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_semantics>and the application
> of category theory to it 
> <https://www.google.es/search?q=denotational+semantics+imperative+monads&sugexp=chrome,mod=11&sourceid=chrome&ie=UTF-8#hl=en&sugexp=efrsh&gs_nf=1&tok=VMyaXoMGarRPPBvFsyx1Cg&pq=denotational%20semantics%20imperative%20monads&cp=49&gs_id=1q&xhr=t&q=denotational+semantics+imperative+category+theory&pf=p&safe=off&sclient=psy-ab&oq=denotational+semantics+imperative+category+theory&gs_l=&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.&fp=4beb944d59246923&biw=1092&bih=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 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.
> If I understand, the self computing universe is still a physicalist view.
It is a reification of objects that compute, the elementary particles  But
really for you what computes the infinity of computations that make us and
the reality that we perceive ( including the elementary particles) is a
different , more basic substance, unknow to us.

But still even if this is true, the study of the (then apparent)
mathematical nature of the phisical reality and their implications is

> 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.
> 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.
> 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.

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