[continued from previous message]   
      
   >>>>>>>>>> but for the purposes of this discussion it doesn't really   
   >>>>>>>>>> matter whether it's space or steps we're talking about   
   >>>>>>>>>>   
   >>>>>>>>>>>   
   >>>>>>>>>>> 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.   
   >>>>> I have been doing this for more than three years.   
   >>>>> We probably should not be spamming alt.buddha.short.fat.guy   
   >>>>>   
   >>>>> int sum(int x, int y){return x + y;}   
   >>>>> sum(3,2) should return 5 and it is incorrect   
      
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