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Path: eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Mikko <mikko.levanto@iki.fi> Newsgroups: comp.theory Subject: =?utf-8?B?UmU6IGVtYmVkZGVkX0ggYXBwbGllZCB0byDin6jEpOKfqSDin6jEpOKfqSBjb21wdXRlcyB0aGUgbWFwcGluZyBmcm9tIGl0cyBpbnB1dCB0byDEpC5xbg==?= Date: Thu, 1 Aug 2024 10:44:12 +0300 Organization: - Lines: 79 Message-ID: <v8fecc$22lpn$1@dont-email.me> References: <v6rg65$32o1o$3@dont-email.me> <e2958e7ea04d53590c79b53bfb4bc9dff468772b@i2pn2.org> <v742r2$s48s$2@dont-email.me> <210383b2ee318f68a96d94aec314ee8b93f79b7f@i2pn2.org> <v75u22$19j7l$4@dont-email.me> <fde630817c49562bc765bdbc98e16a1582bcad53@i2pn2.org> <v78mda$1smtm$2@dont-email.me> <v7d5cl$2t3ja$1@dont-email.me> <v7ds0o$30pvh$3@dont-email.me> <v7fs29$3f4g7$1@dont-email.me> <v7gd17$3hlc2$2@dont-email.me> <v7ikn4$1jv5$1@dont-email.me> <v7j2pg$3o7r$3@dont-email.me> <v7l3di$idv1$1@dont-email.me> <v7lnrf$luh0$1@dont-email.me> <v7niqp$13ghd$1@dont-email.me> <v7obbn$17h8r$1@dont-email.me> <v7qfm6$1m5ce$1@dont-email.me> <v7qvs3$1onhe$2@dont-email.me> <v7vnnn$2os1v$1@dont-email.me> <v80akb$2rabc$5@dont-email.me> <v82751$39qck$1@dont-email.me> <v82v0a$3dftr$4@dont-email.me> <v84tv8$3rmit$1@dont-email.me> <v88f8e$i7kl$1@dont-email.me> <v8a1o6$tvll$1@dont-email.me> <v8asjm$12hr3$1@dont-email.me> <v8cpaf$1g7h6$1@dont-email.me> <v8ds65$1mg72$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 01 Aug 2024 09:44:13 +0200 (CEST) Injection-Info: dont-email.me; posting-host="cf6c3700573d19c81f9562406f33b929"; logging-data="2185015"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19zZ0j1RxxrS/gDapGxuJXH" User-Agent: Unison/2.2 Cancel-Lock: sha1:upKoheJdOkD/BgtNw8O17q5+iPc= On 2024-07-31 17:27:33 +0000, olcott said: > On 7/31/2024 2:32 AM, Mikko wrote: >> On 2024-07-30 14:16:20 +0000, olcott said: >> >>> On 7/30/2024 1:37 AM, Mikko wrote: >>>> On 2024-07-29 16:16:13 +0000, olcott said: >>>> >>>>> On 7/28/2024 3:02 AM, Mikko wrote: >>>>>> On 2024-07-27 14:08:10 +0000, olcott said: >>>>>> >>>>>>> On 7/27/2024 2:21 AM, Mikko wrote: >>>>>>>> On 2024-07-26 14:08:11 +0000, olcott said: >>>>>>>> >>>>>>>>> When Ĥ is applied to ⟨Ĥ⟩ >>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ >>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn >>>>>>>> >>>>>>> >>>>>>> The above is merely simplified syntax for the top of page 3 >>>>>>> https://www.liarparadox.org/Linz_Proof.pdf >>>>>>> The above is the whole original Linz proof. >>>>>> >>>>>> And even more simplified semantics. >>>>>> >>>>>>> (a) Ĥ copies its input ⟨Ĥ⟩ >>>>>>> (b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ >>>>>>> (c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩ >>>>>>> (d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩ >>>>>>> (e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ >>>>>>> (f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩ >>>>>>> (g) goto (d) with one more level of simulation >>>>>>> >>>>>>> You are supposed to evaluate the above as a contiguous >>>>>>> sequence of moves such that non-halting behavior is >>>>>>> identified. >>>>>> >>>>>> The above is an obvious tight loop of (d), (e), (f), and (g). >>>>>> Its relevance (it any) to the topic of the discussion is not >>>>>> obvious. >>>>>> >>>>> >>>>> When we compute the mapping from the input to embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ >>>>> to the behavior specified by this input we know that embedded_H >>>>> is correct to transition to Ĥ.qn. >>>> >>>> The meaning of "correct" in this context is that if the transition of >>>> embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ to Ĥ.qn is correct if H ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to H.qn but >>>> incorrect otherwise. >>> >>> No you are wrong. >> >> Which dictionary (or other authority) disagrees? > > Computable functions are the formalized analogue of the > intuitive notion of algorithms, in the sense that 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 > > The common knowledge that a decider computes the mapping > from its input finite string... > > This is almost always the same as the direct execution of > the machine represented by this finite string. None of above indicates any disagreement by any authority. > The one rare exception is shown above where Ĥ ⟨Ĥ⟩ halts > and the input to embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ cannot possibly reach > its own final state of ⟨Ĥ.qn⟩ when embedded_H acts as if > it was a UTM. That is not supported by any anuthority. -- Mikko