Re: equivalence between math and computations
2012/8/16 Bruno Marchal marc...@ulb.ac.be On 15 Aug 2012, at 15:14, Alberto G. Corona wrote: I ´m seduced and intrigued by the Bruno´s final conclussións of the COMP hypothesis. But I had a certain disconfort with the idea of a simulation of the reality by means of an algorithm for reasons I will describe later. Comp is I am a machine. It is NOT reality is a machine. If comp is true, both reality and physical reality are NOT machine, for the output of the many self-multiplication is NOT emulable by a Turing machine. You might not yet grasp fully the impact of the first person indeterminacy. In a sense: I am a machine implies that everything else is not. Indeed, the apparent computability of nature might in fine be a problem for comp. It is behind the whole measure problem. It is not emulable, I suppose, for the reason that if the physical reality has a underlying mathematical structure, if this is continuous it can not be emulable but in a discrete approximation. This emulation at the substitution level is what may be a physical reality indistinguishableness from the mathematical reality. I found that either if the nature of our perception of reality) can be of the thesis of a simulation at a certain level of substitution of a phisical or mathematical reality, this simulation is, and only is, a discrete manifold, with discreteness defined by the substitution level, which is a subset of a continuous manifold that is the equation M of superstring theory of wathever mathematical structure that describe the universe. The equivalence may be shown as follows: A imperative computation is equivalent to a mathematical structure thanks to the work on denotational semantics http://en.wikipedia.org/wiki/Denotational_semanticsand the application of category theory to it https://www.google.es/search?q=denotational+semantics+imperative+monadssugexp=chrome,mod=11sourceid=chromeie=UTF-8#hl=ensugexp=efrshgs_nf=1tok=VMyaXoMGarRPPBvFsyx1Cgpq=denotational%20semantics%20imperative%20monadscp=49gs_id=1qxhr=tq=denotational+semantics+imperative+category+theorypf=psafe=offsclient=psy-aboq=denotational+semantics+imperative+category+theorygs_l=pbx=1bav=on.2,or.r_gc.r_pw.r_cp.r_qf.fp=4beb944d59246923biw=1092bih=514 . Or just by definition. Suppose that we know the M theory equation. You are still assuming a physical reality. I assume a mathematical reality If the M theory equation is correct, it has to be derived from addition and multiplication ? , and comp at the metalevel. But it has to admit non computable solution, because with comp the physical reality is not computable, a priori. a continuous reality is uncomputable, but this is not a problem for someone who assume a mathematical reality. A particular simulation can be obtained in a straighfordward way by means of an algorithm that compute a sequence of positions and the respective values in the M equation (which must specify wether there is a particle, its nature and state at this point or more precisely the value of the wave equation at this N-position or wathever are the relevant parameters at this level of substitution), perhaps the sucession of points can be let´s say in a progression of concentric n-dimensional circles around the singularity. this algoritm is equivalent to the ordered set obtained by the combination of two kind of functions (1) for obtaining sucessive N-dimensional positions and (2) the function M(pos) itself for that particular point. The simulation then is a mathematical structure composed by the ordered set of these points, which is a subset of the manifold described by the M equation. (When a computation is pure, like this, the arrows between categories are functions). Suppose that we do not know the equation fo the M theory, and maybe it does not exist, but COMP holds and we start with the dovetailer algoritm at a fortunate substitution level. The universal dovetailer simulates all the level, and below a level, we can see only the result of a statistics beaing on infinities of computation. This is NOT simulable by any algorithm, a priori. It don´t have to be a single equation. But it is a mathematical structure, given the above said. Then we are sure that a complete mathematical description of reality exist (perhaps not the more concrete for our local universe), since the imperative algoritm can be (tanks to denotational semantics) described in terms of category theory. Not really. The reality we see result from our first person indeterminacy. You cannot simulate it, and it is not describable by any equation. again it may be aproximated exactly, but discretely, by a mathematical structure. the dovetailer algorithm. At least one of the infinite superpositions that predict the Everett interpretation. Surely, there is a mathematical structure that integrate the infinite set of algoritms for all the superpositions. In any case, I
Re: equivalence between math and computations
On 15 Aug 2012, at 15:14, Alberto G. Corona wrote: I ´m seduced and intrigued by the Bruno´s final conclussións of the COMP hypothesis. But I had a certain disconfort with the idea of a simulation of the reality by means of an algorithm for reasons I will describe later. Comp is I am a machine. It is NOT reality is a machine. If comp is true, both reality and physical reality are NOT machine, for the output of the many self-multiplication is NOT emulable by a Turing machine. You might not yet grasp fully the impact of the first person indeterminacy. In a sense: I am a machine implies that everything else is not. Indeed, the apparent computability of nature might in fine be a problem for comp. It is behind the whole measure problem. I found that either if the nature of our perception of reality) can be of the thesis of a simulation at a certain level of substitution of a phisical or mathematical reality, this simulation is, and only is, a discrete manifold, with discreteness defined by the substitution level, which is a subset of a continuous manifold that is the equation M of superstring theory of wathever mathematical structure that describe the universe. The equivalence may be shown as follows: A imperative computation is equivalent to a mathematical structure thanks to the work on denotational semantics and the application of category theory to it . Or just by definition. Suppose that we know the M theory equation. You are still assuming a physical reality. If the M theory equation is correct, it has to be derived from addition and multiplication, and comp at the metalevel. But it has to admit non computable solution, because with comp the physical reality is not computable, a priori. A particular simulation can be obtained in a straighfordward way by means of an algorithm that compute a sequence of positions and the respective values in the M equation (which must specify wether there is a particle, its nature and state at this point or more precisely the value of the wave equation at this N-position or wathever are the relevant parameters at this level of substitution), perhaps the sucession of points can be let´s say in a progression of concentric n-dimensional circles around the singularity. this algoritm is equivalent to the ordered set obtained by the combination of two kind of functions (1) for obtaining sucessive N-dimensional positions and (2) the function M(pos) itself for that particular point. The simulation then is a mathematical structure composed by the ordered set of these points, which is a subset of the manifold described by the M equation. (When a computation is pure, like this, the arrows between categories are functions). Suppose that we do not know the equation fo the M theory, and maybe it does not exist, but COMP holds and we start with the dovetailer algoritm at a fortunate substitution level. The universal dovetailer simulates all the level, and below a level, we can see only the result of a statistics beaing on infinities of computation. This is NOT simulable by any algorithm, a priori. Then we are sure that a complete mathematical description of reality exist (perhaps not the more concrete for our local universe), since the imperative algoritm can be (tanks to denotational semantics) described in terms of category theory. Not really. The reality we see result from our first person indeterminacy. You cannot simulate it, and it is not describable by any equation. In any case, I believe, similar conclussion holds. Although in the consequence of machine psychology in the case of COMP, the mind imposes a fortunate and robust algoritm as description of our local universe, Not really, for the reason above. We belongs to infinities of computations, and the physical reality is a sum on all those computations existing below our substitution level. QM confirms this. and in the case of a mathematical universe this requirement is substituted by a fortunate and coherent mathematical structure. Anyhow, both are equivalent since one implies the other. Both of them reject phisicalism and the mind stablish requirement for the nature of what we call Physics. Perhaps one may be more general, and the other may bring more details A question open is the nature of time and the progression of the simulation of the points. Theoretically, for obtaining a subset of the points of a mathematical structure, the simulation can proceed in any direction, independent on the gradient of entropy. It can proceed backwards or laterally, since the value of a ndimensional point does not depend on any other point, if we have the M equation. Moreover, time is local, there is no meaning of absolute time for the universe, so the simulation can not progress with a uniform notion of time. A local portion of the universe does make sense to
equivalence between math and computations
I ´m seduced and intrigued by the Bruno´s final conclussións of the COMP hypothesis. But I had a certain disconfort with the idea of a simulation of the reality by means of an algorithm for reasons I will describe later. I found that either if the nature of our perception of reality) can be of the thesis of a simulation at a certain level of substitution of a phisical or mathematical reality, this simulation is, and only is, a discrete manifold, with discreteness defined by the substitution level, which is a subset of a continuous manifold that is the equation M of superstring theory of wathever mathematical structure that describe the universe. The equivalence may be shown as follows: A imperative computation is equivalent to a mathematical structure thanks to the work on denotational semantics http://en.wikipedia.org/wiki/Denotational_semanticsand the application of category theory to it https://www.google.es/search?q=denotational+semantics+imperative+monadssugexp=chrome,mod=11sourceid=chromeie=UTF-8#hl=ensugexp=efrshgs_nf=1tok=VMyaXoMGarRPPBvFsyx1Cgpq=denotational%20semantics%20imperative%20monadscp=49gs_id=1qxhr=tq=denotational+semantics+imperative+category+theorypf=psafe=offsclient=psy-aboq=denotational+semantics+imperative+category+theorygs_l=pbx=1bav=on.2,or.r_gc.r_pw.r_cp.r_qf.fp=4beb944d59246923biw=1092bih=514 . Suppose that we know the M theory equation. A particular simulation can be obtained in a straighfordward way by means of an algorithm that compute a sequence of positions and the respective values in the M equation (which must specify wether there is a particle, its nature and state at this point or more precisely the value of the wave equation at this N-position or wathever are the relevant parameters at this level of substitution), perhaps the sucession of points can be let´s say in a progression of concentric n-dimensional circles around the singularity. this algoritm is equivalent to the ordered set obtained by the combination of two kind of functions (1) for obtaining sucessive N-dimensional positions and (2) the function M(pos) itself for that particular point. The simulation then is a mathematical structure composed by the ordered set of these points, which is a subset of the manifold described by the M equation. (When a computation is pure, like this, the arrows between categories are functions). Suppose that we do not know the equation fo the M theory, and maybe it does not exist, but COMP holds and we start with the dovetailer algoritm at a fortunate substitution level. Then we are sure that a complete mathematical description of reality exist (perhaps not the more concrete for our local universe), since the imperative algoritm can be (tanks to denotational semantics) described in terms of category theory. In any case, I believe, similar conclussion holds. Although in the consequence of machine psychology in the case of COMP, the mind imposes a fortunate and robust algoritm as description of our local universe, and in the case of a mathematical universe this requirement is substituted by a fortunate and coherent mathematical structure. Anyhow, both are equivalent since one implies the other. Both of them reject phisicalism and the mind stablish requirement for the nature of what we call Physics. Perhaps one may be more general, and the other may bring more details A question open is the nature of time and the progression of the simulation of the points. Theoretically, for obtaining a subset of the points of a mathematical structure, the simulation can proceed in any direction, independent on the gradient of entropy. It can proceed backwards or laterally, since the value of a ndimensional point does not depend on any other point, if we have the M equation. Moreover, time is local, there is no meaning of absolute time for the universe, so the simulation can not progress with a uniform notion of time. A local portion of the universe does make sense to have an uniform time, but the level of substitution necessary may force the locality of time to be very small. At the limit, the simulation may be forced to be massively parallel with as many local times as particles, and the model becomes the one of a self computing universe. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
