Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!ncar!gatech!udel!haven.umd.edu!socrates.umd.edu!socrates!rockwell From: rockwell@socrates.umd.edu (Raul Rockwell) Newsgroups: comp.theory Subject: Re: The Ulam Machine (was: Re: Paradox of the non-recursive computer) Message-ID: Date: 15 May 91 04:11:14 GMT References: <11943@uwm.edu> <12089@uwm.edu> <1991May13.192530.27792@unx2.ucc.okstate.edu> Sender: rockwell@socrates.umd.edu (Raul Rockwell) Organization: Traveller Lines: 27 In-Reply-To: unx20491@unx2.ucc.okstate.edu's message of 13 May 91 19: 25:30 GMT Eric Gindrup: (To answer why I think you're being dense...) He [Mark William Hopkins] seems to be producing an arbitrarily random theorem and then determining whether through (not necessarily) finite application of the previous theorems, he can arrive at a previous theorem. Ah, yes, now I _think_ I see the point he was trying to make. To grab a quote from the original article: MWH: Yet at any point in time it has only "computed" a finite set and can thus be emulated by a finite machine. So is this machine actually computing or not? And the answer to that question is: Yes, it's computing, but its computations may take infinite time. The "emulator" is somewhat less well defined (does it also take infinite time where the "ulam machine" would do so?) but it too is computing. If the emulator always takes finite time to produce a result, it would, in finite time, produce an erroneous result (unless it was doing strict construction -- which is a finite computation). Or, maybe I'm still not getting the point. I still don't see the paradox :-( Raul Rockwell