Path: utzoo!mnetor!uunet!mcvax!lambert From: lambert@cwi.nl (Lambert Meertens) Newsgroups: sci.misc Subject: Re: Engines of Creation: Nanotechnology Message-ID: <128@piring.cwi.nl> Date: 30 Nov 87 19:19:49 GMT References: <799@sbcs.sunysb.edu> <2698@drivax.UUCP> <1063@sugar.UUCP> <2411@watcgl.waterloo.edu> <1445@m-net.UUCP> Organization: CWI, Amsterdam Lines: 30 Keywords: nanotechnology foresight drexler In article <1445@m-net.UUCP> russ@m-net.UUCP (Russ Cage) writes: ) The difficulty is that, in order to decide ) if a particular bit of nanomachinery is Gray Goo (or a part thereof), ) you have to analyze its program to see if it ever quits reproducing. ) This is exactly equivalent to the halting problem, which is insoluble. As long as the GG itself is not insoluble ... :-) There are theoretical differences between the GG containment problem and the TM (Turing Machine) halting problem. Suppose the nanoprogram has been proven to stop in a finite time. Only, after the machinery is released, it turns out that the stopping time is 10^79 generations. Not exactly what we want, eh? On the other hand, it does not really matter if the stuff keeps indefinitely "alive" as long as its growth is checked. I can imagine a nanomachined salami sausage that will regrow if you cut slices off, but not beyond one foot. (The problem whether a machine--together with its offspring--will grow beyond a prior established space limit S is algorithmically solvable in theory, but the time this takes is exponential in S, so this is no big help.) Finally, one has to take the (real-time physical) input stream to the machine into account, whereas for the TM case the input is given and finite. Perhaps the growth of my salami sausage is provably checked except if it is kept on a diet of pure caviar. That would not worry me ... until someone markets caviar with checked growth except if fed enough salami. Part of the physical environment is radiation, which will cause random mutations. Most mutations may be indifferent or lethal, but in the analysis we must consider the possibility of malign mutations. Even theoretical analysis can only give probabilistic results here. -- Lambert Meertens, CWI, Amsterdam; lambert@cwi.nl