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.