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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!news.quux.org!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: comp.theory Subject: Re: How computable functions actually work. (was Flibble) Date: Tue, 22 Apr 2025 22:33:11 -0400 Organization: i2pn2 (i2pn.org) Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 23 Apr 2025 02:34:22 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="1482570"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US On 4/22/25 6:19 PM, olcott wrote: > On 4/22/2025 4:58 PM, Andy Walker wrote: >> On 22/04/2025 15:57, Mr Flibble wrote: >>> On Tue, 22 Apr 2025 15:43:27 +0100, Andy Walker wrote: >>>> The "real" Mr Flibble is a malevolent penguin.  I wonder why >>>> contributors take him so seriously?  If you want to debate with a >>>> penguin, that's your prerogative, but to me it makes more sense to add >>>> several pinches of salt and smile or groan as appropriate to everything >>>> he writes.  He has a knack for writing things that are just about >>>> plausible, which is enviable, but one response to anything interesting >>>> is surely enough? >>> Mr Flibble is very cross. >> >>      He shouldn't be.  As hinted above, being able to write successful >> satire is a rare skill.  But it loses its point if too many people take >> it seriously. >> > > Flibble factually correct. > > All computation is defined to be represented as finite string > transformations to finite strings. Except you are doing the logic backward. > > This how Turing Machine computable functions actually work. > Outputs are forced to correspond to inputs when finite string > transformation rules are applied to inputs to derive outputs. And you need to know that the function *IS* computable to use that. What the machine actually produces will be computable. What the machine is SUPPOSED to produce might not be. > >    a function is computable if there exists an algorithm >    that can do the job of the function, i.e. given an input >    of the function domain it can return the corresponding >    output. https://en.wikipedia.org/wiki/Computable_function Which says if a machine exists, it is conputable. The machine does not need to exist. This seems to be a flaw in your logic, you seem to think there is a Truth Faerie that can magically make the impossible happen. > > On Turing Machines inputs finite strings, and > finite string transformation rules applied to > these finite strings to derive corresponding outputs. Yes, so the results can only BE what is computable, but as pointed out, the correct answer need not be. > > People here stupidly assume that the outputs are not > required to correspond to the inputs. That comes from > learn-by-rote with zero depth of understanding. > The outputs DO need to correspond to the input, but not necessarily by a computable transform. That only exists if the function is, in fact, computable. Nearly all "random" functions will not be, by a simple counting argument, There are more functions/mapping (Aleph-1) that can be asked for than machines (Aleph-0) to do the mapping. Therefore only a infintisimal fraction of all possible mappings are in fact computable. Now, when we limit ourselves to mapping that have a use, it seems we find a lot that do have a mapping, but not all. There is no computation that can compute for *ALL* possible programs, if that progran will halt when run. Turing proves that by showing for every possible decider that we might think can do it, that we can make a program for it to decide on that it will get wrong. Thus the mapping must be uncomputable.