On 8/28/22 5:23 PM, Mr Flibble wrote:
> On Sun, 28 Aug 2022 16:56:01 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 8/28/22 4:34 PM, Mr Flibble wrote:
>>> On Sun, 28 Aug 2022 16:30:29 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 8/28/22 3:38 PM, Mr Flibble wrote:
>>>>> On Sun, 28 Aug 2022 15:30:37 -0400
>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>
>>>>>> On 8/28/22 3:21 PM, Mr Flibble wrote:
>>>>>>> On Sun, 28 Aug 2022 15:18:07 -0400
>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>
>>>>>>>> On 8/28/22 2:19 PM, Mr Flibble wrote:
>>>>>>>>> On Sun, 28 Aug 2022 13:33:37 -0400
>>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>>>
>>>>>>>>>> On 8/28/22 1:20 PM, Mr Flibble wrote:
>>>>>>>>>>> On Sun, 28 Aug 2022 13:06:03 -0400
>>>>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>>>>>
>>>>>>>>>>>> On 8/28/22 8:18 AM, Mr Flibble wrote:
>>>>>>>>>>>>> On Sun, 28 Aug 2022 08:10:23 -0400
>>>>>>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>>>>>>>> Which means it doesn't met THE definition from the
>>>>>>>>>>>>>> Classic Theory.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Yes, you can define an alternate problem, and show a
>>>>>>>>>>>>>> solution to that alternate problem, but it becomes a lie
>>>>>>>>>>>>>> to imply that your solution applies to the original
>>>>>>>>>>>>>> classical problem.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> This isn't "my" definition, it is the classical
>>>>>>>>>>>>>> definition, which is presumed by people when you just
>>>>>>>>>>>>>> say "The Halting Problem".
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> You get you choice, chose to be considered a deceitful
>>>>>>>>>>>>>> person by implying something that isn't true, or be
>>>>>>>>>>>>>> careful enough to make yourself clear.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Just use better and clearer terminology, like "The
>>>>>>>>>>>>>> extended Halting Problem", and you won't get complaints
>>>>>>>>>>>>>> of being deceitful.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> This is part of the same problem that Olcott has,
>>>>>>>>>>>>>> although in his case I think he doesn't understand that
>>>>>>>>>>>>>> he HAS tried to extend the definition to something
>>>>>>>>>>>>>> different, and thus gets stuck in lie loops.
>>>>>>>>>>>>>
>>>>>>>>>>>>> What is "classic theory" supposed to be? The very idea
>>>>>>>>>>>>> that definitions and theories cannot be refined is a
>>>>>>>>>>>>> nonsense: this certainly isn't how science is supposed to
>>>>>>>>>>>>> work. Science deals with moving targets as unlike with
>>>>>>>>>>>>> mathematical theories no scientific theory can be proven,
>>>>>>>>>>>>> only falsified. So the question ultimately becomes is the
>>>>>>>>>>>>> Halting Problem a mathematical problem or a computer
>>>>>>>>>>>>> science problem? If the latter then my approach is
>>>>>>>>>>>>> perfectly valid: scientific theories EVOLVE.
>>>>>>>>>>>>>
>>>>>>>>>>>>> /Flibble
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Classical Theory is the Theory that everyone has been
>>>>>>>>>>>> using.
>>>>>>>>>>>>
>>>>>>>>>>>> Changing Definition is rarely actually done because it can
>>>>>>>>>>>> totally break a system, as you need to re-evaluate
>>>>>>>>>>>> EVERYTHING that was done based on the old definition to
>>>>>>>>>>>> see if it still holds, or how it changes.
>>>>>>>>>>>>
>>>>>>>>>>>> Sometimes very minor refinements can be made, clearing up
>>>>>>>>>>>> an ambiguity or loophole in the definition if reviewing
>>>>>>>>>>>> what changed can be easily done.
>>>>>>>>>>>>
>>>>>>>>>>>> A Theory, once proved, is the same. You can remove
>>>>>>>>>>>> restrictions or increase the guaranteed results as that
>>>>>>>>>>>> can't cause a backwards compatibility issue.
>>>>>>>>>>>>
>>>>>>>>>>>> "Improved" Theories can be created, but don't "replace" the
>>>>>>>>>>>> old. Relativity didn't replace classical mechanics, but
>>>>>>>>>>>> just pointed out the limitations of them and showed how to
>>>>>>>>>>>> handle cases that they couldn't.
>>>>>>>>>>>>
>>>>>>>>>>>> As to if it is Mathematics or Computer Science, the answer
>>>>>>>>>>>> is YES, because Computer Science is a BRANCH of
>>>>>>>>>>>> Mathematics, and is thus different than the
>>>>>>>>>>>> "Physical"/Emperical Sciences that aren't (but use a lot
>>>>>>>>>>>> of Mathematics). The Mathematical "Sciences" do deal with
>>>>>>>>>>>> "Proofs".
>>>>>>>>>>>
>>>>>>>>>>> Agree.
>>>>>>>>>>>
>>>>>>>>>>> Given that, I would say the "Halting Problem" *as defined*
>>>>>>>>>>> is uninteresting as it is concerned with the *specific*
>>>>>>>>>>> problem of the contradiction of the "Impossible Program"
>>>>>>>>>>> rather than the far more important *general* problem of
>>>>>>>>>>> determining if a particular program given a particular
>>>>>>>>>>> input halts. I am yet to be convinced that these two
>>>>>>>>>>> problems are one in the same: I maintain that the
>>>>>>>>>>> "Imposssible Program" contradiction is a red herring.
>>>>>>>>>>>
>>>>>>>>>>> /Flibble
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> No, the Halting Problem was a significant problem a century
>>>>>>>>>> ago as people were trying to figure out what was actually
>>>>>>>>>> able to be done with finite work (Computability). Showing
>>>>>>>>>> that not all attributes are computable established that
>>>>>>>>>> there WERE limits to computations, and by some simple
>>>>>>>>>> extensions, provability in logic.
>>>>>>>>>>
>>>>>>>>>> The Halting Problem was a problem BEFORE the specific
>>>>>>>>>> "Impossible Program" was discovered, and it was the discovery
>>>>>>>>>> of it that established the limitation that we know today.
>>>>>>>>>>
>>>>>>>>>> The impossible program is just an example of a particular
>>>>>>>>>> program with a particular input. It should be noted that it
>>>>>>>>>> isn't the ONLY sort of program that can't be decided on, it
>>>>>>>>>> is just a simple enough one that the proof that it can't be
>>>>>>>>>> decided on is simple enough for most people to understand.
>>>>>>>>>> There are many other very different programs that also can
>>>>>>>>>> not be decided if they halt or not by a computation.
>>>>>>>>>
>>>>>>>>> Then why don't you fix the Wikipedia page on the Halting
>>>>>>>>> Problem which explicitly defines it to be based on the
>>>>>>>>> "Impossible Program" contradiction:
>>>>>>>>
>>>>>>>> Why, it seems correct:
>>>>>>>>
>>>>>>>>>
>>>>>>>>> "In computability theory, the halting problem is the problem
>>>>>>>>> of determining, from a description of an arbitrary computer
>>>>>>>>> program and an input, whether the program will finish
>>>>>>>>> running, or continue to run forever. Alan Turing proved in
>>>>>>>>> 1936 that a general algorithm to solve the halting problem
>>>>>>>>> for all possible program-input pairs cannot exist.
>>>>>>>>
>>>>>>>> Which is the basic description of the halting problem, followed
>>>>>>>> by the statement of Alan Turings Proof of the Halting Theorem
>>>>>>>> which says the Problem is not solvable in General (One program
>>>>>>>> to handle all possible inputs)
>>>>>>>>
>>>>>>>>>
>>>>>>>>> For any program f that might determine if programs halt, a
>>>>>>>>> "pathological" program g, called with some input, can pass its
>>>>>>>>> own source and its input to f and then specifically do the
>>>>>>>>> opposite of what f predicts g will do. No f can exist that
>>>>>>>>> handles this case. A key part of the proof is a mathematical
>>>>>>>>> definition of a computer and program, which is known as a
>>>>>>>>> Turing machine; the halting problem is undecidable over Turing
>>>>>>>>> machines. It is one of the first cases of decision problems
>>>>>>>>> proven to be unsolvable. This proof is significant to
>>>>>>>>> practical computing efforts, defining a class of applications
>>>>>>>>> which no programming invention can possibly perform
>>>>>>>>> perfectly."
>>>>>>>>
>>>>>>>> Which is the proof of the Theorem.
>>>>>>>
>>>>>>> That is my point: according to Wikipedia the proof of the
>>>>>>> Theorem is the "Impossible Program" contradiction: nothing else
>>>>>>> is mentioned in these first two paragraphs.
>>>>>>>
>>>>>>>>
>>>>>>>> Only if you think the second paragraph is part of the
>>>>>>>> definition, even though there was a sentence between them
>>>>>>>> stating that the Theorem related to it was proven, do you get
>>>>>>>> your conclusion.
>>>>>>>
>>>>>>> I see no such separating sentence.
>>>>>>>
>>>>>>>>>
>>>>>>>>> -- https://en.wikipedia.org/wiki/Halting_problem
>>>>>>>
>>>>>>> /Flibble
>>>>>>>
>>>>>>
>>>>>> To Quote:
>>>>>>
>>>>>>
>>>>>>> In computability theory, the halting problem is the problem of
>>>>>>> determining, from a description of an arbitrary computer program
>>>>>>> and an input, whether the program will finish running, or
>>>>>>> continue to run forever. Alan Turing proved in 1936 that a
>>>>>>> general algorithm to solve the halting problem for all possible
>>>>>>> program-input pairs cannot exist.
>>>>>>>
>>>>>>> For any program f that might determine if programs halt, a
>>>>>>> "pathological" program g, called with some input, can pass its
>>>>>>> own source and its input to f and then specifically do the
>>>>>>> opposite of what f predicts g will do. No f can exist that
>>>>>>> handles this case. A key part of the proof is a mathematical
>>>>>>> definition of a computer and program, which is known as a
>>>>>>> Turing machine; the halting problem is undecidable over Turing
>>>>>>> machines. It is one of the first cases of decision problems
>>>>>>> proven to be unsolvable. This proof is significant to practical
>>>>>>> computing efforts, defining a class of applications which no
>>>>>>> programming invention can possibly perform perfectly.
>>>>>>
>>>>>> Breaking down into the sections:
>>>>>>
>>>>>> P1S1: The description of the Problem
>>>>>>> In computability theory, the halting problem is the problem of
>>>>>>> determining, from a description of an arbitrary computer program
>>>>>>> and an input, whether the program will finish running, or
>>>>>>> continue to run forever.
>>>>>>
>>>>>> P1S2: The Statment of the Theorem and that it was proven
>>>>>>> Alan Turing proved in 1936 that a general algorithm to solve the
>>>>>>> halting problem for all possible program-input pairs cannot
>>>>>>> exist.
>>>>>>
>>>>>> P2S1: An Overview of the Proof
>>>>>>> For any program f that might determine if programs halt, a
>>>>>>> "pathological" program g, called with some input, can pass its
>>>>>>> own source and its input to f and then specifically do the
>>>>>>> opposite of what f predicts g will do. No f can exist that
>>>>>>> handles this case.
>>>>>
>>>>> Again, my point exactly, "the" Proof is the "Impossible Program"
>>>>> contradiction, no other proofs are mentioned the implication being
>>>>> that the Halting Problem is concerned with the contradiction
>>>>> alone.
>>>>
>>>> So, are you talking about the PROBLEM, or the PROOF of the Theorem
>>>> associated with that Problem?
>>>>
>>>>>
>>>>>>
>>>>>> P2S2: A Summary of the Effect of the Theorem being Proven
>>>>>>> A key part of the proof is a mathematical definition of a
>>>>>>> computer and program, which is known as a Turing machine; the
>>>>>>> halting problem is undecidable over Turing machines. It is one
>>>>>>> of the first cases of decision problems proven to be
>>>>>>> unsolvable. This proof is significant to practical computing
>>>>>>> efforts, defining a class of applications which no programming
>>>>>>> invention can possibly perform perfectly.
>>>>>
>>>>> "the" proof obviously refers to the previous proof and no other
>>>>> proof.
>>>>>
>>>>> /Flibble
>>>>>
>>>>>
>>>>>
>>>>
>>>> Again, are you talking about the PROBLEM, or the PROOF of the
>>>> THEOREM about that Problem.
>>>>
>>>> Your intial statement was about THE PROBLEM.
>>>>
>>>> The Problem has NOTHING about the "Impossible Program" in it.
>>>>
>>>> The PROBLEM came first, as people were wondering it this idea of a
>>>> computing machine might be able to prove some of the problems that
>>>> they were intereseted in but couldn't solve.
>>>>
>>>> THEN came Alan Turing with a formalization of the Turing Machine,
>>>> showed that it could do any form of calculation, and the impossible
>>>> program that no Turing Machine could possible decide.
>>>>
>>>> This is what proved that a Halt Decider couldn't be created, and it
>>>> came AFTER the Halting Problem existed.
>>>>
>>>> Thus, the Halting PROBLEM is not about the Impossible Program, only
>>>> the Proof uses it.
>>>
>>> "the Proof" not "a Proof", ergo the Halting Problem has a symbiotic
>>> relationship with the "Impossible Program" proof alone.
>>>
>>> If you disagree then please present an alternative proof that has no
>>> relationship to the "Impossible Program" whatsoever if we are to
>>> progress this further.
>>>
>>> /Flibble
>>>
>>
>> The big problem is the other proofs tend to require knowledge of some
>> higher level maths.
>>
>> Diagonalization is another simple proof, but that could be looked at
>> as the impossible program just with a different skin.
>>
>> One other source is from the uncomputability of the Busy Beaver
>> function (which is shown non-computable without reference to the
>> Halting Problem) for sufficiently large N.
>>
>> If Halting WAS determinable, then the Busy Beaver Function would be
>> computable by simple enumerating the full set of the finite number of
>> Turing Machines of the given size, weed out those that don't halt,
>> and run the ones that will and see what the longest output is.
>>
>> There are others, but I won't claim to know them well, or the math
>> behind them.
>
> You are failing to present a good case that the Halting Problem isn't
> all about the "Impossible Program" contradiction.
>
> /Flibble
>

The fact that there was a period of time with the Halting Problem but no
Impossible Program in sight should be a key point.

Hard to create something about something you have no concept of.