On 1/30/2022 1:45 PM, Richard Damon wrote:
> On 1/30/22 2:18 PM, olcott wrote:
>> On 1/30/2022 11:41 AM, Richard Damon wrote:
>>> On 1/30/22 12:05 PM, olcott wrote:
>>>> On 1/30/2022 10:40 AM, Richard Damon wrote:
>>>>> On 1/30/22 10:32 AM, olcott wrote:
>>>>>> On 1/30/2022 7:44 AM, Richard Damon wrote:
>>>>>>> On 1/30/22 8:13 AM, olcott wrote:
>>>>>>>> On 1/29/2022 11:34 AM, Ben Bacarisse wrote:
>>>>>>>>> Richard Damon <Richard@Damon-Family.org> writes:
>>>>>>>>>
>>>>>>>>>> And the 'actual behavior of its actual inputs' is DEFINED to
>>>>>>>>>> be what
>>>>>>>>>> the computation the input actually does when run as an
>>>>>>>>>> independent
>>>>>>>>>> machine, or what a UTM will do when simulating that input.
>>>>>>>>>>
>>>>>>>>>> If that isn't the meaning you are using, then you are just
>>>>>>>>>> lying that
>>>>>>>>>> you are working on the halting problem, which is what seems to
>>>>>>>>>> be the
>>>>>>>>>> case. (That you are lying that is).
>>>>>>>>>
>>>>>>>>> It is certainly true that PO is not addressing the halting
>>>>>>>>> problem.  He
>>>>>>>>> has been 100% clear that false is, in his "opinion", the
>>>>>>>>> correct result
>>>>>>>>> for at least one halting computation.  This is not in dispute
>>>>>>>>> (unless
>>>>>>>>> he's retracted that and I missed it).
>>>>>>>>>
>>>>>>>>> To you and I, this means that he's not working on the halting
>>>>>>>>> problem,
>>>>>>>>> but I am not sure you can say he is lying about that.  For one
>>>>>>>>> thing,
>>>>>>>>> how can he be intending to deceive (a core part of lying) when
>>>>>>>>> he's been
>>>>>>>>> clear the he accepts the wrong answer as being the right one?  If
>>>>>>>>> someone claims to be working on "the addition problem", and
>>>>>>>>> also claims
>>>>>>>>> that 2+2=5 is correct, it's hard to consider either claim to be
>>>>>>>>> a lie.
>>>>>>>>> The person is just deeply confused.
>>>>>>>>>
>>>>>>>>> But what sort of confused can explain this nonsense?  I think
>>>>>>>>> the answer
>>>>>>>>> lies in PO's background.  The "binary square root" function is not
>>>>>>>>> computable as far as a mathematician is concerned because no TM
>>>>>>>>> can halt
>>>>>>>>> with, say, sqrt(0b10) on the tape.  But to an engineer, the
>>>>>>>>> function
>>>>>>>>> poses no problem because we can get as close as we like.  If
>>>>>>>>> 0b1.01101010000 is not good enough, just add more digits.
>>>>>>>>>
>>>>>>>>> The point is I think PO does not know what a formal, mathematical
>>>>>>>>> problem really is.  To him, anything about code, machines or
>>>>>>>>> programs is
>>>>>>>>> about solving an engineering problem "well enough" -- with
>>>>>>>>> "well enough"
>>>>>>>>> open to be defined by PO himself.
>>>>>>>>>
>>>>>>>>> More disturbing to me is that he is not even talking about Turing
>>>>>>>>> machines, again as evidenced by his own plain words.  It is not in
>>>>>>>>> dispute that he claims that two (deterministic) TMs, one an
>>>>>>>>> identical
>>>>>>>>> copy of the other, can transition to different states despite
>>>>>>>>> both being
>>>>>>>>> presented with identical input.  These are not Turing machines
>>>>>>>>> but Magic
>>>>>>>>> machines, and I can't see how any discussion can be had while
>>>>>>>>> the action
>>>>>>>>> of the things being considered is not a simple function of the
>>>>>>>>> input and
>>>>>>>>> the state transition graph.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Although Turing machines might not be able to tell that two
>>>>>>>> computations differ on their basis of their machine address x86
>>>>>>>> machines can do this.
>>>>>>>
>>>>>>> But the proof is on Turing Machines, and not all x86 'programs'
>>>>>>> are the equivalent to Turing Machines, only those that meet the
>>>>>>> requirements of being a Computation.
>>>>>>>
>>>>>>> This seems to be the core of your problem, you don't understand
>>>>>>> what a computation actually is, and want to use the WRONG
>>>>>>> definition of it being anything a modern computer does. Wrong
>>>>>>> defintions, wrong results.
>>>>>>>
>>>>>>
>>>>>> When a halt decider bases its halt status decision on the behavior
>>>>>> of the correct simulation of a finite number of N steps of its
>>>>>> input there is nothing about this that is not a computation.
>>>>>
>>>>> Except that that is the WRONG definition of Halting. You can NOT
>>>>> accurate determine halting with only FIXED number N of steps.
>>>>>
>>>>
>>>> This is a stupid mistake on your part.
>>>>
>>>> It is dead obvious that the correct simulation of ⟨Ĥ⟩ applied to ⟨Ĥ⟩
>>>> by embedded_H shows an infinitely repeating pattern in less than
>>>> four simulation cycles.
>>>>
>>>> That you deny things that are dead obvious is what I call your
>>>> mistakes stupid mistakes rather than simply mistakes.
>>>
>>> You need to use the right definition, based on the Halting Problem.
>>>
>>
>> computation that halts … the Turing machine will halt whenever it
>> enters a final state. (Linz:1990:234)
>
> Right, NOT "When a halt decider bases its halt status decision on the
> behavior of the correct simulation of a finite number of N steps of its
> input there is nothing about this that is not a computation."
>
> We need to look at the ACTUAL TURING MACHINE, even if you want to call
> that comming in the 'back door;

Because all simulating halt deciders are deciders they are only
accountable for computing the mapping from their input finite strings to
an accept or reject state on the basis of whether or not their correct
simulation of this input can possibly reach the final state of this
simulated input in any finite number of steps.

>>
>>> The fact that you need to change it just proves that your haven't got
>>> a prayer with the right definitions.
>>>
>>> NOTHING in the actual definition mentions anything about the behavior
>>> of the decider in determining if the computation actually halts.
>>>
>>> In fact, if you knew the first thing of Computation Theory, you would
>>> know that such a definition that includes that would actually be
>>> IMPOSSIBLE, as Halting is a Property of the Computation itself, and
>>> needs to be the same no matter what decider tries to decide on it.
>>>
>>> The fact that you rely on things that seem 'dead obvious' to you
>>> shows that you just don't understand how actual logic and proofs
>>> work. You don't start with things that are 'obvious', you start with
>>> the things DEFINED to be true, and the things that have been proven
>>> to be true based on those definition.
>>>
>>> Using the 'obvious' is one of the biggest sources of fallacies.
>>>
>>>
>>> We can show that your 'claim' is not true, at least for a H that
>>> aborts its simulation and goes to H.Qn,
>>
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>
>> So in other words you believe that when embedded_H aborts the
>> simulation of its input that this aborted input transitions to ⟨Ĥ⟩.qn
>> even though it has been aborted?
>>
>
> You mincing your words again.
>
> The DEFINITION of the operation that determines the 'Halting Behavior of
> the Input', is the ACTUAL RUNNING OF THE MACHINE REPRESENTED BY THE INPUT.
>
> That machine does not halt just because H/embedded_H aborts its
> simulation of its input.
>
> So, YES, when embedded_H aborts ITS PARTIAL simulation of its input,
> that the ACTUAL MACHINE it represents will continue on to H^.Qn.
Because all simulating halt deciders are deciders they are only
accountable for computing the mapping from their input finite strings to
an accept or reject state on the basis of whether or not their correct
simulation of this input can possibly reach the final state of this
simulated input in any finite number of steps.

It is like you put a guard on the front door that is supposed to report
anyone coming in the front door (the actual inputs). Then someone comes
in the back door (non inputs) and the guard does not report this. Since
the guard is only supposed to report people coming in the front door it
is incorrect to say that the guard made a mistake by not reporting
people that came in the back door.

embedded_H is not supposed to report on the halt status of the
computation that it is contained within: Ĥ applied to ⟨Ĥ⟩.

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer