Hello Stephen,
Does there really need to be a single level of the UD?
?
What is the UD is intersecting with itself an infinite number of
times?
The UD emulates itself infinitely often, with all codes, that is:
relatively to all universal numbers.
Is there a relationship. maybe an isomorphism, between the UD and
the set of Godel numbers of the UD?
That depends on how you associate a set of Gödel numbers with the UD.
After all, there does not exist a unique universal Godel code for
the UD, no?
There is an infinity of them, but any one simulates all the others,
and you can't make one more important than another one, at the start.
It is not the same for the internal view in arithmetic, where some
universal number(s) can get local importance in maintaining the right
history measure.
Bruno
On Friday, December 20, 2013 12:08:46 PM UTC-5, Bruno Marchal wrote:
Richard,
On 20 Dec 2013, at 12:40, Richard Ruquist wrote:
What surprises me is that apparently comp predicts a single
multiverse rather than than multiple multiverses.
Interesting problem.
Comp predicts only a single multi-dreams, which is the "universal"
computation made by the UD, or the Sigma_1 complete part of
arithmetic.
I am still not sure if the "material points of view" will give 0, 1,
2, ... aleph_0, ... or more multiverses.
A difficulty relies also in the fact that a "multiverse", or even a
"physical universe" is still not really well defined by the
physicists themselves. In fact in Everett theory, we might also not
be entirely sure if there is a multiverse, or a multi-multiverse,
and such question might need the resolution of the quantum gravity
question.
With comp, we can say things like that: IF there are n multiverses,
THEN they cannot interfere statistically and so "you" are in only
one of them (if not they will comp-interfere), and thus they must be
all "small" (= not emulating a UD). So, only one multiverse might
contain a "physical" universal dovetailing.
Is the quantum vacuum a physical universal dovetailer?
Is the Everett universal wave a physical universal dovetailer?
Is the solution of the comp measure problem a physical universal
dovetailer? Should "nature" compete with the universal dovetailing
to win the measure competition?
Ah! You make me thinking ... What is really a multiverse? Can we
define this in ZF, or in ZF+kappa? Would it makes sense to talk of
alpha-multi-verse for alpha an arbitrary cardinal, or an On-
multiverse, with On being the class of all cardinals?
What if the ultimate structure of the physical reality is non well
founded? That is plausible with comp (despite arithmetic is well
founded). In that case a multiverse could contain another
multiverse, a bit like a black hole could be a door to another
universe.
Keep in mind that for a computationalist (who is aware of the UDA
"reversal") (assuming there is no flaw of course) the physical
reality is the border of the "real" reality where "real" is what the
FPI gives for the "average" universal (and Löbian) numbers.
You can visualized the UD by a cone of length omega (aleph_zero).
Just take a program for a UD implemented in a universal game of life
pattern. Then pile up the planes representing the successive
evolving life pattern. This gives a digital cone (due to the never
ending growing of the life pattern emulating the UD), and you can
"see" the UD* as an infinite tridimensional digital cone. OK?
Now, you can compactify that structure. You identify the planes at
0, 1, 2, 3, ... n, places in the infinite piling with 0, 1/2,
1/2+1/4, 1/2+1/4+1/8, ..., so that the entire infinite UD* is kept
on a finite board of lenght 1: just a cone, or its projection: a
triangle. OK?
Where is the "physical reality" in that picture? Nowhere, as UD* is
purely 3p, and physics is purely 1p. Hopefully: 1p-plural (and
Everett confirms this: our computations are contagious, we cannot
*not* share them when interacting. But that 1p collective structure
must (in comp) emerge at the union of all sets of all computations
(containing our actual states), and this can be described in 3p, and
is in the border which appears when we do the compactification.
That border, the topside of the cone, or the right side of the
triangle of length 1, is an hologram, as each sub-branch infinitely
often generates the UD, and the broder contains the infinite one. It
is a bit like the border (but on dimension 1) of the Mandelbrot set.
The physical realities are dense everywhere "there" and they are
multiplied in hard to conceive magnitude, on that 2-dimensional top
(in that representation of UD*).
Unlike the little mandelbrot sets, they might be non enumerable.
And then you have that things which I tended to hide a little bit,
which is that the hypostases gives three quantizations, like if
there where three type of physical realities (would that mean three
multiverses? In *some* sense to make precise: perhaps).
Not just sensible matter and intelligible matter (Bp & Dt & p, and
Bp & Dt, respectively) provides quantization, on the p sigma_1, the
soul (Bp & p) does too, on the p sigma_1. Apparently Plotinus is
right on this: the soul seems to be born with a foot already in
matter.
I should say more on modal logic and enunciate the theorem of
Solovay. All what I say comes from the fact that meta-arithmetic can
be arithmetized, the main discovery of Gödel. It is the technic
which embeds the "mathematician" in the mathematical reality (indeed
in a tiny arithmetical part), like Everett embeds the physicist in
the physical reality (defined by a solution of the SWE).
It is the technic which makes able to interview, and sum up infinite
interviews with the machine talking about itself.
Monistic theories cannot not embed the observer in the observed, the
spectator in the spectacle, the audience in the show.
Best,
Bruno
Richard
On Fri, Dec 20, 2013 at 5:26 AM, Bruno Marchal <mar...@ulb.ac.be>
wrote:
On 20 Dec 2013, at 02:15, Craig Weinberg wrote:
If it's all just math, what is the unexpected surprise that makes
it funny? Is math surprised that its math?
It is of course only surprising for those deluded (assuming comp)
into thinking that there is some primitive non mathematical
reality, like the aristotelian theologian, who believe in a non
mathematical primitively physical universe.
The real surprise, in the arithmetic internal views, is the
existence of the universe (not the fact that it is not a primitive).
The absence of X, if proved, would surprise the believers in X, in
a same way.
"Surprised" is prejudice dependent.
Bruno
On Wednesday, December 18, 2013 2:07:47 AM UTC-5, Brent wrote:
http://abstrusegoose.com/544
Brent
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