On 9/18/21 1:04 PM, olcott wrote:
> On 9/18/2021 11:32 AM, Richard Damon wrote:
>> On 9/18/21 12:08 PM, olcott wrote:
>>> On 9/18/2021 10:44 AM, Richard Damon wrote:
>>>> On 9/18/21 11:37 AM, olcott wrote:
>>>>> On 9/18/2021 10:25 AM, Richard Damon wrote:
>>>>>> On 9/18/21 11:19 AM, olcott wrote:
>>>>>>> On 9/18/2021 10:13 AM, Richard Damon wrote:
>>>>>>>> On 9/18/21 10:49 AM, olcott wrote:
>>>>>>>>> On 9/18/2021 9:43 AM, Richard Damon wrote:
>>>>>>>>>>
>>>>>>>>>> On 9/18/21 9:54 AM, olcott wrote:
>>>>>>>>>>> On 9/17/2021 11:50 PM, André G. Isaak wrote:
>>>>>>>>>>>> On 2021-09-17 20:40, olcott wrote:
>>>>>>>>>>>>> Why do theory of computation problems require pure functions?
>>>>>>>>>>>>
>>>>>>>>>>>> Because the theory of computation isn't about C or x86. It
>>>>>>>>>>>> isn't
>>>>>>>>>>>> about
>>>>>>>>>>>> computer programs at all, nor about modern computers. Just
>>>>>>>>>>>> because
>>>>>>>>>>>> 'computation' and 'computer' share the same root doesn't mean
>>>>>>>>>>>> they
>>>>>>>>>>>> deal with the same set of phenomena. Remember that the
>>>>>>>>>>>> theory of
>>>>>>>>>>>> computation developed before there even were digital
>>>>>>>>>>>> computers or
>>>>>>>>>>>> programming languages.
>>>>>>>>>>>>
>>>>>>>>>>>> Computational theory is concerned with describing
>>>>>>>>>>>> *mathematical*
>>>>>>>>>>>> functions, and all mathematical functions are pure functions. A
>>>>>>>>>>>> computation is a method for determining the value of the
>>>>>>>>>>>> mathematical
>>>>>>>>>>>> function f(x) for a given x. A computable function is one for
>>>>>>>>>>>> which it
>>>>>>>>>>>> is possible to construct a TM which, given an input string
>>>>>>>>>>>> representing x, will determine the value of f(x).
>>>>>>>>>>>>
>>>>>>>>>>>> You can write computer programs which perform computations,
>>>>>>>>>>>> but the
>>>>>>>>>>>> majority of computer programs don't.
>>>>>>>>>>>>
>>>>>>>>>>>> If you really want to learn about the theory of computation,
>>>>>>>>>>>> I'd
>>>>>>>>>>>> suggest that you forget about C or x86 assembly or any sort of
>>>>>>>>>>>> computer language altogether and focus on Turing Machines.
>>>>>>>>>>>>
>>>>>>>>>>>> And don't try to mentally translate anything you read about
>>>>>>>>>>>> Turing
>>>>>>>>>>>> Machines into computer languages. Don't think about loop
>>>>>>>>>>>> counters, or
>>>>>>>>>>>> calls, or machine addresses, because all of these things
>>>>>>>>>>>> pertain to
>>>>>>>>>>>> computers and computer programming rather than computations and
>>>>>>>>>>>> they
>>>>>>>>>>>> will get in the way of you actually understanding either turing
>>>>>>>>>>>> machines or the theory of computation more generally.
>>>>>>>>>>>>
>>>>>>>>>>>> André
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> I only need to know this for one reason.
>>>>>>>>>>>
>>>>>>>>>>> When my halt decider is examining the behavior of its input and
>>>>>>>>>>> the
>>>>>>>>>>> input calls this halt decider in infinite recursion it cannot
>>>>>>>>>>> keep
>>>>>>>>>>> track
>>>>>>>>>>> of the behavior of this input without having a single pseudo
>>>>>>>>>>> static
>>>>>>>>>>> variable that is directly embedded in its machine code.
>>>>>>>>>>>
>>>>>>>>>>> This pseudo static variable stores the ongoing execution trace.
>>>>>>>>>>> When the
>>>>>>>>>>> variable is an ordinary local variable it loses all of its data
>>>>>>>>>>> between
>>>>>>>>>>> each recursive simulation.
>>>>>>>>>>>
>>>>>>>>>>> It still seems to be a pure function of its input in that
>>>>>>>>>>> (1) The function return values are identical for identical
>>>>>>>>>>> arguments
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> I think the key issue is that if you want to talk about the plain
>>>>>>>>>> behavior of C / x86 code, then you need to talk about the ACTUAL
>>>>>>>>>> behavior of that code, which means that the call to H within the
>>>>>>>>>> simulated machine needs to be seen as a call to H, and NOT some
>>>>>>>>>> logical
>>>>>>>>>> transformation.
>>>>>>>>>>
>>>>>>>>>> If you want to do the transformation, your need to actually PROVE
>>>>>>>>>> that
>>>>>>>>>> this transform is legitimate under the conditions you want to
>>>>>>>>>> make
>>>>>>>>>> it,
>>>>>>>>>> and that needs a very FORMAL argument based on accepted truths
>>>>>>>>>> and
>>>>>>>>>> principles. Your 'argument' based on H not affecting P until
>>>>>>>>>> after it
>>>>>>>>>> makes its decision so it can ignore its effect, is one of those
>>>>>>>>>> arguments that just seems 'obvious' but you haven't actually
>>>>>>>>>> proved it.
>>>>>>>>>> You don't seem to uhderstand that nature of how to prove
>>>>>>>>>> something
>>>>>>>>>> like
>>>>>>>>>> this.
>>>>>>>>>>
>>>>>>>>>> 'Obvious' things can be wrong, like it seems obvious that the
>>>>>>>>>> order you
>>>>>>>>>> add up a series shouldn't affect the result, even if the
>>>>>>>>>> number of
>>>>>>>>>> terms
>>>>>>>>>> in infinite, but there are simple proofs to show that for SOME
>>>>>>>>>> infinite
>>>>>>>>>> sums, the order you take the terms can make a difference,
>>>>>>>>>> dispite it
>>>>>>>>>> seeming contrary to the nature of addition (infinities break a
>>>>>>>>>> lot of
>>>>>>>>>> common sense).
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> A key point about your 'static' variable problem.
>>>>>>>>>
>>>>>>>>> There is only a single question here, not the myriad of questions
>>>>>>>>> that
>>>>>>>>> you refer to.
>>>>>>>>>
>>>>>>>>> Does my use of a single static variable that holds the ongoing
>>>>>>>>> execution
>>>>>>>>> trace by itself necessarily completely disqualify my system from
>>>>>>>>> applying to the halting problem or not?
>>>>>>>>>
>>>>>>>>> a) Yes
>>>>>>>>> b) No
>>>>>>>>
>>>>>>>> Error of the Complex Question, just like the question of "Have you
>>>>>>>> stopped lying about your Halt Decider?".
>>>>>>>>
>>>>>>>> It isn't the existence of a static variable itself that might
>>>>>>>> disqualify
>>>>>>>> your system for applying to the halting problem,
>>>>>>>
>>>>>>> André disagrees so one of you must be wrong.
>>>>>>
>>>>>> Then take his answer and go away as you admit defeat.
>>>>>>
>>>>>
>>>>> That is not how categorically exhaustive reasoning works.
>>>>> Categorically
>>>>> exhaustive reasoning eliminates the possibility of the error of
>>>>> omission. It results in limited subject domain omniscience.
>>>>>
>>>>> It only stops when
>>>>> (1) A solution is found.
>>>>> (2) No solution exist within omniscience.
>>>>
>>>> But your question, as I explained, was not categorically exhaustive.
>>>>
>>>
>>> Polar (yes/no) questions only have {yes, no} answers.
>>> {yes,no} completely exhausts the entire category of answers to polar
>>> (yes/no) questions.
>>
>> As long as you take the answer only for the question exactly as asked.
>>
>> No, the presence of a static local variable doesn't IN ITSELF disqualify
>> a piece of code from being a Computation, but does greatly increase the
>> possibility that it is not.
>>
>>>
>>>> Have you stopped lying about your Halt Decider?
>>>
>>> To the best of my knowledge I have only actually lied once in the last
>>> ten years. I lied to a close friend about a very hurtful truth to
>>> protect them from this very hurtful truth.
>>
>> Since it has been reported that you claimed years ago that you did have
>> a version of your Halt Decider totally coded as a ACTUAL Turing Machine,
>> and you have since retracted that statement, wasn't the first statement
>> a LIE.
>>
>
> Since the key element of the algorithm that correctly decides the halt
> status of the conventional impossible inputs was fully encoded in C and
> code written in C can be applied to Turing machines saying that I had a
> fully encoded Turing machine was poetic license.

No, it is a LIE. Neither C code nor x86 code is an encoded Turing
Machine, any more than your dog spot is a cat.

Unless you have a C compiler that can generate Turing Machine Code, you
didn't have an encoded Turing Machine.

>
> Now that I know that Turing machine equivalence is a concept that does
> exist I can more accurately refer to my code as Turing equivalent. Even
> when I do this I must augment the common notion of Turing equivalence to
> only apply to the subset of computations that have all the memory that
> they need.

So you lied out of ignorance, but it is still a lie.

You made a definitive claim that had a definitive answer, perhaps a
major part of the lie was that you implied that you actually knew what
you were talking about.