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 and
arithmetic -> mind -> physics -> mind -> physics -> ...
For example, does it imply that my 1st person view can make a
supercomputer and then instantiate itself in that supercomputer? Then
there should be two my 1st person views and we seem to come to what you
have referred to as first person indeterminacy.
Could you please relate simulation in simulation with what you are
saying about first person indeterminacy?
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