. remain anyway. Georges. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Fw: Numbers
But the tape can also hold an encoding of the Turing machine to perform the interpretation. This is the essence of the compiler theorem. One can simply iterate this process such that there is no concrete machine interpreting the tape. I think this is another way of putting the UDA. Cheers On Fri, Mar 17, 2006 at 01:31:22PM -0800, Norman Samish wrote: [EMAIL PROTECTED] wrote: Hal Finney wrote: The first is that numbers are really far more complex than they seem. When we think of numbers, we tend to think of simple ones, like 2, or 7. But they are not really typical of numbers. Even restricting ourselves to the integers, the information content of the average number is enormous; by some reasoning, infinite. Most numbers are a lot bigger than 2 or 7! They are big enough to hold all of the information in our whole universe; indeed, all of the information in virtually every possible variant of our universe. A single number can (in some sense) hold this much information. How ? Surely this claim needs justification! ~ The single number can be of infinite length, with infinite digits, and can therefore contain unlimited information. One could compare the single number to a tape to a Universal Turing Machine. Granted, the UTM needs a head and a program to read the tape, so the tape by itself is not sufficient to hold information. Norman ` -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: Fw: Numbers
Are you saying that a tape of infinite length, with infinite digits, is not Turing emulable? I don't understand how the 'compiler theorem' makes a 'concrete' machine unnecessary. I agree that the tape can contain an encoding of the Turing machine - as well as anything else that's describable. Nevertheless, it seems to me there has to be a 'concrete' machine executing the tape, irrespective of the contents of the tape. Norman ~ - Original Message - From: Russell Standish [EMAIL PROTECTED] To: everything-list@googlegroups.com Sent: Friday, March 17, 2006 2:37 PM Subject: Re: Fw: Numbers But the tape can also hold an encoding of the Turing machine to perform the interpretation. This is the essence of the compiler theorem. One can simply iterate this process such that there is no concrete machine interpreting the tape. I think this is another way of putting the UDA. Cheers On Fri, Mar 17, 2006 at 01:31:22PM -0800, Norman Samish wrote: [EMAIL PROTECTED] wrote: Hal Finney wrote: The first is that numbers are really far more complex than they seem. When we think of numbers, we tend to think of simple ones, like 2, or 7. But they are not really typical of numbers. Even restricting ourselves to the integers, the information content of the average number is enormous; by some reasoning, infinite. Most numbers are a lot bigger than 2 or 7! They are big enough to hold all of the information in our whole universe; indeed, all of the information in virtually every possible variant of our universe. A single number can (in some sense) hold this much information. How ? Surely this claim needs justification! ~ The single number can be of infinite length, with infinite digits, and can therefore contain unlimited information. One could compare the single number to a tape to a Universal Turing Machine. Granted, the UTM needs a head and a program to read the tape, so the tape by itself is not sufficient to hold information. Norman ` --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
