# Re: Bruno's mathematical reality

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 <step...@provensecure.com> wrote:
Dear Jason,

Interleaving below.

On Fri, Dec 27, 2013 at 6:20 PM, Jason Resch <jason...@gmail.com> wrote:

On Fri, Dec 27, 2013 at 6:03 PM, LizR <liz...@gmail.com> wrote:
On 28 December 2013 11:55, Stephen Paul King <step...@provensecure.com> 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.

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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