On 11 Jun 2012, at 10:31, Evgenii Rudnyi wrote:
On 10.06.2012 18:49 Bruno Marchal said the following:
On 09 Jun 2012, at 20:57, Evgenii Rudnyi wrote:
On the other hand, if I understand Bruno's theorem correctly a) and
b) imply quite different things. While a) brings no problem, b)
arithmetic -> mind -> physics
That is, I am not sure if according to Bruno, mind simulation in
simulation is possible.
Yes it is possible. And "worth", it is necessary the case.
Let me explain why.
Let us fix a universal system, FORTRAN for example, or c++, game of
life, arithmetic, S & K, etc.
Let us enumerate the one argument programs: p_i, and let us called
phi_i the partial (that include the total) corresponding computable
functions. This is equivalent of choosing a base in linear algebra.
We can associate a number to each partial computable functions.
A universal number (a computer) is a number u such that phi_u(x, y) =
phi_x(y). x is the program, y is the data and u is the computer. In
that case we can say that u emulates the program x (first
approximation of a definition to be sure).
Now, phi_u, to be in the phi_i, needs to be a one variable function,
so we better have a good computable bijection between NxN and N. With
this you can see that a universal emulation can itself be emulated by
yet another universal number, and you can easily understand that the
universal dovetailer generates the infinitely many layers of
simulations, showing that they correspond to true arithmetical
relations. They are solution of a universal diophantine equation. We
cannot avoid them in the measure problem.
The key is that below our substitution level we belong to infinities
computations/emulation, defining our physical realities, and above
the substitution level, it can (re)define our identities. We never
know our level of substitution, but we can know that below, it is a
matter of experience, and above it is a matter of private opinion,
something like that.
In UD*, or in a tiny part of arithmetic, there are a lot of even
infinite trails of simulation in simulation in simulation, etc. with
I do not completely understand consequences from your theorem, sorry.
Does it imply that we have an infinite number of levels between mind
You can say that.
Imagine yourself in front of the UD. By the invariance of the first
person experience for the delays, you have to take into account all
computations accessing to your 3-actual computational states (in comp).
This will include some computation made by some universal number
(computer) u, but also the computation made by the universal number j
when simulating u, and then those made by the universal number k
simulating j simulating u, and so on ad infinitum. So there is an
infinity of dream layers, or mind levels between mind and physics.
Physics does not really relies on any particular computations a
priori, but on *all* computations, as defined by the UD processing (or
equivalently by the true sigma_1 sentences weighted by their proofs).
arithmetic -> mind -> physics -> mind -> physics -> ...
It is more like:
arithmetic -> mind -> mind -> mind -> mind -> ... -> (at the limit
viewed from inside) physics.
(of course it is not that linear, given that it bifurcates and fuses,
and the topology of the local first person neighborhood are
constrained by relatively correct self-reference).
For example, does it imply that my 1st person view can make a
supercomputer and then instantiate itself in that supercomputer?
Only bodies, even if dreamed or relatively virtual, can make other
bodies, like the body of a supercomputer. But that is something that
you can do, by definition of comp. But you cannot do it in a provable
way, so you have to bet on the level, and take your risk and
responsibility. If the doctor says something like "science has proved
that you will survive", without mentioning the theory/hypotheses, it
is better to run away.
Then there should be two my 1st person views and we seem to come to
what you have referred to as first person indeterminacy.
OK. And that happens "naturally" in the realm of the arithmetical
relations. If you accept that truth like "24 is composite" does not
depend on your consciousness, then the whole arithmetical pattern on
which consciousness can differentiated is well defined (through comp).
Could you please relate simulation in simulation with what you are
saying about first person indeterminacy?
It is not really related. I will try. I start from arithmetic, which
contains all computations.
A computation is what universal machine does. Universal machines
emulates other machines. OK?
In particular, a universal machine can emulate another universal
machine. Actually, a universal machine can emulate herself, and even
plays with the levels. This belongs to its 'natural imagination'
Consider U1 emulating M. At base level, like the physical laws if you
want made it "concrete", or in arithmetic (to take a simple base).
This give a sort of level zero of a computation. Now here the
computation is made by U1, emulated by the physical laws (or
arithmetic). But that computations, like any computation, can be done
by any universal numbers/machines. So a second universal machine U2
can emulate U1 emulating M. This will be a more complex computations,
and will appear later in the work of the UD.
Now, the first person indeterminacy, when in "front of a UD, or
arithmetic" bear on all computations leading to your state "as lived
from your first person point of view". So the indeterminacy domain is
somehow trans-level of simulation, making matter emerging from many
computations including infinite sequence of emulation, etc.
The first person indterminacy is illustrate each time bearing on the
same level, or on one level of emulation, in the first six UDA steps.
But on the UD*, or on arithmetic, the first person is dispersed on all
If we look at ourselves below our first person plural substitution
level, we must see the trace of those "competing computations". I
think QM-without-collapse (= Everett) confirms this.
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