[continued from previous message]   
      
   >>>>>>>>>> BB(n) is, by definitiion a "finite" number. Talking about the   
   >>>>>>>>>> "limit" of a finite number is a misuse of the term.   
   >>>>>>>>>   
   >>>>>>>>> i mean the natural number limit L >5 at which point BB(L)   
   >>>>>>>>> becomes fundamentally *unknowable* due to some L-state machine   
   >>>>>>>>> being fundamentally undecidable.   
   >>>>>>>>>   
   >>>>>>>>> if L doesn't exist, that would make halting generally   
   >>>>>>>>> decidable, so therefore L must exist   
   >>>>>>>>>   
   >>>>>>>>> if L does exist, then there must be some L-state machine U   
   >>>>>>>>> which cannot be decided on *by any partial* decider, because   
   >>>>>>>>> the BB computation would find it and use it   
   >>>>>>>>>   
   >>>>>>>>>>   
   >>>>>>>>>> We can sometimes establish upper and lower bounds on the value   
   >>>>>>>>>> of BB(n), is that what you mean by "a limit L"?   
   >>>>>>>>>>   
   >>>>>>>>>>>   
   >>>>>>>>>>> if you believe the halting problem, then BB must have a limit   
   >>>>>>>>>>> L, or else halting becomes generally solvable using the BB   
   >>>>>>>>>>> function. see, if you can compute the BB number for any N-   
   >>>>>>>>>>> state machines, then for any N-state machine u can just run   
   >>>>>>>>>>> the N- state machine until BB number of steps. any machine   
   >>>>>>>>>>> that halts on or before BB(N) steps halts, any that run past   
   >>>>>>>>>>> must be nonhalting   
   >>>>>>>>>>   
   >>>>>>>>>> No, if we could establish an upper limit for BB(n) for all n,   
   >>>>>>>>>> then we could solve the hatling problem, as we have an upper   
   >>>>>>>>>> limit for the number of steps we need to simulate the machine.   
   >>>>>>>>>>   
   >>>>>>>>>> BB(n) has a value, but for sufficiently large values of n, we   
   >>>>>>>>>> don't have an upper bound for BB(n).   
   >>>>>>>>>>   
   >>>>>>>>>>>   
   >>>>>>>>>>> and the problem with allowing for partial decidability is   
   >>>>>>>>>>> that BB can run continually run more and more deciders in   
   >>>>>>>>>>> parallel, on every N- state machine, until one comes back   
   >>>>>>>>>>> with an halting answer, for every N-state machine, which then   
   >>>>>>>>>>> it can the use to decide what the BB number is for any N ...   
   >>>>>>>>>>   
   >>>>>>>>>> So, what BB are you running? Or are you misusing "running" to   
   >>>>>>>>>> try to mean somehow trying to calculate?   
   >>>>>>>>>>>   
   >>>>>>>>>>> contradicting the concept it must have a limit L, where some   
   >>>>>>>>>>> L- state machine cannot be decidable by *any* partial decider   
   >>>>>>>>>>> on the matter,   
   >>>>>>>>>>   
   >>>>>>>>>> No, it can have a limit, just not a KNOWN limit.   
   >>>>>>>>>   
   >>>>>>>>> consensus is there can a known limit L to the BB function, and   
   >>>>>>>>> proofs have been put out in regards to this   
   >>>>>>>>>   
   >>>>>>>>>>   
   >>>>>>>>>>>   
   >>>>>>>>>>> so no richard, partial decidability does not work if BB is to   
   >>>>>>>>>>> have a limit   
   >>>>>>>>>>>   
   >>>>>>>>>>   
   >>>>>>>>>> You only have the problem is BB has a KNOWN limit. Again, you   
   >>>>>>>>>> trip up on assuming you can know any answer you want.   
   >>>>>>>>>>   
   >>>>>>>>>> That some things are not knowable breaks your logic.   
   >>>>>>>>>   
   >>>>>>>>   
   >>>>>>>> I just glanced at your paper and skipped to the conclusion.   
   >>>>>>>> Why do we care about the undecidability of the halting problem?   
   >>>>>>>> Because undecidability in general (if it is correct) shows   
   >>>>>>>> that truth itself is broken. Truth itself cannot be broken.   
   >>>>>>>> This is the only reason why I have worked on these things   
   >>>>>>>> for 28 years.   
   >>>>>>>   
   >>>>>>> because it makes us suck as developing and maintaining software,   
   >>>>>>> and as a 35 year old burnt out SWE, i'm tired of living in a   
   >>>>>>> world running off sucky software. it really is limiting our   
   >>>>>>> potential, and i want my soon to be born son to have a far better   
   >>>>>>> experience with this shit than i did.   
   >>>>>>>   
   >>>>>>> a consequence of accepting the halting problem is then   
   >>>>>>> necessarily accepting proof against *all* semantic deciders,   
   >>>>>>> barring us from agreeing on what such general deciders might be   
   >>>>>>>   
   >>>>>>   
   >>>>>> Exactly: Tarski even "proved" that we can't even directly   
   >>>>>> compute what is true. This lets dangerous liars get away   
   >>>>>> with their dangerous lies.   
   >>>>>>   
   >>>>>>> this has lead to not only an unnecessary explosion in complexity   
   >>>>>>> of software engineering, because we can't generally compute   
   >>>>>>> semantic (turing) equivalence,   
   >>>>>>>   
   >>>>>>> but the general trend in deploying software that doesn't have   
   >>>>>>> computed semantic proofs guaranteeing they actually do what we   
   >>>>>>> want them to do.   
   >>>>>>   
   >>>>>> Yes without computing halting total proof of   
   >>>>>> correctness is impossible.   
   >>>>>>   
   >>>>>>> "testing" is poor substitute for doing so, but that's the most we   
   >>>>>>> can agree upon due to the current theory of computing.   
   >>>>>>>   
   >>>>>>> i think my ideas might contribute to dealing with incompleteness   
   >>>>>>> in fundamental math more generally ... like producing more   
   >>>>>>> refined limits to it's philosophical impact. tho idk if it can be   
   >>>>>>> gotten rid of completely, anymore than we can get rid of the   
   >>>>>>> words "this statement is false"   
   >>>>>>>   
   >>>>>>   
   >>>>>> I don't think that there actually are any limits   
   >>>>>> except for expressions requiring infinite proofs.   
   >>>>>>   
   >>>>>>> but i am currently focused on the theory of computing and not   
   >>>>>>> anything more generally. the fundamental objects comprising the   
   >>>>>>> theory of computing (machines) are far more constrained in their   
   >>>>>>> definitions than what set theory needs to encompass, and within   
   >>>>>>> those constraints i think i can twist the consensus into some   
   >>>>>>> contradiction that are just entirely ignorant of atm   
   >>>>>>>   
   >>>>>>   
   >>>>>> I have explored all of the key areas. None of them   
   >>>>>> can be made as 100% perfectly concrete and unequivocal   
   >>>>>> as computing.   
   >>>>>>   
   >>>>>>> that's the slam dunk left that i need. i have a means to rectify   
   >>>>>>> whatever contradiction we find thru the use of RTMs, but i'm   
   >>>>>>> still teasing out the contradiction that will *force* others to   
   >>>>>>> notice   
   >>>>>>>   
   >>>>>>   
   >>>>>> I do have my refutation of the halting problem itself   
   >>>>>> boiled down to a rough draft of two first principles.   
   >>>>>>   
   >>>>>> When the halting problem requires a halt decider   
   >>>>>> to report on the behavior of a Turing machine this   
   >>>>>> is always a category error because Turing machines   
   >>>>>> only take finite string inputs.   
   >>>>>>   
   >>>>>> The corrected halting problem requires a Turing   
   >>>>>> machine decider to report in the behavior that its   
   >>>>>> actual finite string input actually specifies.   
   >>>>>>   
   >>>>>>   
   >>>>>   
   >>>>> polcott, i'm working on making the halting problem complete and   
   >>>>> consistent in regards to a subset of the improved "reflective   
   >>>>> turing machines" that encompasses all useful computations   
   >>>>>   
   >>>>> i'm sorry, but not about trying to reaffirm the halting function as   
   >>>>> still uncomputable by calling it a category error   
   >>>>>   
   >>>>   
   >>>> I do compute the halting function correctly.   
   >>>   
   >>> the halting *function* is an abstract mathematical object that maps a   
   >>> machine description to whether the machine described halts or not,   
   >>> not the associated machine description that attempts to compute this   
   >>>   
   >>   
   >> All Turing machines only compute the mapping   
   >> from input finite strings to some value.   
   >> On this basis I do compute halting correctly.   
   >>   
   >>>> I have been doing this for more than three years.   
   >>>> We probably should not be spamming alt.buddha.short.fat.guy   
   >>>   
      
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