Re: Asifism revisited.
David Nyman skrev: You have however drawn our attention to something very interesting and important IMO. This concerns the necessary entailment of 'existence'. 1. The relation 1+1=2 is always true. It is true in all universes. Even if a universe does not contain any humans or any observers. The truth of 1+1=2 is independent of all observers. 2. If you have a set of rules and an initial condition, then there exist a universe with this set of rules and this initial condition. Because it is possible to compute a new situation from a situation, and from this new situation it is possible to compute another new situation, and this can be done for ever. This unlimited set of situations will be a universe that exists independent of all humans and all observers. Noone needs to make these computations, the results of the computations will exist anyhow. 3. All mathmatically possible universes exists, and they all exist in the same way. Our universe is one of those possible universes. Our universe exists independant of any humans or any observers. 4. For us humans are the universes that contain observers more interesting. But there is no qualitaive difference between universes with observers and universes without observers. They all exist in the same way. The GoL-universes (every initial condition will span a separate universe) exist in the same way as our universe. But because we are humans, we are more intrested in universes with observers, and we are specially interested in our own universe. But otherwise there is noting special with our universe. -- 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: Asifism revisited.
On 05/07/07, Torgny Tholerus [EMAIL PROTECTED] wrote: TT: All mathmatically possible universes exists, and they all exist in the same way. Our universe is one of those possible universes. Our universe exists independant of any humans or any observers. DN: But here at the heart of your argument is the confusion again over language. If we grant that a mathematically possible universe exists 'independently' (i.e. other than as a sub-structure of the A-Universe) it - and all consequences flowing from it - must exist self-relatively. This is the crucial entailment of 'independent' existence, as we discussed before. And it exposes the confusion of the two distinct senses of 'independent'. The first sense is of course that an independent universe does not 'depend' on any observers it instantiates to grant it existence (i.e. they don't 'cause' it to exist). It's in just this sense that it's 'independent' or self-relative, and this is the sense you rely on. But the second and crucial sense flows directly out of this 'self-relative independence': which is that any self-relative universe capable of generating the necessary structure simply *entails* the existence of 'observers' (i.e. self-relative sub-structures). IOW, self-relation is what observation *is*. It's in precisely this crucial sense that an 'independently existing universe' is not 'independent of observation'. On the contrary: it *entails* observation. And of course our existence as observers in self-relation to the A-Universe demonstrates this 'dependency' in precisely this critical sense. David David Nyman skrev: You have however drawn our attention to something very interesting and important IMO. This concerns the necessary entailment of 'existence'. 1. The relation 1+1=2 is always true. It is true in all universes. Even if a universe does not contain any humans or any observers. The truth of 1+1=2 is independent of all observers. 2. If you have a set of rules and an initial condition, then there exist a universe with this set of rules and this initial condition. Because it is possible to compute a new situation from a situation, and from this new situation it is possible to compute another new situation, and this can be done for ever. This unlimited set of situations will be a universe that exists independent of all humans and all observers. Noone needs to make these computations, the results of the computations will exist anyhow. 3. All mathmatically possible universes exists, and they all exist in the same way. Our universe is one of those possible universes. Our universe exists independant of any humans or any observers. 4. For us humans are the universes that contain observers more interesting. But there is no qualitaive difference between universes with observers and universes without observers. They all exist in the same way. The GoL-universes (every initial condition will span a separate universe) exist in the same way as our universe. But because we are humans, we are more intrested in universes with observers, and we are specially interested in our own universe. But otherwise there is noting special with our universe. -- 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: Some thoughts from Grandma
On 05/07/07, Bruno Marchal [EMAIL PROTECTED] wrote: BM: OK. I would insist that the comp project (extract physics from comp) is really just a comp obligation. This is what is supposed to be shown by the UDA (+ MOVIE-GRAPH). Are you OK with this. It *is* counterintuitive. DN: I believe so - it's what the reductio ad absurdum of the 'physical' computation in the 'grandma' post was meant to show. My version of the 'comp obligation' would then run as follows. Essentially, if comp and number relations are held to be 'real in the sense that I am real', then to use Plato's metaphor, it is numbers that represent the forms outside the cave. If that's so, then physics is represented by the shadows the observers see on the wall of the cave. This is what I mean by 'independent' existence in my current dialogue with Torgny: i.e the 'arithmetical realism' of numbers and their relations in the comp frame equates to their 'independence' or self-relativity. And the existence of 'arithmetical observers' then derives from subsequent processes of 'individuation' intrinsic to such fundamental self-relation. Actually, I find the equation of existence with self-relativity highly intuitive. BM: Then, the interview of the universal machine is just a way to do the extraction of physics in a constructive way. It is really the subtleties of the incompleteness phenomena which makes this interview highly non trivial. DN: This is the technical part. But at this stage grandma has some feeling for how both classical and QM narratives should be what we expect to emerge from constructing physics in this way. BM: There is no direct (still less one-one) correlation between the mental and the physical, that is the physical supervenience thesis is incompatible with the comp hyp. [A quale of a pain] felt at time t in place x, is not a product of the physical activity of a machine, at time t in place x. Rather, it is the whole quale of [a pain felt at time t in place x] which is associated with an (immaterial and necessarily unknown) computational state, itself related to its normal consistent computational continuations. snip Comp makes the yes doctor a gamble, necessarily. That is: assuming the theory comp you have to understand that, by saying yes to the doctor, you are gambling on a level of substitution. At the same time you make a gamble on the theory comp itself. There is double gamble here. Now, the first gamble, IF DONE AT THE RIGHT COMP SUBSTITUTION LEVEL, is comp-equivalent with the natural gamble everybody do when going to sleep, or just when waiting a nanosecond. In some sense nature do that gamble in our place all the time ... But this is somethjng we cannot know, still less assert in any scientific way, and that is why I insist so much on the theological aspect of comp. This is important in practice. It really justify that the truth of the yes doctor entails the absolute fundamental right to say NO to the doctor. The doctor has to admit he is gambling on a substitution level. If comp is true we cannot be sure on the choice of the subst. level. DN: ISTM that a consequence of the above is that the issue of 'substitution level' can in principle be 'gambled' on by cloning, or by evolution (because presumably it has been, even though we can't say how). But by engineering or design??? Would there ever be any justification, in your view, for taking a gamble on being uploaded to an AI program - and if so, on the basis of what theory? Essentially, this is what I've been trying to get at. That is: assuming comp, HOW would we go about making a 'sound bet', founded on a specific AI theory, that some AI program instantiated by a 'physical' computer, will equate to the continuity of our own observation? The second question I have is summarised in my recent posts about 'sense and 'action'. Essentially, I've been trying to postulate that the correlation of consciousness and physics is such that the relations between both sets of phenomena are a necessary entailment, not an additional assumption. ISTM that this is essential to avoid all the nonsense about zombies. And not only this, but to show that the reciprocity between experience - e.g. suffering - and behaviour (indeed the whole entailment of 'intentionality') is a necessary consequence of fundamental self-relation (arithmetical relations, in the comp frame). Now, my attempt to do this has been to postulate that 'sense' and 'action' are simply observer-related aspects of a non-decomposable fundamental self-relation, which in the comp frame would equate to a set of number-relations. But ISTM that for this to be true, the observer and physical narratives would somehow need to follow an 'identical' or isomorphic trajectory for their invariant relation to emerge in the way that it seems to. Do you think that this idea has any specific sense or relevance in the comp frame? BM: Does this help? I assert some propositions without justifying them, because the
Re: Penrose and algorithms
On 29 jun, 19:10, Jesse Mazer [EMAIL PROTECTED] wrote: LauLuna wrote: On 29 jun, 02:13, Jesse Mazer [EMAIL PROTECTED] wrote: LauLuna wrote: For any Turing machine there is an equivalent axiomatic system; whether we could construct it or not, is of no significance here. But for a simulation of a mathematician's brain, the axioms wouldn't be statements about arithmetic which we could inspect and judge whether they were true or false individually, they'd just be statements about the initial state and behavior of the simulated brain. So again, there'd be no way to inspect the system and feel perfectly confident the system would never output a false statement about arithmetic, unlike in the case of the axiomatic systems used by mathematicians to prove theorems. Yes, but this is not the point. For any Turing machine performing mathematical skills there is also an equivalent mathematical axiomatic system; if we are sound Turing machines, then we could never know that mathematical system sound, in spite that its axioms are the same we use. I agree, a simulation of a mathematician's brain (or of a giant simulated community of mathematicians) cannot be a *knowably* sound system, because we can't do the trick of examining each axiom and seeing they are individually correct statements about arithmetic as with the normal axiomatic systems used by mathematicians. But that doesn't mean it's unsound either--it may in fact never produce a false statement about arithmetic, it's just that we can't be sure in advance, the only way to find out is to run it forever and check. Yes, but how can there be a logical impossibility for us to acknowledge as sound the same principles and rules we are using? But Penrose was not just arguing that human mathematical ability can't be based on a knowably sound algorithm, he was arguing that it must be *non-algorithmic*. No, he argues in Shadows of the Mind exactly what I say. He goes on arguing why a sound algorithm representing human intelligence is unlikely to be not knowably sound. And the impossibility has to be a logical impossibility, not merely a technical or physical one since it depends on Gödel's theorem. That's a bit odd, isn't it? No, I don't see anything very odd about the idea that human mathematical abilities can't be a knowably sound algorithm--it is no more odd than the idea that there are some cellular automata where there is no shortcut to knowing whether they'll reach a certain state or not other than actually simulating them, as Wolfram suggests in A New Kind of Science. The point is that the axioms are exactly our axioms! In fact I'd say it fits nicely with our feeling of free will, that there should be no way to be sure in advance that we won't break some rules we have been told to obey, apart from actually running us and seeing what we actually end up doing. I don't see how to reconcile free will with computationalism either. Regards --~--~-~--~~~---~--~~ 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: Penrose and algorithms
LauLuna wrote: On 29 jun, 19:10, Jesse Mazer [EMAIL PROTECTED] wrote: LauLuna wrote: On 29 jun, 02:13, Jesse Mazer [EMAIL PROTECTED] wrote: LauLuna wrote: For any Turing machine there is an equivalent axiomatic system; whether we could construct it or not, is of no significance here. But for a simulation of a mathematician's brain, the axioms wouldn't be statements about arithmetic which we could inspect and judge whether they were true or false individually, they'd just be statements about the initial state and behavior of the simulated brain. So again, there'd be no way to inspect the system and feel perfectly confident the system would never output a false statement about arithmetic, unlike in the case of the axiomatic systems used by mathematicians to prove theorems. Yes, but this is not the point. For any Turing machine performing mathematical skills there is also an equivalent mathematical axiomatic system; if we are sound Turing machines, then we could never know that mathematical system sound, in spite that its axioms are the same we use. I agree, a simulation of a mathematician's brain (or of a giant simulated community of mathematicians) cannot be a *knowably* sound system, because we can't do the trick of examining each axiom and seeing they are individually correct statements about arithmetic as with the normal axiomatic systems used by mathematicians. But that doesn't mean it's unsound either--it may in fact never produce a false statement about arithmetic, it's just that we can't be sure in advance, the only way to find out is to run it forever and check. Yes, but how can there be a logical impossibility for us to acknowledge as sound the same principles and rules we are using? The axioms in a simulation of a brain would have nothing to do with the high-level conceptual principles and rules we use when thinking about mathematics, they would be axioms concerning the most basic physical laws and microscopic initial conditions of the simulated brain and its simulated environment, like the details of which brain cells are connected by which synapses or how one cell will respond to a particular electrochemical signal from another cell. Just because I think my high-level reasoning is quite reliable in general, that's no reason for me to believe a detailed simulation of my brain would be sound in the sense that I'm 100% certain that this precise arrangement of nerve cells in this particular simulated environment, when allowed to evolve indefinitely according to some well-defined deterministic rules, would *never* make a mistake in reasoning and output an incorrect statement about arithmetic (or even that it would never choose to intentionally output a statement it believed to be false just to be contrary). But Penrose was not just arguing that human mathematical ability can't be based on a knowably sound algorithm, he was arguing that it must be *non-algorithmic*. No, he argues in Shadows of the Mind exactly what I say. He goes on arguing why a sound algorithm representing human intelligence is unlikely to be not knowably sound. He does argue that as a first step, but then he goes on to conclude what I said he did, that human intelligence cannot be algorithmic. For example, on p. 40 he makes quite clear that his arguments throughout the rest of the book are intended to show that there must be something non-computational in human mental processes: I shall primarily be concerned, in Part I of this book, with the issue of what it is possible to achieve by use of the mental quality of 'understanding.' Though I do not attempt to define what this word means, I hope that its meaning will indeed be clear enough that the reader will be persuaded that this quality--whatever it is--must indeed be an essentail part of that mental activity needed for an acceptance of the arguments of 2.5. I propose to show that the appresiation of these arguments must involve something non-computational. Later, on p. 54: Why do I claim that this 'awareness', whatever it is, must be something non-computational, so that no robot, controlled by a computer, based merely on the standard logical ideas of a Turing machine (or equivalent)--whether top-down or bottom-up--can achieve or even simulate it? It is here that the Godelian argument plays its crucial role. His whole Godelian argument is based on the idea that for any computational theorem-proving machine, by examining its construction we can use this understanding to find a mathematical statement which *we* know must be true, but which the machine can never output--that we understand something it doesn't. But I think my argument shows that if you were really to build a simulated mathematician or community of mathematicians in a computer, the Godel statement for this system would only be true *if* they never made a mistake in
