Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: Keith Thompson Newsgroups: comp.theory Subject: Re: Flibble's Law Date: Fri, 18 Apr 2025 15:57:05 -0700 Organization: None to speak of Lines: 31 Message-ID: <87fri5nkn2.fsf@nosuchdomain.example.com> References: <19955e68400bc2ad935f413f012fe04011f7cf75@i2pn2.org> <7c47bbe68c1cf317ddb2a0418564127c1471e11b@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain Injection-Date: Sat, 19 Apr 2025 00:57:05 +0200 (CEST) Injection-Info: dont-email.me; posting-host="b62a019a496a9456e80ffe1b61d2a7b5"; logging-data="4175327"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/lsqy9UlDCY8eD+cwkDUmn" User-Agent: Gnus/5.13 (Gnus v5.13) Cancel-Lock: sha1:Fz7bF6eFIKmHvdk3/OS6HjpKLAI= sha1:lYVWy6diZNL7+i4zCjhKoI6I1gs= Mr Flibble writes: [...] > I'm not claiming we can build a decider with infinite resources. > > I'm saying that if the problem permits infinite machines, then infinite > analyzers are fair game in theory. > > The Flibble Reciprocity Principle: > > In theoretical computation, every permitted infinity in problem > formulation implies a permitted infinity in problem analysis. > > It's about playing the game by the rules of the game. No, it seems to be about inventing new rules because you don't like the results you get from the existing rules. There is no "fair game" principle in mathematics. The fact that a Turing machine can have potentially unlimited resources (though any terminating Turing machine can use only finite resources) *does not imply* that "infinite analyzers are fair game". A halt decider that can give a correct answer for any input using only finite time and tape would be extremely interesting and useful, but such a thing has been proven to be impossible. A halt decider that can give a correct answer only, in some cases, after consuming infinite resources is neither interesting nor useful. -- Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com void Void(void) { Void(); } /* The recursive call of the void */