Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Mikko Newsgroups: comp.theory Subject: =?utf-8?B?UmU6IGVtYmVkZGVkX0ggYXBwbGllZCB0byDin6jEpOKfqSDin6jEpOKfqSBjb21wdXRlcyB0aGUgbWFwcGluZyBmcm9tIGl0cyBpbnB1dCB0byDEpC5xbg==?= Date: Fri, 2 Aug 2024 09:28:31 +0300 Organization: - Lines: 89 Message-ID: References: <210383b2ee318f68a96d94aec314ee8b93f79b7f@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 02 Aug 2024 08:28:32 +0200 (CEST) Injection-Info: dont-email.me; posting-host="091c507d5ae6612e3eb2a7bc86b072a3"; logging-data="2834127"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19XLkz2IUMh+MUgrhnJEQ0p" User-Agent: Unison/2.2 Cancel-Lock: sha1:24AnDKWzHeCiqwtj+Xh9kx1toos= Bytes: 5371 On 2024-08-01 11:49:13 +0000, olcott said: > On 8/1/2024 2:44 AM, Mikko wrote: >> 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. >> > > Everyone (even Linz) has the wrong headed idea that a halt > decider must report on the behavior of the computation that > itself is contained within. This has always been wrong. What does "must" mean above? How does that relate to what Linz really says? > A halt decider must always report on the behavior that its > finite string specifies. This is different only when an > input invokes its own decider. The input string cannot "invoke". It only specifies. -- Mikko