Path: utzoo!utgpu!jarvis.csri.toronto.edu!clyde.concordia.ca!uunet!snorkelwacker!think!yale!cmcl2!lanl!opus!ted From: ted@nmsu.edu (Ted Dunning) Newsgroups: comp.ai Subject: Re: Another letter to the New York Review Message-ID: Date: 28 Feb 90 16:00:39 GMT References: <18883@bcsaic.UUCP> <1589@skye.ed.ac.uk> <11488@venera.UUCP> <1754@skye.ed.ac.uk> <90Feb15.231415est.6212@neat.cs.toronto.edu> <2al902Zg8bnn01@amdahl.uts.amdahl.com> <3750@uceng.UC.EDU> dmocsny@uceng.UC.EDU (daniel mocsny) writes: > Can any phenomenon be so truly uncomputable that no logical process > could behave equivalently (if not exactly)? > >yes. I should expand on my use of "equivalently." While I agree that some chaotic systems are probably hopeless to simulate with arbitrary precision, certainly that does not prevent an artificial system from being equivalently "interesting." I.e., the artificial system may not exactly reproduce all the behavior of the chaotic system, but it may satisfy some of the same performance measures, it may exhibit behavior that appears to be similarly complex, or it may spend roughly the same amount of time in the same attractor basins. indeed it has been shown that while a computed simulation of a chaotic system will diverge from the `true' trajectory for a particular initial condition, for many systems it will stay within a small neighborhood of some trajectory of the system. thus simulations can reasonably be used to investigate the behavior of some chaotic systems. If we regard the system of (chaotic system + sensor readout) as a computer giving the state of the system at time t, the question is: "From where does the chaotic system derive its great computing power?" For the chaotic system fits quite nicely into the universe, and yet it performs the equivalent of a seemingly uncountable number of elementary operations. for that matter, if we posit a RAM machine which can manipulate real numbers it _can_ solve the halting problem. real numbwers have strange consequences for the theory of algorithms. not to mention for the hardware types. -- Offer void except where prohibited by law.