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_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>
 .

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.

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