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

A crude sketch of a computational model of Interaction. Stephen Paul King 9/29/2010Might it be possible to model the content of 1st person experienceas acomputationally 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 byDavid Deutsch, such as that found in his book The Fabric of Reality,asproviding some excellent reasoning to at least consider that theanswer toour 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 interactionsbetween such "simulations" in a way that would give us somethingthat coversmany 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 thesimulationsthat they could generate. We know that computers can generatesimulations ofother 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 acomputer X generating a simulation of some other computer Y that isrunninga 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 computationalresources, we could have a computer generating a simulation of acomputergenerating 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 resourcesavailableto the simulation generating computers then such expressions ofinfiniteregress cannot obtain,

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

`referential information.`

but the idea that one computational system cangenerate simulations of other computational systems is notproblematic andmaybe 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 acomputational system from a "real" computational system in mostdiscussionsof 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 candistinguish a simulation from the real thing to require some kind ofnotionof a physical reality that is distinct from simulations of parts ofit.

`Right. But what could *that* mean? With DM that can only emerge from a`

`projection on infinities of computations.`

Inother words that there is something about "reality" that is notcapable ofbeing 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 modallogic, wefind some very good arguments that there does not exist acomputationalmeans to decide which computation might be the one that exactlymatches theworld of experience that I have as a 1-scape. We can conjecture thatthatsomething has to do with the Hard Problem of Consciousness (3), butwe canset that aside for now since we are only considering those aspectsthat arecomputational.

`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 sensetosuspect that some kind of Cartesian-like dualism is involved isimplied.(4)We could go further and borrow from the brilliant writer and thinkerGregEgan (5) the notion of a 1-scape; the landscape of the world as seenby 1person 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 enableus to figure out when and if separate systems can be said tocommunicatewith each other if in the course of a conversation back and forththeirsuccessive simulations of each other match up with the internalsimulationsthat 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 occurredmatchedup with your simulation of yourself telling me that X occurred *and*if yoursimulation of me responding to the occurrence of X matches up with mysimulation of my response to the occurrence of X then we can saythat X iscommunicated 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'snotion ofinformation as the coincidence of joint allowed states between apair ofsystems and if so it may help us to take a step beyond the usualaccount ofcommunication between systems that assumes some kind of substanceexchange.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 ); sincetheseare 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 thatimplies that a"real identity" occurs only when the conjugate of the bisimulationis equalto 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 realidentityof 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 cancome toassociativity.Note that retractable path independence does not necessarily implyclosure: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. --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-l...@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

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