RE: Numbers, Machine and Father Ted
Bruno Marchal writes: Church thesis just assert that a universal turing machine can compute all computable functions from N to N. It relate a mathematical object with a human cognitive notion. It does not invoke physical machine at all. In a sense that is true, but a TM is still a model of what could possibly be built in a physical universe such as ours. Of course the model is still valid irrespective of the existence of a physical machine or indeed a physical universe, but if you abandon the idea of a physical universe there is no need to constrain yourself to models based on one. I am not sure why you say the TM model is based on what we can build in the physical universe. Both with comp and without, the physical universe is a priori far richer than a UTM. The UTM of Turing relies explicitly on an analysis of human capacity for computations. Post universal systems are based on analysis of mathematician psychology. The word machine implies something that can be physically built, even though that definition is stretched a bit when we talk about idealised machines. Geometric compass and ruler proofs are based on what can be done with a physical compass and ruler, even though they are still valid if all the compasses and rulers are destroyed in a big fire, and even though they strictly rely on idealised lines and points. If there is no physical universe, then there is no basis for favouring one mathematical model (of geometry, of computation) over all the other theoretically possible ones, except that it *seems* we are living in such a universe. If we go beyond the apparent to true reality why not say that the requisite computations are just there rather than invoking a TM? So I suppose the two questions I have (which you partly answer below) are, having arrived at step 8 of the UDA could you go back and say that the UD is not really necessary but all the required computations exist eternally without any generating mechanism or program (after all, you make this assumption for the UD itself), or alternatively, could you have started with step 8 and eliminate the need for the UD in the argument at all? This is the way I proceed in Conscience and Mechanism. I begin, by using the movie graph argument MGA, to show that consciousness cannot be attached to physical activities, and then I use the UD to explain that the comp-physics get the form of a measure on all computations. In my Lille thesis I do the opposite because the UDA is simpler than the MGA. It is not so important. UD is needed to justify and to make mathematically precise the ontic 3-observer moments. They correspond to its (the UD) accessible states. But any other mathematical model of computation, even if impossible in the real world, such as infinite parallel computers, would do just as well? It seems that this is the computer you have in mind to run the UD. Only for providing a decor for a story. This assumption is eliminated when we arrive (step eight of UDA-8) at the conclusion that universal digital machine cannot distinguish any reality from an arithmetical one. That's OK and the argument works (assuming comp etc.), but in Platonia you have access to hypercomputers of the best and fastest kind. Fastness is relative in Platonia. Universal machine can always been sped up on almost all their inputs (There is a theorem by Blum and Marquez to that effect). Then indeed there are the angels and hierachies of non-comp machine. A vast category of angels can be shown to have the same hypostases (so we cannot tested by empirical means if we are such angels). Then they are entities very closed to the one, having stronger hypostases, i.e. you need to add axioms to G and G* (or V, V* with explicit comp) to get them. Of course I was joking when I said best and fastest. In Platonia there is no actual time and everything is as fast and as perfect as you want it. OK. But of course there exist notion of relative time: a fast Fourier transform is faster than a slow Fourier transform, even in Platonia. Of course this can be said in term of number of steps in computations (no need to invoke time). OK, I understand that point. Stathis Papaioannou _ Be one of the first to try Windows Live Mail. http://ideas.live.com/programpage.aspx?versionId=5d21c51a-b161-4314-9b0e-4911fb2b2e6d --~--~-~--~~~---~--~~ 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: To observe is to......EC
Colin Hales wrote: When you are in EC it looks like more relative speed (compared your local EC string), time goes slower. Traveling faster than the speed of light is meaningless EC can't 'construct/refresh' you beyond the rate it's () operate at. There's nothing to travel in anything and nothing to travel. It's meaningless. It's hard not to use 'temporal' language, isn't it? So when you say the 'rate' the () operate at, you're referring ultimately to representational granularity? And 'travel' is redistribution of structure over this granularity? In deep 'time' (many more state changes in the proof beyond 'now') EC predicts (I think) the equivalent of approaching the speed of light, only not through moving fast, but by dissipation of the fabric of space/matter (there is no time). To be alive then (see how our words are troublesome?) would feel the same. But if you compared the rate of progress of EC would be different. An EC aging process of the time it takes to write WORD in the year 10^^25 could be our equivalent of 3 months of current EC state evolution. It's the same effect as that got by going really fast. Yes, this would resolve the 'twin paradox' through the way that each twin's structural redistribution is dissipated differentially through its 'systemic acceleration' versus its 'rate of internal change'. If I've followed you, in saying 'there is no time', you're taking the view (e.g. with Barbour) that there is only 'change' in the sense of the sort that we notice in comparing one part of a 4-dimensional *compresent* structure with another, as opposed to change that 'annihilates the prior' in the A-series view of 'time'. So, in this case, the EC 'nows' containing 'me' are identified 'indexically' within a continuous/structural ensemble? David Colin Hales wrote: 3) The current state of the proof is 'now' the thin slice of the present. Just a couple of questions for the moment Colin, until I've a little more time. Actually, that's precisely what it's about - 'time'. Just how thin is this slice of yours? And is it important whether we conceive it as Now-You-See-It-Now-You-Don't time, or does it work in 'block' time? This may be a maths vs. 'primitive' EC issue. Anyway, if NYSINYD, what is the status of the 'thens'? That is, if nothing but a wafer-thin 'now' is actual, how does this effect process-structure at the macro-level, which we encounter as Vast ensembles of events? Does reality work as just the flimsiest meniscus? This is presumably not a problem in a block version. Also, what about STR with respect to 'now' and the present? But perhaps I'm jumping the gun. David Jump away! I'm letting EC 'rules of formation' ferment at the moment Preamble... the mental secret to EC is to attend to one of my all time faves: Leibniz. His approach has always born fruit in my analyses. What he was on about, translated into modern jargon, was that brain operation is a literal metaphor for the deep structure of matter. Brain operation is a whole bunch of nested resonating loops. I have observed in general and found the same pattern in a lot of things - trees, clouds... and most wonderfully in the boiling froth... rice is best. :-) Time. It's important to distinguish between the mental perception of it and the reality of it. * TIME PERCEIVED There is a neurological condition (name escapes me) where the visual field is updated on mass as usual but at a repetition rate much lower than usual. Try pouring a glass of wine you see the glass at one instant and the next time you see it: overfull. Try crossing a road. A car is 200m away... you walk and bang, it's 10m away. All throughout this, EC state changes have been running normally. In a normally operating brain in the face of novelty, where more brain regions are involved as a result of dealing with the novelty (such as when traveling in a new area), more energy is recruited, more brain regions are active and the cognitive update rate is increased. Time feels like its going slower. All throughout this, EC state changes have been running normally. * TIME REALITY - according to EC Time is virtual. There is only EC proof and its current state. The best way of imaging it is to think of it as a nested structure of nearest neighbour interactions according to a local 'energy' optimization rule. 'Energy' is a metric counting how many ()s there are in a given structure and how many it can do without and still remain the same 'thing'. () () could go to (()()) or vice versa. It doesn't matter. Overall it's a one way trip (door slams behind you) depending on what 'nearest neighbour' situation results from the present 'nearest neighbour' situation. Locally there can be lossless EC transformations. Globally the net result is dissipation back to primitive () (and then to its constituents (noise). There is no future, only next state.
Mail problem
Le 23-oct.-06, à 18:52, David Nyman a écrit : Bruno, I think it's the Beta version that's intermittently losing posts - Colin lost one, and I've lost two. I've posted a topic to this effect for the list. You may wish to revert to the old version. That does not work either but apparently my mail problem is due to a massive spam attack on my institution net. I have just answered one of your last post, but I got a message saying it will be send with some important delay. I will get the same message for this one, I guess. Apology for those inconveniences. 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, Machine and Father Ted
Le 23-oct.-06, à 15:58, David Nyman a écrit : Bruno Marchal wrote: Here I disagree, or if you want make that distinction (introduced by Peter), you can sum up the conclusion of the UD Argument by: Computationalism entails COMP. Bruno, could you distinguish between your remarks vis-a-vis comp, that on the one hand: a belief in 'primary' matter can be retained provided it is not invoked in the explanation of consciousness, Imagine someone who has been educated during his entire childhood with the idea that anything moving on the road with wheels is pulled by invisible horses. Imagine then that becoming an adult he decides to study physics and thermodynamics, and got the understanding that there is no need to postulate invisible horses for explaining how car moves around. Would this proves the non existence of invisible horses? Of course no. From a logical point of view you can always add irrefutable hypotheses making some theories as redundant as you wish. The thermodynamician can only say that he does not need the invisible horses hypothesis for explaining the movement of the cars , like Laplace said to Napoleon that he does not need the God hypothesis in his mechanics. And then he is coherent as far as he does not use the God concept in is explanation. The comp hypothesis, which I insist is the same as standard computationalism (but put in a more precise way if only because of the startling consequences) entails that primary matter, even existing, cannot be used to justify anything related to the subjective experience, and this includes any *reading* of pointer needle result of a physical device. So we don't need the postulate it. And that is a good thing because the only definition of primary matter I know (the one by Aristotle in his metaphysics) is already refuted by both experiments and theory (QM or just comp as well). and on the other: that under comp 'matter' emerges from (what I've termed) a recursively prior 1-person level. Why are these two conclusions not contradictory? 'Matter', or the stable appearance of matter has to emerge from the mathematical coherence of the computations. This is what the UDA is supposed to prove. Scientifically it means that you can test comp by comparing some self-observing discourses of digital machines (those corresponding to the arithmetical translation of the UDA (AUDA)) with empirical physics. Again this cannot disprove the (religious) belief in Matter, or in any Gods, for sure. You will have to attach consciousness to actual material infinite. Why is this the case? Because it is a way to prevent the UDA reasoning (at least as currently exibited) to proceed. It makes sense to say that some actual material infinity is not duplicable, for example. To be sure, the AUDA would still work (but could be less well motivated). 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, Machine and Father Ted
Bruno Marchal wrote: Le 23-oct.-06, à 15:58, David Nyman a écrit : Bruno Marchal wrote: Here I disagree, or if you want make that distinction (introduced by Peter), you can sum up the conclusion of the UD Argument by: Computationalism entails COMP. Bruno, could you distinguish between your remarks vis-a-vis comp, that on the one hand: a belief in 'primary' matter can be retained provided it is not invoked in the explanation of consciousness, Imagine someone who has been educated during his entire childhood with the idea that anything moving on the road with wheels is pulled by invisible horses. Imagine then that becoming an adult he decides to study physics and thermodynamics, and got the understanding that there is no need to postulate invisible horses for explaining how car moves around. Would this proves the non existence of invisible horses? Of course no. From a logical point of view you can always add irrefutable hypotheses making some theories as redundant as you wish. The thermodynamician can only say that he does not need the invisible horses hypothesis for explaining the movement of the cars , like Laplace said to Napoleon that he does not need the God hypothesis in his mechanics. And then he is coherent as far as he does not use the God concept in is explanation. The analogy isn't analogous. It is actually the Platonic numbers that are the invisible horses. No-one has ever seen a Platonic object. The vehicle of mathematics is driven by the engine of mathematicians, chalk, blackboards, computers etc -- all material. The comp hypothesis, which I insist is the same as standard computationalism (but put in a more precise way if only because of the startling consequences) entails that primary matter, even existing, cannot be used to justify anything related to the subjective experience, and this includes any *reading* of pointer needle result of a physical device. So we don't need the postulate it. And that is a good thing because the only definition of primary matter I know (the one by Aristotle in his metaphysics) is already refuted by both experiments and theory (QM or just comp as well). Of course QM does not refute materialism. and on the other: that under comp 'matter' emerges from (what I've termed) a recursively prior 1-person level. Why are these two conclusions not contradictory? 'Matter', or the stable appearance of matter has to emerge from the mathematical coherence of the computations. Which emerge from...? This is what the UDA is supposed to prove. Scientifically it means that you can test comp by comparing some self-observing discourses of digital machines (those corresponding to the arithmetical translation of the UDA (AUDA)) with empirical physics. Again this cannot disprove the (religious) belief in Matter, or in any Gods, for sure. The material world is visible, Platonia is not. You will have to attach consciousness to actual material infinite. Why is this the case? Because it is a way to prevent the UDA reasoning (at least as currently exibited) to proceed. It makes sense to say that some actual material infinity is not duplicable, for example. To be sure, the AUDA would still work (but could be less well motivated). It makes sense to say that consciousness depends on levels of emulation -- providing there is a 0-level pinned down by matter. 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, Machine and Father Ted
1Z wrote: Bruno Marchal wrote: Le 23-oct.-06, à 15:58, David Nyman a écrit : Bruno Marchal wrote: Here I disagree, or if you want make that distinction (introduced by Peter), you can sum up the conclusion of the UD Argument by: Computationalism entails COMP. Bruno, could you distinguish between your remarks vis-a-vis comp, that on the one hand: a belief in 'primary' matter can be retained provided it is not invoked in the explanation of consciousness, Imagine someone who has been educated during his entire childhood with the idea that anything moving on the road with wheels is pulled by invisible horses. Imagine then that becoming an adult he decides to study physics and thermodynamics, and got the understanding that there is no need to postulate invisible horses for explaining how car moves around. Would this proves the non existence of invisible horses? Of course no. From a logical point of view you can always add irrefutable hypotheses making some theories as redundant as you wish. The thermodynamician can only say that he does not need the invisible horses hypothesis for explaining the movement of the cars , like Laplace said to Napoleon that he does not need the God hypothesis in his mechanics. And then he is coherent as far as he does not use the God concept in is explanation. The analogy isn't analogous. It is actually the Platonic numbers that are the invisible horses. No-one has ever seen a Platonic object. The vehicle of mathematics is driven by the engine of mathematicians, chalk, blackboards, computers etc -- all material. The comp hypothesis, which I insist is the same as standard computationalism (but put in a more precise way if only because of the startling consequences) entails that primary matter, even existing, cannot be used to justify anything related to the subjective experience, and this includes any *reading* of pointer needle result of a physical device. So we don't need the postulate it. And that is a good thing because the only definition of primary matter I know (the one by Aristotle in his metaphysics) is already refuted by both experiments and theory (QM or just comp as well). Of course QM does not refute materialism. and on the other: that under comp 'matter' emerges from (what I've termed) a recursively prior 1-person level. Why are these two conclusions not contradictory? 'Matter', or the stable appearance of matter has to emerge from the mathematical coherence of the computations. Which emerge from...? This is what the UDA is supposed to prove. Scientifically it means that you can test comp by comparing some self-observing discourses of digital machines (those corresponding to the arithmetical translation of the UDA (AUDA)) with empirical physics. Again this cannot disprove the (religious) belief in Matter, or in any Gods, for sure. The material world is visible, Platonia is not. You will have to attach consciousness to actual material infinite. Why is this the case? Because it is a way to prevent the UDA reasoning (at least as currently exibited) to proceed. It makes sense to say that some actual material infinity is not duplicable, for example. To be sure, the AUDA would still work (but could be less well motivated). It makes sense to say that consciousness depends on levels of emulation -- providing there is a 0-level pinned down by matter. Bruno http://iridia.ulb.ac.be/~marchal/ David and 1Z: How is exploring the Mandelbrot set through computation any different than exploring subatomic particles through computation (needed to successively approach the accuracies needed for the collisions in the linear accelerator)? Is not the only difference that in one case we have a priori labeled the object of study 'matter' and in the other case a 'set of numbers'? Granted, in the matter case we need more energy to explore, but couldn't this be simply from the sheer quantity of number histories we are dealing with compared to the Mandelbrot set? Tom --~--~-~--~~~---~--~~ 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, Machine and Father Ted
Stathis Papaioannou wrote: In an excellent and clear post Peter Jones writes: Matter is a bare substrate with no properties of its own. The question may well be asked at this point: what roles does it perform ? Why not dispense with matter and just have bundles of properties -- what does matter add to a merely abstract set of properties? The answer is that not all bundles of posible properties are instantiated, that they exist. What does it mean to say something exists ? ..exists is a meaningful predicate of concepts rather than things. The thing must exist in some sense to be talked about. But if it existed full, a statement like Nessie doesn't exist would be a contradiction ...it would amount to the existing thing Nessie doesnt exist. However, if we take that the some sense in which the subject of an ...exists predicate exists is only initially as a concept, we can then say whether or not the concept has something to refer to. Thus Bigfoot exists would mean the concept 'Bigfoot' has a referent. What matter adds to a bundle of properties is existence. A non-existent bundle of properties is a mere concept, a mere possibility. Thus the concept of matter is very much tied to the idea of contingency or somethingism -- the idea that only certain possible things exist. So on this basis alone are you opposed to a *physical* multiverse, in which every possibility is physically instantiated somewhere, but some possibilities are more common/ have greater measure than others? No, a Physical multiverse is material and Somethingist. The idea that HP/WR universes are not observed because they have a low, but non-zero measure is an extension of the single universe idea that they are no observed because they have zero measure. The other issue matter is able to explain as a result of having no properties of its own is the issue of change and time. For change to be distinguishable from mere succession, it must be change in something. It could be a contingent natural law that certain properties never change. However, with a propertiless substrate, it becomes a logical necessity that the substrate endures through change; since all changes are changes in properties, a propertiless substrate cannot itself change and must endure through change. In more detail here Why must change... be change in something? It sort of sounds reasonable but it is our duty to question every assumption and weed out the superfluous ones. If there is an object with (space, time, colour) coordinates (x1, t1, red) and another object (x1, t2, orange), then we say that the object has changed from red to orange. If we already know what distinguishes the time co-ordinate from the space co-ordinate. What is our usual way of doing that? The time co-ordinate is the one that is always changing... Time and Possibility Imagine a universe in which there was no change, nothing actually occurs. In the absence of events, it would be imposssible to distinguish any point in timw from any other point. There would be no meaning to time -- such a universe would be timeless. Now imagine a universe which is completely chaotic. Things change so completely from one moment to the next that there are no conistent things. This universe is made up solely of events, which can be labelled with 4 coordinates . [ x,y,z,t]. But which coordinate is the time coordinate ? One could just as well say [ y,t,z,x]. In the absence of persistent ojects there is nothing to single out time as a 'direction' in a coordinate system. So again time is meaingless. In order to have a meaningful Time, you need a combination of sameness (persisitent objects) and change (events). So time is posited on being able to say: Object A changed from state S1 at time T1 to state S2 at time T2. I don't see how a physical multiverse would be distinguishable from a virtual reality or a mathematical reality (assuming the latter is possible, for the sake of this part of the argument). The successive moments of your conscious experience do not need to be explicitly linked together to flow and they do not need to be explicitly separated, either in separate universes or in separate rooms, to be separate. I've never seen an HP universe. Yet they *must* exist in a mathematical reality, because there are no random gaps in Platonia. Since all mathematical structures are exemplified, the structure corresponging to (me up till 1 second ago) + (purple dragons) must exist. If there is nothing mathematical to keep out of HP universe, the fact that I have never seen one is evidence against a mathematical multiverse. If you died today and just by accident a possible next moment of consciousness was generated by a computer a trillion years in the future, then ipso facto you would find yourself a trillion years in the future. That's the whole problem. I could just as easily find myself in an HP universe. But I never do. But if you
Re: Numbers, Machine and Father Ted
Tom Caylor wrote: 1Z wrote: Bruno Marchal wrote: Le 23-oct.-06, à 15:58, David Nyman a écrit : Bruno Marchal wrote: Here I disagree, or if you want make that distinction (introduced by Peter), you can sum up the conclusion of the UD Argument by: Computationalism entails COMP. Bruno, could you distinguish between your remarks vis-a-vis comp, that on the one hand: a belief in 'primary' matter can be retained provided it is not invoked in the explanation of consciousness, Imagine someone who has been educated during his entire childhood with the idea that anything moving on the road with wheels is pulled by invisible horses. Imagine then that becoming an adult he decides to study physics and thermodynamics, and got the understanding that there is no need to postulate invisible horses for explaining how car moves around. Would this proves the non existence of invisible horses? Of course no. From a logical point of view you can always add irrefutable hypotheses making some theories as redundant as you wish. The thermodynamician can only say that he does not need the invisible horses hypothesis for explaining the movement of the cars , like Laplace said to Napoleon that he does not need the God hypothesis in his mechanics. And then he is coherent as far as he does not use the God concept in is explanation. The analogy isn't analogous. It is actually the Platonic numbers that are the invisible horses. No-one has ever seen a Platonic object. The vehicle of mathematics is driven by the engine of mathematicians, chalk, blackboards, computers etc -- all material. The comp hypothesis, which I insist is the same as standard computationalism (but put in a more precise way if only because of the startling consequences) entails that primary matter, even existing, cannot be used to justify anything related to the subjective experience, and this includes any *reading* of pointer needle result of a physical device. So we don't need the postulate it. And that is a good thing because the only definition of primary matter I know (the one by Aristotle in his metaphysics) is already refuted by both experiments and theory (QM or just comp as well). Of course QM does not refute materialism. and on the other: that under comp 'matter' emerges from (what I've termed) a recursively prior 1-person level. Why are these two conclusions not contradictory? 'Matter', or the stable appearance of matter has to emerge from the mathematical coherence of the computations. Which emerge from...? This is what the UDA is supposed to prove. Scientifically it means that you can test comp by comparing some self-observing discourses of digital machines (those corresponding to the arithmetical translation of the UDA (AUDA)) with empirical physics. Again this cannot disprove the (religious) belief in Matter, or in any Gods, for sure. The material world is visible, Platonia is not. You will have to attach consciousness to actual material infinite. Why is this the case? Because it is a way to prevent the UDA reasoning (at least as currently exibited) to proceed. It makes sense to say that some actual material infinity is not duplicable, for example. To be sure, the AUDA would still work (but could be less well motivated). It makes sense to say that consciousness depends on levels of emulation -- providing there is a 0-level pinned down by matter. Bruno http://iridia.ulb.ac.be/~marchal/ David and 1Z: How is exploring the Mandelbrot set through computation any different than exploring subatomic particles through computation (needed to successively approach the accuracies needed for the collisions in the linear accelerator)? Is not the only difference that in one case we have a priori labeled the object of study 'matter' and in the other case a 'set of numbers'? Granted, in the matter case we need more energy to explore, but couldn't this be simply from the sheer quantity of number histories we are dealing with compared to the Mandelbrot set? Tom A number of recent developments in mathematics, such as the increased use of computers to assist proof, and doubts about the correct choice of basic axioms, have given rise to a view called quasi-empiricism. This challenges the traditional idea of mathematical truth as eternal and discoverable apriori. According to quasi-empiricists the use of a computer to perform a proof is a form of experiment. But it remains the case that any mathematical problem that can in principle be solved by shutting you eye and thinking. Computers are used because mathematians do not have infinite mental resources; they are an aid. Contrast this with traditonal sciences like chemistry or biology, where real-world objects have to be studied, and would
Re: Numbers, Machine and Father Ted
Hi, Le Mardi 24 Octobre 2006 18:29, 1Z a écrit : I've never seen an HP universe. Yet they *must* exist in a mathematical reality, because there are no random gaps in Platonia. Since all mathematical structures are exemplified, the structure corresponging to (me up till 1 second ago) + (purple dragons) must exist. If there is nothing mathematical to keep out of HP universe, the fact that I have never seen one is evidence against a mathematical multiverse. I'd say it is evidence that you're not currently in an HP universe. Considering HP universes have low measure (even in mathematical only MWI as COMP), not being in one is not surprising. And if you were in one or noticed weird events you wouldn't writing this... Absence of proof is not proof of absence. Quentin Anciaux --~--~-~--~~~---~--~~ 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, Machine and Father Ted
Quentin Anciaux wrote: Hi, Le Mardi 24 Octobre 2006 18:29, 1Z a écrit : I've never seen an HP universe. Yet they *must* exist in a mathematical reality, because there are no random gaps in Platonia. Since all mathematical structures are exemplified, the structure corresponging to (me up till 1 second ago) + (purple dragons) must exist. If there is nothing mathematical to keep out of HP universe, the fact that I have never seen one is evidence against a mathematical multiverse. I'd say it is evidence that you're not currently in an HP universe. Considering HP universes have low measure (even in mathematical only MWI as COMP), not being in one is not surprising. What measure they have depends on the flavour of MW. In a purely mathematical MW, each configuration of matter is exemplified once. (Barbour's theory is close to this, but he also has mists, quantum probability measures, which are not apriori necessary). And if you were in one or noticed weird events you wouldn't writing this... Absence of proof is not proof of absence. So there *are* unicorns? Quentin Anciaux --~--~-~--~~~---~--~~ 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, Machine and Father Ted
1Z wrote: Tom Caylor wrote: David and 1Z: How is exploring the Mandelbrot set through computation any different than exploring subatomic particles through computation (needed to successively approach the accuracies needed for the collisions in the linear accelerator)? Is not the only difference that in one case we have a priori labeled the object of study 'matter' and in the other case a 'set of numbers'? Granted, in the matter case we need more energy to explore, but couldn't this be simply from the sheer quantity of number histories we are dealing with compared to the Mandelbrot set? Tom A number of recent developments in mathematics, such as the increased use of computers to assist proof, and doubts about the correct choice of basic axioms, have given rise to a view called quasi-empiricism. This challenges the traditional idea of mathematical truth as eternal and discoverable apriori. In either case, with math and matter, our belief is that there is an eternal truth to be discovered, i.e. a truth that is independent of the observer. According to quasi-empiricists the use of a computer to perform a proof is a form of experiment. But it remains the case that any mathematical problem that can in principle be solved by shutting you eye and thinking. Computers are used because mathematians do not have infinite mental resources; they are an aid. In either case, an experiment is a procedure that is followed which outputs information about the truth we are trying to discover. Math problems that we can solve by shutting our eyes are solvable that way because they are simple enough. As you point out, there are math problems that are too complex to solve by shutting our eyes. In fact there are math problems which are unsolvable. I think Bruno hypothesizes that the frontier of solvability/unsolvability in math/logic is complex enough to cover all there is to know about physics. Therefore, what role is left for matter? Contrast this with traditonal sciences like chemistry or biology, where real-world objects have to be studied, and would still have to be studied by super-scientitists with an IQ of a million. In genuinely emprical sciences, experimentation and observation are used to gain information. In mathematics the information of the solution to a problem is always latent in the starting-point, the basic axioms and the formulation of the problem. The process of thinking through a problem simply makes this latent information explicit. (I say simply, but of ocurse it is often very non-trivial). The belief about matter is that there are basic properties of matter which are the starting point for all of physics, and that all of the outcomes of the sciences are latent in this starting point, just as in mathematics. The use of a computer externalises this process. The computer may be outside the mathematician's head but all the information that comes out of it is information that went into it. Mathematics is in that sense still apriori. Having said that, the quasi-empricist still has some points about the modern style of mathematics. Axioms look less like eternal truths and mroe like hypotheses which are used for a while but may eventualy be discarded if they prove problematical, like the role of scientific hypotheses in Popper's philosophy. Thus mathematics has some of the look and feel of empirical science without being empricial in the most essential sense -- that of needing an input of inormation from outside the head.Quasi indeed! I'd say that the common belief of mathematicians is that axioms are just a (temporary) framework with which to think about the invariant truths. And one of the most important (unspoken) axioms is the convenient myth that I don't need any input from outside my head, so that I can have total control of what's going on in my head, an essential element for believing the outcome of my thinking. However, the fact is that a mathematician indeed would not be able to discover anything about math without external input at some point. This is the process of learning to think. Tom --~--~-~--~~~---~--~~ 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, Machine and Father Ted
Le Mardi 24 Octobre 2006 19:25, 1Z a écrit : Quentin Anciaux wrote: Hi, Le Mardi 24 Octobre 2006 18:29, 1Z a écrit : I've never seen an HP universe. Yet they *must* exist in a mathematical reality, because there are no random gaps in Platonia. Since all mathematical structures are exemplified, the structure corresponging to (me up till 1 second ago) + (purple dragons) must exist. If there is nothing mathematical to keep out of HP universe, the fact that I have never seen one is evidence against a mathematical multiverse. I'd say it is evidence that you're not currently in an HP universe. Considering HP universes have low measure (even in mathematical only MWI as COMP), not being in one is not surprising. What measure they have depends on the flavour of MW. In a purely mathematical MW, each configuration of matter is exemplified once. Why is it so ? I'd say at first glance that every configuration of matter is exemplified an infinity of time. Like I can see a video in 320x240, 640x480, 1024x768, x, 10x10... each time it's the same footage but each version differ with the accessible information content of the scene. So for a specified level of information I could agree that there is only one configuration... but there should exists in a mathematical MW an infinity of level. (Barbour's theory is close to this, but he also has mists, quantum probability measures, which are not apriori necessary). And if you were in one or noticed weird events you wouldn't writing this... Absence of proof is not proof of absence. So there *are* unicorns? No, just that you can't conclude that unicorn don't exists only because you've never seen one... You could conclude with an high certainty that unicorn don't exist with more evidences... Have you such evidences ? beside that you've never met Harry Potter ? ;-D Quentin Anciaux --~--~-~--~~~---~--~~ 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, Machine and Father Ted
Quentin Anciaux wrote: Le Mardi 24 Octobre 2006 19:25, 1Z a écrit : Quentin Anciaux wrote: Hi, Le Mardi 24 Octobre 2006 18:29, 1Z a écrit : I've never seen an HP universe. Yet they *must* exist in a mathematical reality, because there are no random gaps in Platonia. Since all mathematical structures are exemplified, the structure corresponging to (me up till 1 second ago) + (purple dragons) must exist. If there is nothing mathematical to keep out of HP universe, the fact that I have never seen one is evidence against a mathematical multiverse. I'd say it is evidence that you're not currently in an HP universe. Considering HP universes have low measure (even in mathematical only MWI as COMP), not being in one is not surprising. What measure they have depends on the flavour of MW. In a purely mathematical MW, each configuration of matter is exemplified once. Why is it so ? I'd say at first glance that every configuration of matter is exemplified an infinity of time. Like I can see a video in 320x240, 640x480, 1024x768, x, 10x10... each time it's the same footage but each version differ with the accessible information content of the scene. But what you call accessible information is the actual , objective configuration. We call them the same footage, but that is a human-centric definition of the same. So for a specified level of information I could agree that there is only one configuration... but there should exists in a mathematical MW an infinity of level. (Barbour's theory is close to this, but he also has mists, quantum probability measures, which are not apriori necessary). And if you were in one or noticed weird events you wouldn't writing this... Absence of proof is not proof of absence. So there *are* unicorns? No, just that you can't conclude that unicorn don't exists only because you've never seen one... But that is the only reason anyone has to conclude that they don't exist. If it isn't a good reason, therefore, they do exist. You could conclude with an high certainty that unicorn don't exist with more evidences... Have you such evidences ? Absence of evidence is good reason. It just isn't logically certain. beside that you've never met Harry Potter ? ;-D Quentin Anciaux --~--~-~--~~~---~--~~ 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, Machine and Father Ted
Tom Caylor wrote: 1Z wrote: Tom Caylor wrote: David and 1Z: How is exploring the Mandelbrot set through computation any different than exploring subatomic particles through computation (needed to successively approach the accuracies needed for the collisions in the linear accelerator)? Is not the only difference that in one case we have a priori labeled the object of study 'matter' and in the other case a 'set of numbers'? Granted, in the matter case we need more energy to explore, but couldn't this be simply from the sheer quantity of number histories we are dealing with compared to the Mandelbrot set? Tom A number of recent developments in mathematics, such as the increased use of computers to assist proof, and doubts about the correct choice of basic axioms, have given rise to a view called quasi-empiricism. This challenges the traditional idea of mathematical truth as eternal and discoverable apriori. In either case, with math and matter, our belief is that there is an eternal truth to be discovered, i.e. a truth that is independent of the observer. Eternal doesn't mean independent of the observer. Empirically-detectable facts are often fleeting. According to quasi-empiricists the use of a computer to perform a proof is a form of experiment. But it remains the case that any mathematical problem that can in principle be solved by shutting you eye and thinking. Computers are used because mathematians do not have infinite mental resources; they are an aid. In either case, an experiment is a procedure that is followed which outputs information about the truth we are trying to discover. Math problems that we can solve by shutting our eyes are solvable that way because they are simple enough. As you point out, there are math problems that are too complex to solve by shutting our eyes. In fact there are math problems which are unsolvable. I think Bruno hypothesizes that the frontier of solvability/unsolvability in math/logic is complex enough to cover all there is to know about physics. Therefore, what role is left for matter? Physical truth is a tiny subset of mathematical truth. Contrast this with traditonal sciences like chemistry or biology, where real-world objects have to be studied, and would still have to be studied by super-scientitists with an IQ of a million. In genuinely emprical sciences, experimentation and observation are used to gain information. In mathematics the information of the solution to a problem is always latent in the starting-point, the basic axioms and the formulation of the problem. The process of thinking through a problem simply makes this latent information explicit. (I say simply, but of ocurse it is often very non-trivial). The belief about matter is that there are basic properties of matter which are the starting point for all of physics, and that all of the outcomes of the sciences are latent in this starting point, just as in mathematics. You can't deduce the state of the universe at time T in any detailed way from the properties of matter, you have to get out your telescope and look. The use of a computer externalises this process. The computer may be outside the mathematician's head but all the information that comes out of it is information that went into it. Mathematics is in that sense still apriori. Having said that, the quasi-empricist still has some points about the modern style of mathematics. Axioms look less like eternal truths and mroe like hypotheses which are used for a while but may eventualy be discarded if they prove problematical, like the role of scientific hypotheses in Popper's philosophy. Thus mathematics has some of the look and feel of empirical science without being empricial in the most essential sense -- that of needing an input of inormation from outside the head.Quasi indeed! I'd say that the common belief of mathematicians is that axioms are just a (temporary) framework with which to think about the invariant truths. The truths are not invariant with regard to choice of axioms. Consider Euclid's fifth postulate. And one of the most important (unspoken) axioms is the convenient myth that I don't need any input from outside my head, so that I can have total control of what's going on in my head, an essential element for believing the outcome of my thinking. However, the fact is that a mathematician indeed would not be able to discover anything about math without external input at some point. This is the process of learning to think. You need to learn axioms and rules of inference. Everything else is implicit in them. Tom --~--~-~--~~~---~--~~ 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
Re: Numbers, Machine and Father Ted
Le Mardi 24 Octobre 2006 21:00, 1Z a écrit : Quentin Anciaux wrote: Le Mardi 24 Octobre 2006 19:25, 1Z a écrit : Quentin Anciaux wrote: Hi, Le Mardi 24 Octobre 2006 18:29, 1Z a écrit : I've never seen an HP universe. Yet they *must* exist in a mathematical reality, because there are no random gaps in Platonia. Since all mathematical structures are exemplified, the structure corresponging to (me up till 1 second ago) + (purple dragons) must exist. If there is nothing mathematical to keep out of HP universe, the fact that I have never seen one is evidence against a mathematical multiverse. I'd say it is evidence that you're not currently in an HP universe. Considering HP universes have low measure (even in mathematical only MWI as COMP), not being in one is not surprising. What measure they have depends on the flavour of MW. In a purely mathematical MW, each configuration of matter is exemplified once. Why is it so ? I'd say at first glance that every configuration of matter is exemplified an infinity of time. Like I can see a video in 320x240, 640x480, 1024x768, x, 10x10... each time it's the same footage but each version differ with the accessible information content of the scene. But what you call accessible information is the actual , objective configuration. We call them the same footage, but that is a human-centric definition of the same. Still I don't see why in a mathematical MW each actual , objective configuration should be unique and have the same measure... specifically in Bruno's UD. It's like you're saying that no mathematical MW theory could have a valid measure function associated to it (which is needed to explain why WR is not experienced). Also I don't see how a physical MW theory shouldn't need such a measure function (for the same reason, exclude WR). Quentin Anciaux --~--~-~--~~~---~--~~ 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, Machine and Father Ted
1Z wrote: Tom Caylor wrote: 1Z wrote: Tom Caylor wrote: David and 1Z: How is exploring the Mandelbrot set through computation any different than exploring subatomic particles through computation (needed to successively approach the accuracies needed for the collisions in the linear accelerator)? Is not the only difference that in one case we have a priori labeled the object of study 'matter' and in the other case a 'set of numbers'? Granted, in the matter case we need more energy to explore, but couldn't this be simply from the sheer quantity of number histories we are dealing with compared to the Mandelbrot set? Tom A number of recent developments in mathematics, such as the increased use of computers to assist proof, and doubts about the correct choice of basic axioms, have given rise to a view called quasi-empiricism. This challenges the traditional idea of mathematical truth as eternal and discoverable apriori. In either case, with math and matter, our belief is that there is an eternal truth to be discovered, i.e. a truth that is independent of the observer. Eternal doesn't mean independent of the observer. Empirically-detectable facts are often fleeting. We're getting into the typical bifurcation of interpretation of terms. When you used the term eternal to describe math truth, I assumed you were talking about something that is independent of time. According to quasi-empiricists the use of a computer to perform a proof is a form of experiment. But it remains the case that any mathematical problem that can in principle be solved by shutting you eye and thinking. Computers are used because mathematians do not have infinite mental resources; they are an aid. In either case, an experiment is a procedure that is followed which outputs information about the truth we are trying to discover. Math problems that we can solve by shutting our eyes are solvable that way because they are simple enough. As you point out, there are math problems that are too complex to solve by shutting our eyes. In fact there are math problems which are unsolvable. I think Bruno hypothesizes that the frontier of solvability/unsolvability in math/logic is complex enough to cover all there is to know about physics. Therefore, what role is left for matter? Physical truth is a tiny subset of mathematical truth. This agrees with what I am saying. Contrast this with traditonal sciences like chemistry or biology, where real-world objects have to be studied, and would still have to be studied by super-scientitists with an IQ of a million. In genuinely emprical sciences, experimentation and observation are used to gain information. In mathematics the information of the solution to a problem is always latent in the starting-point, the basic axioms and the formulation of the problem. The process of thinking through a problem simply makes this latent information explicit. (I say simply, but of ocurse it is often very non-trivial). The belief about matter is that there are basic properties of matter which are the starting point for all of physics, and that all of the outcomes of the sciences are latent in this starting point, just as in mathematics. You can't deduce the state of the universe at time T in any detailed way from the properties of matter, This is a subject of debate. you have to get out your telescope and look. A telescope could be a way of looking at the state of the computation of the universe. This doesn't preclude being able to in theory compute the universe (in 3rd pov). The use of a computer externalises this process. The computer may be outside the mathematician's head but all the information that comes out of it is information that went into it. Mathematics is in that sense still apriori. Having said that, the quasi-empricist still has some points about the modern style of mathematics. Axioms look less like eternal truths and mroe like hypotheses which are used for a while but may eventualy be discarded if they prove problematical, like the role of scientific hypotheses in Popper's philosophy. Thus mathematics has some of the look and feel of empirical science without being empricial in the most essential sense -- that of needing an input of inormation from outside the head.Quasi indeed! I'd say that the common belief of mathematicians is that axioms are just a (temporary) framework with which to think about the invariant truths. The truths are not invariant with regard to choice of axioms. Consider Euclid's fifth postulate. Euclid's fifth postulate is an axiom. And one of the most important (unspoken) axioms is the convenient myth that I don't need any input from outside my head, so that I can have total control of what's going on in my head, an essential element
Re: Numbers, Machine and Father Ted
Tom Caylor wrote: 1Z wrote: Tom Caylor wrote: 1Z wrote: Tom Caylor wrote: David and 1Z: How is exploring the Mandelbrot set through computation any different than exploring subatomic particles through computation (needed to successively approach the accuracies needed for the collisions in the linear accelerator)? Is not the only difference that in one case we have a priori labeled the object of study 'matter' and in the other case a 'set of numbers'? Granted, in the matter case we need more energy to explore, but couldn't this be simply from the sheer quantity of number histories we are dealing with compared to the Mandelbrot set? Tom A number of recent developments in mathematics, such as the increased use of computers to assist proof, and doubts about the correct choice of basic axioms, have given rise to a view called quasi-empiricism. This challenges the traditional idea of mathematical truth as eternal and discoverable apriori. In either case, with math and matter, our belief is that there is an eternal truth to be discovered, i.e. a truth that is independent of the observer. Eternal doesn't mean independent of the observer. Empirically-detectable facts are often fleeting. We're getting into the typical bifurcation of interpretation of terms. When you used the term eternal to describe math truth, I assumed you were talking about something that is independent of time. According to quasi-empiricists the use of a computer to perform a proof is a form of experiment. But it remains the case that any mathematical problem that can in principle be solved by shutting you eye and thinking. Computers are used because mathematians do not have infinite mental resources; they are an aid. In either case, an experiment is a procedure that is followed which outputs information about the truth we are trying to discover. Math problems that we can solve by shutting our eyes are solvable that way because they are simple enough. As you point out, there are math problems that are too complex to solve by shutting our eyes. In fact there are math problems which are unsolvable. I think Bruno hypothesizes that the frontier of solvability/unsolvability in math/logic is complex enough to cover all there is to know about physics. Therefore, what role is left for matter? Physical truth is a tiny subset of mathematical truth. This agrees with what I am saying. Contrast this with traditonal sciences like chemistry or biology, where real-world objects have to be studied, and would still have to be studied by super-scientitists with an IQ of a million. In genuinely emprical sciences, experimentation and observation are used to gain information. In mathematics the information of the solution to a problem is always latent in the starting-point, the basic axioms and the formulation of the problem. The process of thinking through a problem simply makes this latent information explicit. (I say simply, but of ocurse it is often very non-trivial). The belief about matter is that there are basic properties of matter which are the starting point for all of physics, and that all of the outcomes of the sciences are latent in this starting point, just as in mathematics. You can't deduce the state of the universe at time T in any detailed way from the properties of matter, This is a subject of debate. you have to get out your telescope and look. A telescope could be a way of looking at the state of the computation of the universe. This doesn't preclude being able to in theory compute the universe (in 3rd pov). The use of a computer externalises this process. The computer may be outside the mathematician's head but all the information that comes out of it is information that went into it. Mathematics is in that sense still apriori. Having said that, the quasi-empricist still has some points about the modern style of mathematics. Axioms look less like eternal truths and mroe like hypotheses which are used for a while but may eventualy be discarded if they prove problematical, like the role of scientific hypotheses in Popper's philosophy. Thus mathematics has some of the look and feel of empirical science without being empricial in the most essential sense -- that of needing an input of inormation from outside the head.Quasi indeed! I'd say that the common belief of mathematicians is that axioms are just a (temporary) framework with which to think about the invariant truths. The truths are not invariant with regard to choice of axioms. Consider Euclid's fifth postulate. Euclid's fifth postulate is an axiom. And one of the most important (unspoken) axioms is the convenient myth that I don't need any input from outside my head, so that I can have total control of what's going on in my head, an essential element for believing the outcome of my thinking. However, the fact is that a mathematician indeed would not be able to
Re: Numbers, Machine and Father Ted
Brent Meeker wrote: Tom Caylor wrote: 1Z wrote: Tom Caylor wrote: 1Z wrote: Tom Caylor wrote: David and 1Z: How is exploring the Mandelbrot set through computation any different than exploring subatomic particles through computation (needed to successively approach the accuracies needed for the collisions in the linear accelerator)? Is not the only difference that in one case we have a priori labeled the object of study 'matter' and in the other case a 'set of numbers'? Granted, in the matter case we need more energy to explore, but couldn't this be simply from the sheer quantity of number histories we are dealing with compared to the Mandelbrot set? Tom A number of recent developments in mathematics, such as the increased use of computers to assist proof, and doubts about the correct choice of basic axioms, have given rise to a view called quasi-empiricism. This challenges the traditional idea of mathematical truth as eternal and discoverable apriori. In either case, with math and matter, our belief is that there is an eternal truth to be discovered, i.e. a truth that is independent of the observer. Eternal doesn't mean independent of the observer. Empirically-detectable facts are often fleeting. We're getting into the typical bifurcation of interpretation of terms. When you used the term eternal to describe math truth, I assumed you were talking about something that is independent of time. According to quasi-empiricists the use of a computer to perform a proof is a form of experiment. But it remains the case that any mathematical problem that can in principle be solved by shutting you eye and thinking. Computers are used because mathematians do not have infinite mental resources; they are an aid. In either case, an experiment is a procedure that is followed which outputs information about the truth we are trying to discover. Math problems that we can solve by shutting our eyes are solvable that way because they are simple enough. As you point out, there are math problems that are too complex to solve by shutting our eyes. In fact there are math problems which are unsolvable. I think Bruno hypothesizes that the frontier of solvability/unsolvability in math/logic is complex enough to cover all there is to know about physics. Therefore, what role is left for matter? Physical truth is a tiny subset of mathematical truth. This agrees with what I am saying. Contrast this with traditonal sciences like chemistry or biology, where real-world objects have to be studied, and would still have to be studied by super-scientitists with an IQ of a million. In genuinely emprical sciences, experimentation and observation are used to gain information. In mathematics the information of the solution to a problem is always latent in the starting-point, the basic axioms and the formulation of the problem. The process of thinking through a problem simply makes this latent information explicit. (I say simply, but of ocurse it is often very non-trivial). The belief about matter is that there are basic properties of matter which are the starting point for all of physics, and that all of the outcomes of the sciences are latent in this starting point, just as in mathematics. You can't deduce the state of the universe at time T in any detailed way from the properties of matter, This is a subject of debate. you have to get out your telescope and look. A telescope could be a way of looking at the state of the computation of the universe. This doesn't preclude being able to in theory compute the universe (in 3rd pov). The use of a computer externalises this process. The computer may be outside the mathematician's head but all the information that comes out of it is information that went into it. Mathematics is in that sense still apriori. Having said that, the quasi-empricist still has some points about the modern style of mathematics. Axioms look less like eternal truths and mroe like hypotheses which are used for a while but may eventualy be discarded if they prove problematical, like the role of scientific hypotheses in Popper's philosophy. Thus mathematics has some of the look and feel of empirical science without being empricial in the most essential sense -- that of needing an input of inormation from outside the head.Quasi indeed! I'd say that the common belief of mathematicians is that axioms are just a (temporary) framework with which to think about the invariant truths. The truths are not invariant with regard to choice of axioms. Consider Euclid's fifth postulate. Euclid's fifth postulate is an axiom. And one of the most important (unspoken) axioms is the convenient myth that I don't need any input from outside my head, so that I can have total control of what's going on in my head, an essential
RE: Numbers, Machine and Father Ted
Peter Jones writes: The other issue matter is able to explain as a result of having no properties of its own is the issue of change and time. For change to be distinguishable from mere succession, it must be change in something. It could be a contingent natural law that certain properties never change. However, with a propertiless substrate, it becomes a logical necessity that the substrate endures through change; since all changes are changes in properties, a propertiless substrate cannot itself change and must endure through change. In more detail here Why must change... be change in something? It sort of sounds reasonable but it is our duty to question every assumption and weed out the superfluous ones. If there is an object with (space, time, colour) coordinates (x1, t1, red) and another object (x1, t2, orange), then we say that the object has changed from red to orange. If we already know what distinguishes the time co-ordinate from the space co-ordinate. What is our usual way of doing that? The time co-ordinate is the one that is always changing... Time and Possibility Imagine a universe in which there was no change, nothing actually occurs. In the absence of events, it would be imposssible to distinguish any point in timw from any other point. There would be no meaning to time -- such a universe would be timeless. Now imagine a universe which is completely chaotic. Things change so completely from one moment to the next that there are no conistent things. This universe is made up solely of events, which can be labelled with 4 coordinates . [ x,y,z,t]. But which coordinate is the time coordinate ? One could just as well say [ y,t,z,x]. In the absence of persistent ojects there is nothing to single out time as a 'direction' in a coordinate system. So again time is meaingless. In order to have a meaningful Time, you need a combination of sameness (persisitent objects) and change (events). So time is posited on being able to say: Object A changed from state S1 at time T1 to state S2 at time T2. You're just stating that time is different from space. Time and space are also different from colour, or any other property an object may have. If we didn't have time there would be no change, if we didn't have height everything would be flat, and if we didn't have colour everything would be black. I don't see how a physical multiverse would be distinguishable from a virtual reality or a mathematical reality (assuming the latter is possible, for the sake of this part of the argument). The successive moments of your conscious experience do not need to be explicitly linked together to flow and they do not need to be explicitly separated, either in separate universes or in separate rooms, to be separate. I've never seen an HP universe. Yet they *must* exist in a mathematical reality, because there are no random gaps in Platonia. Since all mathematical structures are exemplified, the structure corresponging to (me up till 1 second ago) + (purple dragons) must exist. If there is nothing mathematical to keep out of HP universe, the fact that I have never seen one is evidence against a mathematical multiverse. That you don't experience HP universes is as much an argument against a physical multiverse as it is an argument against a mathematical multiverse. If a physical MV exists, then in some branch you will encounter purple dragons in the next second. The fact that you don't means that either there is no physical multiverse or there is a physical multiverse but the purple dragon experience is of low measure. Similarly in a mathematical multiverse the HP experiences may be of low measure. If you died today and just by accident a possible next moment of consciousness was generated by a computer a trillion years in the future, then ipso facto you would find yourself a trillion years in the future. That's the whole problem. I could just as easily find myself in an HP universe. But I never do. Not just as easily. If you are destructively scanned and a moment from now 2 copies of you are created in Moscow and 1 copy created in Washington, you have a 2/3 chance of finding yourself in Moscow and a 1/3 chance of finding yourself in Washington. It is a real problem to explain why the HP universes are less likely to be experienced than the orderly ones (see chapter 4.2 of Russell Standish' book for a summary of some of the debates on this issue), but it is not any more of a problem for a mathematical as opposed to a physical multiverse. But if you had the successive moments of your consciousness implemented in parallel, perhaps as a simulation on a powerful computer, it would be impossible to tell that this was the case. For all you are aware, there may not *be* any past moments: your present experience may include false memories of your past, and whole
