One thing I thought of recently which is a good way of showing how computation occurs due to the objective truth or falsehood of mathematical propositions is as follows:

Most would agree that a statement such as "8 is composite" has an eternal objective truth. Likewise the statement: the Nth fibbinacci number is X. Has an objective truth for any integer N no matter how large. Let's say N=10 and X = 55. The truth of this depends on the recursive definition of the fibbinacci sequence, where future states depend on prior states, and is therefore a kind if computation. Since N may be infinitely large, then in a sense this mathematical computation proceeds forever. Likewise one might say that chaitin's constant = Y has some objective mathematical truth. For chaintons constant to have an objective value, the execution of all programs must occur.


Simple recursive relations can lead to exraordinary complexity, consider the universe of the Mandelbrot set implied by the simple relation Z(n+1)= Z(n)^2 + C. Other recursive formulae may result in the evolution of structures such as our universe or the computation of your mind.

Jason

On Jun 4, 2011, at 4:09 AM, Felix Hoenikker <fhoenikk...@gmail.com> wrote:

Sorry again, but I want to add one thing:

The broadest mathematical closure of "the existence of computation",
"the observation of consciousness anywhere" suggests the following, in
my mind: all possible numbers (including transfinite-ones) are, in
fact, self aware substructures in the mathematical universe,
recursively "communicating" to "each other" by exchanging bits in an
attempt to develop the algorithm which compresses themselves to a
single state, which represents the number "one", after which it
promptly forgets and starts all over again, everywhere, and all at
once.

---------- Forwarded message ----------
From: Felix Hoenikker <fhoenikk...@gmail.com>
Date: Sat, Jun 4, 2011 at 3:03 AM
Subject: The final TOE?
To: Everything List <everything-list@googlegroups.com>


Hi all,

Consider the following fully general way of saying this is the
following: quantum mechanics and general relativity are symmetrically
"the exact same theory", modulo the additional "bit" of information
that quantum entanglement reduces net gravitational energy.  This is
the EXACT answer to the EPR paradox, and all paradoxes about
singularities, and consistent with our picture of reality in every
respect, as it "necessarily must be" since it follows exactly from the
asssumption of 3+1 spacetime embedded within some higher dimensional
structure of "any" form (i.e. including string theory).

Since no "true" gravitational singularities exist, then "every point
in space is an apparent black hole" because "no point in space is an
apparent black hole".  Thus, at every point in space, a "bit" of
information (or a "photon") can escape from the "observable" universe
on our scale, "go into the past", and come out "in the future" in a
symmetric manner for all observers, without considering your frame of
reference in 3+1 space time.  This qualitatively predicts all features
of GR without QCD or QFT.  However, since photons travelling through
locally closed loops can look like "point" particles with some net
entanglement coming out, then they can look like bundles that, for all
intents and purposes, appear to randomly add information in some way,
and in some spherically symmetric fashion, which predicts the
divergence and appearance of other "fundamental forces" early in the
inflating universe.

It is often said that QM and GR differ from each other exactly by the
contemplation of the "singularity", and that our inability to discover
the "true" laws of the universe has been limited by our lack of
knowledge about the twin singularities: the inflationary bubble and
the black hole.  It follows that this fact was "exactly true" all
along, and the laws of physics are a completely dimensionless
consequences of our "local" geometry of space, and our civilization
has, in fact, rather than been trying to "discover" the next laws of
physics, has in fact been struggling to "unlearn" the concept of
"Indeterminacy" and "quantum mechanics", since QM follows from GR, the
postulate of 3+1 spacetime and E = mc^2 (a nice, dimensionless
equation).  Einstein, in fact, was right all along, and successfully
completed the "fully" deterministic general laws of physics.

Consider then, the reason why indeterministic QM was ever suggested:
the apparently subjective indeterminacy of the universe from each
"observer" point of view (i.e. the uncertainty principle).  Or
actually, consider the fact that, if the universe is completely
deterministic, and "you" for any defined "you" is getting non-random
information from any source, then that information must, in fact, be
added to you by the "rest of the universe" in some systematic fashion,
down to the tiniest quantum of "universe".  This implies that there
"is" actually, some "quanta" of the universe, a "photon", and each
"photon" is having information added to "it" from the "rest of the
universe", in a systematic fashion, and recursively so for every
"observer".  This is actually a fully generic model for the universe,
and the absolute generalization of QM and SR.

Next, consider the fact that you are "conscious" and possibly
"indeterminstic" (i.e. have subjective free will).  I think I do.
Therefore, I am not a "quanta" of information, or a "bit", but it was
"added to me" from "somewhere".  No, consider the mathematical closure
of this observation.  What does this imply about and anthropic
principle and "fine tuning"? Does that make sense anymore.  Also, does
this not mean that our "observable universe", for "some definition of
observable", from "any subjective observer's point of view", is
constantly being added non-random information from "outside".

I truly beg you all to consider this argument fully.

Please let me know what you think,
F.H.

On Fri, Jun 3, 2011 at 7:16 PM, Felix Hoenikker <fhoenikk...@gmail.com> wrote:
Every "apparent" event horizon is really a separation of two
universes, where the outside universe is entangled geometrically with
the inside universe. The Hubble volume is sitting inside of an
expanding supermassive black hole, of another universe. However, by
the uncertainty principle, this means the "outside universe" is
"really" simultaneously in a superposition of a large but countably
finite many possible universes (i.e. bitstates), with the net
information between the "inside" and "outside" views cancelling out to
zero. Equivalently, every "classical" black hole is really in a
microscopic superposition of countably finite many bitstates, again
with the net information "inside" and "outside" cancelling zero.
However, it cannot converge to a singularity, because it cannot encode
"bitstates" forever in the same volume, therefore it must leak
information in the form of "photons" (i.e. Hawking radiation).

Equivalently, the Hubble volume receives information one photon at a
time from the "outside" in the form of cosmic background radiation,
that information being about the prior state of the otherwise casually
disconnected universe. (i.e. CMB == Hawking radiation). The
equivalence principle implies length contraction and time dilation.
Gravity mediated by photons is the single fundamental force of the
universe. All other sources of apparent information and causal
connectivity (i.e. all other forces) are the result of the initial
state of the universe at the Big Bang, the only true singularity. The
laws of the universe are extremely simple.

This is the digital unification of GR and QM.  What do you think?

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