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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott <polcott2@gmail.com> Newsgroups: comp.theory,sci.logic Subject: Re: Linz's proofs. --- Good catch ! Date: Thu, 7 Mar 2024 15:08:48 -0600 Organization: A noiseless patient Spider Lines: 112 Message-ID: <usdad0$18hee$2@dont-email.me> References: <877cj0g0bw.fsf@bsb.me.uk> <urogvi$1aeb$1@news.muc.de> <87v868ksuy.fsf@bsb.me.uk> <uromc0$5stj$1@dont-email.me> <o-mdnTMhKdsmcUL4nZ2dnZfqnPWdnZ2d@brightview.co.uk> <urpm5s$fi17$1@dont-email.me> <87edcokhy2.fsf@bsb.me.uk> <us896f$g09$1@dont-email.me> <87il1yi8fj.fsf@bsb.me.uk> <uscjr5$13k1e$1@dont-email.me> <877ciehvab.fsf@bsb.me.uk> <uscqu4$1565a$1@dont-email.me> <usd152$16fuu$1@dont-email.me> <usd22a$14o2s$11@i2pn2.org> <usd3h2$173nr$1@dont-email.me> <usd3pf$14t3b$2@i2pn2.org> <usd511$179na$1@dont-email.me> <usd675$150h1$1@i2pn2.org> <usd7eq$17ueg$1@dont-email.me> <usd9r9$150h1$4@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 7 Mar 2024 21:08:48 -0000 (UTC) Injection-Info: dont-email.me; posting-host="991a76fa9aa76d17f8f6286f1a0a882d"; logging-data="1328590"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19Dhq/2RgpOrBmxHnPkHEe5" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:5Bi5zbs2wKFyLqb//tEK1V7/Yow= Content-Language: en-US In-Reply-To: <usd9r9$150h1$4@i2pn2.org> Bytes: 6139 On 3/7/2024 2:59 PM, Richard Damon wrote: > On 3/7/24 12:18 PM, olcott wrote: >> On 3/7/2024 1:57 PM, Richard Damon wrote: >>> On 3/7/24 11:37 AM, olcott wrote: >>>> On 3/7/2024 1:15 PM, Richard Damon wrote: >>>>> On 3/7/24 11:11 AM, olcott wrote: >>>>>> On 3/7/2024 12:46 PM, Richard Damon wrote: >>>>>>> On 3/7/24 10:30 AM, olcott wrote: >>>>>>>> On 3/7/2024 10:44 AM, immibis wrote: >>>>>>>>> On 7/03/24 17:16, Ben Bacarisse wrote: >>>>>>>>>> immibis <news@immibis.com> writes: >>>>>>>>>> >>>>>>>>>>> On 7/03/24 12:32, Ben Bacarisse wrote: >>>>>>>>>>>> The students I taught seemed to have no problem with this >>>>>>>>>>>> sort of case >>>>>>>>>>>> analysis. But the "assume H does X" argument lead to lots >>>>>>>>>>>> of "but H1 >>>>>>>>>>>> could be better" arguments. >>>>>>>>>>> >>>>>>>>>>> They aren't satisfied with "we can do the exact same thing >>>>>>>>>>> with H1 to prove >>>>>>>>>>> that H1 doesn't work either"? >>>>>>>>>> >>>>>>>>>> In the vast majority of cases, yes, but even then there is a >>>>>>>>>> logical >>>>>>>>>> problem with going down that route -- there is no H so there >>>>>>>>>> can't be an >>>>>>>>>> H1 that does better. Once this objection is properly >>>>>>>>>> examined, it turns >>>>>>>>>> out to be the argument I ended up preferring anyway. H isn't >>>>>>>>>> a halt >>>>>>>>>> decider, it's just any old TM and we show it can't be halt >>>>>>>>>> decider for >>>>>>>>>> one reason or another. >>>>>>>>>> >>>>>>>>> >>>>>>>>> Unless your students are extremely pedantic... maybe they >>>>>>>>> are... I don't see what's illogical with: >>>>>>>>> >>>>>>>>> "I think H is a halt decider." >>>>>>>>> "But it doesn't: see this proof." >>>>>>>>> "Oh. Well, even though H isn't a halt decider, how do we know >>>>>>>>> there isn't a program H1 which is a halt decider?" >>>>>>>>> "The proof would still work for H1, or H2, or any other program >>>>>>>>> you think is a halt decider." >>>>>>>>> >>>>>>>>> >>>>>>>> >>>>>>>> It is an easily verified fact that: >>>>>>>> H(D,D) Sees that D(D) is calling H(D,D) at machine address 00001522 >>>>>>>> H1(D,D) Sees that D(D) is NOT calling H1(D,D) at machine address >>>>>>>> 00001422 >>>>>>>> *different machine addresses is the reason for different return >>>>>>>> values* >>>>>>>> >>>>>>>> >>>>>>> >>>>>>> Which proves that H1 and H are different computation and thus >>>>>>> different Turing Machines, so H1 getting the right answer doesn't >>>>>>> "fix" H's getting the wrong answer. >>>>>>> >>>>>> >>>>>> Good catch !!! >>>>>> >>>>>> For Olcott machines Linz H ⟨Ĥ⟩ ⟨Ĥ⟩ would map its input with >>>>>> its own TMD concatenated to this input to its Boolean result. >>>>>> >>>>>> Linz Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ would map its input with its own TMD >>>>>> concatenated to this input to its Boolean result. >>>>>> >>>>>> thus finally explaining how Linz H ⟨Ĥ⟩ ⟨Ĥ⟩ can correctly >>>>>> determine the halt status of its input while Linz Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ >>>>>> cannot. >>>>> >>>>> Which only indicates that either you built your H^ incorrectly, as >>>>> H^.H is supposed to do exactly the same thing as H itself, >>>> >>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ is supposed to do exactly the same things as H ⟨Ĥ⟩ ⟨Ĥ⟩ >>>> only if they have the same input. >>>> >>>> When Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ are Olcott machines they always >>>> have an additional input that makes the input to Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ >>>> and H ⟨Ĥ⟩ ⟨Ĥ⟩ different. >>> >>> And a machone that depends on anythohng other than the description of >>> the input is provvably NOT a Halt Decider, >> >> When it correctly determines the actual halt status of an >> actual input TMD+Finite_String then it correctly decided >> this TMD+Finite_String. > > And the finite string needs to be EXACTLY the input given to that Turing > Machine that was Described. > >> >> No one can say that it gets the wrong answer when it >> gets the right answer. > > > But if H, given the description of H^ applied to its description says it > doesn't halt, but when H^ is applied to its description it does, then it > was wrong. > New thread has all of the relevant details in one place [We finally know exactly how H1(D,D) derives a different result than H(D,D)] This make it much easier for people seeing this for the first time. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer