----- Original Message ----- From: "Ben Goertzel" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Sunday, January 12, 2003 10:50 AM Subject: RE: [agi] AI and computation (was: The Next Wave)
> > Once again, the interesting question is not "Is NARS a TM?", but > > "Is NARS a > > TM with respect to problem P?" If the problem is "To answer > > Ben's email on > > `AI and compuation'", then the system is not a TM (though it may > > be a TM in > > many other senses). For this reason, to discuss the computability and > > computational complexity of P because meaningless for such a system. > > > > Pei > > I'm sorry but I still don't understand exactly what you mean by "Is computer > program-instance X a TM with respect to problem P" Each TM (or algorithm) is defined with respect to a "problem", which is set of valid input strings. Each string in the set is a problem instance, ans the system's output at a final state is the solution to that problem instance. When we discuss whether a system can be seen as a TM, it is always respect to a problem in this sense. > Is this different from "Is computer program-instance X, at time t, a TM with > respect to problem P presented to it at time t"? Problem is defined independent of time or internal state. > Because it seems like any computer program-instance X, at a given point in > time, is modelable as a TM with respect to a problem P presented to it at > time t. > > To get more concrete, suppose we carry out the following experiment: > > "Take a specific NARS instance in a particular state. Call it X. Give it a > query in a specific format, which asks it to sort a list of n numbers. > Then, calculate the amount of time X takes before it delivers a correct > answer to the question (a correct sorting of the list) in a specified > format." This is a bad example --- you are asking NARS to simulate a TM. In doing so, of course it behaves like one. When I say NARS is not a TM, I'm not saying that it cannot simulate a TM in certain situations (and you know this for sure). The interesting situation is when it doesn't silutate a TM. Soring is a problem for it "correct answer" is well-defined, and the system can have sufficient knowledge and resources to solve it. When NARS is given such a problem, and a problem-specific algorithm, it can follow the algorithm, and behaves like a TM. However, for problems for which no algorithm exist in the system, it will "use its intelligence", and behaves in a way that doen't fit any single TM. > We can replicate the NARS instance X on many different machines, hence we > can make a statistical study of this. With insanely machines, we could try > it for every possible list of n numbers. > > By carrying out this experiment, we could calculate the worst case and > average case time complexity of this particular NARS instance as a sorting > algorithm. > > This seems to me to be "discussing the computational complexity of a problem > for NARS", and it doesn't seem to be meaningless... > > The conceptual problem here is the "particular state" assumption, right? > You can't get rid of it by averaging over all particular states, all > particular environments in the history of the system, whatever -- because > you wouldn't know what realistic pdf to use in doing the > weighted-averaging... Yes. Usually such averaging make lettle sense. When I claim that my reply to your email doesn't follow a predetermined algorithm, and therefore has no fixed complexity (instend, it depends on my changing internal state), you cannot reply by averaging many people's processing time on the same email, and call it the "computational complexity of the problem" (under the assumption that my mind is just an instance of human mind). Pei > -- Ben G > > > > > > > > > -- Ben > > > ------- > To unsubscribe, change your address, or temporarily deactivate your subscription, > please go to http://v2.listbox.com/member/?[EMAIL PROTECTED] > ------- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/?[EMAIL PROTECTED]
