On 28 Dec 2013, at 02:03, Edgar L. Owen wrote:
Jason,
You state "The UD is a comparatively short program, and provably
contains the program that is identical to your mind."
You can't be serious! As stated that's the most ridiculous statement
I've heard here today in all manner of respects!
If you believe this, you cannot believe in computationalism. If your
brain work is Turing emulable, that emulation is provably in
arithmetic, which emulates all (it is a theorem in arithmetic) all
computations. It is long to prove, but not so much difficult if you
add some axioms like the exponentiation axioms. It is a hell of a
difficulty to eliminate that exponentiation axioms, but that has been
done, even in some strong way (eliminating universal quantifiers
altogether) by Matiyasevitch, and that is well known (by logicians).
That the UD itself exist is a consequence of Church thesis, and is
obvious to many for wrong reason. If you know Cnator diagonalization,
then at first sight, it looks we can diagonalized against the UD
existence, but it happens that the UD and arithmetic is close for the
diagonalization procedure, making the UD, or equivalently the sigma_1
part of arithmetic, complete for the computational reality (of course
not complete for truth: that never happens by incompleteness à-la
Gödel).
Bruno
Edgar
On Friday, December 27, 2013 7:56:44 PM UTC-5, Jason wrote:
On Fri, Dec 27, 2013 at 6:33 PM, Stephen Paul King
<[email protected]> wrote:
Dear Jason,
Interleaving below.
On Fri, Dec 27, 2013 at 6:20 PM, Jason Resch <[email protected]>
wrote:
On Fri, Dec 27, 2013 at 6:03 PM, LizR <[email protected]> wrote:
On 28 December 2013 11:55, Stephen Paul King
<[email protected]> wrote:
Hi LizR,
That is what is not explicitly explained! I could see how one
might make an argument based on Godel numbers and a choice of a
numbering scheme could show the existence of a string of numbers
that, if run on some computer, would generate a description of the
interaction of several actors. But this ignores the problems of
concurrency and "point of view". The best one might be able to do,
AFAIK, is cook up a description of the interactions of many
"observers" -each one is an intersection of infinitely many
computations, but such a description would itself be the content of
some observer's point of view that assumes a choice of Godel
numbering scheme.
Something doesn't seem right about this!
It seems to suggest "multi-solipsism" or something along those lines
- which doesn't make it wrong, of course.
I await Bruno's answer with interest. I think he has already said
something about this, but I don't recall it being satisfactory, at
least to my limited understanding.
I am also interested to hear what Bruno has to say. My perspective
is that most of the computations that support you and I are not
isolated and short-lived "computational Boltzmann brains" but much
larger, long-running computations such as those that correspond to a
universe in which life adapts and evolves.
I agree. I have never been happy with the Boltzman brain argument
because it seems to assume that the probability distribution of
"spontaneous" BBs is independent of the complexity of the content of
the minds associated with those brains. I have been studying this
relationship between complexity or "expressiveness" of a B.B. My
first guesstimation is that there is something like a Zift's Law in
the distribution: the more expressive a BB the less chance it has to
exist and evolve at least one "cycle" of its computation. (After
all, computers have to be able to run one clock cycle to be said
that they actually "compute" some program...)
The starting conditions for these is much less constrained, and
therefore it is far more probable to result in conscious
computations such as ours than the case where the computation
supporting your brain experiencing this moment is some initial
condition of a very specific program. Certainly, those programs
exist too, but they are much rarer.
RIght, but how fast do they get rarer?
It's hard to say. We would have to develop some model for estimating
the Kolmogorov complexity (and maybe also incorporate frequency) of
different programs and their relation to a given mind.
They appear in the UD much less frequently than say the program
corresponding to the approximate laws of physics of this universe.
It takes far more data to describe your brain than it does to
describe the physical system on which it is based.
How do you estimate this?
The UDA is a comparatively short program, and provably contains the
program that is identical to your mind. Similarly, all of the known
laws of physics could fit on a couple sheets of paper. QM seems to
suggest that all possible solutions to certain equations exist, and
so there is no need to specify the initial conditions of the
universe (which would require much more information to describe than
your brain).
Are you assuming that a lot of data can be compressed using
symmetries and redundancies. This looks like a Kolmogorov complexity/
entropy...
Somewhat. I think how frequently a program is referenced /
instantiated by other non-halting programs may play a role.
So we are (mostly) still "in the same universe", and so we can
interact with and affect the consciousness of other people.
From my reasoning, the appearance that we are "in the same universe"
is a by product of bisimilarities in the infinity of computations
that are each of us. In other words, there are many computations
that are running Stephen that are identical to and thus are the same
computation to many of the computations that are running Jason.
Yes. We would be programs instantiated within a (possibly but not
necessarily) shared, larger program.
This gives an overlap between our worlds and thus the appearance
of a common world for some collection of "observers".
Right.
The cool thing is that this implies that there are underlaps;
computations that are not shared or bisimilar between all of us.
Yes, I agree. In some branches of the MW, perhaps you were born but
I was not, or I was, and you weren't.
COuld those be the ones that we identify as "ourselves"?
Personal identity can become a very difficult subject, since there
may be paths through which my program evolves to become you, and
vice versa.
Jason
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