On 4/4/2022 5:41 PM, wij wrote:
> On Tuesday, 5 April 2022 at 06:32:34 UTC+8, olcott wrote:
>> On 4/4/2022 5:23 PM, wij wrote:
>>> On Tuesday, 5 April 2022 at 04:47:42 UTC+8, olcott wrote:
>>>> On 4/4/2022 3:36 PM, olcott wrote:
>>>>> On 4/4/2022 2:51 PM, Ben Bacarisse wrote:
>>>>>> olcott <No...@NoWhere.com> writes:
>>>>>>
>>>>>>> On 4/4/2022 11:23 AM, Ben Bacarisse wrote:
>>>>>>>> olcott <No...@NoWhere.com> writes:
>>>>>>>>
>>>>>>>>> On 4/4/2022 10:32 AM, Ben Bacarisse wrote:
>>>>>>>>>> olcott <No...@NoWhere.com> writes:
>>>>>>>>>>
>>>>>>>>>>> On 4/4/2022 5:14 AM, Ben Bacarisse wrote:
>>>>>>>>>>>> olcott <No...@NoWhere.com> writes:
>>>>>>>>>>>>
>>>>>>>>>>>>> On 4/3/2022 8:14 PM, Ben Bacarisse wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>>> It might be time to skip ahead because the next exercise is to
>>>>>>>>>>>>>> do the
>>>>>>>>>>>>>> same for P, a TM that decides if a string encodes a prime
>>>>>>>>>>>>>> number. Can
>>>>>>>>>>>>>> you think of how to specify that without giving an algorithm?
>>>>>>>>>>>>>> P.q0 ??? ⊦* P.qy if ???
>>>>>>>>>>>>>> P.q0 ??? ⊦* P.qn otherwise.
>>>>>>>>>>>>>> (The three ??? won't all be the same things.) Any idea how to
>>>>>>>>>>>>>> flesh
>>>>>>>>>>>>>> this out? If you can, you will be able to do it for E very
>>>>>>>>>>>>>> easily too.
>>>>>>>>>>>>>
>>>>>>>>>>>>> P.q0 S ⊦* P.qy if Is-Prime-Number(S)
>>>>>>>>>>>>> P.q0 S ⊦* P.qn otherwise.
>>>>>>>>>>>> That's getting close. We know, from how the notation works,
>>>>>>>>>>>> that S is a
>>>>>>>>>>>> string of symbols in the TM's alphabet. But writing
>>>>>>>>>>>> Is-Prime-Number(S)
>>>>>>>>>>>> suggests that is not natural language. That's a very hard route
>>>>>>>>>>>> to go
>>>>>>>>>>>> down. I'd have to ask you for the definition of Is-Prime-Number.
>>>>>>>>>>>> Defining it symbolically is messy and if the definition is /not/
>>>>>>>>>>>> formal,
>>>>>>>>>>>> dressing the definition up with a formal-looking name is just
>>>>>>>>>>>> superficial.
>>>>>>>>>>>
>>>>>>>>>>> It goes through some tedious steps to see if it is a prime number:
>>>>>>>>>>>
>>>>>>>>>>> A prime number is a natural number greater than 1 that is not a
>>>>>>>>>>> product of two smaller natural numbers.
>>>>>>>>>> We've hit a bit of a road-block rather sooner that I had expected.
>>>>>>>>>> First off, there's no need to define what a prime number is. If
>>>>>>>>>> at some
>>>>>>>>>> point it turns out that your readers do not know, go ahead and define
>>>>>>>>>> it, but it's too widely understood by comp.theory readers to bother
>>>>>>>>>> about.
>>>>>>>>>> But writing (as I think you are suggesting)
>>>>>>>>>> P.q0 S ⊦* P.qy it goes through some tedious steps to see
>>>>>>>>>> if it is a
>>>>>>>>>> prime number
>>>>>>>>>> is not really adequate. There are two 'it'. To what do they refer?
>>>>>>>>>
>>>>>>>>> You told me to make sure that I do not provide an algorithm.
>>>>>>>> Yes, that good. You didn't.
>>>>>>>> Now, to what do the two 'it's refer?
>>>>>>
>>>>>> OK, maybe things have gone too far already, but why are you ignoring my
>>>>>> questions? Your phrase used 'it' twice. What did you intend to refer
>>>>>> to by these two pronouns? It was not an idle question. I think when
>>>>>> you answer it, at least one problem will become clear.
>>>>>>
>>>>>>>>> This is somewhat algorithmic:
>>>>>>>> No, no. The non-algorithmic way is best. You should be able to
>>>>>>>> specific what a computation does even when yo have no idea how to write
>>>>>>>> the an algorithm to do it. Sometimes there isn't ad algorithm!
>>>>>>>>
>>>>>>>>>> and nothing in P.q0 S ⊦* P.qy is a number so there is nothing
>>>>>>>>>> there to
>>>>>>>>>> be a prime number.
>>>>>>>>>> Can you see how you (a) make it shorter, (b) make it clearer?
>>>>>>>> My reply has three questions in it (depending on how you count) but you
>>>>>>>> didn't answer any of them. This will only work if you try to answer
>>>>>>>> these questions. Sometimes the answer will be "I don't know what you
>>>>>>>> mean", but that's a perfectly good answer.
>>>>>>>
>>>>>>> Anything besides the bare function name is somewhat algorithmic so
>>>>>>> what you are asking for seems impossible.
>>>>>>
>>>>>> Here's a supporting exercise. Write down at least half a dozen strings
>>>>>> that might be passed to P. At least one of them should be a string that
>>>>>> P must accept and at least one must be a string the P should reject, but
>>>>>> you should say, for each one, whether P accepts of rejects it.
>>>>>>
>>>>>> Be prepared for me to raise questions about what the strings represent.
>>>>>> It's easy to assume conventions from everyday life that should be stated
>>>>>> explicitly. You must have come across this in software: "the manual
>>>>>> said the input should be a number but it went wrong for सहस्र."
>>>>>>
>>>>>> Finally, don't fuss about the prime bit. Just use the word prime.
>>>>>> Everyone one knows what it means. The key thing here is to state /what/
>>>>>> must be prime for P to correctly accept a string.
>>>>>>
>>>>>
>>>>> I am estimating that we will finally achieve closure on this.
>>>>> Creating a common language between us will achieve the basis for mutual
>>>>> understanding.
>>>>>
>>>> The process that we are doing looks like it will be effective on the
>>>> basis of eliminating all hidden assumptions.
>>>> --
>>>> Copyright 2022 Pete Olcott
>>>>
>>>> "Talent hits a target no one else can hit;
>>>> Genius hits a target no one else can see."
>>>> Arthur Schopenhauer
>>>
>>> No use. Even all the people you find agree with you is still useless. To claim
>>> you solved the HP problem, you have to show ALL your H first. People cannot
>>> judge or teach 'claims'. But your P already showed wrong, no need to publish H.
>> My analysis is based on this model: If "an X is a Y" and Z says that "an
>> X is a Y" then anything in the universe that disagrees is necessarily
>> incorrect.
>>
>> "an X is a Y" =
>> The input to embedded_H specifies a non-halting sequence of
>> configurations. (input is non-halting)
>>
>> Z says that "an X is a Y" =
>> embedded_H rejects its input.
>>
>> If you can think of a case where
>> "an X is a Y" is simultaneously true and false then you have a rebuttal,
>> otherwise not so much.
>> --
>> Copyright 2022 Pete Olcott
>>
>> "Talent hits a target no one else can hit;
>> Genius hits a target no one else can see."
>> Arthur Schopenhauer
>
> You simply do not have H. What you say? If you say yes, then show it to prove.

Whether or not I have H is moot at this point in the dialogue, the Linz
proof is refuted either way.

Showing that an H is possible and answering Ben's question will be
postponed until after it is fully understood that embedded_H is
necessarily correct to reject its input: ⟨Ĥ⟩ ⟨Ĥ⟩.

--
Copyright 2022 Pete Olcott

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