### Re: Introduction (Digital Physics)

Brent Meeker wrote: OK. So do you invoke an anthropic principle in the step (computer law) = (mind law) ... Let us a say a Church Turing Markov -tropic principle, eventually. If you want I (re)define the physical by what is observable by a sound universal machine. And observable is eventually defined by a measure on her set on consistent extension, and I must add as seen by her. and then hope to show that will entail the step (mind law) = (physical law)? It seems to me that the UDA entails that reversal. We must recover physical laws and physical sensations from the discourse of average sound universal machine about their most probable computational neighborhood. And why do you take this approach rather than (number law) = (computer law) = (physical law) = (mind law)? Just for the kantian reason that I can access only to my first person knowledge, even when I just look to a needle of a physical measuring apparatus. The UDA shows I must integrate on all computational histories going through, similar enough, from a first person point of view, states. Those states-point of view are psychological concept. It could still be possible that, in fine, (physical law) = (mind law) That could happen if our level of description is very low. But then we will know it, without having put the mind-body problem under the rug. What is very promising with the arithmetical transformation is that all logics are doubled (G and G*, Z and Z*, ...) so that we get information on both communicable and incommunicable propositions. The arithmetical quantisation seems to put light on both qualia and quanta. Also, independently, Maudlin and me have shown in some more direct way that, with comp, there is no hope for (physical law) = (mind law). (It is the crackpot proof in Jacques Mallah's terms!, look in the archive at key words like Maudlin, movie, crackpot. (But with Occam it is not necessary). Perhaps you could briefly elucidate what you think goes into each = ? For example, I assume that the step (number law) = (computer law) is motivated by saying our TOE must be finitely describable and so it must lie in a subset of all mathematics that is most explicitly defined by computation. Is this right? Mmh ... Arithmetical truth is not finitely describable and I doubt there is a TOE for any first person plenitude (Levy's term). You should realise that Godel shows that the structure (N, +, x, , =, 0) is far more complex than the equivalent structure for the reals, which are completely captured by the notion of archimedian algebraicaly closed field. Natural numbers are in a sense much more complex than reals. We have no TOE for them. The step (number law) = (computer law) comes from the fact that you can, by chosing some number encoding (like Godel's one) embed proposition on programs in pure arithmetical terms. An example is Godel's encoding of provability, which I promise George to discuss about, and so will I ASAP or perhaps later. But in a nutshell, Godel did build, uniquely from the symbole O, =, X, +, x, s, (intended for the successor function) an arithmetical predicate B(x,y) meaning x is the godel number of a proof for the formula with godel number y. So that provable(y) is just the arithmetical sentence ExB(x,y). (E = the existencial quantifier). I'm not sure I can give precise meaning to an expression like all mathematics. Perhaps this is the Cantor inconsistenz. But I don't ask mathematics to be made explicit by computations. In fact most of the truth *about* computations are not reachable by univoquely determined computations. This is the foremost origin of the gap between G and G*. Computerland, which is just an intentional variant of numberland, is not computable, not finitely describable. A brain, or any implementation of a universal machine is really nothing other than a door on many (many) realities. Bruno

### Re: Introduction (Digital Physics)

Brent Meeker wrote (out of line, but I guess it is by error): I'm a little unclear on the ontological hierarchy of your TOE. Do you propose to show that, out of all computations, all our conscious experiences are recovered (by somehow identifying appropriate histories corresponding to us in this world). And then, from our common experiences, physics is inferred. Yes. (Number law) = (computer law) = (mind law) = (physical law) roughly speaking. Or - do you propose to show that, out of all computations, almost all of them entail a regular physics and in particular a physics similar to that which we observe, and from this physics arises our being and consciousness according to the scientific processes which we already understand. No. Actually most consistent continuations have white rabbits, and white noise. I am still open that the little program, if it exists is any QUD, i.e. any Quantum Universal Dovetailer. Not because it generates less white rabbits, but because it generates *much more* white rabbits! The reason is that it generates also much more -anti white rabbits- so that there are eliminated in the average. But even this idea I feel it necessary to deduce it from the universal interview. (look at my post to Georges Levy containing a partial technical result in that direction which gives the embryo of the reason why point of views makes angles, and why interference of the probabilities are possibly necessary http://www.escribe.com/science/theory/m2855.html) Bruno

### Re: Introduction (Digital Physics)

Check out The Whipping Star by Frank Herbert. A neat story but kind of twisted. The story is about stars that are conscious. Robert W. could be conscious/aware in a way that we might recognize. If so, then stars too would probably have a very different idea about foundations than we planetary dwellers do. But still, I find it almost impossible to imagine that there is no underlying principle that runs everything. Maybe I've been living on the surface too long. Joel _ Do You Yahoo!? Get your free @yahoo.com address at http://mail.yahoo.com

### Re: Introduction (Digital Physics)

Hi Fred, I think relying on the sum/integral over all possible programs as the FINAL explanation would lead to avoiding the questions about details of the criteria. We are safe because we are included in the overall sum. True, for the general purpose of explaining our existence, we don't know the details of the criteria. But if we are deeply involved in modeling specific fundamental phenomena, or are just extremely curious, we are led to pursue the details of the criteria, instead of staying satisfied with the top-down result. But then you should say that to James Higgo or to other antimeasurist, to coin Jesse Mazer expression. It seems to me that comp, thanks to computer science eventually, gives all the constraints needed for making converging the top down approach toward the specific details. That is I think the main goal of the UDA. True, there could be ironical but logical reasons why the average relative universal machine state remember having discover some truth empiricaly, but that would be nice because it would explain why consciousness evolves among apparently empirical world. True, we will never succeed in finding out the actual program, ... If there is one. But with comp any bottoms is a name for deeper bottoms. The phenomenological laws of physics transcend those bottoms. I am willing to believe that the quantum is such a very deep invariant tarnscending bottoms. But then I must extract from the stable predictable machine belief. This would show that quantum logic would be a logical necessity from machine's pov. So we can have precise laws relating experiences, but no bottom. Also, when you find a bottom you get insecure. On what could that bottom rely? I would be astonished if there was an (absolute) nameable bottom. but I would also be astonished if there was an (absolute) nameable top. but we can speculate about it, and could try to approach it asymptotically (that is what I meant by narrowing down the infinite subset of options) from a bottom-up approach. I feel that is what science is all about. Yes, sure, but with comp, this gives an infinite zoom. An infinite exploration. Science do that, but science try to collect the invariants, and sometimes science discovers deeper explanation of the origine (of the belief) in those invariants, etc. Bruno

### Re: Introduction (Digital Physics)

Fred Chen wrote: I appreciate how something like the Universal Dovetailer or equivalent programs can generate an infinite set of programs that could include the one that describes our universe (including our consciousness). You are confusing Schmidhuber-like theories with me-like theories (if I can say). In Schmidhuber-like theories there are indeed a program which generates an infinite set of programs that could include the one that describes our universe (including our consciousness). I have explained in length why such approach fails to explain what is matter, what is consciousness, what is time, what is a universe. And also that such approach buries the mind body problem. What I just show is that if we are machines then the physical appearances *must* emerges from *all* computations *at once*, and that the physical discourses, both first person (including uncommunicable qualia) and third person (communicable quanta) must be defined with a sort of sum on all computations. However, Godel's theorem applied to this top-down approach would prevent us from being able to recognize that program, or even knowing how to recognize that program. You are right! That the first law of machine psychology. It is related to what I call Post-Benaceraff principle. See http://www.escribe.com/science/theory/m2487.html. It can be dangerous for Schmidhuber-like approach. It does not threat my theorem :-) Quite the contrary: Godel's theorem is generalised by the modal logic G and G*, which axiomatises completely propositional psychology machine, from which portion of physics can be derived. The best we can do is continually narrow down the options, from an infinite subset to a smaller infinite subset, as we add more parameters for description. No. Read carefully the recent UDA thread to understand. To reconcile with anthropic fine-tuning without white rabbits, I had bought into the postulate that we were in the simplest possible universe, in the absence of knowing the exact criteria for developing self-aware consciousness, but just assuming that some absolute criteria exist. But this begs the questions, what are those criteria and why those criteria? Without knowing these criteria, we cannot tell what is the simplest possible universe containing consciousness. With comp we don't need such criteria. We sum on all program executions. It really looks like a generalisation of Feynman integral. In particular it should be an integral ... Bruno

### Re: Introduction (Digital Physics)

Fred: Without knowing these criteria, we cannot tell what is the simplest possible universe containing consciousness. I don't see why we should limit ourselves to the simplest possible universe containing consciousness. I would think that all worlds containing consciousness would be inhabited naturally. Joel

### Re: Introduction (Digital Physics)

I don't see why we should limit ourselves to the simplest possible universe containing consciousness. I would think that all worlds containing consciousness would be inhabited naturally. Joel Actually I agree, fundamentally. Perhaps, there is just a gut feeling around that simplest possible goes hand-in-hand with more instances, and hence, a greater likelihood that that description is accurate for our world. In physics and cosmology, and even in many engineering siutations, we have always tried to avoid fine-tuning, which is associated with greater complexity. The best models have the least need for fine-tuning. So that is where I am coming from. The all-universes (and related) approaches have appeal precisely for this reason. Fred

### Re: Introduction (Digital Physics)

Bruno, Joel, et. al., I appreciate how something like the Universal Dovetailer or equivalent programs can generate an infinite set of programs that could include the one that describes our universe (including our consciousness). However, Godel's theorem applied to this top-down approach would prevent us from being able to recognize that program, or even knowing how to recognize that program. The best we can do is continually narrow down the options, from an infinite subset to a smaller infinite subset, as we add more parameters for description. To reconcile with anthropic fine-tuning without white rabbits, I had bought into the postulate that we were in the simplest possible universe, in the absence of knowing the exact criteria for developing self-aware consciousness, but just assuming that some absolute criteria exist. But this begs the questions, what are those criteria and why those criteria? Without knowing these criteria, we cannot tell what is the simplest possible universe containing consciousness. Fred

### Re: Introduction (Digital Physics)

Bruno: I should have been more clear. I put at the (3-) bottom arithmetical truth. It just means I believe sentence like 2+2=4, Fermat theorem, ... Yes, I think we agree on this point. I gave the example of the minimal cellular automaton as another third-person verifiable structure. We can all start with the simple one-dimensional automata (Rules 0..255) and notice that some of them do certain things, and some of them do EVERYTHING (e.g. Rule 30). Also, how would a friendly entity manages bottom-up links between a universal automata and the observers it generates? Ahh... sorry. I did not express this clearly. I believe that NO entity is responsible for the automaton that is the Universe (the WHOLE thing). As I said, I feel that the Universe is a simple mathematical structure that generates all things - and is something that all sentient entities can discover. The friendly entity I speak of lives WITHIN the automaton - and creates new worlds (virtual realities) within it. This complicated entity, living naturally within the automaton (like everything else), creates new artificial realities where different games are played. In some of these worlds, gravity is attractive (like the Earth 2001 simulation). But in other worlds, gravity is repulsive. And in still other worlds, there is no gravity at all - and white rabbits are abundant. So again, such a wise and old and friendly natural entity could create an artificial simulation in which the laws of physics in that world were closely related to the structure and behavior of the universal automaton outside. Maybe such an entity would choose to do this in order to reeducate itself about the greater truth outside. Or, just for te fun of it! Note: I have neglected to mention explicitly that I believe this complicated, god-like friendly entity is *us*. We have chosen to enter this simulation - and divide our awareness into separate people - in order to once again appreciate the natural wonder and complexity that WE are - collectively. Collectively, we are one organism. Playing games... dreaming. If I understand your work correctly, Bruno, you are not far from this idea as well. As you say, our physics (the world we see now) is just a branch of machine psychology. We are all mecha - pretending to be orga. Joel

### Re: Introduction (Digital Physics)

Joel wrote: Bruno: I am not sure there is any (absolute) bottom. Mustn't we assume there is? If there is no bottom, what will we stand on? How can we understand anything at all? I should have been more clear. I put at the (3-) bottom arithmetical truth. It just means I believe sentence like 2+2=4, Fermat theorem, Goldbach conjecture, or like the machine with Goedel number 42 does not stop on 24, etc. are true or false independently of my ability to prove them or not. I am trying to show you (in the UDA threads) that physics is a 1-phenomenon and it will appear that 1-phenomenon truly lacks bottom. If we live in a world that is designed by a friendly entity, then s/he might make things purposely related to the bottom, and easy to figure out. But if, as you say, there is no bottom layer, then all of this speculation is sortof meaningless. There are 3-bottoms, no 1-bottoms. This is not unrelated to incompleteness phenomena but the UDA illustrates that quite well. Well, let us hope. Also, how would a friendly entity manages bottom-up links between a universal automata and the observers it generates? Bruno

### Re: Introduction (Digital Physics)

Joel wrote: This may be true, but has anyone here (or anywhere else) ever checked to see that we can't program the universe exactly with simple algorithms? I think this is something new. (Check out what Stephen Wolfram has been doing lately: http://www.wolframscience.com) Everyone's talking about quantum consciousness and other nebulous words, but it seems no one has tried to build the universe from the ground up - on absolute principles and no uncertainties. Now, I know I'm not asking everyone to give up their most cherished beliefs and all their hard work forever. I'm just asking for SOMEONE to stop and take a look with me to see if we haven't missed something really simple - something so obviousthat everyone just dismissed it without asking, Why not? Maybe it's not as hard as we think. Maybe we CAN obtain some real, final answers. It's just crazy enough to work! Joel Interestingly 't Hooft (one of the Nobel-Prize winners of 1999) has formulated deterministic models that reduce to quantum mechanics when described statistically. See e.g. this article: ``How Does God Play Dice? (Pre-)Determinism at the Planck Scale´´: http://xxx.lanl.gov/abs/hep-th/0104219 Saibal

### Re: Introduction (Digital Physics)

Bruno: See http://www.escribe.com/science/theory/m2793.html for a universal dovetailer written in LISP. Among the LISP programs you have all the simulation of Fortran programs, Joel's minimal cellular automata, etc. Yes, this is true. But (of course :) I would like to argue in favor of cellular automata over Turing Machines and even the Universal Dovetailer. Somehow, though I can't fully express the idea in my head, they seem more natural to me... and perhaps more obvious to other sentient entities. Some of my reasons are as follows... Turing Machines usually require many internal states, while CA need only two. TMs also contain a *moving* part - the read/write head, and it's not exactly clear how to implement such a gizmo outside of physics, or justify such complexity when simpler machines exist. (Depending on your idea of simplicity of course!) You could imagine, for example, a cellular automaton that could run a Turing Machine with a real read-write head that moved and everything - but with no moving parts. Yes, I know these things are all equivalent, but to me, CA require fewer assumptions or explanations. Furthermore, Turing Machines tend to slow down as the size of the universe grows larger, while cellular automata may be made arbitrarily fast, once the synchronization problem is addressed. (Plamen showed me how this is not too difficult to do actually.) Finally, CA require no (3rd person) interpretation as to the special relationships between bit patterns. They are represented naturally in the geometric cellular space. All of this may seem academic really, since we all know that any universal computer is as good as any other. It's kindof like arguing about the kind of wood God's stool is made out of! But there MAY be some reasons to want to know exactly which algorithm is really being run on the bottom... Because all of these implementations have slight differences as to the core informational process they represent. Yes, they all do the same thing in the long run, but the order in which they do things may be different. And if we are anywhere near the bottom of it all, then we may be able to take advantage of knowing that order. For example, suppose we run my cellular automaton and find certain core particle interactions that are extremely common. We might then recognize these in a laboratory and better understand conventional physics. Ok, that's a really weak argument, since I also believe that this world is made up and that its physics is rather arbitrary. But if it IS made up, and we are SUPPOSED to figure out the workings of the automaton, then MAYBE ... the simulation would be made to resemble the workings of the machine down below. Ok, I'm rambling. I'll stop. Joel

### Re: Introduction (Digital Physics)

Joel: ... But there MAY be some reasons to want to know exactly which algorithm is really being run on the bottom... Bruno: I am not sure there is any (absolute) bottom. Joel: Mustn't we assume there is? If there is no bottom, what will we stand on? How can we understand anything at all? I wrote this to the list a while ago: Gerard O'Neill, the late Princeton physicist best known for his space colony studies, once said that if you met a race that insisted that logical developments must be built step by step from a firm foundation, you could be pretty sure they were planet dwellers. Races that live in space realize that it's perfectly OK to build structures that have no foundation at all. They can be circular and unsupported, yet if you spin them they'll have gravity just like the ponderous planetary piles! The context, related to the discussion above, was the need for a logical foundation for objective attributions of consciousness. more: Many of the people on this list (in common with a lot of western philosophy at least since Descartes) are hoping to construct their existence measures on the bedrock of the objectively decidable self-awareness. They've built very interesting structures, but you may notice there's been no progress at all on stabilizing the foundation. Instead we have on this list the same debates that endlessly, repetitively and inconclusively flood comp.ai.philosophy, never mind philosophy journals and books. I think the insistence on the absolute underpinning of an objective consciousness is just planet-bound thinking. Bruno's, Juergen's, Russell's or Max Tegmark's analyses can just as well be built on arbitrary selections of what's conscious (Turing test passers? biological brains? red-haired people? teddy bears?). The teddy bear universes may have different probabilities than the biological brain universes or the Turing test universes, but so what? Each is as likely to be self-consistent as another. i.e. You don't have to give up the goals of this list just because you don't believe there is an objective fact of the matter to consciousness.

### Re: Introduction (Digital Physics)

hpm: Races that live in space realize that it's perfectly OK to build structures that have no foundation at all. They can be circular and unsupported, yet if you spin them they'll have gravity just like the ponderous planetary piles! This is a clever argument, but I think it's just a trick. Races that live in space will have built their science(s) from the ground up just like us - on first principles, and extensions of those principles. It wasn't wishful thinking that allowed them to escape their planet's gravity! Many of the people on this list (in common with a lot of western philosophy at least since Descartes) are hoping to construct their existence measures on the bedrock of the objectively decidable self-awareness. They've built very interesting structures, but you may notice there's been no progress at all on stabilizing the foundation. Instead we have on this list the same debates that endlessly, repetitively and inconclusively flood comp.ai. philosophy, never mind philosophy journals and books. This may be true, but has anyone here (or anywhere else) ever checked to see that we can't program the universe exactly with simple algorithms? I think this is something new. (Check out what Stephen Wolfram has been doing lately: http://www.wolframscience.com) Everyone's talking about quantum consciousness and other nebulous words, but it seems no one has tried to build the universe from the ground up - on absolute principles and no uncertainties. Now, I know I'm not asking everyone to give up their most cherished beliefs and all their hard work forever. I'm just asking for SOMEONE to stop and take a look with me to see if we haven't missed something really simple - something so obviousthat everyone just dismissed it without asking, Why not? Maybe it's not as hard as we think. Maybe we CAN obtain some real, final answers. It's just crazy enough to work! Joel

### Re: Introduction (Digital Physics)

Bruno: All of this may seem academic really, since we all know that any universal computer is as good as any other. It's kindof like arguing about the kind of wood God's stool is made out of! But there MAY be some reasons to want to know exactly which algorithm is really being run on the bottom... I am not sure there is any (absolute) bottom. Mustn't we assume there is? If there is no bottom, what will we stand on? How can we understand anything at all? Ok, that's a really weak argument, since I also believe that this world is made up and that its physics is rather arbitrary. Physics should emerge from *all computations and I don't think it is arbitrary. What I mean is that the physics of our world may be so far removed from the bottom that we have no hope of seeing any meaningful relationships. For example, if we live in a world that is designed by a malicious entity, s/he might make things purposely confusing or misleading. It is true that the program that computes everything will completely explain the mad scientist and the world s/he designs (including us), but our computers might be, for all practical purposes, useless in figuring out his/her intentions. HOWEVER... If we live in a world that is designed by a friendly entity, then s/he might make things purposely related to the bottom, and easy to figure out. But if, as you say, there is no bottom layer, then all of this speculation is sortof meaningless. Down below (actually just below our correct computationalist level of description) you will discover the many interfering computations. Why interference? That is what I actually try to explain in the UDAs posts. Empirical discovery of many computations is what seems to happen with empirical Quantum Mechanics (cf quantum computers). Ok. I am skeptical about this approach, but I'll wait and see where your Universal Dovetailer Argument takes us. Joel

### Re: Introduction (Digital Physics)

Fred: Perhaps you are saying all worlds have some commonality eventually? Such as the program you mention below? Yes, I suppose so. If you'd like something to visualize... Imagine a huuuge Game of Life grid. Some regions of space will contain worlds that are relatively self-contained for long periods of time - being located very far from other goings-on in other parts of the grid. But eventually, maybe after such a region has mostly died out, some of the gliders and such that were generated in the localized region will travel and reach other regions of space where other local worlds exist. That's where they interact. But like I said, this might be totally out of view of any observers in the first world. Sounds like you are going after some magic program that generates all possible programs. Yes. And, perhaps surprisingly, it might not be that hard to do. Others here have mentioned various Turing Machines that will do the same thing, and (if I understand it correctly) the Universal Dovetailer qualifies as well. And while these are perfectly acceptable programs, we (my friend Plamen and I) try to make some arguments for the slight preference of cellular automata over the others. (See my arguments in my next reply to Bruno.) Would this program be a logical necessity in and of itself? That is, must it necessarily exist? Or would it just happen to exist? I can't think of any reason to justify the existence of the program itself. This is the classic question: Why does anything exit at all? To that question, I can imagine no reasonable answer. But since we are here to discuss things, we can only conclude: something exists. And let me say this... No matter what you experience, no matter what you see -- this program can account for it. Joel

### Re: Introduction (Digital Physics)

Bruno: The mind body admit a lot of subproblem, like what is free-will An illusion. An illusion? That is a rather quick answer. Let us not enter into that perenial debate. Perhaps I should ask you exemple of what is not an illusion, what is your ontology. Good idea. Let me just say that I believe the world is deterministic. But in my mind, this is not incompatible with freewill. For example, I believe the things I WANT to do are determined by the computation... and then I act out the action to obtain what I want. Though technically, I can only WANT one thing at a time. But I realize most people do not feel this way, and they see determinism as incompatible with freewill. So that's why I call it an illusion. It seems like we are making decisions, but in reality, there is no alternatives. I should have you ask this before, if your TOE is a cellular automata, what does execute it? Nothing. Cellular automata simply exist - in the abstract sense - just like the number 3, or the concept of the circle. These objects are merely out there for all to discover, and reason about. is there an afterdeath, Yes. That rather quick too! Amazing for a materialist, plausible for a computationalist, I guess. But then I don't believe materialism being compatible with computationalism. As I've said, I think this world is just a game. New games await us when this one is over. But this idea should not be too tightly connected to cellular automata. It is only my own personal philosophy and not part of the science, per se. Qualia are internal states. Right! (imo). But internal in which sense? Would you agree that it is related with the first person viewpoint. I'm not sure. Ok, thank you Bruno. I think I understand the terminology now (first and third person viewpoints), but I fail to see the importance of it all. If you want I open a new thread. I send you a post with one question. Normally if you are computationalist you will answer yes. The same for the second post, etc. At the end you will understand (or at least to have an idea) the importance of it all. OK? Ok, sounds fun! (I didn't quite understand the UDA - universal dovetailer argument). What is the question? (yes, start a new thread if you prefer) Nevertheless I believe that the fact that 17 is prime is 3-person (objective) verifiable. It is a sharable reality. Yes, I agree. This is a good example. In a similar way, I believe minimal cellular automata are objective reality. We can all think about, for example, the one-dimensional automaton Rule-30. This automaton is exactly the same for everyone, and independent of any simulation you may find yourself in. Let us take your cellular automata which generates everything. You will be generated at some moment (where the moment can be defined in the universal cellular automata terms). The problem is that you will be generated infinitely often, and your average next first person point of view depends on all the consistent computational continuations generated by your universal automata. Hmmm... Yes, you are generated infinitely often, but those copies are not (usually) in communication with one another. In general, each one has its own history and own future. I don't see how there is any synthesis of these experiences. They are (again, usually) independent. Joel

### Re: Introduction (Digital Physics)

Joel, thanks for your clarification. Fred: If two worlds within this everything are contradictory or not consistent with each other, with no common ground, how exactly do they interact? Well I believe the universe is strictly local and completely homogeneous at the bottommost layer. So even though two worlds/cosmoses may be very far apart, eventually the information from one will reach the other. There they will interact, although the result may be completely unexpected from anything that was happening in the two worlds when they were apart, and their inhabitants may be long since gone. Perhaps you are saying all worlds have some commonality eventually? Such as the program you mention below? I imagine all possible programs for all possible universes. If there were a single program running the whole show, I would ask, why that program? Because that one program runs all the others. All the others are embodied by the larger computation. Any program that instantiates all programs should be as good as any other, don't you think? All of these superprograms souuld be equivalent, since they all do exactly the same thing. Yes? As I mentioned in my reply to scerir, we can't avoid self-referential problems, however, if we try to represent or describe ourselves. But if we are merely three-dimensional bit sequences - 3D movies, then all we have to do is find a program that generates our movie. But instead of looking for our particular movie, it's easier to find the program that generates all movies... which must necessarily also generate ours. I don't see any problem with that description. It's all bits. Joel Sounds like you are going after some magic program that generates all possible programs. Would this program be a logical necessity in and of itself? That is, must it necessarily exist? Or would it just happen to exist? Fred

### Re: Introduction (Digital Physics)

Fred: If two worlds within this everything are contradictory or not consistent with each other, with no common ground, how exactly do they interact? Well I believe the universe is strictly local and completely homogeneous at the bottommost layer. So even though two worlds/cosmoses may be very far apart, eventually the information from one will reach the other. There they will interact, although the result may be completely unexpected from anything that was happening in the two worlds when they were apart, and their inhabitants may be long since gone. I imagine all possible programs for all possible universes. If there were a single program running the whole show, I would ask, why that program? Because that one program runs all the others. All the others are embodied by the larger computation. Any program that instantiates all programs should be as good as any other, don't you think? All of these superprograms souuld be equivalent, since they all do exactly the same thing. Yes? As I mentioned in my reply to scerir, we can't avoid self-referential problems, however, if we try to represent or describe ourselves. But if we are merely three-dimensional bit sequences - 3D movies, then all we have to do is find a program that generates our movie. But instead of looking for our particular movie, it's easier to find the program that generates all movies... which must necessarily also generate ours. I don't see any problem with that description. It's all bits. Joel

### Re: Introduction (Digital Physics)

Robert: I object to what I see as an attempt to constrain all viewpoints to a particular way of seeing. I think your idea is fine. A tool for seeing things from a given vantage point. I'm sure there are other vantage points worth visiting, and tools needed to see from those perspectives as well. I don't think anyone would arge against descretization as a tool for seeing. I think people would complain loudly if one insisted his way of seeing was the only way. Wow. Yes. You are absolutely right Robert! Thanks for pointing this out. Understanding the world, whatever it turns out to be, will require lots of different points of view, and different sets of tools. I'm sorry I've been so inflexible. As I've hinted before, I honestly think this world is a kind of puzzle/game that we've created for ourselves to figure out. This has the effect of making me somewhat fearless - trying to knock down well-established castles - but also sometimes reckless and insensitive to those with alternative views. My passion for the game, I think, makes me a better player... but a terrible scientist! In any case, I'll try to be more respectful of the other participants. Regards, Joel

### Re: Introduction (Digital Physics)

Serafino Cerulli-Irelli (scerir) wrote: Christof Schmidhuber wrote an interesting paper, along that path: Strings from Logic http://arxiv.org/abs/hep-th/0011065 What are strings made of? The possibility is discussed that strings are purely mathematical objects, made of logical axioms. More precisely, proofs in simple logical calculi are represented by graphs that can be interpreted as the Feynman diagrams of certain large-N field theories. Each vertex represents an axiom. Strings arise, because these l arge-N theories are dual to string theories. These ``logical quantum field theories'' map theorems into the space of functions of two parameters: N and the coupling constant. Undecidable theorems might be related to nonperturbative field theory effects. Thanks for this interesting reference. It seems more readable than other papers by Christof Schmidhuber. Bruno

### Re: Introduction (Digital Physics)

Christof and Juergen are brothers, aren't they? Marchal wrote: Serafino Cerulli-Irelli (scerir) wrote: Christof Schmidhuber wrote an interesting paper, along that path: Strings from Logic http://arxiv.org/abs/hep-th/0011065 What are strings made of? The possibility is discussed that strings are purely mathematical objects, made of logical axioms. More precisely, proofs in simple logical calculi are represented by graphs that can be interpreted as the Feynman diagrams of certain large-N field theories. Each vertex represents an axiom. Strings arise, because these l arge-N theories are dual to string theories. These ``logical quantum field theories'' map theorems into the space of functions of two parameters: N and the coupling constant. Undecidable theorems might be related to nonperturbative field theory effects. Thanks for this interesting reference. It seems more readable than other papers by Christof Schmidhuber. Bruno Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile) UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 () Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02

### Re: Introduction (Digital Physics)

Joel, let's clarify our positions: To be clear, I envision just one universe that contains everything. Within it may be many worlds or sub-worlds, but these are not independent. They interact. If two worlds within this everything are contradictory or not consistent with each other, with no common ground, how exactly do they interact? I feel two such worlds must be independent entities within the set. This is different from the case of universes which may be linked by wormholes or MWI splittings or whatever. Furthermore, I imagine there is a single program that runs the whole universe, and that we can know that program exactly. I'm not sure what Godel is doing here. I imagine all possible programs for all possible universes. If there were a single program running the whole show, I would ask, why that program? As I mentioned in my reply to scerir, we can't avoid self-referential problems, however, if we try to represent or describe ourselves. Adopting that perspective, we should be able to justify that a simulation of our universe does not appear overly fine-tuned. At least that would suit my aesthetic tastes. As in fine-tuned to support life, etc.? No, I don't see any necessity in that either. Where there is life, there is life. That's enough for me! Joel True, there is no necessity in avoiding fine-tuning. It just makes the model more compelling in my opinion. Fred

### Re: Introduction (Digital Physics)

Hi Fred: I agree that any useful TOE should be able to be implemented on a (large enough) computer. Yes, I agree. This computation can then SIMULATE the relevant or important aspects of the universe we observe, or all aspects of other possible universes, with their APPARENT real-number continua and infinite sets. Godel's theorem prevents us from simulating all aspects of our universe. Hmm.. Sounds like we might be talking about different things. Or maybe it's just our terminology... To be clear, I envision just one universe that contains everything. Within it may be many worlds or sub-worlds, but these are not independent. They interact. Furthermore, I imagine there is a single program that runs the whole universe, and that we can know that program exactly. I'm not sure what Godel is doing here. Adopting that perspective, we should be able to justify that a simulation of our universe does not appear overly fine-tuned. At least that would suit my aesthetic tastes. As in fine-tuned to support life, etc.? No, I don't see any necessity in that either. Where there is life, there is life. That's enough for me! Joel

### Re: Introduction (Digital Physics)

Let us take the realist approach and focus on the things we can actually compute fully. Joel Godel's theorem prevents us from simulating all aspects of our universe. Fred Is that true? Goedel's argument does not prove the existence of absolutely unprovable (arithmetical) truths. Its conclusion is relative to some first-order axiom system (of elementary arithmetic), and proves only that there is a true proposition unprovable in that system. But there are plenty of other systems in wich that proposition is provable (mechanically too). The existence of a proposition unprovable in a given system requires, also, that the system is consistent. But how is a computer supposed to know that? Does the universe know Goedel's theorems? - Scerir

### Re: Introduction (Digital Physics)

Bruno: Would you formalise that by the total (defined everywhere) functions from N to N, or do you accept the partial computable functions as well? And why would you not accept also the functions computable relatively to the halting problem? They correspond naturally to the function computable in the limit and are quite usefull if you accept infinite histories ... Hmmm... As you can probably tell, I'm not big on proofs or expressing things formally, so maybe it will be safer if I continue to talk plainly. When devising a Theory of Everything, anything goes, except you must be able to demonstrate the universe in action. At least the beginning part. You must specify, exactly, what the initial conditions are, and what the procedure is for transforming the initial conditions into the future states. Following the instructions you specify, we should be able (in principle) to see everything we see now. The ground, the sky, the sea, people, plants, and animals. Joel

### Re: Introduction (Digital Physics)

Joel wrote: If we cannot program it... it's not a Theory of EVERYTHING. It's just a description. You really should be an intuitionist mathematicien. It is consistent with most intuitionist mathematical system that 1) all function from N to N is computable. 2) all function from R to R is continuous. In my approach the intuitionist philosophy correspond to the first person viewpoint. But I'm a Platonist, at least about numbers and functions from N to N. This includes a lot of uncomputable functions. For exemple the function which gives for each n the greatest number you can compute in fortran with program of length n. (This function grows quickly than any computable function; you can approximate it, in a very weak sense by using transfinite induction: this illustrates that higher infinities can help to manage finite combinatorial problems). Let us take the realist approach and focus on the things we can actually compute fully. Would you formalise that by the total (defined everywhere) functions from N to N, or do you accept the partial computable functions as well? And why would you not accept also the functions computable relatively to the halting problem? They correspond naturally to the function computable in the limit and are quite usefull if you accept infinite histories ... Bruno PS I will comment you other post (from the same thread), where you say you are a materialist, ASAP.

### Re: Introduction (Digital Physics)

Hi Scerir. Thanks for your explanation of Godel's theorem. Goedel's argument does not prove the existence of absolutely unprovable (arithmetical) truths. Its conclusion is relative to some first-order axiom system (of elementary arithmetic), and proves only that there is a true proposition unprovable in that system. But there are plenty of other systems in wich that proposition is provable (mechanically too). If we exclude ourselves from the part of the universe we attempt to simulate, I think we can avoid the self-referential paradox brought up by Godel. This is probably okay for simulating unconscious phenomena, like in physics or biology or engineering. But if we include our consciousness in the simulation, I imagine we would surely have a problem describing our thought processes, especially the thought of how to simulate the thought process, etc. The existence of a proposition unprovable in a given system requires, also, that the system is consistent. I am indeed assuming the universe is consistent. But how is a computer supposed to know that? Does the universe know Goedel's theorems? - Scerir Well, we know Goedels' theorem, so if we include our knowledge into the universe simulation, then we have this barrier. Despite this, Godel does not bar us from stumbling upon a truth without proving it. Fred

### Re: Introduction (Digital Physics)

Hi Brent: I find myself agreeing with you on your general point that any computational theory of everything must be strictly finite - not just countable. Thank goodness! I was beginning to think I was all alone!! On the other hand I think you are missing the point about pi. Pi can be represented by a short program that will compute pi to however many decimal places are required in any given calculation. Yes, I do understand this. I've just done a lousy job explaining it. That program, not the decimal representation, can be inserted in place of pi in any calculation where we would write pi. So in that sense it has a finite, even small, representation. Ahhh... but does that little program ever return a value? Does it ever finish? No. So if this tiny pi program is required as a step in a larger program (like my little example that uses the function pi() ), then main program will never get beyond the first call to the function pi(). The universe would enter this function and never return. Sure, we can use the tiny pi program to symbolically represent the idea of pi. And there may even be some things we can learn from that little program. We can even manipulate it by concatinating it with other programs or some piece of prose text, etc. But we must never be allowed to RUN that program (as a step in a larger program), or else we won't be able to do any other calculations. We can never use the RESULT in a larger program, since the result is infinite. If we cannot program it... it's not a Theory of EVERYTHING. It's just a description. I'm not so sure about this. A program is also just a description. But it's not only a description... it's a perfect description. It's an implementation. And it is identical to the workings of the universe it instantiates. Whereas formulas based on continuous or non-local ideas (e.g. Newtonian Mechanics) only give a rough picture - and leave out the all-important details. Joel

### Re: Introduction (Digital Physics)

Joel wrote Bruno: The formulations are as numerous than the philosophical systems. For a materialist the problem is to explain what are the necessary and sufficient conditions for having the feeling of pain in a leg. Consider me a materialist then, I suppose. In the literature a materialist is someone who believes in a physical (or material) universe, and nothing else. I called ``weak materialist someone who believes in a physical universe and also in something else (number, game, justice, for naming a few examples). Now I am afraid that even ``weak materialism is hardly compatible with computationalism (which you are using in your TOE approach). Most on this list, I think, are willing to accept the idea that materiality occurs in mathematical structures, as seen from inside by some SSA. What I try to show is that, if you accept the comp hypothesis (under the form of the survival through digital substitution, with survival in the great mother psychology sense) then you must substitute the mathematical structure by sort of continuous sheaf of possible first person histories. This happens at a very basic level, and I illustrate it formally with the logic of self-reference in my thesis). In the process I illustrate the loss of explicativeness of the concept of empirical realities, but I have also a direct argument. The mind body admit a lot of subproblem, like what is free-will An illusion. An illusion? That is a rather quick answer. Let us not enter into that perenial debate. Perhaps I should ask you exemple of what is not an illusion, what is your ontology. I should have you ask this before, if your TOE is a cellular automata, what does execute it? is there an afterdeath, Yes. That rather quick too! Amazing for a materialist, plausible for a computationalist, I guess. But then I don't believe materialism being compatible with computationalism. Qualia are internal states. Right! (imo). But internal in which sense? Would you agree that it is related with the first person viewpoint. Ok, thank you Bruno. I think I understand the terminology now (first and third person viewpoints), but I fail to see the importance of it all. If you want I open a new thread. I send you a post with one question. Normally if you are computationalist you will answer yes. The same for the second post, etc. At the end you will understand (or at least to have an idea) the importance of it all. OK? If you prefer, read the UDA. You can ask me question or challenge me on the reasoning. For the record: I think the third person point of view does not exist. Confirmation is never permanent and can always be unconfirmed. (i.e. One of the observers on the phone can later admit that she or he was lying, or confused.) For each of us, there is only the first person. We certainly have some acquaintance with ourself from the first person point of view (and even the third ). I dont' see why we should not trying most objective possible theories of realities, though. Of course such theories are always sort of anticipation, but that game is part of science and even consciousness. Nevertheless I believe that the fact that 17 is prime is 3-person (objective) verifiable. It is a sharable reality. If your cellular automata generates everythings it will do it in an extraordinary terrible redundant way. The computational indeterminacy must be quantified on the set of *all* consistent continuations. Huh? What does that mean? Let us take your cellular automata which generates everything. You will be generated at some moment (where the moment can be defined in the universal cellular automata terms). The problem is that you will be generated infinitely often, and your average next first person point of view depends on all the consistent computational continuations generated by your universal automata. (See the UDA, or answer yes for my thread proposition if you want). The basic point comes from the fact that from you first person point of view you cannot be aware of 10^billion moments between the generation of similar next instant. Like in quantum physics there is eventually a sum over infinities of histories which are needed here. Bruno http://iridia.ulb.ac.be/~marchal

### Re: Introduction (Digital Physics)

Joel: It seems to me there is a great deal more information in PI than just the 2 bytes it takes to convey it in an email message. Russell: Not much more. One could express pi by a short program - eg the Wallis formula, that would be a few tens of bytes on most Turing machines. Even expressing it as a pattern on your beloved CA, it would probably not consume more that a few hundred bytes. Yes, I see. Juergen pointed this out too, and I think it's a valid point to make the distinction between different representations of the same mathematical object. You are both correct - Pi can in fact be represented nicely (as a program) in a finite way. But I don't dispute this, as I wasn't talking about the finite representation. I was talking about the infinite process / function that pi represents. Maybe this is obvious, but my whole point is that we are fooling ourselves if we think we can compute physics using expressions that consume infinite resources (memory, or computing time). Yes, I understand that the universe as a whole may grow without bound (infinite history), but at any given moment, it must be a finite size. Otherwise we can't compute it! For example, if somehow the universe requires computations like the following: x = 0 do x = x + pi() print x loop Then we are doomed. We cannot run this kind of program. Yes, I know we can find a finite representation like this: x = 0 do x = x + 1 print x; pi loop But does this REALLY make use of the details of pi? I don't think so. I'm simply trying to get people to confront the truth that we humans are incapable of devising Theories of Everything that are NOT run on a universal computer. That's all. Many will say, Of course! We know that!. And then they go on, as if nothing happened, talking about the probabilities of items in infinite sets, and independent tosses of a fair coin, and quantum indeterminacy, and the continuum of the real numbers, as if these things exist! If we cannot program it... it's not a Theory of EVERYTHING. It's just a description. Let us take the realist approach and focus on the things we can actually compute fully. Joel

### Re: Introduction (Digital Physics)

Joel Dobrzelewski wrote: And please explain for me how this calculation involved the continuum or infinite binary expansion of the symbol pi in any meaningful way. Sorry, missed getting in this riposte in the last post. What does a binary expansion have to with the calculation .1 * 10 = 1? (I am assuming the usual decimal base convention). Binary representations are no more real than pencil marks on a paper. As far as the continuum is concerned, calculations involving pi do not involve the continuum. There is a whole lot of mathematics in between the discrete and the continuous (pretty much all of it I'm afraid!). Cheers Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967 UNSW SYDNEY 2052 Fax 9385 6965 Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks

### Re: Introduction (Digital Physics)

Joel Dobrzelewski wrote: Ok, sorry for being a smart-ass. Instead of baiting the discussion to make my point, I'll try to simply state the position clearly. We humans cannot deal with infinite structures, like pi. Numbers like pi and e and Omega and all the others are the devil! :) And we all know the devil is in the details... I think I made it obvious that pi and e are pretty simple objects, and humans are quite capable of dealing with them (OK maybe not all humans :). Omega, on the other hand, is quite a different beast again! We carry them along in our mathematics all the way to the end so that they can be evaluated in the final step. But I ask you: When does the universe evaluate its expressions? AFAIC, this is a meaningless question. ... Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967 UNSW SYDNEY 2052 Fax 9385 6965 Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks

### Re: Introduction (Digital Physics)

Hello again Joel. I think I can agree with you, in a pragmatic sense, with what you state below. I agree that any useful TOE should be able to be implemented on a (large enough) computer. This computation can then SIMULATE the relevant or important aspects of the universe we observe, or all aspects of other possible universes, with their APPARENT real-number continua and infinite sets. Godel's theorem prevents us from simulating all aspects of our universe. Adopting that perspective, we should be able to justify that a simulation of our universe does not appear overly fine-tuned. At least that would suit my aesthetic tastes. Fred I'm simply trying to get people to confront the truth that we humans are incapable of devising Theories of Everything that are NOT run on a universal computer. That's all. Many will say, Of course! We know that!. And then they go on, as if nothing happened, talking about the probabilities of items in infinite sets, and independent tosses of a fair coin, and quantum indeterminacy, and the continuum of the real numbers, as if these things exist! If we cannot program it... it's not a Theory of EVERYTHING. It's just a description. Let us take the realist approach and focus on the things we can actually compute fully. Joel

### Re: Introduction (Digital Physics)

Joel Dobrzelewski wrote: And please explain for me how this calculation involved the continuum or infinite binary expansion of the symbol pi in any meaningful way. All you have really said was: 2 * broccoli = 2 broccoli No - I said the circumference of a circle of diameter 1 is pi. Not the same thing at all. :) I am unimpressed. It seems to me there is a great deal more information in PI than just the 2 bytes it takes to convey it in an email message. Not much more. One could express pi by a short program - eg the Wallis formula, that would be a few tens of bytes on most Turing machines. Even expressing it as a pattern on your beloved CA, it would probably not consume more that a few hundred bytes. Maybe Mathematica was a poor choice for your counterexample, since it too runs on discrete hardware and software that could easily be run on a CA. I chose my example wisely So far you have not convinced me that a CA could not perform these same calculations. That was not my point... Do you have some other example? Joel Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967 UNSW SYDNEY 2052 Fax 9385 6965 Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks

### Re: Introduction (Digital Physics)

Joel Dobrzelewski wrote: But I don't dispute this, as I wasn't talking about the finite representation. I was talking about the infinite process / function that pi represents. Maybe this is obvious, but my whole point is that we are fooling ourselves if we think we can compute physics using expressions that consume infinite resources (memory, or computing time). Yes, I understand that the universe as a whole may grow without bound (infinite history), but at any given moment, it must be a finite size. Otherwise we can't compute it! Yes - I understand that is your point of view, as it is also that of Hal Ruhl's. It is not shared by the majority - eg myself, Juergen or Bruno. To be quite frank, whether something can be computed using 32 bit integers, or IEEE floating point numbers or not is rather irrelevant to fundamental theories of reality. This is why Juergen's all possible descriptions approach has more legs. As an instance of the sort of problems you face, the number 0.1 can be represented as a finite string in base 10, but cannot be represented as a finite binary string (floating point number). Is 0.1 a valid number then? Unless you completely do the Kronecker thing, or course Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967 UNSW SYDNEY 2052 Fax 9385 6965 Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks

### Re: Introduction (Digital Physics)

[EMAIL PROTECTED] wrote: Bruno Marchal: 1) The Schmidhuber-Ruhl-Dobrzelewski-... approaches (SRD) 2) The other approaches, which take into account the fact that we have not yet solved the mind body problem. Von Weizsaecker said, long time ago, that Nature is earlier than man. But man is earlier than natural science. Is that a third approach? Reminder: first person plural point of views arise when entire population of machines are multiplied, like in the quantum MWI. In that case the indeterminacy is sharable, (like in quantum computing, or like in EPR-Bell type of experiences). Von Weizsaecker's sentence is third or first-plural approach. I don't know. I would bet on first-plural. The existence of empirical quantum indeterminacy is evidence that we share some sort of self-multiplication since a long time. Of course natural science is an ambiguous experience. I suppose you mean Human Natural Science. God's treatise on General Possible Science belongs to Babel Library in Plato Heaven, out of time. Math makes possible (for relative UTMs) to glimpse a little bit of those atemporal realities. Note that the devil's treatise belong in Babel too, btw. Note also that no glimpse can be enough deep for making possible for a UTM to distinguish those treatise with *complete* confidence ... The sound universal machine cannot not be modest and prudent. Er... Sorry for the digression :-) Bruno

### Re: Introduction (Digital Physics)

Joel: What is the mind-body problem? Bruno: The formulations are as numerous than the philosophical systems. For a materialist the problem is to explain what are the necessary and sufficient conditions for having the feeling of pain in a leg. Consider me a materialist then, I suppose. The mind body admit a lot of subproblem, like what is free-will An illusion. is there an afterdeath, Yes. what is the nature of qualia, etc. Qualia are internal states. A third person description is a verifiable one by an external (not duplicated) observer. It can contain something like Joel wakes up successfully in both Washington and Moscow. It has been confirmed by two phonecalls, etc. Ok, thank you Bruno. I think I understand the terminology now (first and third person viewpoints), but I fail to see the importance of it all. For the record: I think the third person point of view does not exist. Confirmation is never permanent and can always be unconfirmed. (i.e. One of the observers on the phone can later admit that she or he was lying, or confused.) For each of us, there is only the first person. If your cellular automata generates everythings it will do it in an extraordinary terrible redundant way. The computational indeterminacy must be quantified on the set of *all* consistent continuations. Huh? What does that mean? Joel

### Re: Introduction (Digital Physics)

Von Weizsaecker said, long time ago, that Nature is earlier than man. But man is earlier than natural science. and Bruno wrote: Of course natural science is an ambiguous experience. I suppose you mean Human Natural Science. Yes. I think so. Christof Schmidhuber wrote an interesting paper, along that path: Strings from Logic http://arxiv.org/abs/hep-th/0011065 What are strings made of? The possibility is discussed that strings are purely mathematical objects, made of logical axioms. More precisely, proofs in simple logical calculi are represented by graphs that can be interpreted as the Feynman diagrams of certain large-N field theories. Each vertex represents an axiom. Strings arise, because these l arge-N theories are dual to string theories. These ``logical quantum field theories'' map theorems into the space of functions of two parameters: N and the coupling constant. Undecidable theorems might be related to nonperturbative field theory effects. God's treatise on General Possible Science belongs to Babel Library in Plato Heaven, out of time. Math makes possible (for relative UTMs) to glimpse a little bit of those atemporal realities. Note that the devil's treatise belong in Babel too, btw. Note also that no glimpse can be enough deep for making possible for a UTM to distinguish those treatise with *complete* confidence ... The sound universal machine cannot not be modest and prudent. Er... Sorry for the digression :-) Very nice digression. Read with much pleasure. A very interesting lecture, about Babel languages dreams, et cetera, was this one, http://www.italynet.com/columbia/dream.htm by Umberto Eco. - Serafino Cerulli-Irelli (scerir) [Once a physicist, at Rome Un., now just a farmer]

### Re: Introduction (Digital Physics)

Joel wrote: What is the mind-body problem? The formulations are as numerous than the philosophical systems. For a materialist the problem is to explain what are the necessary and sufficient conditions for having the feeling of pain in a leg. For an idealist the problem is to explain what are the necessary and sufficient conditions for having the feeling that there exists things like electrons, waves, chairs, and neurons... For an dualist the problem is to explain the relationship between mind and matter. (cf Descartes modern formulation). In general the mind body problem is tackle by religion. Some scientist does not believe there is a mind body problem because they are unaware that they believed in the matter religion. The mind body admit a lot of subproblem, like what is free-will, is there an afterdeath, what is the nature of qualia, etc. What does first person and third person mean? I know from your post that you are computationalist, i.e. you can imagine that our consciousness is can be retrieved from the working of a pure finite computation (by a universal minimal cellular automaton for instance). Then you agree that in principle you are duplicable (at some level of description). Suppose you take on you a intime diary where you note the result of your personal experience. Now I make here (at Brussels) a copy of your actual description, then I annihilate you, and then I make you reconstituted at both Washington and Moscow. A first approximation of the first person is given by the content of your diary. Because you keep your diary with you, it will be duplicated too. It will contain either I wake up in Moscow, what a nice city, etc., or I wake up in Washington, what a nice city, etc.. A third person description is a verifiable one by an external (not duplicated) observer. It can contain something like Joel wakes up successfully in both Washington and Moscow. It has been confirmed by two phonecalls, etc. This gives a striking illustration of the difference between the two discourses. What is an and (Moscow and Washington) in the 3-description becomes an or (I wake up in Moscow or in Washington) in the 1-description. It is easy (for some at least!) to realise that (with comp) we cannot predict the result of experience for self-multiplication experiments. This indeterminacy can be shown not depending of the contingent feature of the reconstitutions. Look at the UDA for a description of the consequences of that proposition. It entails a priori explosive sets of possible 1-continuations. There is a kind of complementarity/duality between 1-3 description versus discrete/continuum. If we can be captured by a finite discrete code, then we cannot avoid some confrontation with the continuum under one form or another. Sometimes I summarise that view on the foundation of math by paraphrasing Kronecker : God creates the Natural Numbers, all the rest are ... dreams by Natural Numbers. (Kronecker says ... all the rest are human inventions; I generalise Kronecker by replacing human by universal turing machines). Now, with comp dreams obeys the laws of dreams (the laws of the consistent computational extensions), and the appearance of the physical must be explained by the logical structures of those sheaves of dreams. If your cellular automata generates everythings it will do it in an extraordinary terrible redundant way. The computational indeterminacy must be quantified on the set of *all* consistent continuations. Bruno http://iridia.ulb.ac.be/~marchal

### Re: Introduction (Digital Physics)

George: My position, is that there are no separations between worlds. There is only one single huge world, the plenitude and we live in it. The plenitude is choke full of white rabbits. In fact most of it is white rabbit stuff. I very much agree. The reason we don't see them is that our consciousness anthropically constrains what we can observe and filters out the white rabbits just like inhabitants of Flat Land can only see objects in two dimentions. What do you mean by consciousness here? If you mean simply beliefs then I might agree. But if you mean consciousness in general, then I think I disagree. The reason we haven't seen any is simply because we haven't seen any. (yet) Necessarily, there will be some worlds where white flying rabbits aren't seen for trillions of years. By the way... I'm curious why we are using the example of white rabbits. White rabbits are quite common in the laboratory. Is that why we use them as an example? Because they are uncommon in nature? Greek philosophers would have called White Rabbits devices like cars, TVs and flashlights. Of course, after an expossure to twentieth century science, their beliefs would be modified and what used to be White Rabbits would become hackneyed household hare. So the perception of white rabbits is definitely in the eyes of the beholder. A very relativistic attitude. Now this is a good example. So maybe white rabbits are just around the corner. You raise a good question regarding the probability of infinite sets. It has been the subject of infinite discussions on this list dismissing it as meaningless does not solve the problem of why event A may be more proable than event B even though both may have infinite measure in the plenitude. I still have a problem with this concept. If I have a bag with an infinite number of apples and oranges, and I keep pulling out an orange for a billion years... what use is the information that both apple and orange are equally likely? Maybe all the oranges are on top! That's what I mean by meaningless. Joel

### Re: Introduction (Digital Physics)

Fred: Your cellular automaton demos look pretty neat, but how can you tell if they are conscious or self-aware? Do two of these interact in a social manner? Well, in the 3D version there must exist (if these automata are indeed minimal) configurations that look just like you and me discussing this very topic. I consider that proof enough that they are self-aware. (In the 2D version there are just pictures of these entities.) Do they interact with the programmer? No. There is no programmer. These automata are simply out there, waiting to be discovered. Anyone can discover them. And the inhabitants of cellular automata worlds can reason about the automaton they live in. That's as close as they can get to talking with a programmer. (A scenario where reality is 'put up' is entertaining, but it would be more convincing if a sign were received from beyond, so to speak.). Though I don't expect them to convince anyone else, I have received all the signs I need. I conclude that in fact this world is 'set up' for us to topple down! (Yes, I realize it's statements like these that jeopardize my credibility. :) Joel

### Re: Introduction (Digital Physics)

Joel wrote: What is weird from one perspective is not too weird in another. Some might thing it's strange, and others might not. I agree. So what I say is that we must explain why the world seems to *remain* normal to us. Suppose you have a theory of elementary particles, and that your theory predicts that if you send a neutron on a proton with enough energy, then you get a virtual mad cows lasting for 0.00134sec. And then you do the experiment, and you get nothing (except the proton and neutron). You agree that you must explain the absence of madcows, I guess. Well, with everything-like type of TOEs, there is a necessity to explain the apparence of lawfull regularities, because those TOEs (like the Everett one) a priori entails to much possible continuations, there is an induction-inflation. In this list, oversimplifying a little bit, there are two sort of approaches with respect to that inflation. 1) The Schmidhuber-Ruhl-Dobrzelewski-... approaches (SRD). (Please don't take such denomination too seriously). The SRD makes abstraction of the first person and does not take into account the first person description. There is some agreement that there are still third person white rabbits, and they hunt them by using some absolute self-sampling assumption (Nick Bostrom SSA, see http://www.analytic.org/) based on universal prior. 2) The other approaches, which take into account the fact that we have not yet solved the mind body problem. In particular if we accept the computationalist thesis, then it is possible to show explicitily that consciousness cannot be associate neither with physical activity, nor even with any single computation, but only to dense and continuous sheaves of infinite computations. You still have to explain the absence of the third person whabbits (and universal prior could still be useful although my own track of 3-whabbits is more based on Bennett notion of depth), but, you get 1-person whabbits too (and a priori vastly numerous, at least 2^aleph0). To track them you need a refined *relative SSA*, which can be seen as a conditionalisation on your actual states. Some are hunting the 3-whabbits, and some are hunting the 3-whabbits + the 1-whabbits. No doubt that that summary is rough, but I wanted to be short. Bruno

### Re: Introduction (Digital Physics)

Joel, Your cellular automaton demos look pretty neat, but how can you tell if they are conscious or self-aware? Do two of these interact in a social manner? Do they interact with the programmer? True, it is hard to determine probabilities in an infinite set, but we get a feel for how likely something is, in terms of ratios of possibilities. So universes perceived to be simple and lawlike outnumber those perceived to be contrived and lawless, for example. (A scenario where reality is 'put up' is entertaining, but it would be more convincing if a sign were received from beyond, so to speak.). Once we get a better understanding of the laws in our universe, I think we can get a better picture of the whole thing. Fred

### Re: Introduction (Digital Physics)

Scerir: Thanks for your thoughtful reply. Today is commonly accepted that the QM domain is incompatible with that local realism. That is because Bell inequalities actually are violated. Local hidden variables do not exist. I know this is not a popular view, but I am not convinced of the validity of such experiments. One proponent of the realist opinion, who has better arguments than I, is Caroline Thompson: http://users.aber.ac.uk/cat/ But, fortunately, Bell inequalities imply a Kolmogorovian probability model. So we can keep that local realism and say that probability is truly non-Kolmogorovian. But, wait. Ehe. There is another problem. The Bohm-Aharonov effect is truly non-local. And that is hard, very hard to avoid. I admit I'm not too familiar with these concepts or terms. I'll try to understand them a little better. In the mean time, my main objection to non-local phenomena is, once again, our inability to formally implement it. Challenge: write a set of non-local equations or a non-local computer program that isn't implemented locally. For example: It would be easy enough to program a virtual reality simulation to exhibit seemingly non-local behaviors. We could even do something extremely macroscopic like joining the motion of two pool balls firmly together - so that whenever one was moved, the other moved also - seemingly instantaneously. From all indications, to the inhabitants of our virtual reality, their world is non-local. But they should know better. They must realize that even though they may see non-local phenomena happening around them, they could always be fooled by SOME local communication happening behind the scenes. And so... our virtual reality simulation, being run on a conventional computer, literally has HIDDEN VARIABLES that the inhabitants don't see, but we can. It seems a popular fallacy to say that Bell proved that no local theory can account for the experiments. But this is not true at all. From what I can tell, Bell only showed that Quantum Mechanics, as it is formulated, is non-local. But this is a far cry from showing it in the real world. If we're intent on looking for magic, we needn't go so far as quantum mechanics. For that matter, we could say that Newton proved that gravity is a non-local phenomenon. And, to some extent, we would be correct. Experiments show that gravity travels instantaneously from the Earth to the Sun... and all the bodies of the cosmos simultaneously. But we know better... We know that SOMETHING must carry the information from one place to another - even if it appears to be happening instantaneously *from our point of view*. Joel

### Re: Introduction (Digital Physics)

Hi Fred: I have not corresponded with the distribution in quite a while. Your posting below seems to have caused some furor. That's good, right?! I tend to feel that the position that our universe is a digital cellular automaton is vulnerable, mainly because it implies that we can create universes containing self-aware structures (SAS's) that our much simpler than the one we inhabit, by using some multi-dimensional analogue to Rule-30 below. I don't see why our being able to create life within cellular automata makes the view that we too live in a cellular automaton weak or vulnerable. There is no reason why a self-aware entity within cellular automaton wouldn't be interested in cellular automata too. Within the Universe that generates all things... All things will happen. A resolution to the White Rabbits problem accepted by most on the distribution requires us to insist that we live in the simplest possible universe containing SAS's. So it would be impossible or highly improbable that we can create universes with SAS's (e.g., by constructing cellular automata). I just don't understand the White Rabbit problem. Again, in a Universe where Everything happens, some worlds are going to have white rabbits, and others blue, and others flying, and others hopping. Probability has nothing to do with it. (And is meaningless, in my opinion, when it comes to infinite collections of things.) We happen to find ourselves in a world where most rabbits stay on the ground. But to conclude that it has always been so, or that it will always remain so, or that it is somehow more likely than the alternatives is just plain silly. No justification is needed for what we see. As I suggested in my other post, leaping Leporidae, each of us has little idea what 'really' happened before we were born... or what will happen when we die. Are you absolutely sure the world is what you think it is? See 'The Matrix', or 'The Thirteenth Floor', or 'eXistenZ', or 'The Truman Show', or better yet: all of them. Now stir gently. If you could, and you could prove that you have created a universe inhabited by SAS's, that would indeed be some achievement, and it would force a change of thinking in many. That's what I'm here for - to change the thinking of many! Anyway, I don't have a mathematical proof yet, but I do have some nice, ultra-high-resolution photographs of these SAS's: http://cvm.msu.edu/~dobrzele/ideas/dp/leo/2dRule30.htm And some exquisitely animated 3D models that are so lifelike, you cannot tell that they aren't real: http://digitalphysics.org/Automata/Triangle/ Whether our universe is digital or continuous is harder to decide. Even with a set of quantized universes, we could have a continuum of 'different sized' quanta building blocks, though it may not affect the physics for each of the universes. That's a great way of putting it! Different sized quanta. -- Philosophically speaking, challenging the idea of white rabbits... What if our current world was deliberately made ordinary and regular so that we can get our bearings among all the multitudes of crazy realities out there? A kind of VR training ground for digital spirits that had grown tired of VR heaven and purposely instantiated themselves into corporeal (but still digital) bodies in order to fully experience the pleasures of freedom outside? Outside of gravity and bills and carpel tunnel syndrome. What if our world is just a puzzle we've constructed for ourselves to keep us busy for a few decades? And when we solve it, and learn the truth that all is virtual, we'll be set free to create new worlds of our own design and safely explore the fantastic worlds of others? Just wondering... Joel

### Re: Introduction (Digital Physics)

Joel Dobrzelewski: I know this is not a popular view, but I am not convinced of the validity of such experiments. One proponent of the realist opinion, who has better arguments than I, is Caroline Thompson: http://users.aber.ac.uk/cat/ Yes, I know. But chances for loopholes are very narrow, after 20 years, unfortunately. I admit I'm not too familiar with these concepts or terms. I'll try to read up and understand them a little better. In the mean time, my main objection to non-local phenomena is, once again, our inability to formally implement it. Challenge: write a set of non-local equations or a non-local computer program that isn't implemented locally. For example: It would be easy enough to program a virtual reality simulation to exhibit seemingly non-local behaviors. We could even do something extremely macroscopic like joining the motion of two pool balls firmly together - so that whenever one was moved, the other moved also - seemingly instantaneously. Very interesting. For local vs non-local experiments and effects with (two separated) computers see: www.maths.nottingham.ac.uk/personal/sjw/abstracts/accardi.html http://volterra.mat.uniroma2.it/ the link probability and quantum Have a look also to: http://arxiv.org/abs/quant-ph/0007019 Non-locality and quantum theory: new experimental evidence Luigi Accardi, Massimo Regoli Starting from the late 60's many experiments have been performed to verify the violation Bell's inequality by Einstein-Podolsky-Rosen (EPR) type correlations. The idea of these experiments being that: (i) Bell's inequality is a consequence of locality, hence its experimental violation is an indication of non locality; (ii) this violation is a typical quantum phenomenon because any classical system making local choices (either deterministic or random) will produce correlations satisfying this inequality. Both statements (i) and (ii) have been criticized by quantum probability on theoretical grounds (not discussed in the present paper) and the experiment discussed below has been devised to support these theoretical arguments. We emphasize that the goal of our experiment is not to reproduce classically the EPR correlations but to prove that there exist perfectly local classical dynamical systems violating Bell's inequality. http://arxiv.org/abs/quant-ph/0007005 Locality and Bell's inequality Luigi Accardi, Massimo Regoli We prove that the locality condition is irrelevant to Bell in equality. We check that the real origin of the Bell's inequality is the assumption of applicability of classical (Kolmogorovian) probability theory to quantum mechanics. We describe the chameleon effect which allows to construct an experiment realizing a local, realistic, classical, deterministic and macroscopic violation of the Bell inequalities. http://arxiv.org/abs/quant-ph/9606019 A Proposed Experiment Showing that Classical Fields Can Violate Bell's Inequalities Patrick Suppes (Stanford University, USA), J. Acacio de Barros (Federal University at Juiz de Fora, Brazil), Adonai S. Sant'Anna (Federal University at Parana, Brazil) We show one can use classical fields to modify a quantum optics experiment so that Bell's inequalities will be violated. This happens with continuous random variables that are local, but we need to use the correlation matrix to prove there can be no joint probability distribution of the observables. For joining the motion of two pool balls firmly together, etc. see http://arxiv.org/abs/quant-ph/0007044 The Violation of Bell Inequalities in the Macroworld Diederik Aerts, Sven Aerts, Jan Broekaert, Liane Gabora We show that Bell inequalities can be violated in the macroscopic world. The macroworld violation is illustrated using an example involving connected vessels of water. We show that whether the violation of inequalities occurs in the microworld or in the macroworld, it is the identification of nonidentical events that plays a crucial role. Specifically, we prove that if nonidentical events are consistently differentiated, Bell-type Pitowsky inequalities are no longer violated, even for Bohm's example of two entangled spin 1/2 quantum particles. We show how Bell inequalities can be violated in cognition, specifically in the relationship between abstract concepts and specific instances of these concepts. This supports the hypothesis that genuine quantum structure exists in the mind. We introduce a model where the amount of nonlocality and the degree of quantum uncertainty are parameterized, and demonstrate that increasing nonlocality increases the degree of violation, while increasing quantum uncertainty decreases the degree of violation. and for Bohm-Aharonov effect and weird jamming: http://arxiv.org/abs/quant-ph/9605004 Action and Passion at a Distance: An Essay in Honor of Professor Abner Shimony Sandu Popescu, Daniel Rohrlich Quantum mechanics permits nonlocality---both nonlocal correlations and

### Re: Introduction (Digital Physics)

Joel : And non-local effects must be similarly ruled out, as they too are forbidden to our intellect. Just as it is impossible for us to create non-discrete (i.e. continuous) theories, it is also not possible for humans to construct truly non-local theories. I hope so. But there are difficulties. In QM, Bell's theorem states that statistical results of experiments performed on a certain physical entity satisfy his inequalities iff the physical reality in which that physical entity is embedded is local (local hidden variables). Today is commonly accepted that the QM domain is incompatible with that local realism. That is because Bell inequalities actually are violated. Local hidden variables do not exist. But, fortunately, Bell inequalities imply a Kolmogorovian probability model. So we can keep that local realism and say that probability is truly non-Kolmogorovian. But, wait. Ehe. There is another problem. The Bohm-Aharonov effect is truly non-local. And that is hard, very hard to avoid. And, again, Bell inequalities are (also and much more) violated in CM. In our macro-world. Weird. Unbelievable. Is our macro-world non-local ? Is our universe non-Kolmogorovian ? Or is our (my) mind stupid ? Or is our logic poor ? - S.

### Re: Introduction (Digital Physics)

Ok, sorry for being a smart-ass. Instead of baiting the discussion to make my point, I'll try to simply state the position clearly. We humans cannot deal with infinite structures, like pi. Numbers like pi and e and Omega and all the others are the devil! :) And we all know the devil is in the details... We carry them along in our mathematics all the way to the end so that they can be evaluated in the final step. But I ask you: When does the universe evaluate its expressions? Is there an end to the universe when all the values for pi and e are fully computed and all their magic is brought to life? If we simply carry these finite expressions along so that they can be evaluated later, if we choose to, but they don't really make a big difference anyway, then what use did we make of the continuum? Maybe we were just fooling ourselves and delaying the inevitable. F = G * m1 * m2 / r^2 That's a finite expression. We always assume that we can calculate F and to any degree of precision we like. But then does this capture the whole picture? If we are guaranteed to have rounding errors because our computers only have so much RAM, then have we really explained all there is to explain? No. Something more (or less!) is necessary... When searching for a Theory of Everything, we need an expression, a formula, a program that doesn't have any rounding errors. I still claim... it must be finite and discrete. Does this make any more sense now? Chasing the real devil / details of pi is a hopeless task. It would be better to just acknowledge that we can never *implement* pi and resolve to work with finite expressions and finite mathematics. I feel that this bottom up approach is our only chance fr success. Joel

### Re: Introduction (Digital Physics)

Hello, --- Joel Dobrzelewski [EMAIL PROTECTED] wrote: Russell and Brent: I understand this is an extreme position, but I state it this way on purpose: to bring the issue to the foreground and get to the heart of the problem of science today. As long as we insist that continuous objects really exist - we will always* No, we're finite and discrete remember? be fooling ourselves and forever chasing an unobtainable ghost. Descriptions of continuous structures are only that - descriptions. And they will *always* remain finite and discrete. Discrete and finite viewpoints are an artifact of a finite consciousness. The symbol PI is a finite description for an infinite *process*. No sheet of paper or gigabyte of RAM can contain PI. It can, just not all at once. YOu could say Ram and paper are temporally challenged entities. And thus, any theory we create or program we write MUST truncate PI at come point... otherwise we will forever be waiting for the theory to produce its first result. const PI = 3.1415926535 These descriptions are entirely misleading - only approximations - never reality. I strongly disagree. Reality is a relative construct anyway, a construction, and agreement by a group of people large enough to enforce it. It would be better to do this... const PI = 1110101100010000111 But even this is wrong. To truly illustrate the point, we must do the following... function PI () as string do 'calculate PI loop end function Does the function PI() ever return a value? No. It is not within our reach. This is not proof that there is no continuum. Only evidence that there can be no continuum FOR US. *ouch* I just don't agree. If anything, your pi illustration is a demonstration of a kind of continuum. We are forced to interpret this infinite string in finite terms because we *think* in finite terms. One can train his brain to interpret any equation that fits in his field of view simultaneously. That is, the entire equation front to back as one visual/symbolic entity. From there, the information would trickle back through the neurons to form an expression the interpreter disires. So in effect, to the limit of his field of view, he sees the equation in it's entirety simultaneously without delay. Only processing depth incurs any delay. This person could also see a limited sequence of numbers produced by the equation, in this case pi, to the extent of his field of usable vision, and interpret this finite sequence, simultaneousy from paper to brain. Only depth of processing delays would be incurred. Now assume someone with a field of view that is infinite in one direction along with the required neurons for processing. This person could interpret a continuous infinite number set simultaneously. We assume we cannot do this because we assume we are finite and discrete. I say this thinking is limited to self limited consciousness. We might view another concept. This idea assumes that are finite nature is illusory. Our brains made up of ~10^9 neurons and 10^12 connections exist as an intersection into a conscious realm that only sees discretely. We see a single neuron but in fact a single neuron would be (in this concept) an intersection into a preceptual space where discrete conscousness exists. So to our equation to evaluate pi, simply an intersection into discrete perceptual space if something continuous and infinite. This concept allows one to interpret infinite number sets without constraint to time. Assuming time itself is an illusion of descrete/finite perceptual space, our way of thinking may be the exception, and not the rule of all possible perceptional and thinking spaces. For us, there can only be one infinite process in the Universe - the universe itself. Are we truely seperate from the universe that gave birth to us? Could it be, we and are finite/discrete thinking and perceptional viewpoints are simply a snapshot, an intersection of the universe's expression of intelligence? I assert that even our own existence is a continuum, we only happen to be conscious at this point of our development. In that, we are not seperate from the universe that gave birth to us, every atom in our bodies a mini-contimuum of existence, forming a singular (aprently) expression of intelligence. Robert W. __ Do You Yahoo!? Spot the hottest trends in music, movies, and more. http://buzz.yahoo.com/

### Re: Introduction (Digital Physics)

Russell and Brent: I understand this is an extreme position, but I state it this way on purpose: to bring the issue to the foreground and get to the heart of the problem of science today. As long as we insist that continuous objects really exist - we will always be fooling ourselves and forever chasing an unobtainable ghost. Descriptions of continuous structures are only that - descriptions. And they will *always* remain finite and discrete. The symbol PI is a finite description for an infinite *process*. No sheet of paper or gigabyte of RAM can contain PI. And thus, any theory we create or program we write MUST truncate PI at come point... otherwise we will forever be waiting for the theory to produce its first result. const PI = 3.1415926535 These descriptions are entirely misleading - only approximations - never reality. It would be better to do this... const PI = 1110101100010000111 But even this is wrong. To truly illustrate the point, we must do the following... function PI () as string do 'calculate PI loop end function Does the function PI() ever return a value? No. It is not within our reach. This is not proof that there is no continuum. Only evidence that there can be no continuum FOR US. For us, there can only be one infinite process in the Universe - the universe itself. The one calculation that never ceases... but always remains FINITE in extent and always DISCRETE. Always calculating PI to ever more decimal places... Joel

### Re: Introduction (Digital Physics)

Hi Robert: Discrete and finite viewpoints are an artifact of a finite consciousness. I agree. It can, just not all at once. You could say Ram and paper are temporally challenged entities. Do you have an example of something (other than the universe itself) that is not temporally challenged? We are forced to interpret this infinite string in finite terms because we *think* in finite terms. Again, I agree. One can train his brain to interpret any equation that fits in his field of view simultaneously. That is, the entire equation front to back as one visual/symbolic entity. From there, the information would trickle back through the neurons to form an expression the interpreter disires. So in effect, to the limit of his field of view, he sees the equation in it's entirety simultaneously without delay. Yes, the equation fits in the mind without problem. But it's the implementation that's going to get you. At some point the simulation is going to deviate from nature at the point where the field of view ends. Such a view is only an approximation to what is actually happening. If our goal is a Theory of Everything, then those missing bits of PI are going to come back to haunt us at some point. Maybe it is this goal where our views have departed. I want to implement nature precisely - with no rounding errors. Others seem content in describing it with broad mathematical statements that are illustrative of the whole, but lacking in the details. Only processing depth incurs any delay. Yes, but we're not talking about a couple of seconds while god's computer displays an hourglass. We're talking about an eternity. And if our Theory of Everything makes use of the whole PI - crust and all - then that hourglass is going to be on the screen for a very long time... forever. The burden of proof lies with those who claim that infinity exists. I say... show it to me/us. Challenge: Try to write a program or come up with a set of equations that makes use of the continuum. Otherwise, our words are only pieces of dreams in the mind of god. Are we truely seperate from the universe that gave birth to us? Not at all, and this is my point. When creating our Theories of Everything, there is no need to rely on a multitude of infinite structures. (PI, e, etc.) One infinite structure is as good as any other. The universe itself, because it DOES exist forever, IS a continuum. But it need be the only one. Everything else inside can be discrete and finite... parts of the whole. Meanwhile, we have found a simple process... the minimal cellular automaton... that generates all variations of finite structures. Taken as a whole, this object is infinitely complex. There is no need to search for anything more. Is there? Joel

### Re: Introduction (Digital Physics)

You picked a bad example with pi. Many mathematicians manipulate pi with exact precision in their calculations. Many use computer programs to do this also, eg Mathematica. The lack of any possible representation as a rational number does not prove a barrier to this. Your point would be better made with an object such as Omega, or countless other numbers that defy description. My point was that discrete grids omit many objects that are within the domain of describability. You cannot map the set of rational numbers onto a grid, whilst preserving the ordering property. You you can describe them, and enumerate them. Whilst a continuum may not exist in itself, discrete CA models do not capture everything that lies in the domain of discrete describability. I've had a lengthy and exhausting argument with Hal Ruhl over this issue - I don't really feel like repeating it. Cheers Joel Dobrzelewski wrote: Russell and Brent: I understand this is an extreme position, but I state it this way on purpose: to bring the issue to the foreground and get to the heart of the problem of science today. As long as we insist that continuous objects really exist - we will always be fooling ourselves and forever chasing an unobtainable ghost. Descriptions of continuous structures are only that - descriptions. And they will *always* remain finite and discrete. The symbol PI is a finite description for an infinite *process*. No sheet of paper or gigabyte of RAM can contain PI. And thus, any theory we create or program we write MUST truncate PI at come point... otherwise we will forever be waiting for the theory to produce its first result. const PI = 3.1415926535 These descriptions are entirely misleading - only approximations - never reality. It would be better to do this... const PI = 1110101100010000111 But even this is wrong. To truly illustrate the point, we must do the following... function PI () as string do 'calculate PI loop end function Does the function PI() ever return a value? No. It is not within our reach. This is not proof that there is no continuum. Only evidence that there can be no continuum FOR US. For us, there can only be one infinite process in the Universe - the universe itself. The one calculation that never ceases... but always remains FINITE in extent and always DISCRETE. Always calculating PI to ever more decimal places... Joel Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967 UNSW SYDNEY 2052 Fax 9385 6965 Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks

### Re: Introduction (Digital Physics)

Joel Dobrzelewski wrote: I stand by my original claim: Any successful human Theory of Everything must recognize the discrete nature of the human intellect, and our inability to express or engage the continuum in any meaningful way. That is a particularly extreme way of putting it. All descriptions must be discrete, but this doesn't mean the continuum is not engaged. For one thing, it does not require a discrete space time. There are plenty of examples of non-discrete countable sets (eg the rational numbers), and plenty of examples of discrete descriptions of continuous objects, albeit incomplete ones. Cheers Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967 UNSW SYDNEY 2052 Fax 9385 6965 Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks

### Re: Introduction (Digital Physics)

Robert: but my view is that consciousness does'nt need descretization to function. Yes, I think we agree here. But I must admit, I am at a loss as to imagine what non-discrete might be. It's more likely that a more fluid view of the universe is the accurate model. Why? If we cannot formally implement fluid or continuum, then these will forever be out of our reach. We might as well give up. We may have *descriptions* of the continuum. But they are just descriptions... and remain, finite. I stand by my original claim: Any successful human Theory of Everything must recognize the discrete nature of the human intellect, and our inability to express or engage the continuum in any meaningful way. Joel

### Re: Introduction (Digital Physics)

On 17-Jun-01, Russell Standish wrote: Joel Dobrzelewski wrote: I stand by my original claim: Any successful human Theory of Everything must recognize the discrete nature of the human intellect, and our inability to express or engage the continuum in any meaningful way. That is a particularly extreme way of putting it. All descriptions must be discrete, but this doesn't mean the continuum is not engaged. For one thing, it does not require a discrete space time. There are plenty of examples of non-discrete countable sets (eg the rational numbers), and plenty of examples of discrete descriptions of continuous objects, albeit incomplete ones. Cheers Not only that, I think Joel is placing far to much emphasis on computational theory. People draw pictures and imagine images which are continuous in 2D. I know that these can always be digitized and if done on a sufficiently fine level the result is indistinguisable from continuous - but this doesn't prove that there is no continuum. Even quantum mechanics still relies on a continuous psi functions defined over continuous space-time. It may be possible to *represent* this discretely, but even if that is possible it doesn't mean it is impossible to represent it using a continuum or that there is no underlying continuum. The argument that our understanding or our descriptions must be discrete is not convincing because it is equal true (or false) that our descriptions must be finite and even *small*. Brent Meeker Seven is the most belivable number. --- Joe Semonian

### Re: Introduction (Digital Physics)

Hi George: You say that you believe that our universe is discrete. I agree with this... but I believe that discreteness is itself a mystery. Why discrete? It may very well be that discreteness is a necessary condition for consciousness and therefore anthropically driven. Discreteness necessary for consciousness? I don't see why. But our minds do appear to be discrete - and therefore, the continuum will forever be unknown to us. Discreteness may simply be a fact of life (for humans anyway). And so it seems to me that any successful human theory of everything must acknowledge this. We perceive a discrete world, but the number of variations in the MW may very well be continuous since this characteristics does not seem to affect consciousness. Thus discreteness may be just a constraint on the plenitude imposed by our consciousness. Well if the continuum doesn't affect our minds, then we needn't consider it. We will never experience it, so for us... it doesn't exist. Joel

### Re: Introduction (Digital Physics)

Thanks for your reply, Bruno... All this for reasons similar to those made by Everett in his many world papers. Have you read Everett ? (or at least Tegmark? or Deutsch?) Just Tegmark. I'm looking into the others... Is it more impressioning than the (binary) counting algorithm, which just counts: 0, 1, 10, 11, 100, 101, etc. It generates (after the first 1) every strings too. And you can implement it in a reversible way with a reversible universal turing machine. Well, there may be some reasons to think that cellular automata are more fundamental, computationally speaking, than even Turing Machines. For instance, a Turing Machine has a moving part (the read/write head) and usually a complicated state transition table, perhaps requiring a physics all its own. While the cellular automaton has no moving parts at all - just two states and the transition rule. And consider the economy of its description. Suppose you needed to send a computer program to an alien civilization. Describing the workings of a Turing Machine might be a little tricky, while a few simple pictures can convey the idea of a cellular automaton and its initial configuration. Since CA can do everything TMs can do, and because of their simple implementation, I tend to prefer them. But the advantage here is that we can more easily envision the existence of such a miraculous object like a minimal cellular automaton than, say, a Universal Turing Machine. Cellular automata naturally implement physical universes without any interpretation. How? Implementations are interpretations. Yes, I suppose so. I simply mean that that the cellular automaton has a direct mapping to 3D physical space. It's just easier for me to envision. The bits merely exist... and we can see them with our digital eyes - and the patterns they generate. Where? Well I suppose I was trying to be poetic. :) The cellular automaton, I believe, exists in Platonic Heaven as you described it. It really doesn't matter. It is not the solution. It is the problem. Your type of approach like Schmidhuber's one is based on a naive association between the first person view and some third person description (brain, machine, automata). See http://www.escribe.com/science/theory/m1726.html for an attempt to explain how non trivial the mind body problem becomes when the computationalist hypothesis is taken seriously. Wow, that is quite some post. =) It's almost overwhelming. Can you try to describe, in simple terms: what is the mind/body problem? And how does it relate to cellular automata? I always assumed that the automaton merely exists... and we (our minds and bodies) simply emerge from the bits. Thanks again for your thoughts, Joel