# Re: equivalence between math and computations

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On 15 Aug 2012, at 15:14, Alberto G. Corona wrote:```
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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.
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Comp is "I am a machine". It is NOT "reality is a machine".

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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.
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In a sense: "I am a machine" implies that everything else is not.

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Indeed, the apparent computability of nature might in fine be a problem for comp. It is behind the whole measure problem.
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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:
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A imperative computation is equivalent to a mathematical structure thanks to the work on denotational semantics and the application of category theory to it .
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Or just by definition.

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Suppose that we know the M theory equation.
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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.
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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).
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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.
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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.
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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.
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Not really. The reality we see result from our first person indeterminacy. You cannot simulate it, and it is not describable by any equation.
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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,
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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.
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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
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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.
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With comp physical reality, and even more the whole of reality (physical + theological) is even beyond the whole of mathematics. All physical and psychological notion, like perhaps time and surely space, have to be derived from the logic of self-reference only. Subjective time is explained by the Bp & p modality, but physical time seems to vanish completely (a bit like in Wheeler Dewitt equation H = 0). Obviously, there are tuns of open problem to proceed.
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To sum up again: IF I am a machine, then whatever I am confront too cannot be a machine. A bit like the arithmetical truth cannot be defined in arithmetic. The same for arithmetical knowledge and arithmetical observability. Arithmetic viewed from inside is *vastly bigger* than third person describable Arithmetic, which is already far beyond algorithm. It is a sort of "Skolem paradox". It is not easy to explain to non logicians.
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Bruno

http://iridia.ulb.ac.be/~marchal/

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