On 01 Oct 2013, at 17:43, Richard Ruquist wrote:

According to Max Tegmark, a Swedish-American MIT cosmologist, “only Godel-complete (fully decidable) mathematical structures have physical existence” http://arxiv.org/pdf/0704.0646v2.p df
Here is his abstract:

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and G¨odel incompleteness. I hypothesize that only computable and decidable (in G¨odel’s sense) structures exist, which alleviates the cosmological measure problem and may help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical
structures, computations, simulations and physical systems.

Richard Ruquist: This is not Bruno's comp because of the assumption of ERH.


It is quite close, though, or can be get arithmetically interpreted so. Indeed comp interpreted in arithmetic is really a completeness axiom: p -> Bp. (but not completeness in 1930 sense, it is more Turing completeness). (Gödel's completeness is used, but only as a a simplifying tool). Comp forces the choice of a Turing complete system, which is complete on the computable, but not at all on the provable. Glad to see that Tegmark at last don't take the MUH as axiom. It follows indeed from deeper consideration (on the computable, notably).



My paper http://vixra.org/pdf/1303.0194v1.pdf, based on Tegmark's Hypotheses, conjectures that only a holographic Metaverse containing many holographic Universes, contains a sufficient number of bits for computations in it to be effectively complete and decidable to compute matter and energy; whereas the computations in any Universe having a relatively limited number of bits for computation (ie., ~10^122) are relatively incomplete, and that incompleteness hypothetically results in emergent consciousness. BTW, Ruquist is a Swedish-American name, having been anglicized on Ellis Island.

That is a complex theory, which if correct, and comp compatible should be derivable from elementary arithmetic. But I am afraid that it negates comp, and is a form of physicalist ultra-finitism. But fair enough, it seems to work (up to now).

I am not sure neither you nor Tegmark really appreciate the depth of the FPI rabbit hole in arithmetic, when taking comp enough seriously into account.

Tegmark progress in the right direction, but still miss the comp reversal.

The physical reality is only in the head ... of the universal machines. Both informally (UDA), and formally (AUDA, the universal- machine's interview, the invariance of physics for the change of the basic phi_i, etc.).

There remains an external physical reality, but it is a part of a (greater) real and objective arithmetical reality seen from inside. (and I just argue that this *has to be* the case if we are correct when saying "yes" to the doctor).

Bruno






On Tue, Oct 1, 2013 at 11:04 AM, Roger Clough <rclo...@verizon.net> wrote:
A Platonic, singularity theory of space

Plato envisioned the One, a singularity from which the pluralistic world
emerged(s).

Big Bang theories of Creation point back to such a singularity
from which space emerged, and black hole or white hole theories
also point to singularities possibly related to creations.
Penrose has also proposed the twister, an entity
which might possibly have similarities to those events.

Recently I have also presented a Platonic, singularity theory
of mind, in which the mental or nonphysical produces the
phjysical.

What if we take Plato seriously and examine the possibility
that physical space (spaetime) emerged from the nonphysical ?
One might express this is that physical existence has
emerged from nonphysical Being or Mind.

I am no mathematician, perhaps a mathematical physicist could
construct such a theory. Entanglement and Bell's Theorem
could be related to this.


Dr. Roger B Clough NIST (ret.) [1/1/2000]
See my Leibniz site at
http://independent.academia.edu/RogerClough

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