On 30 Sep 2010, at 04:25, Stephen P. King wrote:

A crude sketch of a computational model of Interaction.

Stephen Paul King
9/29/2010

Might it be possible to model the content of 1st person experience as a
computationally generated "simulation"?

Yes and no.
Yes: that is a way to express digital mechanism.
No: IF you express mechanism through "yes doctor", which makes it possible to separate more clearly the first person from its "third person describable bodies at the hopefullly correct level", THEN, strictly speaking, the first person become attached to all its possible bodies, below its substitution level. So it can be argued that the first person and its content is distributed in the whole space of all computations. This include oracles and is a priori not an enumerable space. In a sense, all bodies are zombie, "we" are always elsewhere. In a sense, DM makes the first person NOT being a machine, from her/his/its point of view.




We can point to the body of work by
David Deutsch, such as that found in his book The Fabric of Reality, as providing some excellent reasoning to at least consider that the answer to
our question might be: Yes.

Deutsch accepts mechanism. He seems to even accept classical mechanism (the brain is a classical computer, roughly speaking). This is not postulated in the UDA reasoning. The consequences of DM I point too does not depend on classical or quantum mechanism in cognitive science.



OK, given that, how might we model interactions
between such "simulations" in a way that would give us something that covers
many situations including those where we have events that cannot occur
simultaneously? I think there is.

That seems obvious for me. Cellular automate interacts, subroutine interacts, all computations are, or can be, defined as elementary actions and interaction. They look more physical when linearity is introduced, which give a notion of resource.
Sub lambda calculus and sub combinator algebra are similarly linear.



Let us first point out some features of computations and the simulations that they could generate. We know that computers can generate simulations of
other computational systems.

Yes. Computers are universal simulators. Universal is really *universal*, if we think twice on Church thesis.




We see this when we consider how one computer
can run software that emulates of some other computer.
What about a computer generating a simulation of itself?

No problem. Well, there are some problems, or impossibilities. You cannot write a stopping program with output its own complete trace of its actual behavior. But you can write a program a which output a program b capable of given the trace of the program a, in finite steps. Solovay, inspired by Hofstadter, makes relation between virus, and a form of constructive lobianity. The Löbian sentence is the sentence which says of itself that she is provable: "I am provable". Amazingly Löb showed those sentences to be true, and of course, then, provable. Hofstadter Solovay virus not only asserts that they are true, but try, some with success, to actually provide a proof of themselves.




What about a
computer X generating a simulation of some other computer Y that is running
a simulation of X?

No problem with unbounded 'tape'. You machine might ask for more memory. Let her write on the wall.



It seems that if we allow for unlimited computational
resources, we could have a computer generating a simulation of a computer
generating a simulation of a computer generating a simulation .

Yes. Like the universal dovetailer which runs all computations on all oracles, including itself an infinity of times.

All the combinators equation admits always solution, but some can give non terminating computations.


What about a
computer X generating a simulation of computer Y that is generating a
simulation of X as it generates a simulation of Y . As so forth.

No problems.



We can see that if there is a finite upper bound on the resources available to the simulation generating computers then such expressions of infinite
regress cannot obtain,

It depends! In some case self-referential programs stop, with self- referential information.





but the idea that one computational system can
generate simulations of other computational systems is not problematic and
maybe even useful to model interactions between computational system.

I don't see the problem with simulating interaction (with fortran, lisp or just numbers with + and x). The conceptual problem is the peculiar symmetrical multi-universal ways interaction seems to occur in our neighborhood, and in the neighborhood of the first persons.



Now we need to ask how it is that we distinguish a simulation of a
computational system from a "real" computational system in most discussions
of this idea?

When I hear the word "real", I take my gun .... :)




Given that we have the notion of Universal Computers and even
Universal Virtual Reality Machines (1)

Assuming the physicalist "Church Turing principle", I think. Which I think might be hard to maintain with digital mechanism. Again, the problem is in the word 'reality'. David Deutsch seems to believe that there is a machine capable to emulate all physical phenomenon. Needless to say, that is an open problem with DM, but it might seems unreasonable to believe that we could have both Church thesis true and the Church Turing principle true too. Below our level of substitution there are too many white rabbits. In my opinion mechanism go in the direction that "matter, time consciousness, etc.' are NOT computable things. You can run the universal dovetailer, but there are no step at which you can say "that first person is emulated" (only its relative bodies). the first person itself is distributed in the whole UD*, and its internal logic reflects that facts.




we find that the idea that we can
distinguish a simulation from the real thing to require some kind of notion of a physical reality that is distinct from simulations of parts of it.

Right. But what could *that* mean? With DM that can only emerge from a projection on infinities of computations.



In
other words that there is something about "reality" that is not capable of
being simulated by a computational system in principle.

That's right again. But then since some times we know that the arithmetical reality is the union of the Sigma_1 (computable) with the Pi_1 (already not computable), and the Sigma_2 (not computable) and the Pi_2 , well all the non computable true Sigma_i (ExAyEzArEsAtEuAj...P(x,y,z,j, ...) and Pi_i (AEAEAEA...P) propositions. Arithmetical truth extends widely the computable. Only the sigma_1 reality is partially computable, (p -> Bp)




In the work of Bruno Marchal (2), building on prior work in modal logic, we find some very good arguments that there does not exist a computational means to decide which computation might be the one that exactly matches the world of experience that I have as a 1-scape. We can conjecture that that something has to do with the Hard Problem of Consciousness (3), but we can set that aside for now since we are only considering those aspects that are
computational.

Why? The whole problem is there. How could a first person (conscious) attaches her consciousness to any particular bodies, given that (from a DM third person view) she got an infinity of bodies, relatively to an infinity of universal numbers. The hard problem of consciousness, assuming DM, is shown to be an hard problem of matter.



Additionally there are some other reasoning as to why it makes sense to suspect that some kind of Cartesian-like dualism is involved is implied.(4) We could go further and borrow from the brilliant writer and thinker Greg Egan (5) the notion of a 1-scape; the landscape of the world as seen by 1
person and communicated about in the 1st person sense.

Hmm... that looks like telepathy. Communication are third person things, emerging at some level from the many computations that we share.




3-scapes would then
be considered as emerging from the intercommunications between many
1-scapes.

OK.




We now move to considerations of multiple separate computational
simulations.

The UD does that. It makes the steps of the computations of all phi_i on all numbers and numbers stream. But this includes all the computational means of all possible forms of interaction too. Right? This includes Romeo and Juliette type of interaction at the level of quark and electrons, in some computations.




I suspect that we can use the notion of bisimulation to enable
us to figure out when and if separate systems can be said to communicate with each other if in the course of a conversation back and forth their successive simulations of each other match up with the internal simulations
that they might have of each other.

All you need is some good tensor products. With the X and Z logic, I have searched for Temperley-Lieb algebra rich enough for having projective structures, braids and knots, but the emergence of space remains quite a mystery. But you are already supposing some good tensor products. I can' do that with the DM 'deontology' (that would be treachery)




In other words, if my simulation of you telling me that X occurred matched up with your simulation of yourself telling me that X occurred *and* if your
simulation of me responding to the occurrence of X matches up with my
simulation of my response to the occurrence of X then we can say that X is
communicated to me by you.

OK. In a third person sense of communication.

I have to go now, but I send the message anyway. I may comment on what you write below, if I succeed in making some sense of it. How should I read A ~ B ~ A? as (A ~ B )~ A, or A ~ (B ~ A) ? I guess A ~ (B ~ A) A = (A ~ A) for all A? This would not be a simulation in the usual computer science meaning of the word. A program which simulates a simulation of itself by itself would be a very special program. But I will read this at ease soon.

Bruno



I strongly suspect that this idea is consistent with Shannon's notion of information as the coincidence of joint allowed states between a pair of systems and if so it may help us to take a step beyond the usual account of communication between systems that assumes some kind of substance exchange.
Some of the algebra (6) of this idea if bisimulation is as follows.

Let "A simulation of B" be denoted  A ~ B.

Further, let ( B ~ A ) be called the "conjugate" of ( A ~ B ); since these
are not equal, the simulation is not commutative in general.

We see that  A = A ~ A  is the "real identity bisimulation" since the
simulation is equal to its' conjugate.


Then we state the "Woolsey identity":

        A ~ A  =  A ~ B ~ A

That is:  real identity bisimulation = simulation of the conjugate
simulation.


This is a law of identity for computational bisimulation that implies that a "real identity" occurs only when the conjugate of the bisimulation is equal
to itself.

This "law of real identity bisimulation" would then imply:
A ~ B ~ C ~ A not=  A ~ A, since A ~ B ~ C ~ A not= A ~ C ~ B ~ A ;
the conjugate is not equal to itself and so does not form the real identity
of A ~ A  =  A.

But the law of real identity bisimulation would validate the following
statement:
A ~ B ~ B ~ A  =  A ~ A,

and this is seen to be consistent with
A ~ B ~ B ~ A  =  A ~ B ~ A  =  A ~A

since B ~ B  =  B.

Also, due to the law of conjugate bisimulation identity:

        A ~ A  =  A ~ B ~ C ~ B ~ A  =  A ~ B ~ A

this is "retractable path independence": path independence only over
retrace-able paths.
This is consistent since B = B ~ C ~ B, and is the closest I can come to
associativity.
Note that retractable path independence does not necessarily imply closure:

A ~ C  not=  A ~ B ~ C,
since closure is assuming something beyond the law of real identity
bisimulation.  It seems likely that bisimulation between
three observers (or more) is not in general closed.

Notes:
1.      http://everything2.com/title/Turing+principle
2.      http://iridia.ulb.ac.be/~marchal/
3.      http://en.wikipedia.org/wiki/Hard_problem_of_consciousness
4.      See http://xxx.lanl.gov/abs/math.HO/9911150 and
http://boole.stanford.edu/pub/ratmech.pdf for more.
5) http://gregegan.customer.netspace.net.au/
6) As developed and communicated to me by Paul Hanna.


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http://iridia.ulb.ac.be/~marchal/



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