Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: dbush Newsgroups: comp.theory Subject: Re: DDD simulated by HHH cannot possibly halt (Halting Problem) --- mindless robots Date: Mon, 14 Apr 2025 18:18:09 -0400 Organization: A noiseless patient Spider Lines: 106 Message-ID: References: <852f89c9196e0261b8156050fea4572fe886933f@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 15 Apr 2025 00:18:09 +0200 (CEST) Injection-Info: dont-email.me; posting-host="7a693fffeb8cb3d93ca8829962a38503"; logging-data="2372117"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/pyHGCLAdQaQr4l4f9/ZNM" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:/JU7gMubBYdJle8oSBfPKSPI/Ik= Content-Language: en-US In-Reply-To: On 4/14/2025 5:40 PM, olcott wrote: > On 4/14/2025 7:22 AM, dbush wrote: >> On 4/14/2025 8:01 AM, olcott wrote: >>> On 4/13/2025 9:13 PM, dbush wrote: >>>> On 4/13/2025 10:11 PM, olcott wrote: >>>>> On 4/13/2025 6:11 PM, Richard Damon wrote: >>>>>> On 4/13/25 5:00 PM, olcott wrote: >>>>>>> On 4/13/2025 3:00 PM, dbush wrote: >>>>>>>> On 4/13/2025 3:59 PM, olcott wrote: >>>>>>>>> On 4/13/2025 3:54 AM, joes wrote: >>>>>>>>>> Am Fri, 11 Apr 2025 10:56:32 -0500 schrieb olcott: >>>>>>>>>>> On 4/11/2025 3:24 AM, Richard Heathfield wrote: >>>>>>>>>>>> On 11/04/2025 08:57, Mikko wrote: >>>>>>>>>> >>>>>>>>>>>>> No proof of this principle has been shown so its use is not >>>>>>>>>>>>> valid. >>>>>>>>>>>> >>>>>>>>>>>> No proof of Peano's axioms or Euclid's fifth postulate has >>>>>>>>>>>> been shown. >>>>>>>>>>>> That doesn't mean we can't use them. >>>>>>>>>>>> Mr Olcott can have his principle if he likes, but only by >>>>>>>>>>>> EITHER >>>>>>>>>>>> proving it (which, as you say, he has not yet done) OR by >>>>>>>>>>>> taking it as >>>>>>>>>>>> axiomatic, leaving the world of mainstream computer science >>>>>>>>>>>> behind him, >>>>>>>>>>>> constructing his own computational 'geometry' so to speak, and >>>>>>>>>>>> abandoning any claim to having overturned the Halting >>>>>>>>>>>> Problem. Navel >>>>>>>>>>>> contemplation beckons. >>>>>>>>>>>> Axioms are all very well, and he's free to invent as many as >>>>>>>>>>>> he wishes, >>>>>>>>>>>> but nobody else is obliged to accept them. >>>>>>>>>>>> >>>>>>>>>>> *Simulating termination analyzer Principle* >>>>>>>>>>> It is always correct for any simulating termination analyzer >>>>>>>>>>> to stop >>>>>>>>>>> simulating and reject any input that would otherwise prevent >>>>>>>>>>> its own >>>>>>>>>>> termination. >>>>>>>>>> Sure. Why doesn’t the STA simulate itself rejecting its input? >>>>>>>>>> >>>>>>>>> >>>>>>>>> Because that is a STUPID idea and categorically impossible >>>>>>>>> because the outermost HHH sees its needs to stop simulating >>>>>>>>> before any inner HHH can possibly see this. >>>>>>>>> >>>>>>>> >>>>>>>> In other words, you agree that Linz and others are correct that >>>>>>>> no H exists that satisfies these requirements: >>>>>>>> >>>>>>>> >>>>>>>> Given any algorithm (i.e. a fixed immutable sequence of >>>>>>>> instructions) X described as with input Y: >>>>>>>> >>>>>>>> A solution to the halting problem is an algorithm H that >>>>>>>> computes the following mapping: >>>>>>>> >>>>>>>> (,Y) maps to 1 if and only if X(Y) halts when executed directly >>>>>>>> (,Y) maps to 0 if and only if X(Y) does not halt when >>>>>>>> executed directly >>>>>>>> >>>>>>> >>>>>>> No stupid! Those freaking requirements are wrong and* >>>>>>> anchored in the ignorance  of rejecting the notion >>>>>>> of a simulating termination analyzer OUT-OF-HAND WITHOUT REVIEW. >>>>>> >>>>>> No, those "freeking requirement" *ARE* the requirements >>>>> >>>>> >>>>> AND AS STUPID AS {REQUIRING} A GEOMETRIC SQUARE >>>>> CIRCLE IN THE SAME TWO-DIMENSIONAL PLANE. >>>>> >>>> >>>> In other words, you think something that would make all formal >>>> systems complete would be stupid. >>> >>> Formal systems are only incomplete[math] because >> >> They contain unknowable truths. > > Undecidability Is not incompleteness, which is the current topic. Formal systems are defined to be incomplete if they contain unknowable truths. An H that satisfies the below requirements would make them knowable and therefore the system would be complete. > >>  An H that meets these requirements would make those unknowable truths >> knowable: >> >> >> Given any algorithm (i.e. a fixed immutable sequence of instructions) >> X described as with input Y: >> >> A solution to the halting problem is an algorithm H that computes the >> following mapping: >> >> (,Y) maps to 1 if and only if X(Y) halts when executed directly >> (,Y) maps to 0 if and only if X(Y) does not halt when executed >> directly >> > >