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"? 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. 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. 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. 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? What about a computer X generating a simulation of some other computer Y that is running a simulation of X? 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 . 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. 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, 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. 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? Given that we have the notion of Universal Computers and even Universal Virtual Reality Machines (1) 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. In other words that there is something about "reality" that is not capable of being simulated by a computational system in principle. 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. 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. 3-scapes would then be considered as emerging from the intercommunications between many 1-scapes. We now move to considerations of multiple separate computational simulations. 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. 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. 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. -- You received this message because you are subscribed to the Google Groups "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.