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
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
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
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
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
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
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.
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