On 5/3/2022 5:21 PM, Python wrote:
> Peter Olcott wrote:
>> On 5/3/2022 1:59 PM, Mr Flibble wrote:
>>> On Tue, 3 May 2022 11:57:39 -0500
>>> olcott <polcott2@gmail.com> wrote:
> ...
>>>> I don't buy into the whole imaginary numbers game.
>>>> We could imagine that 2 + 3 = 17 and call that an imaginary sum.
> ...
>>
>> Nice to know, thanks. Thus your rebuttal seems complete it is not an
>> infinite anything. Imagining the square root of a negative number or
>> that parallel lines meet seems a little nuts to me.
>
> Before jumping to such outrageously uninformed conclusions you may want
> to learn how complex numbers are actually defined nowadays.
>

They are defined to directly contradict the verified facts.
I really hate anything that directly contradicts the verified facts
because this can result in:
(a) Climate change making humans extinct quite soon,

(b) Nazi "big lie" propaganda about election fraud is making very
significant inroads to transforming Democracy ion the USA to Fascism.

(c) It directly resulted in many covid-19 deaths

> It is true that, at first, it was used without any proper definition
> better than "let's assume we can deal with sqrt(-1) as usual". The
> surprising point at that time is it works pretty well.
>

We can see what happens when we hypothesize (against the facts) that
square roots of negative numbers and parallel lines that meet exist
simply to see where this leads. I am sure that this is the intent.

> *Then*, in the XIXth Century, Gallois showed how to define complex
> numbers rigorously.
>
> You've never heard of that, Peter, really?
>
> [for the record: C is the set of equivalence classes of polynomials
> on R by the relation p ~ q iff p - q = 0 [mod x^2+1], compatibility
> of + and * on R and C can be proven easily, R is naturally injected
> into C as a set of constant polynomials, i is the equivalence class of
> the polynomial x]
>
>

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

Peter Olcott wrote:
> On 5/3/2022 5:21 PM, Python wrote:
>> Peter Olcott wrote:
>>> On 5/3/2022 1:59 PM, Mr Flibble wrote:
>>>> On Tue, 3 May 2022 11:57:39 -0500
>>>> olcott <polcott2@gmail.com> wrote:
>> ...
>>>>> I don't buy into the whole imaginary numbers game.
>>>>> We could imagine that 2 + 3 = 17 and call that an imaginary sum.
>> ...
>>>
>>> Nice to know, thanks. Thus your rebuttal seems complete it is not an
>>> infinite anything. Imagining the square root of a negative number or
>>> that parallel lines meet seems a little nuts to me.
>>
>> Before jumping to such outrageously uninformed conclusions you may want
>> to learn how complex numbers are actually defined nowadays.
>>
>
> They are defined to directly contradict the verified facts.
> I really hate anything that directly contradicts the verified facts
> because this can result in:
> (a) Climate change making humans extinct quite soon,
>
> (b) Nazi "big lie" propaganda about election fraud is making very
> significant inroads to transforming Democracy ion the USA to Fascism.
>
> (c) It directly resulted in many covid-19 deaths

You should definitely call a doctor and ask for help, your mental
state is utterly ill. What the f* are complex numbers related to
your rants on politics?

>> It is true that, at first, it was used without any proper definition
>> better than "let's assume we can deal with sqrt(-1) as usual". The
>> surprising point at that time is it works pretty well.
>>
>
> We can see what happens when we hypothesize (against the facts) that
> square roots of negative numbers and parallel lines that meet exist
> simply to see where this leads. I am sure that this is the intent.

Not quite you're wrong. The intent was to find *real* roots of degree 3
polynomials even if square root of negative quantities appears at
intermediary steps.

You know *nothing* about history of Science, Peter. Guessing is quite
absurd when it comes to History.

>> *Then*, in the XIXth Century, Gallois showed how to define complex
>> numbers rigorously.
>>
>> You've never heard of that, Peter, really?
>>
>> [for the record: C is the set of equivalence classes of polynomials
>> on R by the relation p ~ q iff p - q = 0 [mod x^2+1], compatibility
>> of + and * on R and C can be proven easily, R is naturally injected
>> into C as a set of constant polynomials, i is the equivalence class of
>> the polynomial x]

No reaction? Well... Not a big surprise, your eyes cancel out any
sensible arguments proving you wrong, as usual.

Die in Hell, idiotic annoying crank. You deserve it.

On 5/3/2022 5:46 PM, Python wrote:
> Peter Olcott wrote:
>> On 5/3/2022 5:21 PM, Python wrote:
>>> Peter Olcott wrote:
>>>> On 5/3/2022 1:59 PM, Mr Flibble wrote:
>>>>> On Tue, 3 May 2022 11:57:39 -0500
>>>>> olcott <polcott2@gmail.com> wrote:
>>> ...
>>>>>> I don't buy into the whole imaginary numbers game.
>>>>>> We could imagine that 2 + 3 = 17 and call that an imaginary sum.
>>> ...
>>>>
>>>> Nice to know, thanks. Thus your rebuttal seems complete it is not an
>>>> infinite anything. Imagining the square root of a negative number or
>>>> that parallel lines meet seems a little nuts to me.
>>>
>>> Before jumping to such outrageously uninformed conclusions you may want
>>> to learn how complex numbers are actually defined nowadays.
>>>
>>
>> They are defined to directly contradict the verified facts.
>> I really hate anything that directly contradicts the verified facts
>> because this can result in:
>> (a) Climate change making humans extinct quite soon,
>>
>> (b) Nazi "big lie" propaganda about election fraud is making very
>> significant inroads to transforming Democracy ion the USA to Fascism.
>>
>> (c) It directly resulted in many covid-19 deaths
>
> You should definitely call a doctor and ask for help, your mental
> state is utterly ill. What the f* are complex numbers related to
> your rants on politics?
>
>>> It is true that, at first, it was used without any proper definition
>>> better than "let's assume we can deal with sqrt(-1) as usual". The
>>> surprising point at that time is it works pretty well.
>>>
>>
>> We can see what happens when we hypothesize (against the facts) that
>> square roots of negative numbers and parallel lines that meet exist
>> simply to see where this leads. I am sure that this is the intent.
>
>
> Not quite you're wrong. The intent was to find *real* roots of degree 3
> polynomials even if square root of negative quantities appears at
> intermediary steps.
>

None-the-less as I just said this whole think relies on accepting a
known false premise.

> You know *nothing* about history of Science, Peter. Guessing is quite
> absurd when it comes to History.
>
>>> *Then*, in the XIXth Century, Gallois showed how to define complex
>>> numbers rigorously.
>>>
>>> You've never heard of that, Peter, really?
>>>
>>> [for the record: C is the set of equivalence classes of polynomials
>>> on R by the relation p ~ q iff p - q = 0 [mod x^2+1], compatibility
>>> of + and * on R and C can be proven easily, R is naturally injected
>>> into C as a set of constant polynomials, i is the equivalence class of
>>> the polynomial x]
>
> No reaction? Well... Not a big surprise, your eyes cancel out any
> sensible arguments proving you wrong, as usual.
>
> Die in Hell, idiotic annoying crank. You deserve it.
>
>
>
>

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

Peter Olcott wrote:
> On 5/3/2022 5:46 PM, Python wrote:
>> Peter Olcott wrote:
>>> On 5/3/2022 5:21 PM, Python wrote:
>>>> Peter Olcott wrote:
>>>>> On 5/3/2022 1:59 PM, Mr Flibble wrote:
>>>>>> On Tue, 3 May 2022 11:57:39 -0500
>>>>>> olcott <polcott2@gmail.com> wrote:
>>>> ...
>>>>>>> I don't buy into the whole imaginary numbers game.
>>>>>>> We could imagine that 2 + 3 = 17 and call that an imaginary sum.
>>>> ...
>>>>>
>>>>> Nice to know, thanks. Thus your rebuttal seems complete it is not
>>>>> an infinite anything. Imagining the square root of a negative
>>>>> number or that parallel lines meet seems a little nuts to me.
>>>>
>>>> Before jumping to such outrageously uninformed conclusions you may want
>>>> to learn how complex numbers are actually defined nowadays.
>>>>
>>>
>>> They are defined to directly contradict the verified facts.
>>> I really hate anything that directly contradicts the verified facts
>>> because this can result in:
>>> (a) Climate change making humans extinct quite soon,
>>>
>>> (b) Nazi "big lie" propaganda about election fraud is making very
>>> significant inroads to transforming Democracy ion the USA to Fascism.
>>>
>>> (c) It directly resulted in many covid-19 deaths
>>
>> You should definitely call a doctor and ask for help, your mental
>> state is utterly ill. What the f* are complex numbers related to
>> your rants on politics?
>>
>>>> It is true that, at first, it was used without any proper definition
>>>> better than "let's assume we can deal with sqrt(-1) as usual". The
>>>> surprising point at that time is it works pretty well.
>>>>
>>>
>>> We can see what happens when we hypothesize (against the facts) that
>>> square roots of negative numbers and parallel lines that meet exist
>>> simply to see where this leads. I am sure that this is the intent.
>>
>>
>> Not quite you're wrong. The intent was to find *real* roots of degree 3
>> polynomials even if square root of negative quantities appears at
>> intermediary steps.
>>
>
> None-the-less as I just said this whole think relies on accepting a
> known false premise.

Let me guess, you are some kind of "information engineer" and consider
yourself also as "one of the greatest logicians Humanity ever had",
right? There is a demented guy of this kind on sci.physics.relativity,
his name is Maciej Wozniak. You guys should definitely mate (NOT).

>> You know *nothing* about history of Science, Peter. Guessing is quite
>> absurd when it comes to History.
>>
>>>> *Then*, in the XIXth Century, Gallois showed how to define complex
>>>> numbers rigorously.
>>>>
>>>> You've never heard of that, Peter, really?
>>>>
>>>> [for the record: C is the set of equivalence classes of polynomials
>>>> on R by the relation p ~ q iff p - q = 0 [mod x^2+1], compatibility
>>>> of + and * on R and C can be proven easily, R is naturally injected
>>>> into C as a set of constant polynomials, i is the equivalence class of
>>>> the polynomial x]
>>
>> No reaction? Well... Not a big surprise, your eyes cancel out any
>> sensible arguments proving you wrong, as usual.
>>
>> Die in Hell, idiotic annoying crank. You deserve it.

(bis)

On 5/3/2022 6:05 PM, Python wrote:
> Peter Olcott wrote:
>> On 5/3/2022 5:46 PM, Python wrote:
>>> Peter Olcott wrote:
>>>> On 5/3/2022 5:21 PM, Python wrote:
>>>>> Peter Olcott wrote:
>>>>>> On 5/3/2022 1:59 PM, Mr Flibble wrote:
>>>>>>> On Tue, 3 May 2022 11:57:39 -0500
>>>>>>> olcott <polcott2@gmail.com> wrote:
>>>>> ...
>>>>>>>> I don't buy into the whole imaginary numbers game.
>>>>>>>> We could imagine that 2 + 3 = 17 and call that an imaginary sum.
>>>>> ...
>>>>>>
>>>>>> Nice to know, thanks. Thus your rebuttal seems complete it is not
>>>>>> an infinite anything. Imagining the square root of a negative
>>>>>> number or that parallel lines meet seems a little nuts to me.
>>>>>
>>>>> Before jumping to such outrageously uninformed conclusions you may
>>>>> want
>>>>> to learn how complex numbers are actually defined nowadays.
>>>>>
>>>>
>>>> They are defined to directly contradict the verified facts.
>>>> I really hate anything that directly contradicts the verified facts
>>>> because this can result in:
>>>> (a) Climate change making humans extinct quite soon,
>>>>
>>>> (b) Nazi "big lie" propaganda about election fraud is making very
>>>> significant inroads to transforming Democracy ion the USA to Fascism.
>>>>
>>>> (c) It directly resulted in many covid-19 deaths
>>>
>>> You should definitely call a doctor and ask for help, your mental
>>> state is utterly ill. What the f* are complex numbers related to
>>> your rants on politics?
>>>
>>>>> It is true that, at first, it was used without any proper definition
>>>>> better than "let's assume we can deal with sqrt(-1) as usual". The
>>>>> surprising point at that time is it works pretty well.
>>>>>
>>>>
>>>> We can see what happens when we hypothesize (against the facts) that
>>>> square roots of negative numbers and parallel lines that meet exist
>>>> simply to see where this leads. I am sure that this is the intent.
>>>
>>>
>>> Not quite you're wrong. The intent was to find *real* roots of degree 3
>>> polynomials even if square root of negative quantities appears at
>>> intermediary steps.
>>>
>>
>> None-the-less as I just said this whole think relies on accepting a
>> known false premise.
>
> Let me guess, you are some kind of "information engineer" and consider
> yourself also as "one of the greatest logicians Humanity ever had",
> right? There is a demented guy of this kind on sci.physics.relativity,
> his name is Maciej Wozniak. You guys should definitely mate (NOT).
>

I consider myself to have made significant unique advancements on the
single subject on the philosophical foundation of the notion of logical
truth.

One of my key breakthroughs is redefining the analytic / synthetic
distinction such that analytic means (the same as it did) any expression
of formal or natural language that can be verified as true entirely on
the basis of its meaning. "Dogs are animals"

The somewhat vaguely defined synthetic is renamed as empirical and it is
the same sort of thing as analytic that additionally requires sense data
from the sense organs as an aspect of the truth verification process.
"There is a dog in my living room right now."

This is the most important paper on the subject
Two Dogmas of Empiricism by Willard Van Orman Quine
(Harvard University Press, 1953; second, revised, edition 1961)
https://www.theologie.uzh.ch/dam/jcr:ffffffff-fbd6-1538-0000-000070cf64bc/Quine51.pdf

Quine didn't seem to understand that bachelors are necessarily unmarried.

Meaning Postulates by RUDOLF CARNAP
https://liarparadox.org/Meaning_Postulates_Rudolf_Carnap_1952.pdf
conclusively proved the complete basis of how we know that bachelors are
necessarily unmarried. Quine didn't want to hear this because it
contradicted his paper.

>>> You know *nothing* about history of Science, Peter. Guessing is quite
>>> absurd when it comes to History.
>>>
>>>>> *Then*, in the XIXth Century, Gallois showed how to define complex
>>>>> numbers rigorously.
>>>>>
>>>>> You've never heard of that, Peter, really?
>>>>>
>>>>> [for the record: C is the set of equivalence classes of polynomials
>>>>> on R by the relation p ~ q iff p - q = 0 [mod x^2+1], compatibility
>>>>> of + and * on R and C can be proven easily, R is naturally injected
>>>>> into C as a set of constant polynomials, i is the equivalence class of
>>>>> the polynomial x]
>>>
>>> No reaction? Well... Not a big surprise, your eyes cancel out any
>>> sensible arguments proving you wrong, as usual.
>>>
>>> Die in Hell, idiotic annoying crank. You deserve it.
>
> (bis)
>
>

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

On 5/3/22 2:13 PM, olcott wrote:
> On 5/3/2022 12:27 PM, Mikko wrote:
>> On 2022-05-03 14:42:32 +0000, olcott said:
>>
>>> On 5/3/2022 4:31 AM, Mikko wrote:
>>>> On 2022-05-02 15:47:32 +0000, Mr Flibble said:
>>>>
>>>>> Not all infinitely recursive definitions are invalid however
>>>>> infinitely
>>>>> recursive definitions that arise out of a category error (as is the
>>>>> case with the halting problem) are invalid.
>>>>
>>>> An infinite recursion cannot arise out of a category error as the
>>>> recursion
>>>> stops at the category error.
>>>>
>>>> Mikko
>>>>
>>>
>>> The category error is that an expression of language X is construed
>>> as a logic sentence / truth bearer that is true or false. It is
>>> because of the infinitely recursive definition that X is neither of
>>> these.
>>
>> Only if the recursive expression is used as if it were a truth bearer.
>> Definitions usually don't use expression that way.
>>
>> Mikko
>>
>
> Expressions of language can only be correctly construed as true:
> (a) if they are defined to be true
> (b) have no contradictory elements in (a)
> (c) are derived by applying true preserving operations to (a) or (c)
>

So, you don't believe the Bible verse you like to Quote is actually true?

Then why do you quote it?

There is no "Definiton" that it must be true, or how do you decide WHICH
writings get that status.

And you certainly can't derive it from things actually defined to be true.

This seems to say you have a contradiction in your logic system, so I
guess that mean your logic system isn't correct.

On 5/3/22 10:42 AM, olcott wrote:
> On 5/3/2022 4:31 AM, Mikko wrote:
>> On 2022-05-02 15:47:32 +0000, Mr Flibble said:
>>
>>> Not all infinitely recursive definitions are invalid however infinitely
>>> recursive definitions that arise out of a category error (as is the
>>> case with the halting problem) are invalid.
>>
>> An infinite recursion cannot arise out of a category error as the
>> recursion
>> stops at the category error.
>>
>> Mikko
>>
>
> The category error is that an expression of language X is construed as a
> logic sentence / truth bearer that is true or false. It is because of
> the infinitely recursive definition that X is neither of these.
>
> https://en.wikipedia.org/wiki/Sentence_(mathematical_logic)#:~:text=In%20mathematical%20logic%2C%20a%20sentence,must%20be%20true%20or%20false.
>
>

Except that neither G (in F) or the Halting Problem as properly defined
has a recursive definition, so you have no grounds to call it infinitely
recursive.

Yes, G may become recursive in F', but it isn't in F.

On 5/3/22 6:32 PM, olcott wrote:
> On 5/3/2022 5:21 PM, Dennis Bush wrote:
>> On Tuesday, May 3, 2022 at 6:08:33 PM UTC-4, olcott wrote:
>>> On 5/3/2022 4:49 PM, Dennis Bush wrote:
>>>> On Tuesday, May 3, 2022 at 12:39:49 PM UTC-4, olcott wrote:
>>>>> On 5/3/2022 10:36 AM, Dennis Bush wrote:
>>>>>> On Tuesday, May 3, 2022 at 11:19:33 AM UTC-4, olcott wrote:
>>>>>>> On 5/3/2022 9:47 AM, Dennis Bush wrote:
>>>>>>>> On Tuesday, May 3, 2022 at 10:31:21 AM UTC-4, olcott wrote:
>>>>>>>>> On 5/3/2022 7:12 AM, wij wij wrote:
>>>>>>>>>> Richard Damon 在 2022年5月3日 星期二上午8:48:57 [UTC+8] 的信中
>>>>>>>>>> 寫道：
>>>>>>>>>>> On 5/2/22 8:35 PM, olcott wrote:
>>>>>>>>>>>> On 5/2/2022 5:47 PM, Mr Flibble wrote:
>>>>>>>>>>>>> On Mon, 2 May 2022 18:46:00 -0400
>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> On 5/2/22 6:38 PM, Mr Flibble wrote:
>>>>>>>>>>>>>>> On Mon, 2 May 2022 18:32:16 -0400
>>>>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>>>> On 5/2/22 11:47 AM, Mr Flibble wrote:
>>>>>>>>>>>>>>>>> Not all infinitely recursive definitions are invalid
>>>>>>>>>>>>>>>>> however
>>>>>>>>>>>>>>>>> infinitely recursive definitions that arise out of a
>>>>>>>>>>>>>>>>> category
>>>>>>>>>>>>>>>>> error (as is the case with the halting problem) are
>>>>>>>>>>>>>>>>> invalid.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> The halting problem (as currently defined) is invalid
>>>>>>>>>>>>>>>>> due to the
>>>>>>>>>>>>>>>>> invalid "impossible program" [Strachey, 1965] that is
>>>>>>>>>>>>>>>>> actually
>>>>>>>>>>>>>>>>> impossible due to the category error present in its
>>>>>>>>>>>>>>>>> definition and
>>>>>>>>>>>>>>>>> *not* because of any function call-like recursion;
>>>>>>>>>>>>>>>>> confusion
>>>>>>>>>>>>>>>>> between these two types of recursion are why Olcott is
>>>>>>>>>>>>>>>>> having
>>>>>>>>>>>>>>>>> difficulty communicating his ideas with the rest of you
>>>>>>>>>>>>>>>>> shower.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> The categories involved in the category error are the
>>>>>>>>>>>>>>>>> decider and
>>>>>>>>>>>>>>>>> that which is being decided. Currently extant attempts to
>>>>>>>>>>>>>>>>> conflate the decider with that which is being decided are
>>>>>>>>>>>>>>>>> infinitely recursive and thus invalid.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> /Flibble
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Except that the "impossible program" isn't part of the
>>>>>>>>>>>>>>>> definition
>>>>>>>>>>>>>>>> of the Halting Problem.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> It is according to [Wikipedia, 2022].
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> /Flibble
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Nope, you comprehend worse that PO.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Note, and Encyclopedic entery, like Wikipedia, is NOT just a
>>>>>>>>>>>>>> definition but a full article explaining the subject.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Maybe if you look for a FORMAL source, that states what is
>>>>>>>>>>>>>> the ACTUAL
>>>>>>>>>>>>>> definition, you would learn something.
>>>>>>>>>>>>>
>>>>>>>>>>>>> If Wikipedia is wrong then correct it and have your
>>>>>>>>>>>>> corrections
>>>>>>>>>>>>> reviewed; until then please shut the fuck up.
>>>>>>>>>>>>>
>>>>>>>>>>>>> /Flibble
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> I think that the problem is that Richard has disagreeably as
>>>>>>>>>>>> his highest
>>>>>>>>>>>> priority, thus doesn't really give a rat's ass for the
>>>>>>>>>>>> truth. An
>>>>>>>>>>>>
>>>>>>>>>>>> An impossible program C. Strachey
>>>>>>>>>>>> The Computer Journal, Volume 7, Issue 4, January 1965, Page
>>>>>>>>>>>> 313,
>>>>>>>>>>>> Published: 01 January 1965
>>>>>>>>>>>> https://academic.oup.com/comjnl/article/7/4/313/354243
>>>>>>>>>>>>
>>>>>>>>>>>> It is very common knowledge that the Wikipedia description
>>>>>>>>>>>> is true and
>>>>>>>>>>>> this is affirmed in Sipser.
>>>>>>>>>>>>
>>>>>>>>>>>> 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.
>>>>>>>>>>>> https://en.wikipedia.org/wiki/Halting_problem
>>>>>>>>>>>>
>>>>>>>>>>>> Now we construct a new Turing machine D with H as a
>>>>>>>>>>>> subroutine. This new
>>>>>>>>>>>> TM calls H to determine what M does when the input to M is
>>>>>>>>>>>> its own
>>>>>>>>>>>> description ⟨M⟩. Once D has determined this information, it
>>>>>>>>>>>> does the
>>>>>>>>>>>> opposite. https://www.liarparadox.org/Sipser_165_167.pdf
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>> Thus you have shown you don't even know what a "Definition"
>>>>>>>>>>> is, so it is
>>>>>>>>>>> impossible for you to reason by the meaning of the words.
>>>>>>>>>>>
>>>>>>>>>>> You have just proved yourself to be an IDIOT.
>>>>>>>>>>
>>>>>>>>>> PO is incapable of logic reasoning (PO had shown he cannot
>>>>>>>>>> even get the truth
>>>>>>>>>> table of logical implication/AND right). All he said is
>>>>>>>>>> delusion including when
>>>>>>>>>> words from him happen to be correct to others (no real meaning).
>>>>>>>>>>
>>>>>>>>>> IIRC, PO's revision that H(P,P) has no relation with P(P) is
>>>>>>>>>> deliberately
>>>>>>>>>> fabricated this recent year after PO ran out his reasons to
>>>>>>>>>> explain why HP is
>>>>>>>>>> wrong and he is correct. PO has no trouble to 'lie' to his
>>>>>>>>>> bible (he can read
>>>>>>>>>> it his way), the HP thing is just piece of cake.
>>>>>>>>> It is an easily verified fact that P(P) and the correct
>>>>>>>>> simulation of
>>>>>>>>> the input to H(P,P) specify different sequences of
>>>>>>>>> configurations, thus
>>>>>>>>> have different halting behavior.
>>>>>>>>
>>>>>>>> The easily verified fact is that the correct simulation to
>>>>>>>> H(P,P) is performed by Hb(P,P) (which simulates for k more steps
>>>>>>>> than H) which remains in UTM mode while simulating the same
>>>>>>>> input to a final state.
>>>>>>>>
>>>>>>> I have no idea what you mean.
>>>>>>
>>>>>> In other words you don't want to admit that this proves you are
>>>>>> wrong.
>>>>>>
>>>>> No I can't understand what you mean.
>>>>> I think that I see it now, I had forgotten the notation.
>>>>>
>>>>> An input having a pathological self-reference relationship to its
>>>>> decider H would necessarily derive a different halt status than an
>>>>> input
>>>>> not having a pathological self-reference relationship to its
>>>>> decider Hb.
>>>>>
>>>>> The P having a pathological self-reference relationship to H is not
>>>>> the
>>>>> same as the Px NOT having a pathological self-reference
>>>>> relationship to
>>>>> Hb. Because P.H calls itself and Px.Hb does not call itself P is
>>>>> not the
>>>>> same input as Px.
>>>>
>>>> The P we're talking about is a *specific* P, namely Pa which is
>>>> built from Ha, and Ha is a *specific* H. So Pa and Px are the *same*.
>>> Not at all because H(P,P) has itself as part of its input and Hb(P,P)
>>> does not have itself as part of its input.
>>>>
>>>> So just because Pa contains an embedded copy of Ha but not an
>>>> embedded copy of Hb doesn't means that it's not the same.
>>>>
>>> Sure it does. The correctly simulated input to H(P,P) specifies
>>> infinitely nested simulation where as correctly simulated input to
>>> Hb(P,P) DOES NOT specify infinitely nested simulation.
>>>
>>> How much longer are you going to continue the verified facts?
>>> This does make you look quite foolish or dishonest.
>>>> Ha(Pa,Pa) and Hb(Pa,Pa) have the *exact* same input.
>>>>
>>> The correctly simulated input to Ha(Pa,Pa) specifies infinitely nested
>>> simulation where as correctly simulated input to Hb(Pa,Pa) DOES NOT
>>> specify infinitely nested simulation.
>>>
>>> How much longer are you going to continue the verified facts?
>>> This does make you look quite foolish or dishonest.
>>>> Just because it appears from a glance that Ha is starting its
>>>> simulation of Pa "in the middle" doesn't mean that's what's actually
>>>> happening. That's just how the incorrect simulation is manifesting
>>>> itself. It's kind of like undefined behavior in a C program.
>>> You only have to do a correct execution trace of Ha(Pa,Pa) and Hb(Pa,Pa)
>>> to see that:
>>>
>>> The correctly simulated input to Ha(Pa,Pa) specifies infinitely nested
>>> simulation where as correctly simulated input to Hb(Pa,Pa) DOES NOT
>>> specify infinitely nested simulation.
>>>
>>> How much longer are you going to continue the verified facts?
>>> This does make you look quite foolish or dishonest.
>>>>>>
>>>>>>>> Because H and Hb and both simulating halt deciders and are given
>>>>>>>> the same input, they are deciding on the same sequence of
>>>>>>>> configurations (namely starting with the first instruction of
>>>>>>>> P). Because one answers false and one answers true, one must be
>>>>>>>> wrong.
>>>>>>>>
>>>>>>> It is ridiculously stupid to assume that an input having
>>>>>>> pathological
>>>>>>> self-reference to its decider would have the same behavior as an
>>>>>>> input
>>>>>>> NOT having pathological to its decider.
>>>>>>
>>>>>> Which is another way of saying that H can't give a correct answer
>>>>>> for (P,P).
>>>>>>
>>>>> Different computations must give different answers.
>>>>> That you don't fully understand all of the nuances of how this applies
>>>>> to H/P and Hb/Px is OK, it is difficult to understand.
>>>>
>>>> Just because Pa contains an embedded copy of Ha but not an embedded
>>>> copy of Hb doesn't means that it's not the same.
>>> You only have to do a correct execution trace of Ha(Pa,Pa) and Hb(Pa,Pa)
>>> to see that:
>>>
>>> The correctly simulated input to Ha(Pa,Pa) specifies infinitely nested
>>> simulation where as correctly simulated input to Hb(Pa,Pa) DOES NOT
>>> specify infinitely nested simulation.
>>>
>>> How much longer are you going to continue the verified facts?
>>> This does make you look quite foolish or dishonest.
>>>>>>>> Since a simulating halt decider that simulates its input to a
>>>>>>>> final state while remaining in UTM mode is necessarily correct,
>>>>>>>> this proves that Hb(P,P) == true is correct and that H(P,P) ==
>>>>>>>> false is incorrect, and that H(P,P) does *not* in fact perform a
>>>>>>>> correct simulation of its input because it aborts too soon.
>>>>>>>>
>>>>>>> It is very easy to verify the fact that the simulated input to
>>>>>>> H(P,P)
>>>>>>> would never stop unless aborted. It is pretty psychotic that many
>>>>>>> of my
>>>>>>> reviewers deny easily verified facts.
>>>>>>
>>>>>> There is no "unless". The fixed algorithm of H, which will
>>>>>> henceforth be referred to as Ha and similarly P will be referred
>>>>>> to as Pa, *does* abort.
>>>>> Which is *NOT* halting. A halting input must reach its own final
>>>>> state.
>>>>>> Because of this, Hb(Pa,Pa) explicitly shows that the simulated
>>>>>> input to Ha(Pa,Pa) *does* stop. The fact that Pn(Pn) does not halt
>>>>>> and that Hn(Pn,Pn) does not halt is irrelevant.
>>>>> It it not Hb(Pa,Pa) it is Hb(Px,Px). That P calls H makes it an
>>>>> entirely
>>>>> different input than Px that does not call Hb.
>>>>
>>>> No it is *exactly* Hb(Pa,Pa). The same encoding passed to Ha is
>>>> passed to Hb.
>>> You only have to do a correct execution trace of Ha(Pa,Pa) and Hb(Pa,Pa)
>>> to see that:
>>>
>>> The correctly simulated input to Ha(Pa,Pa) specifies infinitely nested
>>> simulation where as correctly simulated input to Hb(Pa,Pa) DOES NOT
>>> specify infinitely nested simulation.
>>
>> Hb(Pa,Pa) proves that Ha(Pa,Pa) does NOT perform a correct simulation.
> By looking at the actual execution trace of the simulation of Hb(Pa,Pa)
> and Ha(Pa,Pa) it is easy to determine that the simulations are correct
> on the basis of the x86 source code of Pa.

On 5/3/22 3:06 PM, Mr Flibble wrote:
> On Mon, 2 May 2022 20:40:13 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 5/2/22 7:30 PM, Mr Flibble wrote:
>>> On Mon, 2 May 2022 19:16:03 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 5/2/22 6:47 PM, Mr Flibble wrote:
>>>>> On Mon, 2 May 2022 18:46:00 -0400
>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>
>>>>>> On 5/2/22 6:38 PM, Mr Flibble wrote:
>>>>>>> On Mon, 2 May 2022 18:32:16 -0400
>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>
>>>>>>>> On 5/2/22 11:47 AM, Mr Flibble wrote:
>>>>>>>>> Not all infinitely recursive definitions are invalid however
>>>>>>>>> infinitely recursive definitions that arise out of a category
>>>>>>>>> error (as is the case with the halting problem) are invalid.
>>>>>>>>>
>>>>>>>>> The halting problem (as currently defined) is invalid due to
>>>>>>>>> the invalid "impossible program" [Strachey, 1965] that is
>>>>>>>>> actually impossible due to the category error present in its
>>>>>>>>> definition and *not* because of any function call-like
>>>>>>>>> recursion; confusion between these two types of recursion are
>>>>>>>>> why Olcott is having difficulty communicating his ideas with
>>>>>>>>> the rest of you shower.
>>>>>>>>>
>>>>>>>>> The categories involved in the category error are the decider
>>>>>>>>> and that which is being decided. Currently extant attempts to
>>>>>>>>> conflate the decider with that which is being decided are
>>>>>>>>> infinitely recursive and thus invalid.
>>>>>>>>>
>>>>>>>>> /Flibble
>>>>>>>>>
>>>>>>>>
>>>>>>>> Except that the "impossible program" isn't part of the
>>>>>>>> definition of the Halting Problem.
>>>>>>>
>>>>>>> It is according to [Wikipedia, 2022].
>>>>>>>
>>>>>>> /Flibble
>>>>>>>
>>>>>>
>>>>>> Nope, you comprehend worse that PO.
>>>>>>
>>>>>> Note, and Encyclopedic entery, like Wikipedia, is NOT just a
>>>>>> definition but a full article explaining the subject.
>>>>>>
>>>>>> Maybe if you look for a FORMAL source, that states what is the
>>>>>> ACTUAL definition, you would learn something.
>>>>>
>>>>> If Wikipedia is wrong then correct it and have your corrections
>>>>> reviewed; until then please shut the fuck up.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> It isn't that the article is "Wrong", it is a fairly good
>>>> Encyclpedic article. It just is that the first two paragraphs
>>>> aren't all a definition, and it doesn't say they are.
>>>
>>> The first two paragraphs define the halting problem as that is what
>>> the currently extant halting problem "proofs" are predicated on
>>> (and why they are invalid).
>>>
>>> /Flibble
>>>
>>
>> No, lets actually look at what is says, and parse it:
>>
>> 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.
>>
>> Jack Copeland attributes the introduction of the term halting problem
>> to the work of Martin Davis in the 1950s.[1]
>>
>>
>>
>> The FIRST SENTENCE is the definition of the Problem.
>>
>> The Second Sentence is the Theorem about it that says that no
>> solution exists.
>>
>> That ends the first paragraph.
>>
>> The Second Paragraph, is a continuation of the idea of the Second
>> Sentence, giving a summary of the proof that no solution exist.
>>
>> It is a category error to confuse the Statement of the Problem with
>> the Proof of the Theorem that not answer to the Problem exists.
>>
>> A Proof is NOT a Problem.
>
> Wrong; the wording in the third paragraph suggests the prior
> paragraphs refer to the halting problem itself, i.e. its definition.
>
> Stop playing word games. The halting problem as defined in [Wikipedia,
> 2022] is erroneous as it contains a category error in the form of an
> erroneous infinite recursion. The fact that currently extant halting
> problem proofs are predicated on this erroneous infinite recursion
> tells us that the second paragraph *is* part of the halting problem
> definition and thus are invalid.
>
> /Flibble
>

So the second sentence of the first paragraph is part of the definition,
so BY DEFINITON, no answer exists to the Halting Problem?

You can't say that paragraph 2 is part of the definiton and exclude the
end of paragraph 1.

The only reasonable parsing is:

Sentence 1: the Defintion of the Problem
Sentence 2: The Theorem about the Problem
Paragraph 2: A sketch of the proof of the Theorem
Paragraph 3: History of how it got its common name.

You confuse the "Halting Problem" with the Theorem about the Halting
Problem that states that no machine can exist to compute the answer to
the problem (and its proof).

On 5/3/22 2:13 PM, olcott wrote:
> On 5/3/2022 12:17 PM, Mikko wrote:
>> On 2022-05-03 14:38:57 +0000, olcott said:
>>
>>> On 5/3/2022 4:36 AM, Mikko wrote:
>>>> On 2022-05-02 16:18:36 +0000, olcott said:
>>>>
>>>>> It seems to me that all infinitely recursive definitions are
>>>>> invalid and I am having an excellent dialogue with some Prolog
>>>>> folks about this in comp.lang.prolog.
>>>>
>>>> One of the rules that define Prolog language is
>>>>
>>>>  arguments ::= argument | argument "," arguments
>>>>
>>>> which is infinitely recursive. Is it invalid? Is Prolog invalid because
>>>> of this and other infinitely recursive rules?
>>>>
>>>> Mikko
>>>>
>>>
>>> If would have to be invalid because it can never be resolved.
>>
>> What would be invalid? Prolog? Definition of Prolog?
>> Why "would be" and not "is"?
>>
>> Mikko
>>
>
> Failing a unify_with_occurs_check which would otherwise derive this:
>
> [trace]  ?- LP = \+(LP).
> LP =  (\+LP).
>
> [trace]  ?- LP.
> % ... 1,000,000 ............ 10,000,000 years later
> %
> %       >> 42 << (last release gives the question)
> [trace]  ?-
>

So, it just says that the question is beyond Prolog ability to process.

Doesn't mean it is an invalid logical sentence.

Prolog has a VERY limited form of logic, and can't express a LOT of true
propositions.

On 5/2/2022 6:10 PM, Ben wrote:
> olcott <polcott2@gmail.com> writes:
>
>> On 5/2/2022 11:39 AM, Ben wrote:
>>> olcott <polcott2@gmail.com> writes:
>>>
>>>> It is clear that the input to H(P,P) specifies infinitely nested
>>>> simulation to H.
>>> What two pointers must be passed to H for H to tell up about the halting
>>> of P(P)? If H can't report on the halting of the computation P(P) it is
>>> not a halt decider, and you have already told use that H(P,P) == false
>>> and that P(P) halts.
>>
>> If H can report on the halting of non-input P(P) then it is not a
>> decider because deciders only compute the mapping from inputs to final
>> states.
>
> TM deciders compute mappings from inputs to final states /according to
> some property of the inputs/

That par is exactly correct.

> -- whether the input represents, for

That part has been the key error of everyone in that they all believe
that is can represent something other than what it actually specifies.
The correct simulation of the input to H(P,P) specifies non-halting
behavior.

Clueless wonders that don't know the first thing about the x86 language
assume that this simulation is incorrect even though is is nearly
trivial to determine that the simulation is correct as a verified fact.

That they contradict verified facts entirely one the basis that they are
incompetent to verify that it is a fact is the worst hubris.

> example, an even number, a prime number or a halting computation.
>
> According to you there is no "input" (in reality a pair of pointers)
> that represents the halting computation P(P). Why should anyone care
> about this H if it does not decide what we want -- the halting of the
> function call represented by the two arguments to H? Whatever H is
> actually deciding is not interesting.

(a) H does correctly decide its input
(b) H is only required to decide its input.
(c) Therefore H(P,P) is entirely correct on the "impossible" input.

> Also, I wonder why you wasted so much time justifying the fact that
> H(P,P) == false "even though P(P) halts" when H(P,P) is, apparently, not
> even supposed to be deciding the halting P(P). Well, we know, of
> course. You realised you were in a hole so you started to dig sideways.
> You used to know that H(X,Y) had to decide the halting of X(Y). You're
> now pretending it never did!
>

>> That you expect a halt decider to compute the mapping from non-inputs
>> is a little nuts when you know that deciders can't possibly do this.
>
> Don't be silly. They decide properties of inputs -- parity, halting and
> so on. You'd know this if you'd done even the warm-up exercises I set.

The problem here is that you expect that the property of an input not be
the actual property of the actual input but the property of a non-input.

The halting property of the input to H(P,P) is the actual behavior of
the correct simulation of this input and thus not at all what you simply
imagine this property should be.

> How are they coming along? It looks like you have found an excuse to
> bail out again:
>

It is coming along great and it is wonderful fun.
I think that it is a great idea to move in this direction.
I may eventually convert C copy of the TM into a RASP machine.
I probably won't begin to do that until after we finish our exercises.

>> It turns out that I can create a whole TM interpreter from scratch
>> quicker than I can learn the extraneous complexity of the TM
>> Interpreter http://www.lns.mit.edu/~dsw/turing/turing.html
>
> I doubt it. But I suppose you think that's a reasonable excuse. Of
> course, some of us remember you saying writing such a thing would take
> about a week three years ago. I remember wondering how such a simple
> program could take you a week to write.

As soon as I complete the detailed design I should have an accurate
estimate of the total time. It currently looks like < 4 hours. I have
spent 15 minutes on the detailed design and it looks like it will take
45 more minutes.

One thing that is great is that I have fully recovered from what could
have been a life threatening infection. I was in the hospital getting IV
antibiotics for nearly two days. Chemotherapy patients have a few days
after chemotherapy where their immune system is very close to zero.

>
> Of course you don't need an interpreter to write E or specify P, but you
> must find some excuse for bailing out.
>

It is much better (and more fun) if I make this totally concrete.
One can not effectively debug code by desk checking.

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

On 2022-05-03 18:06:24 +0000, olcott said:

> On 5/3/2022 12:17 PM, Mikko wrote:
>> On 2022-05-03 14:38:57 +0000, olcott said:
>>
>>> On 5/3/2022 4:36 AM, Mikko wrote:
>>>> On 2022-05-02 16:18:36 +0000, olcott said:
>>>>
>>>>> It seems to me that all infinitely recursive definitions are invalid
>>>>> and I am having an excellent dialogue with some Prolog folks about this
>>>>> in comp.lang.prolog.
>>>>
>>>> One of the rules that define Prolog language is
>>>>
>>>>  arguments ::= argument | argument "," arguments
>>>>
>>>> which is infinitely recursive. Is it invalid? Is Prolog invalid because
>>>> of this and other infinitely recursive rules?
>>>>
>>>> Mikko
>>>>
>>>
>>> If would have to be invalid because it can never be resolved.
>>
>> What would be invalid? Prolog? Definition of Prolog?
>> Why "would be" and not "is"?
>>
>> Mikko
>>
>
> Expressions that cannot be resolved in Prolog that fail the
> unify_with_occurs_check test proves that these expressions are
> semantically incorrect.

No, it does not mean anything like that. It only means that no well founded
data structure matches both arguments.

For example, unify_with_occurs_check(1, 2) fails but there is nothing
sematically incorrect in 1, 2.

> It is generally the case that every expression of any natural of formal
> language that cannot be derived by applying truth preserving operations
> (such as Prolog rules) to expressions known to be true (such as Prolog
> facts) cannot possibly be correctly construed as true.
>
> Dogs are animals (purely analytic)
> There is a small dog in my living room right now (Empirical).
>
> This is true for the entire body of analytic knowledge which only
> excludes expressions of language that rely on sense data from the sense
> organs to verify truth.
>
> The proof that this is correct is that no counter-examples exist.
> When G is considered true and unprovable there is some way the "true"
> is derived, it is not merely a wild guess.
>
> Just like Prolog databases True is limited to a specific formal system,
> one formal system is the entire body of analytic knowledge: EBAK. This
> is an entirely different formal system than PA.
>
> unprovable in PA and true in EBAC is not the same thing as true and
> unprovable. unprovable in PA means not true in PA, and true in EBAC
> means provable in EBAC.

Nothing in this response is relevant to the responded message.
In particular, none of the simple questions were answered.

Mikko

On 2022-05-03 18:26:21 +0000, Mr Flibble said:

> On Tue, 3 May 2022 12:31:44 +0300
> Mikko <mikko.levanto@iki.fi> wrote:
>
>> On 2022-05-02 15:47:32 +0000, Mr Flibble said:
>>
>>> Not all infinitely recursive definitions are invalid however
>>> infinitely recursive definitions that arise out of a category error
>>> (as is the case with the halting problem) are invalid.
>>
>> An infinite recursion cannot arise out of a category error as the
>> recursion stops at the category error.
>
> Which is kind of my point: the category error is what makes the
> infinite recursion invalid thus rendering the halting problem
> definition itself invalid and any proofs predicated on it.

Category error does not make the infinite recursion invalid, just
irrelevant. The sentence containing the category error wourld be
invalid even whithout the infinite recursion.

There is no category error in the Halting problem. Neither Mr Flibble
nor anyone else has identified a word of wrong category in the problem.

Mikko

Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:

> Zero doesn't have a physical representation. So Roman numbers didn't have
> the concept.

I think this is a common myth. The concept of zero is quite different
from the numeral. The Romans used abacuses for calculations so there
was a very natural physical representation both for zero (an empty
counting board) and for zero counters in one or other column.

--
Ben.

olcott <polcott2@gmail.com> writes:

> Even infinitely recursive math expressions are semantically incorrect
> in that they can never be evaluated.

Someone with no education in mathematics makes a bold claim about
mathematical concepts without defining any of then, and for some reason
a discussion ensues on Usenet. Let me get snacks...

--
Ben.
"le génie humain a des limites, quand la bêtise humaine n’en a pas"
Alexandre Dumas (fils)

Python <python@example.invalid> writes:

> You cranks are really unsufferable idiots...

To make it more fun, play crank bingo. All cards include "category
error", "ad hominem" and "straw man" along with "I've answered that a
thousand times". The maths crank bingo card includes "isomorphic",
"0.999... =/= 1" and "Cantor". What else?

--
Ben.

On 04/05/2022 12:04, Ben wrote:
> Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:
>> Zero doesn't have a physical representation. So Roman numbers didn't have
>> the concept.
> I think this is a common myth. The concept of zero is quite different
> from the numeral. The Romans used abacuses for calculations so there
> was a very natural physical representation both for zero (an empty
> counting board) and for zero counters in one or other column.

Partly agreed. But there are other myths and confusions which are
quite near the surface in the above. Zero as a placeholder in a column of
an abacus is quite different from zero as a number. If you ask a farmer
how many sheep he has, he might say "four" or "216"; he is unlikely to
say "zero" [rather, "I don't have any sheep"], and [FWIW] very unlikely to
say "minus three". Even if 0 and -3 exist for some purposes, they were not
thought to be /numbers/ until relatively recently, whereas the answer to
"How many ...?" is expected to be a number. So 0 and -3 were as "nutty"
to most people, however useful in mathematics, as "i" is to PO and others
today. Luckily, I doubt whether PO has yet discovered "j" and "k" as
further square roots of -1, or his "nuttiness" would know no bounds; yet
quaternions are a natural route into [very practical!] relativity.

One of the problems with 0 as a number is that inventories and
other lists become ill-specified. It's one thing to say that this farm
has 216 sheep, 42 cows and three horses, but once you start adding in
that there are zero pigs, zero giraffes, zero unicorns, ..., where do
you stop?

Separately, there is a persistent myth that Roman numerals are
unsuitable for use in arithmetic. Not so. As long as your numbers don't
exceed a few thousand, they are as easy to use as Arabic numerals; and
for large/tiny numbers, you can do what everyone did until recently and
invent new units [such as acres rather than square yards].

--
Andy Walker, Nottingham.
Andy's music pages: www.cuboid.me.uk/andy/Music
Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Mozart,L

Andy Walker <anw@cuboid.co.uk> writes:

> On 04/05/2022 12:04, Ben wrote:
>> Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:
>>> Zero doesn't have a physical representation. So Roman numbers didn't have
>>> the concept.
>> I think this is a common myth. The concept of zero is quite different
>> from the numeral. The Romans used abacuses for calculations so there
>> was a very natural physical representation both for zero (an empty
>> counting board) and for zero counters in one or other column.
>
> Partly agreed. But there are other myths and confusions which are
> quite near the surface in the above. Zero as a placeholder in a column of
> an abacus is quite different from zero as a number.

I hope you don't think I implied they were the same. My point was that
the concept of zero things is very natural, even if it expressed without
that word.

> If you ask a farmer
> how many sheep he has, he might say "four" or "216"; he is unlikely to
> say "zero" [rather, "I don't have any sheep"], and [FWIW] very unlikely to
> say "minus three". Even if 0 and -3 exist for some purposes, they were not
> thought to be /numbers/ until relatively recently, whereas the answer to
> "How many ...?" is expected to be a number.

I think that some quite old Chinese, Indian and Mayan text would suggest
otherwise. Of course it's hard to cross the cultural chasm and work out
who had the concept of zero "as a number", but even if you don't rate my
interpretation of the textual evidence, every culture will have had an
answer to "how many sheep do you have now that they've all starved?".
Is that "none as a number"? I don't think that's an easy question to
answer.

> So 0 and -3 were as "nutty"
> to most people, however useful in mathematics, as "i" is to PO and others
> today. Luckily, I doubt whether PO has yet discovered "j" and "k" as
> further square roots of -1, or his "nuttiness" would know no bounds; yet
> quaternions are a natural route into [very practical!] relativity.
>
> One of the problems with 0 as a number is that inventories and
> other lists become ill-specified. It's one thing to say that this farm
> has 216 sheep, 42 cows and three horses, but once you start adding in
> that there are zero pigs, zero giraffes, zero unicorns, ..., where do
> you stop?
>
> Separately, there is a persistent myth that Roman numerals are
> unsuitable for use in arithmetic. Not so. As long as your numbers don't
> exceed a few thousand, they are as easy to use as Arabic numerals; and
> for large/tiny numbers, you can do what everyone did until recently and
> invent new units [such as acres rather than square yards].

Yes, and the calculations where often done with a place-holder abacus.
The subtractive notation for numbers like IX and IV was a relatively
late contraction and, I believe, not universally used even when it
became common for ceremonial use (for dates and names and the like).

--
Ben.

olcott <polcott2@gmail.com> writes:

> On 5/2/2022 6:10 PM, Ben wrote:
>> olcott <polcott2@gmail.com> writes:
>>
>>> On 5/2/2022 11:39 AM, Ben wrote:
>>>> olcott <polcott2@gmail.com> writes:
>>>>
>>>>> It is clear that the input to H(P,P) specifies infinitely nested
>>>>> simulation to H.
>>>> What two pointers must be passed to H for H to tell up about the halting
>>>> of P(P)? If H can't report on the halting of the computation P(P) it is
>>>> not a halt decider, and you have already told use that H(P,P) == false
>>>> and that P(P) halts.
>>>
>>> If H can report on the halting of non-input P(P) then it is not a
>>> decider because deciders only compute the mapping from inputs to final
>>> states.
>> TM deciders compute mappings from inputs to final states /according to
>> some property of the inputs/
>
> That par is exactly correct.
>
>> -- whether the input represents, for
>
> That part has been the key error of everyone in that they all believe
> that is can represent something other than what it actually specifies.

So now, after thinking otherwise for years, you claim that there is no
way to even specify the computation P(P) for you pseudo-C halt decider
H. At least that is a clear admission that the halting of function
calls like P(P) can not be decided because, apparently, passing P and P
to H does not specify that computation, and you can't say what two
arguments /would/ specify it.

A clear and unambiguous statement that no D such that D(X,Y) == true if
and only if X(Y) halts and false otherwise is possible would be the
honest way to move things on. If you were clear about this, maybe
someone will talk to you about whether it is that your H is deciding.

>> example, an even number, a prime number or a halting computation.
>> According to you there is no "input" (in reality a pair of pointers)
>> that represents the halting computation P(P). Why should anyone care
>> about this H if it does not decide what we want -- the halting of the
>> function call represented by the two arguments to H? Whatever H is
>> actually deciding is not interesting.
>
> (a) H does correctly decide its input

But no one cares about that as it's not what we want a decider for.

> (b) H is only required to decide its input.

And it seems that you agree that no D such that D(X,Y) == true if and
only if X(Y) halts and false otherwise is possible. That's the D that
the world cares about.

> (c) Therefore H(P,P) is entirely correct on the "impossible" input.

It decides some property of the pair of pointers P and P, but not the
one people care about: the halting or otherwise of the function call
P(P).

>> Also, I wonder why you wasted so much time justifying the fact that
>> H(P,P) == false "even though P(P) halts" when H(P,P) is, apparently, not
>> even supposed to be deciding the halting P(P). Well, we know, of
>> course. You realised you were in a hole so you started to dig sideways.
>> You used to know that H(X,Y) had to decide the halting of X(Y). You're
>> now pretending it never did!

Why /did/ you waste so much time trying to convince us that H(P,P) ==
false was correct even though P(P) halted if you never intended H(P,P)
to report on the halting of P(P)?

>> You'd know this if you'd done even the warm-up exercises I set.

<snip the usual waffle>

>> How are they coming along? It looks like you have found an excuse to
>> bail out again:
>
> It is coming along great and it is wonderful fun.

It's good that it's fun, but it seems to be taking a long time. I'd
expect students to be able to write E and specify P "live" in a tutorial
-- i.e. it would take a couple of minutes and we could the discuss more
interesting examples.

The specification of TM's is your stumbling block, so you could be doing
that in parallel.

> I think that it is a great idea to move in this direction.
> I may eventually convert C copy of the TM into a RASP machine.

Do ever read what you write? What is a "C copy of the TM"? I think you
mean the TM interpreter that you've decided to write so as to delay
actually writing even a trivial TM.

--
Ben.
"le génie humain a des limites, quand la bêtise humaine n’en a pas"
Alexandre Dumas (fils)

On 5/4/2022 6:15 AM, Ben wrote:
> olcott <polcott2@gmail.com> writes:
>
>> Even infinitely recursive math expressions are semantically incorrect
>> in that they can never be evaluated.
>
> Someone with no education in mathematics makes a bold claim about
> mathematical concepts without defining any of then, and for some reason
> a discussion ensues on Usenet. Let me get snacks...
>

I have spent thousands of hours on this point.
When the evaluation directed graph of an expression has an infinite
cycle. See page 4.

https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

On Tue, 3 May 2022 21:54:42 -0400
Richard Damon <Richard@Damon-Family.org> wrote:

> On 5/3/22 3:06 PM, Mr Flibble wrote:
> > On Mon, 2 May 2022 20:40:13 -0400
> > Richard Damon <Richard@Damon-Family.org> wrote:
> >
> >> On 5/2/22 7:30 PM, Mr Flibble wrote:
> >>> On Mon, 2 May 2022 19:16:03 -0400
> >>> Richard Damon <Richard@Damon-Family.org> wrote:
> >>>
> >>>> On 5/2/22 6:47 PM, Mr Flibble wrote:
> >>>>> On Mon, 2 May 2022 18:46:00 -0400
> >>>>> Richard Damon <Richard@Damon-Family.org> wrote:
> >>>>>
> >>>>>> On 5/2/22 6:38 PM, Mr Flibble wrote:
> >>>>>>> On Mon, 2 May 2022 18:32:16 -0400
> >>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
> >>>>>>>
> >>>>>>>> On 5/2/22 11:47 AM, Mr Flibble wrote:
> >>>>>>>>> Not all infinitely recursive definitions are invalid however
> >>>>>>>>> infinitely recursive definitions that arise out of a
> >>>>>>>>> category error (as is the case with the halting problem)
> >>>>>>>>> are invalid.
> >>>>>>>>>
> >>>>>>>>> The halting problem (as currently defined) is invalid due to
> >>>>>>>>> the invalid "impossible program" [Strachey, 1965] that is
> >>>>>>>>> actually impossible due to the category error present in its
> >>>>>>>>> definition and *not* because of any function call-like
> >>>>>>>>> recursion; confusion between these two types of recursion
> >>>>>>>>> are why Olcott is having difficulty communicating his ideas
> >>>>>>>>> with the rest of you shower.
> >>>>>>>>>
> >>>>>>>>> The categories involved in the category error are the
> >>>>>>>>> decider and that which is being decided. Currently extant
> >>>>>>>>> attempts to conflate the decider with that which is being
> >>>>>>>>> decided are infinitely recursive and thus invalid.
> >>>>>>>>>
> >>>>>>>>> /Flibble
> >>>>>>>>>
> >>>>>>>>
> >>>>>>>> Except that the "impossible program" isn't part of the
> >>>>>>>> definition of the Halting Problem.
> >>>>>>>
> >>>>>>> It is according to [Wikipedia, 2022].
> >>>>>>>
> >>>>>>> /Flibble
> >>>>>>>
> >>>>>>
> >>>>>> Nope, you comprehend worse that PO.
> >>>>>>
> >>>>>> Note, and Encyclopedic entery, like Wikipedia, is NOT just a
> >>>>>> definition but a full article explaining the subject.
> >>>>>>
> >>>>>> Maybe if you look for a FORMAL source, that states what is the
> >>>>>> ACTUAL definition, you would learn something.
> >>>>>
> >>>>> If Wikipedia is wrong then correct it and have your corrections
> >>>>> reviewed; until then please shut the fuck up.
> >>>>>
> >>>>> /Flibble
> >>>>>
> >>>>
> >>>> It isn't that the article is "Wrong", it is a fairly good
> >>>> Encyclpedic article. It just is that the first two paragraphs
> >>>> aren't all a definition, and it doesn't say they are.
> >>>
> >>> The first two paragraphs define the halting problem as that is
> >>> what the currently extant halting problem "proofs" are predicated
> >>> on (and why they are invalid).
> >>>
> >>> /Flibble
> >>>
> >>
> >> No, lets actually look at what is says, and parse it:
> >>
> >> 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.
> >>
> >> Jack Copeland attributes the introduction of the term halting
> >> problem to the work of Martin Davis in the 1950s.[1]
> >>
> >>
> >>
> >> The FIRST SENTENCE is the definition of the Problem.
> >>
> >> The Second Sentence is the Theorem about it that says that no
> >> solution exists.
> >>
> >> That ends the first paragraph.
> >>
> >> The Second Paragraph, is a continuation of the idea of the Second
> >> Sentence, giving a summary of the proof that no solution exist.
> >>
> >> It is a category error to confuse the Statement of the Problem with
> >> the Proof of the Theorem that not answer to the Problem exists.
> >>
> >> A Proof is NOT a Problem.
> >
> > Wrong; the wording in the third paragraph suggests the prior
> > paragraphs refer to the halting problem itself, i.e. its definition.
> >
> > Stop playing word games. The halting problem as defined in
> > [Wikipedia, 2022] is erroneous as it contains a category error in
> > the form of an erroneous infinite recursion. The fact that
> > currently extant halting problem proofs are predicated on this
> > erroneous infinite recursion tells us that the second paragraph
> > *is* part of the halting problem definition and thus are invalid.
> >
> > /Flibble
> >
>
> So the second sentence of the first paragraph is part of the
> definition, so BY DEFINITON, no answer exists to the Halting Problem?
>
> You can't say that paragraph 2 is part of the definiton and exclude
> the end of paragraph 1.
>
> The only reasonable parsing is:
>
> Sentence 1: the Defintion of the Problem
> Sentence 2: The Theorem about the Problem
> Paragraph 2: A sketch of the proof of the Theorem
> Paragraph 3: History of how it got its common name.
>
> You confuse the "Halting Problem" with the Theorem about the Halting
> Problem that states that no machine can exist to compute the answer
> to the problem (and its proof).

Sentence 2 merely states that Turing provided a proof: a proof is not a
theory, a proof proves a theory.

I see you wish to continue to play word games; I can play word games
too, and win.

If I accept your assertion as true (which is reasonable) then the facts
on the ground haven't actually changed: I merely have to make minor
modifications to my original assertion. See my "reprise #2" post which I
will post shortly.

/Flibble

On 5/4/2022 11:40 AM, Mr Flibble wrote:
> On Tue, 3 May 2022 21:54:42 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 5/3/22 3:06 PM, Mr Flibble wrote:
>>> On Mon, 2 May 2022 20:40:13 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 5/2/22 7:30 PM, Mr Flibble wrote:
>>>>> On Mon, 2 May 2022 19:16:03 -0400
>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>
>>>>>> On 5/2/22 6:47 PM, Mr Flibble wrote:
>>>>>>> On Mon, 2 May 2022 18:46:00 -0400
>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>
>>>>>>>> On 5/2/22 6:38 PM, Mr Flibble wrote:
>>>>>>>>> On Mon, 2 May 2022 18:32:16 -0400
>>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>>>
>>>>>>>>>> On 5/2/22 11:47 AM, Mr Flibble wrote:
>>>>>>>>>>> Not all infinitely recursive definitions are invalid however
>>>>>>>>>>> infinitely recursive definitions that arise out of a
>>>>>>>>>>> category error (as is the case with the halting problem)
>>>>>>>>>>> are invalid.
>>>>>>>>>>>
>>>>>>>>>>> The halting problem (as currently defined) is invalid due to
>>>>>>>>>>> the invalid "impossible program" [Strachey, 1965] that is
>>>>>>>>>>> actually impossible due to the category error present in its
>>>>>>>>>>> definition and *not* because of any function call-like
>>>>>>>>>>> recursion; confusion between these two types of recursion
>>>>>>>>>>> are why Olcott is having difficulty communicating his ideas
>>>>>>>>>>> with the rest of you shower.
>>>>>>>>>>>
>>>>>>>>>>> The categories involved in the category error are the
>>>>>>>>>>> decider and that which is being decided. Currently extant
>>>>>>>>>>> attempts to conflate the decider with that which is being
>>>>>>>>>>> decided are infinitely recursive and thus invalid.
>>>>>>>>>>>
>>>>>>>>>>> /Flibble
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Except that the "impossible program" isn't part of the
>>>>>>>>>> definition of the Halting Problem.
>>>>>>>>>
>>>>>>>>> It is according to [Wikipedia, 2022].
>>>>>>>>>
>>>>>>>>> /Flibble
>>>>>>>>>
>>>>>>>>
>>>>>>>> Nope, you comprehend worse that PO.
>>>>>>>>
>>>>>>>> Note, and Encyclopedic entery, like Wikipedia, is NOT just a
>>>>>>>> definition but a full article explaining the subject.
>>>>>>>>
>>>>>>>> Maybe if you look for a FORMAL source, that states what is the
>>>>>>>> ACTUAL definition, you would learn something.
>>>>>>>
>>>>>>> If Wikipedia is wrong then correct it and have your corrections
>>>>>>> reviewed; until then please shut the fuck up.
>>>>>>>
>>>>>>> /Flibble
>>>>>>>
>>>>>>
>>>>>> It isn't that the article is "Wrong", it is a fairly good
>>>>>> Encyclpedic article. It just is that the first two paragraphs
>>>>>> aren't all a definition, and it doesn't say they are.
>>>>>
>>>>> The first two paragraphs define the halting problem as that is
>>>>> what the currently extant halting problem "proofs" are predicated
>>>>> on (and why they are invalid).
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> No, lets actually look at what is says, and parse it:
>>>>
>>>> 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.
>>>>
>>>> Jack Copeland attributes the introduction of the term halting
>>>> problem to the work of Martin Davis in the 1950s.[1]
>>>>
>>>>
>>>>
>>>> The FIRST SENTENCE is the definition of the Problem.
>>>>
>>>> The Second Sentence is the Theorem about it that says that no
>>>> solution exists.
>>>>
>>>> That ends the first paragraph.
>>>>
>>>> The Second Paragraph, is a continuation of the idea of the Second
>>>> Sentence, giving a summary of the proof that no solution exist.
>>>>
>>>> It is a category error to confuse the Statement of the Problem with
>>>> the Proof of the Theorem that not answer to the Problem exists.
>>>>
>>>> A Proof is NOT a Problem.
>>>
>>> Wrong; the wording in the third paragraph suggests the prior
>>> paragraphs refer to the halting problem itself, i.e. its definition.
>>>
>>> Stop playing word games. The halting problem as defined in
>>> [Wikipedia, 2022] is erroneous as it contains a category error in
>>> the form of an erroneous infinite recursion. The fact that
>>> currently extant halting problem proofs are predicated on this
>>> erroneous infinite recursion tells us that the second paragraph
>>> *is* part of the halting problem definition and thus are invalid.
>>>
>>> /Flibble
>>>
>>
>> So the second sentence of the first paragraph is part of the
>> definition, so BY DEFINITON, no answer exists to the Halting Problem?
>>
>> You can't say that paragraph 2 is part of the definiton and exclude
>> the end of paragraph 1.
>>
>> The only reasonable parsing is:
>>
>> Sentence 1: the Defintion of the Problem
>> Sentence 2: The Theorem about the Problem
>> Paragraph 2: A sketch of the proof of the Theorem
>> Paragraph 3: History of how it got its common name.
>>
>> You confuse the "Halting Problem" with the Theorem about the Halting
>> Problem that states that no machine can exist to compute the answer
>> to the problem (and its proof).
>
> Sentence 2 merely states that Turing provided a proof: a proof is not a
> theory, a proof proves a theory.
>
> I see you wish to continue to play word games; I can play word games
> too, and win.
>
> If I accept your assertion as true (which is reasonable) then the facts
> on the ground haven't actually changed: I merely have to make minor
> modifications to my original assertion. See my "reprise #2" post which I
> will post shortly.
>
> /Flibble
>

I made this same mistake for many years.
Now I refer to the conventional HP proof counter-examples.

On 5/4/2022 2:19 AM, Mikko wrote:
> On 2022-05-03 18:06:24 +0000, olcott said:
>
>> On 5/3/2022 12:17 PM, Mikko wrote:
>>> On 2022-05-03 14:38:57 +0000, olcott said:
>>>
>>>> On 5/3/2022 4:36 AM, Mikko wrote:
>>>>> On 2022-05-02 16:18:36 +0000, olcott said:
>>>>>
>>>>>> It seems to me that all infinitely recursive definitions are
>>>>>> invalid and I am having an excellent dialogue with some Prolog
>>>>>> folks about this in comp.lang.prolog.
>>>>>
>>>>> One of the rules that define Prolog language is
>>>>>
>>>>>  arguments ::= argument | argument "," arguments
>>>>>
>>>>> which is infinitely recursive. Is it invalid? Is Prolog invalid
>>>>> because
>>>>> of this and other infinitely recursive rules?
>>>>>
>>>>> Mikko
>>>>>
>>>>
>>>> If would have to be invalid because it can never be resolved.
>>>
>>> What would be invalid? Prolog? Definition of Prolog?
>>> Why "would be" and not "is"?
>>>
>>> Mikko
>>>
>>
>> Expressions that cannot be resolved in Prolog that fail the
>> unify_with_occurs_check test proves that these expressions are
>> semantically incorrect.
>
> No, it does not mean anything like that. It only means that no well founded
> data structure matches both arguments.
>
> For example, unify_with_occurs_check(1, 2) fails but there is nothing
> sematically incorrect in 1, 2.
>

BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the
unification used in Resolution. Most Prolog systems will allow you to
satisfy goals like:

equal(X, X).
?- equal(foo(Y), Y).

that is, they will allow you to match a term against an uninstantiated
subterm of itself. In this example, foo(Y) is matched against Y, which
appears within it. As a result, Y will stand for foo(Y), which is
foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))),
and so on. So Y ends up standing for some kind of infinite structure.

<inserted for clarity>
foo(foo(foo(foo(foo(foo(foo(foo(foo(foo(foo(foo(...))))))))))))
</inserted for clarity>

Note that, whereas they may allow you to construct something like this,
most Prolog systems will not be able to write it out at the end.
According to the formal definition of Unification, this kind of
“infinite term” should never come to exist. Thus Prolog systems that
allow a term to match an uninstantiated subterm of itself do not act
correctly as Resolution theorem provers. In order to make them do so, we
would have to add a check that a variable cannot be instantiated to
something containing itself. Such a check, an occurs check, would be
straightforward to implement, but would slow down the execution of
Prolog programs considerably. Since it would only affect very few
programs, most implementors have simply left it out 1.

1 The Prolog standard states that the result is undefined if a Prolog
system attempts to match a term against an uninstantiated subterm of
itself, which means that programs which cause this to happen will not
be portable. A portable program should ensure that wherever an occurs
check might be applicable the built-in predicate
unify_with_occurs_check/2 is used explicitly instead of the normal
unification operation of the Prolog implementation. As its name
suggests, this predicate acts like =/2 except that it fails if an occurs
check detects an illegal attempt to instantiate a variable.
END:(Clocksin & Mellish 2003:254)

Clocksin, W.F. and Mellish, C.S. 2003. Programming in Prolog Using the
ISO Standard Fifth Edition, 254. Berlin Heidelberg: Springer-Verlag.

>> It is generally the case that every expression of any natural of
>> formal language that cannot be derived by applying truth preserving
>> operations (such as Prolog rules) to expressions known to be true
>> (such as Prolog facts) cannot possibly be correctly construed as true.
>>
>> Dogs are animals (purely analytic)
>> There is a small dog in my living room right now (Empirical).
>>
>> This is true for the entire body of analytic knowledge which only
>> excludes expressions of language that rely on sense data from the
>> sense organs to verify truth.
>>
>> The proof that this is correct is that no counter-examples exist.
>> When G is considered true and unprovable there is some way the "true"
>> is derived, it is not merely a wild guess.
>>
>> Just like Prolog databases True is limited to a specific formal
>> system, one formal system is the entire body of analytic knowledge:
>> EBAK. This is an entirely different formal system than PA.
>>
>> unprovable in PA and true in EBAC is not the same thing as true and
>> unprovable. unprovable in PA means not true in PA, and true in EBAC
>> means provable in EBAC.
>
> Nothing in this response is relevant to the responded message.
> In particular, none of the simple questions were answered.
>
> Mikko
>

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

On 5/4/2022 2:31 AM, Mikko wrote:
> On 2022-05-03 18:26:21 +0000, Mr Flibble said:
>
>> On Tue, 3 May 2022 12:31:44 +0300
>> Mikko <mikko.levanto@iki.fi> wrote:
>>
>>> On 2022-05-02 15:47:32 +0000, Mr Flibble said:
>>>
>>>> Not all infinitely recursive definitions are invalid however
>>>> infinitely recursive definitions that arise out of a category error
>>>> (as is the case with the halting problem) are invalid.
>>>
>>> An infinite recursion cannot arise out of a category error as the
>>> recursion stops at the category error.
>>
>> Which is kind of my point: the category error is what makes the
>> infinite recursion invalid thus rendering the halting problem
>> definition itself invalid and any proofs predicated on it.
>
> Category error does not make the infinite recursion invalid, just
> irrelevant. The sentence containing the category error wourld be
> invalid even whithout the infinite recursion.
>

Infinite recursion prevents an expression of language from being a logic
sentence.

https://en.wikipedia.org/wiki/Sentence_(mathematical_logic)#:~:text=In%20mathematical%20logic%2C%20a%20sentence,must%20be%20true%20or%20false.

When we try to evaluate an expression of language that is not a logic
sentence / truth bearer for its truth value that is just like asking:
Is this banana true?

> There is no category error in the Halting problem. Neither Mr Flibble
> nor anyone else has identified a word of wrong category in the problem.
>
> Mikko
>

Flibble was very helpful with his use of the term Category Error here is
one very great way to apply it:

There is certainly a category error in:
(a) The formalized Liar Paradox
(b) Gödel 1931 Incompleteness
(c) 1936 Tarski undefinability

In each of these cases the respective LP, G, and P are assumed to belong
in the category of logic sentence, and they do not actually belong in
this category.

In English only declarative sentences have a truth value. Trying to
determine the truth value of an interrogatory sentence is a category
error. Likewise the same error occurs when trying to determine the truth
value of an expression of formal language that is not a logic sentence.

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

On 5/4/2022 9:16 AM, Ben wrote:
> olcott <polcott2@gmail.com> writes:
>
>> On 5/2/2022 6:10 PM, Ben wrote:
>>> olcott <polcott2@gmail.com> writes:
>>>
>>>> On 5/2/2022 11:39 AM, Ben wrote:
>>>>> olcott <polcott2@gmail.com> writes:
>>>>>
>>>>>> It is clear that the input to H(P,P) specifies infinitely nested
>>>>>> simulation to H.
>>>>> What two pointers must be passed to H for H to tell up about the halting
>>>>> of P(P)? If H can't report on the halting of the computation P(P) it is
>>>>> not a halt decider, and you have already told use that H(P,P) == false
>>>>> and that P(P) halts.
>>>>
>>>> If H can report on the halting of non-input P(P) then it is not a
>>>> decider because deciders only compute the mapping from inputs to final
>>>> states.
>>> TM deciders compute mappings from inputs to final states /according to
>>> some property of the inputs/
>>
>> That par is exactly correct.
>>
>>> -- whether the input represents, for
>>
>> That part has been the key error of everyone in that they all believe
>> that is can represent something other than what it actually specifies.
>
> So now, after thinking otherwise for years, you claim that there is no
> way to even specify the computation P(P) for you pseudo-C halt decider
> H. At least that is a clear admission that the halting of function
> calls like P(P) can not be decided because, apparently, passing P and P
> to H does not specify that computation, and you can't say what two
> arguments /would/ specify it.
>
> A clear and unambiguous statement that no D such that D(X,Y) == true if
> and only if X(Y) halts and false otherwise is possible would be the
> honest way to move things on. If you were clear about this, maybe
> someone will talk to you about whether it is that your H is deciding.
>

I adapted my system so that I could empirically test this:
H1(P,P)==true is empirically proven to be correct
H(P,P)==false is empirically proven to be correct

Both deciders correctly report on the actual behavior of their actual
input. This can be verified by carefully studying their execution trace.

>>> example, an even number, a prime number or a halting computation.
>>> According to you there is no "input" (in reality a pair of pointers)
>>> that represents the halting computation P(P). Why should anyone care
>>> about this H if it does not decide what we want -- the halting of the
>>> function call represented by the two arguments to H? Whatever H is
>>> actually deciding is not interesting.
>>
>> (a) H does correctly decide its input
>
> But no one cares about that as it's not what we want a decider for.
>
>> (b) H is only required to decide its input.
>
> And it seems that you agree that no D such that D(X,Y) == true if and
> only if X(Y) halts and false otherwise is possible. That's the D that
> the world cares about.
>
>> (c) Therefore H(P,P) is entirely correct on the "impossible" input.
>
> It decides some property of the pair of pointers P and P, but not the
> one people care about: the halting or otherwise of the function call
> P(P).
>
>>> Also, I wonder why you wasted so much time justifying the fact that
>>> H(P,P) == false "even though P(P) halts" when H(P,P) is, apparently, not
>>> even supposed to be deciding the halting P(P). Well, we know, of
>>> course. You realised you were in a hole so you started to dig sideways.
>>> You used to know that H(X,Y) had to decide the halting of X(Y). You're
>>> now pretending it never did!
>
> Why /did/ you waste so much time trying to convince us that H(P,P) ==
> false was correct even though P(P) halted if you never intended H(P,P)
> to report on the halting of P(P)?
>
>>> You'd know this if you'd done even the warm-up exercises I set.
>
> <snip the usual waffle>
>
>>> How are they coming along? It looks like you have found an excuse to
>>> bail out again:
>>
>> It is coming along great and it is wonderful fun.
>
> It's good that it's fun, but it seems to be taking a long time. I'd
> expect students to be able to write E and specify P "live" in a tutorial
> -- i.e. it would take a couple of minutes and we could the discuss more
> interesting examples.

I have had some serious health issues that could have killed me last week.

>
> The specification of TM's is your stumbling block, so you could be doing
> that in parallel.

I like to go through all of the best steps in order. Having a machine to
execute TM's is the first step.

(a) Deciding to get around to start this project took weeks when dealing
with my other issues.

(b) No setting up the tedious syntax of reading a file of text lines
took much longer than usual, I usually cut-and-paste.

(c) I studied enough of the
http://www.lns.mit.edu/~dsw/turing/turing.html
To realize it was a superb architecture yet an overly complex
implementation.

Other people can read much faster than me, yet they lose a lot of
meaning when they read this fast. I usually read something over and over
until I have 100% complete understanding.

When I was reading the specs for how VISA changed their system so that I
could adapt the bank's system to meet these changed specs I had to read
the VISA material 17 times. I only had to read the Discover card changes
three times.

>
>> I think that it is a great idea to move in this direction.
>> I may eventually convert C copy of the TM into a RASP machine.
>
> Do ever read what you write? What is a "C copy of the TM"? I think you
> mean the TM interpreter that you've decided to write so as to delay
> actually writing even a trivial TM.
>

I am going to write a TM interpreter in C++. Sometime after I get done
with this I may adapt it to becoming an RASP machine. I will keep the
original TM interpreter and not simply overwrite it with the RASP
machine. This requires that the changes must be to a copy of the TM
interpreter.

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer