On 7/10/22 8:55 AM, wij wrote:
> On Sunday, 10 July 2022 at 04:21:34 UTC+8, Andy Walker wrote:
>> On 09/07/2022 20:21, Malcolm McLean wrote:
>>> Humans seem to be able to do things that Turing machines can't.
>> Well, of course. We can sing and dance, cook, go to parties,
>> etc., etc. But in terms of effective computations, not so much. We're
>> in Church-Turing territory. AFAIK, there is no evidence at all that
>> things we could [eg] imagine robots being programmed to do differ in
>> any interesting [visible] way from the things humans do; but it all
>> depends on your view of the Chinese Room [thought] experiment. None
>> of that is relevant to the things usually being discussed here; there
>> is no evidence [none, nil, nada] that the standard theory of the HP is
>> in any way wrong. People who nevertheless waste their time trying to
>> construct halt deciders [or near equivalents thereto] are barking at
>> the moon. Nothing to see here, move along.
>> --
>> Andy Walker, Nottingham.
>> Andy's music pages: www.cuboid.me.uk/andy/Music
>> Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Balakirev
>
> The sentence "No halt decider exists" may be misleading without further
> understanding (Bacon classified as knowledge of/from market place, theater...).
> The HP proof only proves in its definition. It does not rule out a H (in its definition)
> of 99.999...% accuracy, which is desirable in practice. In theory, well, that depends.
> People learning by rote (most knowledge is hear and say, school, the education
> system?) usually has such synoptic tendency that we all have, more or less.
> (like the 0.999... problem and infinity, seems only I understand more,:-))

Yes, the definition of a Halt Decider in the theory is a Turing Machine
that with 100% accuracy decides for EVERY Turing Machine and Input.

That is the type of Halt Decider wanted in Computation Theory. Deciders
that are just almost always right, or always right but only handle
"most" machines aren't really interesting to the theory, even if they
might be useful for many "practical" applications.

In Mathematics, there is a vast gulf between things that are ALWAYS, and
things that are SOMETIMES (and often little difference between 0.001%
and 99.999% for sometimes).

On Sunday, 10 July 2022 at 13:19:08 UTC+1, Ben Bacarisse wrote:
> Ben Bacarisse <ben.u...@bsb.me.uk> writes:
>
> > Malcolm McLean <malcolm.ar...@gmail.com> writes:
> >
> >> Humans seem to be able to do things that Turing machines can't. So it's
> >> possible that the Turing machine isn't the last word in symbol
> >> processing.
> >
> > What sort of thing are you thinking of here?
> Jeff's reply may a derailed things. I really did want to know what sort
> of human symbol processing you were thinking of here. I'm sure we'll
> disagree but, as always, I'm curious about what facts led to you making
> that statement.
>
One feature of computer programming is that hard problems (for a human)
are easy, easy problems are hard. If you ask the average person to solve
an equation, they would glaze over and say that you need high intelligence
and many years of maths education to do that. If you ask them to look at
a series of pictures and pick out the ones with dogs in them, that's easy.

To get a computer to do the same problems, and the difficulty is
reversed.

So it's reasonable to suppose that humans and computers work in fundamentally
different ways. That's particularly true when we get to natural language. We
code natural language using a discrete set of symbols, so reading and writing
is definitely a "symbol processing exercise" (it's less clear when you consider spoken
language). Computers can't do it. You can sometimes create the illusion that
the computer is speaking, like with Eliza, but all it does is throw your own words
back at you, "tell me about your father" "pink unicorns must be important to you",
and so on. And you can have a tinned "abort, retry, fail?" dialogue. But it can't
actually talk, as you soon realise.

On 7/11/2022 7:11 AM, Malcolm McLean wrote:
> On Sunday, 10 July 2022 at 13:19:08 UTC+1, Ben Bacarisse wrote:
>> Ben Bacarisse <ben.u...@bsb.me.uk> writes:
>>
>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>
>>>> Humans seem to be able to do things that Turing machines can't. So it's
>>>> possible that the Turing machine isn't the last word in symbol
>>>> processing.
>>>
>>> What sort of thing are you thinking of here?
>> Jeff's reply may a derailed things. I really did want to know what sort
>> of human symbol processing you were thinking of here. I'm sure we'll
>> disagree but, as always, I'm curious about what facts led to you making
>> that statement.
>>
> One feature of computer programming is that hard problems (for a human)
> are easy, easy problems are hard. If you ask the average person to solve
> an equation, they would glaze over and say that you need high intelligence
> and many years of maths education to do that. If you ask them to look at
> a series of pictures and pick out the ones with dogs in them, that's easy.
>
> To get a computer to do the same problems, and the difficulty is
> reversed.
>
> So it's reasonable to suppose that humans and computers work in fundamentally
> different ways. That's particularly true when we get to natural language. We
> code natural language using a discrete set of symbols, so reading and writing
> is definitely a "symbol processing exercise" (it's less clear when you consider spoken
> language). Computers can't do it. You can sometimes create the illusion that
> the computer is speaking, like with Eliza, but all it does is throw your own words
> back at you, "tell me about your father" "pink unicorns must be important to you",
> and so on. And you can have a tinned "abort, retry, fail?" dialogue. But it can't
> actually talk, as you soon realise.
>

The cyc project encodes human knowledge in its knowledge tree.

--
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 Monday, 11 July 2022 at 14:26:43 UTC+1, olcott wrote:
> On 7/11/2022 7:11 AM, Malcolm McLean wrote:
> > On Sunday, 10 July 2022 at 13:19:08 UTC+1, Ben Bacarisse wrote:
> >> Ben Bacarisse <ben.u...@bsb.me.uk> writes:
> >>
> >>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
> >>>
> >>>> Humans seem to be able to do things that Turing machines can't. So it's
> >>>> possible that the Turing machine isn't the last word in symbol
> >>>> processing.
> >>>
> >>> What sort of thing are you thinking of here?
> >> Jeff's reply may a derailed things. I really did want to know what sort
> >> of human symbol processing you were thinking of here. I'm sure we'll
> >> disagree but, as always, I'm curious about what facts led to you making
> >> that statement.
> >>
> > One feature of computer programming is that hard problems (for a human)
> > are easy, easy problems are hard. If you ask the average person to solve
> > an equation, they would glaze over and say that you need high intelligence
> > and many years of maths education to do that. If you ask them to look at
> > a series of pictures and pick out the ones with dogs in them, that's easy.
> >
> > To get a computer to do the same problems, and the difficulty is
> > reversed.
> >
> > So it's reasonable to suppose that humans and computers work in fundamentally
> > different ways. That's particularly true when we get to natural language. We
> > code natural language using a discrete set of symbols, so reading and writing
> > is definitely a "symbol processing exercise" (it's less clear when you consider spoken
> > language). Computers can't do it. You can sometimes create the illusion that
> > the computer is speaking, like with Eliza, but all it does is throw your own words
> > back at you, "tell me about your father" "pink unicorns must be important to you",
> > and so on. And you can have a tinned "abort, retry, fail?" dialogue. But it can't
> > actually talk, as you soon realise.
> >
> The cyc project encodes human knowledge in its knowledge tree.
>

‘Girl number twenty unable to define a horse!’ said Mr. Gradgrind, for the general behoof of all the little pitchers. ‘Girl number twenty possessed of no facts, in reference to one of the commonest of animals! Some boy’s definition of a horse. Bitzer, yours.’

....

‘Bitzer,’ said Thomas Gradgrind. ‘Your definition of a horse.’

‘Quadruped. Graminivorous. Forty teeth, namely twenty-four grinders, four eye-teeth, and twelve incisive. Sheds coat in the spring; in marshy countries, sheds hoofs, too. Hoofs hard, but requiring to be shod with iron. Age known by marks in mouth.’ Thus (and much more) Bitzer.

‘Now girl number twenty,’ said Mr. Gradgrind. ‘You know what a horse is.’

On Monday, 11 July 2022 at 09:25:19 UTC+8, richar...@gmail.com wrote:
> On 7/10/22 8:55 AM, wij wrote:
> > On Sunday, 10 July 2022 at 04:21:34 UTC+8, Andy Walker wrote:
> >> On 09/07/2022 20:21, Malcolm McLean wrote:
> >>> Humans seem to be able to do things that Turing machines can't.
> >> Well, of course. We can sing and dance, cook, go to parties,
> >> etc., etc. But in terms of effective computations, not so much. We're
> >> in Church-Turing territory. AFAIK, there is no evidence at all that
> >> things we could [eg] imagine robots being programmed to do differ in
> >> any interesting [visible] way from the things humans do; but it all
> >> depends on your view of the Chinese Room [thought] experiment. None
> >> of that is relevant to the things usually being discussed here; there
> >> is no evidence [none, nil, nada] that the standard theory of the HP is
> >> in any way wrong. People who nevertheless waste their time trying to
> >> construct halt deciders [or near equivalents thereto] are barking at
> >> the moon. Nothing to see here, move along.
> >> --
> >> Andy Walker, Nottingham.
> >> Andy's music pages: www.cuboid.me.uk/andy/Music
> >> Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Balakirev
> >
> > The sentence "No halt decider exists" may be misleading without further
> > understanding (Bacon classified as knowledge of/from market place, theater...).
> > The HP proof only proves in its definition. It does not rule out a H (in its definition)
> > of 99.999...% accuracy, which is desirable in practice. In theory, well, that depends.
> > People learning by rote (most knowledge is hear and say, school, the education
> > system?) usually has such synoptic tendency that we all have, more or less.
> > (like the 0.999... problem and infinity, seems only I understand more,:-))
> Yes, the definition of a Halt Decider in the theory is a Turing Machine
> that with 100% accuracy decides for EVERY Turing Machine and Input.
>
> That is the type of Halt Decider wanted in Computation Theory. Deciders
> that are just almost always right, or always right but only handle
> "most" machines aren't really interesting to the theory, even if they
> might be useful for many "practical" applications.
>
> In Mathematics, there is a vast gulf between things that are ALWAYS, and
> things that are SOMETIMES (and often little difference between 0.001%
> and 99.999% for sometimes).

I know the conventional HP proofs are 100% correct.

The intent was asking YOU for possible ways(tricks) to refute the HP.

On 11/07/2022 14:54, wij wrote:
[to RD:]
> I know the conventional HP proofs are 100% correct.
> The intent was asking YOU for possible ways(tricks) to refute the HP.

If something is "100% correct", then, by construction, everyone would
be wasting their time trying to refute it. If you mean something else, such
as "are there useful subsets of programs/data for which the HP can be solved",
then everyone here already knows that the answer is "yes". If ever it is
proved that "P /= NP", then much the same will apply to polynomial algorithms
for NP-complete problems; people already solve "Travelling Salesman" problems
efficiently every day.

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

On 10/07/2022 19:34, wij wrote:
> My eccentric math. is improving everyday (not in a hurry to develop it) while
> you standstill with only 'eccentric' in mind.

Not so. I know a /lot/ of maths now of which I had not the slightest
notion either when I was a student or even when I embarked on my career as a
university lecturer. This includes great swathes of [in particular] graph
theory, statistics and algebra that was not on even a postgraduate syllabus
in my time; but also such things as complexity theory, fractals and the
surreals that are more recent inventions. None of that material comes from
a "standstill", and only a tiny part was ever considered "eccentric" [or
"wrong"] even at the time; the more usual reaction was "Oh, interesting,
what happens if ...", or "Can that be integrated with the theory of ...",
and similar.

Produce something interesting, and I [and perhaps others here] will
be interested. Produce something plainly wrong, and someone here will point
out the mistake. The incidence of mistakes would be greatly reduced if
you and others had a better idea of what is already known. Maths [and CS]
at the research level is a very different subject from what was taught in
schools when you were young. Even if you are still young.

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

On 7/11/22 9:54 AM, wij wrote:
> On Monday, 11 July 2022 at 09:25:19 UTC+8, richar...@gmail.com wrote:
>> On 7/10/22 8:55 AM, wij wrote:
>>> On Sunday, 10 July 2022 at 04:21:34 UTC+8, Andy Walker wrote:
>>>> On 09/07/2022 20:21, Malcolm McLean wrote:
>>>>> Humans seem to be able to do things that Turing machines can't.
>>>> Well, of course. We can sing and dance, cook, go to parties,
>>>> etc., etc. But in terms of effective computations, not so much. We're
>>>> in Church-Turing territory. AFAIK, there is no evidence at all that
>>>> things we could [eg] imagine robots being programmed to do differ in
>>>> any interesting [visible] way from the things humans do; but it all
>>>> depends on your view of the Chinese Room [thought] experiment. None
>>>> of that is relevant to the things usually being discussed here; there
>>>> is no evidence [none, nil, nada] that the standard theory of the HP is
>>>> in any way wrong. People who nevertheless waste their time trying to
>>>> construct halt deciders [or near equivalents thereto] are barking at
>>>> the moon. Nothing to see here, move along.
>>>> --
>>>> Andy Walker, Nottingham.
>>>> Andy's music pages: www.cuboid.me.uk/andy/Music
>>>> Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Balakirev
>>>
>>> The sentence "No halt decider exists" may be misleading without further
>>> understanding (Bacon classified as knowledge of/from market place, theater...).
>>> The HP proof only proves in its definition. It does not rule out a H (in its definition)
>>> of 99.999...% accuracy, which is desirable in practice. In theory, well, that depends.
>>> People learning by rote (most knowledge is hear and say, school, the education
>>> system?) usually has such synoptic tendency that we all have, more or less.
>>> (like the 0.999... problem and infinity, seems only I understand more,:-))
>> Yes, the definition of a Halt Decider in the theory is a Turing Machine
>> that with 100% accuracy decides for EVERY Turing Machine and Input.
>>
>> That is the type of Halt Decider wanted in Computation Theory. Deciders
>> that are just almost always right, or always right but only handle
>> "most" machines aren't really interesting to the theory, even if they
>> might be useful for many "practical" applications.
>>
>> In Mathematics, there is a vast gulf between things that are ALWAYS, and
>> things that are SOMETIMES (and often little difference between 0.001%
>> and 99.999% for sometimes).
>
> I know the conventional HP proofs are 100% correct.
>
> The intent was asking YOU for possible ways(tricks) to refute the HP.

As Andy said, if the proof is correct, why do you expect someone to put
effort trying to refute it?

Peter is wasting a lot of time on that because, due to is other mistaken
beliefs, he can't allow himself to accept the Halt Problem results,
because it shows that he is wrong.

Yes, there are ways you could alter the definition of the Halting
Problem to allow that modified Halting Problem to be possibly
"solvable", but such alternatives aren't actually interesting for
Computation Theory.

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

> On Sunday, 10 July 2022 at 13:19:08 UTC+1, Ben Bacarisse wrote:
>> Ben Bacarisse <ben.u...@bsb.me.uk> writes:
>>
>> > Malcolm McLean <malcolm.ar...@gmail.com> writes:
>> >
>> >> Humans seem to be able to do things that Turing machines can't. So it's
>> >> possible that the Turing machine isn't the last word in symbol
>> >> processing.
>> >
>> > What sort of thing are you thinking of here?
>> Jeff's reply may a derailed things. I really did want to know what sort
>> of human symbol processing you were thinking of here. I'm sure we'll
>> disagree but, as always, I'm curious about what facts led to you making
>> that statement.
>>
> One feature of computer programming is that hard problems (for a human)
> are easy, easy problems are hard. If you ask the average person to solve
> an equation, they would glaze over and say that you need high intelligence
> and many years of maths education to do that. If you ask them to look at
> a series of pictures and pick out the ones with dogs in them, that's easy.
>
> To get a computer to do the same problems, and the difficulty is
> reversed.
>
> So it's reasonable to suppose that humans and computers work in
> fundamentally different ways. That's particularly true when we get to
> natural language. We code natural language using a discrete set of
> symbols, so reading and writing is definitely a "symbol processing
> exercise" (it's less clear when you consider spoken
> language). Computers can't do it.

Ah, I thought you were making a theoretical point about Turing
machines, not a practical one about current hardware and software.

--
Ben.

On Tuesday, 12 July 2022 at 02:05:26 UTC+1, Ben Bacarisse wrote:
> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>
> > On Sunday, 10 July 2022 at 13:19:08 UTC+1, Ben Bacarisse wrote:
> >> Ben Bacarisse <ben.u...@bsb.me.uk> writes:
> >>
> >> > Malcolm McLean <malcolm.ar...@gmail.com> writes:
> >> >
> >> >> Humans seem to be able to do things that Turing machines can't. So it's
> >> >> possible that the Turing machine isn't the last word in symbol
> >> >> processing.
> >> >
> >> > What sort of thing are you thinking of here?
> >> Jeff's reply may a derailed things. I really did want to know what sort
> >> of human symbol processing you were thinking of here. I'm sure we'll
> >> disagree but, as always, I'm curious about what facts led to you making
> >> that statement.
> >>
> > One feature of computer programming is that hard problems (for a human)
> > are easy, easy problems are hard. If you ask the average person to solve
> > an equation, they would glaze over and say that you need high intelligence
> > and many years of maths education to do that. If you ask them to look at
> > a series of pictures and pick out the ones with dogs in them, that's easy.
> >
> > To get a computer to do the same problems, and the difficulty is
> > reversed.
> >
> > So it's reasonable to suppose that humans and computers work in
> > fundamentally different ways. That's particularly true when we get to
> > natural language. We code natural language using a discrete set of
> > symbols, so reading and writing is definitely a "symbol processing
> > exercise" (it's less clear when you consider spoken
> > language). Computers can't do it.
> Ah, I thought you were making a theoretical point about Turing
> machines, not a practical one about current hardware and software.
>
Some people think that you can scale up current hardware to solve
these problems. We know that the central nervous system is massively
parallel, which current computers only have a few parallel elements.
So maybe by using parallel algorithms we can build computers that talk.

But that doesn't seem to be the case..

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

> On Tuesday, 12 July 2022 at 02:05:26 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>> > On Sunday, 10 July 2022 at 13:19:08 UTC+1, Ben Bacarisse wrote:
>> >> Ben Bacarisse <ben.u...@bsb.me.uk> writes:
>> >>
>> >> > Malcolm McLean <malcolm.ar...@gmail.com> writes:
>> >> >
>> >> >> Humans seem to be able to do things that Turing machines can't. So it's
>> >> >> possible that the Turing machine isn't the last word in symbol
>> >> >> processing.
>> >> >
>> >> > What sort of thing are you thinking of here?
>> >> Jeff's reply may a derailed things. I really did want to know what sort
>> >> of human symbol processing you were thinking of here. I'm sure we'll
>> >> disagree but, as always, I'm curious about what facts led to you making
>> >> that statement.
>> >>
>> > One feature of computer programming is that hard problems (for a human)
>> > are easy, easy problems are hard. If you ask the average person to solve
>> > an equation, they would glaze over and say that you need high intelligence
>> > and many years of maths education to do that. If you ask them to look at
>> > a series of pictures and pick out the ones with dogs in them, that's easy.
>> >
>> > To get a computer to do the same problems, and the difficulty is
>> > reversed.
>> >
>> > So it's reasonable to suppose that humans and computers work in
>> > fundamentally different ways. That's particularly true when we get to
>> > natural language. We code natural language using a discrete set of
>> > symbols, so reading and writing is definitely a "symbol processing
>> > exercise" (it's less clear when you consider spoken
>> > language). Computers can't do it.
>> Ah, I thought you were making a theoretical point about Turing
>> machines, not a practical one about current hardware and software.
>>
> Some people think that you can scale up current hardware to solve
> these problems.

I often don't know what to make of your remarks. I'm not really
interested in what some people think about future hardware.

I thought you were making a point about a finite state, unbounded
storage model of computation and human cognitive abilities, but I don't
think you were.

--
Ben.

On Tuesday, 12 July 2022 at 11:08:21 UTC+1, Ben Bacarisse wrote:
> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>
> > On Tuesday, 12 July 2022 at 02:05:26 UTC+1, Ben Bacarisse wrote:
> >> Malcolm McLean <malcolm.ar...@gmail.com> writes:
> >>
> >> > On Sunday, 10 July 2022 at 13:19:08 UTC+1, Ben Bacarisse wrote:
> >> >> Ben Bacarisse <ben.u...@bsb.me.uk> writes:
> >> >>
> >> >> > Malcolm McLean <malcolm.ar...@gmail.com> writes:
> >> >> >
> >> >> >> Humans seem to be able to do things that Turing machines can't. So it's
> >> >> >> possible that the Turing machine isn't the last word in symbol
> >> >> >> processing.
> >> >> >
> >> >> > What sort of thing are you thinking of here?
> >> >> Jeff's reply may a derailed things. I really did want to know what sort
> >> >> of human symbol processing you were thinking of here. I'm sure we'll
> >> >> disagree but, as always, I'm curious about what facts led to you making
> >> >> that statement.
> >> >>
> >> > One feature of computer programming is that hard problems (for a human)
> >> > are easy, easy problems are hard. If you ask the average person to solve
> >> > an equation, they would glaze over and say that you need high intelligence
> >> > and many years of maths education to do that. If you ask them to look at
> >> > a series of pictures and pick out the ones with dogs in them, that's easy.
> >> >
> >> > To get a computer to do the same problems, and the difficulty is
> >> > reversed.
> >> >
> >> > So it's reasonable to suppose that humans and computers work in
> >> > fundamentally different ways. That's particularly true when we get to
> >> > natural language. We code natural language using a discrete set of
> >> > symbols, so reading and writing is definitely a "symbol processing
> >> > exercise" (it's less clear when you consider spoken
> >> > language). Computers can't do it.
> >> Ah, I thought you were making a theoretical point about Turing
> >> machines, not a practical one about current hardware and software.
> >>
> > Some people think that you can scale up current hardware to solve
> > these problems.
> I often don't know what to make of your remarks. I'm not really
> interested in what some people think about future hardware.
>
> I thought you were making a point about a finite state, unbounded
> storage model of computation and human cognitive abilities, but I don't
> think you were.
>
The central nervous system is massively parallel whilst Turing machines are
single-threaded. However you can convert any parallel algorithm to a
single-threaded algorithm.
It has been proposed that the reason that computers can't match human
cognitive abilities is that the algorithms are not parallel enough. Whilst theoretically
this is nothing to do with hardware, in practice of course it is, because you can't
be hanging around for the results.

What I am saying is that it doesn't seem to be the case that by making the
Turing machine bigger and the symbols on the tape more complicated, to
emulate things like artificial neural networks, you can match humans, or
indeed animals. Minds seem to work on a fundamentally different principle.
Evidence for this is that many easy problems (for minds) are hard for computers,
whilst many problems that are hard, for minds, are easy for computers.
However what that principle is, I don't know.

On 7/12/22 7:20 AM, Malcolm McLean wrote:
> On Tuesday, 12 July 2022 at 11:08:21 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>>> On Tuesday, 12 July 2022 at 02:05:26 UTC+1, Ben Bacarisse wrote:
>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>>
>>>>> On Sunday, 10 July 2022 at 13:19:08 UTC+1, Ben Bacarisse wrote:
>>>>>> Ben Bacarisse <ben.u...@bsb.me.uk> writes:
>>>>>>
>>>>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>>>>>
>>>>>>>> Humans seem to be able to do things that Turing machines can't. So it's
>>>>>>>> possible that the Turing machine isn't the last word in symbol
>>>>>>>> processing.
>>>>>>>
>>>>>>> What sort of thing are you thinking of here?
>>>>>> Jeff's reply may a derailed things. I really did want to know what sort
>>>>>> of human symbol processing you were thinking of here. I'm sure we'll
>>>>>> disagree but, as always, I'm curious about what facts led to you making
>>>>>> that statement.
>>>>>>
>>>>> One feature of computer programming is that hard problems (for a human)
>>>>> are easy, easy problems are hard. If you ask the average person to solve
>>>>> an equation, they would glaze over and say that you need high intelligence
>>>>> and many years of maths education to do that. If you ask them to look at
>>>>> a series of pictures and pick out the ones with dogs in them, that's easy.
>>>>>
>>>>> To get a computer to do the same problems, and the difficulty is
>>>>> reversed.
>>>>>
>>>>> So it's reasonable to suppose that humans and computers work in
>>>>> fundamentally different ways. That's particularly true when we get to
>>>>> natural language. We code natural language using a discrete set of
>>>>> symbols, so reading and writing is definitely a "symbol processing
>>>>> exercise" (it's less clear when you consider spoken
>>>>> language). Computers can't do it.
>>>> Ah, I thought you were making a theoretical point about Turing
>>>> machines, not a practical one about current hardware and software.
>>>>
>>> Some people think that you can scale up current hardware to solve
>>> these problems.
>> I often don't know what to make of your remarks. I'm not really
>> interested in what some people think about future hardware.
>>
>> I thought you were making a point about a finite state, unbounded
>> storage model of computation and human cognitive abilities, but I don't
>> think you were.
>>
> The central nervous system is massively parallel whilst Turing machines are
> single-threaded. However you can convert any parallel algorithm to a
> single-threaded algorithm.
> It has been proposed that the reason that computers can't match human
> cognitive abilities is that the algorithms are not parallel enough. Whilst theoretically
> this is nothing to do with hardware, in practice of course it is, because you can't
> be hanging around for the results.
>
> What I am saying is that it doesn't seem to be the case that by making the
> Turing machine bigger and the symbols on the tape more complicated, to
> emulate things like artificial neural networks, you can match humans, or
> indeed animals. Minds seem to work on a fundamentally different principle.
> Evidence for this is that many easy problems (for minds) are hard for computers,
> whilst many problems that are hard, for minds, are easy for computers.
>
> However what that principle is, I don't know.
>
>

One possible answer is that "Thought" isn't a deterministic process, but
a randomized one. Running many parrallel random processes does make it
so that if the answer is likely found, then at least one of the
parrallel processes will find it, so things seem at least mostly
deterministic.

On Tuesday, 12 July 2022 at 12:45:14 UTC+1, richar...@gmail.com wrote:
> On 7/12/22 7:20 AM, Malcolm McLean wrote:
> > On Tuesday, 12 July 2022 at 11:08:21 UTC+1, Ben Bacarisse wrote:
> >> Malcolm McLean <malcolm.ar...@gmail.com> writes:
> >>
> >>> On Tuesday, 12 July 2022 at 02:05:26 UTC+1, Ben Bacarisse wrote:
> >>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
> >>>>
> >>>>> On Sunday, 10 July 2022 at 13:19:08 UTC+1, Ben Bacarisse wrote:
> >>>>>> Ben Bacarisse <ben.u...@bsb.me.uk> writes:
> >>>>>>
> >>>>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
> >>>>>>>
> >>>>>>>> Humans seem to be able to do things that Turing machines can't. So it's
> >>>>>>>> possible that the Turing machine isn't the last word in symbol
> >>>>>>>> processing.
> >>>>>>>
> >>>>>>> What sort of thing are you thinking of here?
> >>>>>> Jeff's reply may a derailed things. I really did want to know what sort
> >>>>>> of human symbol processing you were thinking of here. I'm sure we'll
> >>>>>> disagree but, as always, I'm curious about what facts led to you making
> >>>>>> that statement.
> >>>>>>
> >>>>> One feature of computer programming is that hard problems (for a human)
> >>>>> are easy, easy problems are hard. If you ask the average person to solve
> >>>>> an equation, they would glaze over and say that you need high intelligence
> >>>>> and many years of maths education to do that. If you ask them to look at
> >>>>> a series of pictures and pick out the ones with dogs in them, that's easy.
> >>>>>
> >>>>> To get a computer to do the same problems, and the difficulty is
> >>>>> reversed.
> >>>>>
> >>>>> So it's reasonable to suppose that humans and computers work in
> >>>>> fundamentally different ways. That's particularly true when we get to
> >>>>> natural language. We code natural language using a discrete set of
> >>>>> symbols, so reading and writing is definitely a "symbol processing
> >>>>> exercise" (it's less clear when you consider spoken
> >>>>> language). Computers can't do it.
> >>>> Ah, I thought you were making a theoretical point about Turing
> >>>> machines, not a practical one about current hardware and software.
> >>>>
> >>> Some people think that you can scale up current hardware to solve
> >>> these problems.
> >> I often don't know what to make of your remarks. I'm not really
> >> interested in what some people think about future hardware.
> >>
> >> I thought you were making a point about a finite state, unbounded
> >> storage model of computation and human cognitive abilities, but I don't
> >> think you were.
> >>
> > The central nervous system is massively parallel whilst Turing machines are
> > single-threaded. However you can convert any parallel algorithm to a
> > single-threaded algorithm.
> > It has been proposed that the reason that computers can't match human
> > cognitive abilities is that the algorithms are not parallel enough. Whilst theoretically
> > this is nothing to do with hardware, in practice of course it is, because you can't
> > be hanging around for the results.
> >
> > What I am saying is that it doesn't seem to be the case that by making the
> > Turing machine bigger and the symbols on the tape more complicated, to
> > emulate things like artificial neural networks, you can match humans, or
> > indeed animals. Minds seem to work on a fundamentally different principle.
> > Evidence for this is that many easy problems (for minds) are hard for computers,
> > whilst many problems that are hard, for minds, are easy for computers.
> >
> > However what that principle is, I don't know.
> >
> >
> One possible answer is that "Thought" isn't a deterministic process, but
> a randomized one. Running many parrallel random processes does make it
> so that if the answer is likely found, then at least one of the
> parrallel processes will find it, so things seem at least mostly
> deterministic.
>
Yes, that would be a simple way in which a mind differs from a Turing machine.
And it's obviously true on some level. Your attention is caught by a leaf
blowing in the breeze, and your train of thought goes off in a different
direction.
Gerald Edelman suggested that the mind worked by having many circuits
competing for control. He called it "Neural Darwinism". Basically random
solutions compete, and the best one wins.

On 7/12/2022 6:20 AM, Malcolm McLean wrote:
> On Tuesday, 12 July 2022 at 11:08:21 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>>> On Tuesday, 12 July 2022 at 02:05:26 UTC+1, Ben Bacarisse wrote:
>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>>
>>>>> On Sunday, 10 July 2022 at 13:19:08 UTC+1, Ben Bacarisse wrote:
>>>>>> Ben Bacarisse <ben.u...@bsb.me.uk> writes:
>>>>>>
>>>>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>>>>>
>>>>>>>> Humans seem to be able to do things that Turing machines can't. So it's
>>>>>>>> possible that the Turing machine isn't the last word in symbol
>>>>>>>> processing.
>>>>>>>
>>>>>>> What sort of thing are you thinking of here?
>>>>>> Jeff's reply may a derailed things. I really did want to know what sort
>>>>>> of human symbol processing you were thinking of here. I'm sure we'll
>>>>>> disagree but, as always, I'm curious about what facts led to you making
>>>>>> that statement.
>>>>>>
>>>>> One feature of computer programming is that hard problems (for a human)
>>>>> are easy, easy problems are hard. If you ask the average person to solve
>>>>> an equation, they would glaze over and say that you need high intelligence
>>>>> and many years of maths education to do that. If you ask them to look at
>>>>> a series of pictures and pick out the ones with dogs in them, that's easy.
>>>>>
>>>>> To get a computer to do the same problems, and the difficulty is
>>>>> reversed.
>>>>>
>>>>> So it's reasonable to suppose that humans and computers work in
>>>>> fundamentally different ways. That's particularly true when we get to
>>>>> natural language. We code natural language using a discrete set of
>>>>> symbols, so reading and writing is definitely a "symbol processing
>>>>> exercise" (it's less clear when you consider spoken
>>>>> language). Computers can't do it.
>>>> Ah, I thought you were making a theoretical point about Turing
>>>> machines, not a practical one about current hardware and software.
>>>>
>>> Some people think that you can scale up current hardware to solve
>>> these problems.
>> I often don't know what to make of your remarks. I'm not really
>> interested in what some people think about future hardware.
>>
>> I thought you were making a point about a finite state, unbounded
>> storage model of computation and human cognitive abilities, but I don't
>> think you were.
>>
> The central nervous system is massively parallel whilst Turing machines are
> single-threaded. However you can convert any parallel algorithm to a
> single-threaded algorithm.
> It has been proposed that the reason that computers can't match human
> cognitive abilities is that the algorithms are not parallel enough. Whilst theoretically
> this is nothing to do with hardware, in practice of course it is, because you can't
> be hanging around for the results.
>

That is the dead end that neural network programming took.
The actual issue is that we must have something like Doug Lenat's cyc
project where all human knowledge has been transformed into HOL.
The deep learning algorithms are currently very terrible at learning the
meaning of words.

> What I am saying is that it doesn't seem to be the case that by making the
> Turing machine bigger and the symbols on the tape more complicated, to
> emulate things like artificial neural networks, you can match humans, or
> indeed animals. Minds seem to work on a fundamentally different principle.
> Evidence for this is that many easy problems (for minds) are hard for computers,
> whilst many problems that are hard, for minds, are easy for computers.
>
> However what that principle is, I don't know.
>
>

--
Copyright 2022 Pete Olcott

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

Demented bigot Peter Olcott wrote:
....
> The deep learning algorithms are currently very terrible at learning the
> meaning of words.

You and them do have a point in common then.

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

> On Tuesday, 12 July 2022 at 11:08:21 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>> > On Tuesday, 12 July 2022 at 02:05:26 UTC+1, Ben Bacarisse wrote:
>> >> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>> >>
>> >> > On Sunday, 10 July 2022 at 13:19:08 UTC+1, Ben Bacarisse wrote:
>> >> >> Ben Bacarisse <ben.u...@bsb.me.uk> writes:
>> >> >>
>> >> >> > Malcolm McLean <malcolm.ar...@gmail.com> writes:
>> >> >> >
>> >> >> >> Humans seem to be able to do things that Turing machines can't. So it's
>> >> >> >> possible that the Turing machine isn't the last word in symbol
>> >> >> >> processing.
>> >> >> >
>> >> >> > What sort of thing are you thinking of here?
>> >> >> Jeff's reply may a derailed things. I really did want to know what sort
>> >> >> of human symbol processing you were thinking of here. I'm sure we'll
>> >> >> disagree but, as always, I'm curious about what facts led to you making
>> >> >> that statement.
>> >> >>
>> >> > One feature of computer programming is that hard problems (for a human)
>> >> > are easy, easy problems are hard. If you ask the average person to solve
>> >> > an equation, they would glaze over and say that you need high intelligence
>> >> > and many years of maths education to do that. If you ask them to look at
>> >> > a series of pictures and pick out the ones with dogs in them, that's easy.
>> >> >
>> >> > To get a computer to do the same problems, and the difficulty is
>> >> > reversed.
>> >> >
>> >> > So it's reasonable to suppose that humans and computers work in
>> >> > fundamentally different ways. That's particularly true when we get to
>> >> > natural language. We code natural language using a discrete set of
>> >> > symbols, so reading and writing is definitely a "symbol processing
>> >> > exercise" (it's less clear when you consider spoken
>> >> > language). Computers can't do it.
>> >> Ah, I thought you were making a theoretical point about Turing
>> >> machines, not a practical one about current hardware and software.
>> >>
>> > Some people think that you can scale up current hardware to solve
>> > these problems.
>> I often don't know what to make of your remarks. I'm not really
>> interested in what some people think about future hardware.
>>
>> I thought you were making a point about a finite state, unbounded
>> storage model of computation and human cognitive abilities, but I don't
>> think you were.
>>
> The central nervous system is massively parallel whilst Turing machines are
> single-threaded.

But since a TM has no notion of time, this hardly matters. TMs are
about what's possible.

> However you can convert any parallel algorithm to a single-threaded
> algorithm. It has been proposed that the reason that computers can't
> match human cognitive abilities is that the algorithms are not
> parallel enough. Whilst theoretically this is nothing to do with
> hardware, in practice of course it is, because you can't be hanging
> around for the results.

There's no "hanging around" with a TM.

> What I am saying is that it doesn't seem to be the case that by making the
> Turing machine bigger and the symbols on the tape more complicated, to
> emulate things like artificial neural networks, you can match humans, or
> indeed animals.

What symbol processing task do you have in mind when you say this, and
how do you reach this conclusion?

Consider just the tiny TMs with, say, 10^100 states and 2 symbols. How
many distinct TMs are there of this size? How do you know that none of
these can perform the symbol processing you had in mind when you made
the remark that caught my attention?

> Minds seem to work on a fundamentally different principle.

It seems to me a trivial remark that a warm, wet collection of cells,
works in a fundamentally different way that a mathematical abstraction,
but your original remark was about tasks. I took that to mean that some
comparison was possible because you were thinking about something
abstract ("symbol processing") that both wet brains and mathematical TMs
"do".

> Evidence for this is that many easy problems (for minds) are hard for
> computers, whilst many problems that are hard, for minds, are easy for
> computers.

Do you mean TMs when you say computers? If so, you seem to be confusing
what is TM computable with what we know how to program. To limit what
task are TM computable to those that our puny brains can devise
algorithms for is a kind of begging the question.

--
Ben.

On Wednesday, 13 July 2022 at 02:29:13 UTC+1, Ben Bacarisse wrote:
> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>
> > On Tuesday, 12 July 2022 at 11:08:21 UTC+1, Ben Bacarisse wrote:
> >> Malcolm McLean <malcolm.ar...@gmail.com> writes:
> >>
> >> > On Tuesday, 12 July 2022 at 02:05:26 UTC+1, Ben Bacarisse wrote:
> >> >> Malcolm McLean <malcolm.ar...@gmail.com> writes:
> >> >>
> >> >> > On Sunday, 10 July 2022 at 13:19:08 UTC+1, Ben Bacarisse wrote:
> >> >> >> Ben Bacarisse <ben.u...@bsb.me.uk> writes:
> >> >> >>
> >> >> >> > Malcolm McLean <malcolm.ar...@gmail.com> writes:
> >> >> >> >
> >> >> >> >> Humans seem to be able to do things that Turing machines can't. So it's
> >> >> >> >> possible that the Turing machine isn't the last word in symbol
> >> >> >> >> processing.
> >> >> >> >
> >> >> >> > What sort of thing are you thinking of here?
> >> >> >> Jeff's reply may a derailed things. I really did want to know what sort
> >> >> >> of human symbol processing you were thinking of here. I'm sure we'll
> >> >> >> disagree but, as always, I'm curious about what facts led to you making
> >> >> >> that statement.
> >> >> >>
> >> >> > One feature of computer programming is that hard problems (for a human)
> >> >> > are easy, easy problems are hard. If you ask the average person to solve
> >> >> > an equation, they would glaze over and say that you need high intelligence
> >> >> > and many years of maths education to do that. If you ask them to look at
> >> >> > a series of pictures and pick out the ones with dogs in them, that's easy.
> >> >> >
> >> >> > To get a computer to do the same problems, and the difficulty is
> >> >> > reversed.
> >> >> >
> >> >> > So it's reasonable to suppose that humans and computers work in
> >> >> > fundamentally different ways. That's particularly true when we get to
> >> >> > natural language. We code natural language using a discrete set of
> >> >> > symbols, so reading and writing is definitely a "symbol processing
> >> >> > exercise" (it's less clear when you consider spoken
> >> >> > language). Computers can't do it.
> >> >> Ah, I thought you were making a theoretical point about Turing
> >> >> machines, not a practical one about current hardware and software.
> >> >>
> >> > Some people think that you can scale up current hardware to solve
> >> > these problems.
> >> I often don't know what to make of your remarks. I'm not really
> >> interested in what some people think about future hardware.
> >>
> >> I thought you were making a point about a finite state, unbounded
> >> storage model of computation and human cognitive abilities, but I don't
> >> think you were.
> >>
> > The central nervous system is massively parallel whilst Turing machines are
> > single-threaded.
> But since a TM has no notion of time, this hardly matters. TMs are
> about what's possible.
> > However you can convert any parallel algorithm to a single-threaded
> > algorithm. It has been proposed that the reason that computers can't
> > match human cognitive abilities is that the algorithms are not
> > parallel enough. Whilst theoretically this is nothing to do with
> > hardware, in practice of course it is, because you can't be hanging
> > around for the results.
> There's no "hanging around" with a TM.
>
Of course there is. You build it, and set it running, and some time later it
comes back with the results. Or never stops. Time is inherent in the model.
>
> > What I am saying is that it doesn't seem to be the case that by making the
> > Turing machine bigger and the symbols on the tape more complicated, to
> > emulate things like artificial neural networks, you can match humans, or
> > indeed animals.
> What symbol processing task do you have in mind when you say this, and
> how do you reach this conclusion?
>
An example would be image recognition. So, for the sake of argument, the task
is to recognise a dog. Now we can create a set of 512 x 512 rgb images, and
say the the "dog function" is to return "true" for those images that show dogs,
and false for those that don't.
Now some initial comments. The way we have framed the task is suitable for
Turing machines. For humans, it's rather artificial. Humans recognise dogs all
the time, but they don't sit in front of stacks of identically framed images, classifying
them. And an on the ball human will tell you that whilst there are images that
clearly show dogs, and images that clearly don't, there are also marginal cases.
They can explain why a case is marginal, but they can't easily assign a number
0.0 to 1.0 to say how marginal the image is. If you specify that the Turing machine
explain why marginal cases are marginal, you've blown up the problem into something
else entirely.

Another question is whether we mean images of dogs, or images containing dogs.
The difference is that in an image of a dog, the dog is the central element in the
image. That's easy enough for humans to understand. A Turing machine can't
easily make the distinction.

Anyway, we can build a Turing machine that can have a reasonable shot at the dog
recognition problem. Since the problem is finite, there must exist a machine which
classifies all possible images in the set as we want, but that's not helpful to us.
Clearly a real classifier cannot work by brute force. And humans recognise dogs
easily - even mentally disabled humans can usually do this task - and with
only a few presentations. Turing machines that attempt dog recongition are very
hard to build, and typically they do one of two things. Either they have a massive
database of training images pre-classified by a human, or they use a trick by
focusing in on certain characteristics of dog images - eyes are easy to recognise,
for example, and then you can draw a triangle to the nose. However whilst the trick
will usually work, it will fail on images that are clearly non-dog, but have the eyes
and nose relationship.

Basically the Turing machine dog classifier doesn't work a bit like the human
dog classifier, and it's clearly inferior.
Now is that because, as you suggest, that we just don't know enough about how
the human system works, and we could imitate it with sufficient knowledge
and a sufficiently big Turing machine? Or is it because what the human is doing
fundamentally cannot be reduced to Turing machine-like mechanical operations?

> > Evidence for this is that many easy problems (for minds) are hard for
> > computers, whilst many problems that are hard, for minds, are easy for
> > computers.
> Do you mean TMs when you say computers? If so, you seem to be confusing
> what is TM computable with what we know how to program. To limit what
> task are TM computable to those that our puny brains can devise
> algorithms for is a kind of begging the question.
>
It is kind of. If we can produce a Turing machine that computes a function,
then we know that that function is computable. If we can't, but we can't
prove that no such machine exists, you can always say that "the machine
exists but you lack the skills to construct it". However if don't really know
how to even set about building the machine, then to claim to know the
fundamental mathematical principle on which such a machine would work
is to claim an understanding of the way the world works that you don't
really have.

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

> On Wednesday, 13 July 2022 at 02:29:13 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>> > On Tuesday, 12 July 2022 at 11:08:21 UTC+1, Ben Bacarisse wrote:
>> >> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>> >>
>> >> > On Tuesday, 12 July 2022 at 02:05:26 UTC+1, Ben Bacarisse wrote:
>> >> >> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>> >> >>
>> >> >> > On Sunday, 10 July 2022 at 13:19:08 UTC+1, Ben Bacarisse wrote:
>> >> >> >> Ben Bacarisse <ben.u...@bsb.me.uk> writes:
>> >> >> >>
>> >> >> >> > Malcolm McLean <malcolm.ar...@gmail.com> writes:
>> >> >> >> >
>> >> >> >> >> Humans seem to be able to do things that Turing machines can't. So it's
>> >> >> >> >> possible that the Turing machine isn't the last word in symbol
>> >> >> >> >> processing.
>> >> >> >> >
>> >> >> >> > What sort of thing are you thinking of here?
>> >> >> >> Jeff's reply may a derailed things. I really did want to know what sort
>> >> >> >> of human symbol processing you were thinking of here. I'm sure we'll
>> >> >> >> disagree but, as always, I'm curious about what facts led to you making
>> >> >> >> that statement.
>> >> >> >>
>> >> >> > One feature of computer programming is that hard problems (for a human)
>> >> >> > are easy, easy problems are hard. If you ask the average person to solve
>> >> >> > an equation, they would glaze over and say that you need high intelligence
>> >> >> > and many years of maths education to do that. If you ask them to look at
>> >> >> > a series of pictures and pick out the ones with dogs in them, that's easy.
>> >> >> >
>> >> >> > To get a computer to do the same problems, and the difficulty is
>> >> >> > reversed.
>> >> >> >
>> >> >> > So it's reasonable to suppose that humans and computers work in
>> >> >> > fundamentally different ways. That's particularly true when we get to
>> >> >> > natural language. We code natural language using a discrete set of
>> >> >> > symbols, so reading and writing is definitely a "symbol processing
>> >> >> > exercise" (it's less clear when you consider spoken
>> >> >> > language). Computers can't do it.
>> >> >> Ah, I thought you were making a theoretical point about Turing
>> >> >> machines, not a practical one about current hardware and software.
>> >> >>
>> >> > Some people think that you can scale up current hardware to solve
>> >> > these problems.
>> >> I often don't know what to make of your remarks. I'm not really
>> >> interested in what some people think about future hardware.
>> >>
>> >> I thought you were making a point about a finite state, unbounded
>> >> storage model of computation and human cognitive abilities, but I don't
>> >> think you were.
>> >>
>> > The central nervous system is massively parallel whilst Turing machines are
>> > single-threaded.
>> But since a TM has no notion of time, this hardly matters. TMs are
>> about what's possible.
>> > However you can convert any parallel algorithm to a single-threaded
>> > algorithm. It has been proposed that the reason that computers can't
>> > match human cognitive abilities is that the algorithms are not
>> > parallel enough. Whilst theoretically this is nothing to do with
>> > hardware, in practice of course it is, because you can't be hanging
>> > around for the results.
>>
>> There's no "hanging around" with a TM.
>>
> Of course there is. You build it, and set it running, and some time later it
> comes back with the results. Or never stops. Time is inherent in the
> model.

No. I can't imagine how you can think this, but it seems there is no
common ground for this discussion.

--
Ben.

On Thursday, 14 July 2022 at 00:17:00 UTC+1, Ben Bacarisse wrote:
> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>
> > On Wednesday, 13 July 2022 at 02:29:13 UTC+1, Ben Bacarisse wrote:
> >> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>
> >> > However you can convert any parallel algorithm to a single-threaded
> >> > algorithm. It has been proposed that the reason that computers can't
> >> > match human cognitive abilities is that the algorithms are not
> >> > parallel enough. Whilst theoretically this is nothing to do with
> >> > hardware, in practice of course it is, because you can't be hanging
> >> > around for the results.
> >>
> >> There's no "hanging around" with a TM.
> >>
> > Of course there is. You build it, and set it running, and some time later it
> > comes back with the results. Or never stops. Time is inherent in the
> > model.
> No. I can't imagine how you can think this, but it seems there is no
> common ground for this discussion.
>
You can't distinguish, in the general case, a TM that doesn't halt from
one that you can't hang round for. That's a fundamental characteristic of
the model and means that TMs cannot be used to prove hypotheses in
number theory. You can't get away from the fact that, to know the configuration
at step three, which is wholly determined by the configuration at step one,
you absolutely have to calculate the configuration at step two (in the
general case again). That's how the model works. Time is inherent to it.

On 7/15/22 6:13 AM, Malcolm McLean wrote:
> On Thursday, 14 July 2022 at 00:17:00 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>>> On Wednesday, 13 July 2022 at 02:29:13 UTC+1, Ben Bacarisse wrote:
>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>>>>> However you can convert any parallel algorithm to a single-threaded
>>>>> algorithm. It has been proposed that the reason that computers can't
>>>>> match human cognitive abilities is that the algorithms are not
>>>>> parallel enough. Whilst theoretically this is nothing to do with
>>>>> hardware, in practice of course it is, because you can't be hanging
>>>>> around for the results.
>>>>
>>>> There's no "hanging around" with a TM.
>>>>
>>> Of course there is. You build it, and set it running, and some time later it
>>> comes back with the results. Or never stops. Time is inherent in the
>>> model.
>> No. I can't imagine how you can think this, but it seems there is no
>> common ground for this discussion.
>>
> You can't distinguish, in the general case, a TM that doesn't halt from
> one that you can't hang round for. That's a fundamental characteristic of
> the model and means that TMs cannot be used to prove hypotheses in
> number theory. You can't get away from the fact that, to know the configuration
> at step three, which is wholly determined by the configuration at step one,
> you absolutely have to calculate the configuration at step two (in the
> general case again). That's how the model works. Time is inherent to it.
>

Which is precisely the effect of the Halting Theorem.

If we COULD tell the diference between a machine that just won't EVER
halt, and one that hasn't halted yet, then Turing Machines could be used
to prove hypotheses.

If you are currently waiting for the halt decider to decide, but
actually KNOW that it will at some point, you know you just need to
crank on that computation longer (or get a faster computation engine) to
get the answer, and it WILL eventually arrive.

Thus we know the problem to be at least theoretically solved (but don't
know the answer yet).

You still have the practical problem that it might be that doing the
computation is totally out of the ability of ANYTHING we might be able
to actually do (like it needs more storage than could exist in the
universe) but that is just the line between theory and practice.

Once something is shown possible, it seems often even if the first
solution was impractical, better methods are found and many thing that
were impractical become practical. The big step is showing it is possible.

On Friday, 15 July 2022 at 12:34:30 UTC+1, richar...@gmail.com wrote:
> On 7/15/22 6:13 AM, Malcolm McLean wrote:
> > On Thursday, 14 July 2022 at 00:17:00 UTC+1, Ben Bacarisse wrote:
> >> Malcolm McLean <malcolm.ar...@gmail.com> writes:
> >>
> >>> On Wednesday, 13 July 2022 at 02:29:13 UTC+1, Ben Bacarisse wrote:
> >>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
> >>
> >>>>> However you can convert any parallel algorithm to a single-threaded
> >>>>> algorithm. It has been proposed that the reason that computers can't
> >>>>> match human cognitive abilities is that the algorithms are not
> >>>>> parallel enough. Whilst theoretically this is nothing to do with
> >>>>> hardware, in practice of course it is, because you can't be hanging
> >>>>> around for the results.
> >>>>
> >>>> There's no "hanging around" with a TM.
> >>>>
> >>> Of course there is. You build it, and set it running, and some time later it
> >>> comes back with the results. Or never stops. Time is inherent in the
> >>> model.
> >> No. I can't imagine how you can think this, but it seems there is no
> >> common ground for this discussion.
> >>
> > You can't distinguish, in the general case, a TM that doesn't halt from
> > one that you can't hang round for. That's a fundamental characteristic of
> > the model and means that TMs cannot be used to prove hypotheses in
> > number theory. You can't get away from the fact that, to know the configuration
> > at step three, which is wholly determined by the configuration at step one,
> > you absolutely have to calculate the configuration at step two (in the
> > general case again). That's how the model works. Time is inherent to it.
> >
> Which is precisely the effect of the Halting Theorem.
>
> If we COULD tell the diference between a machine that just won't EVER
> halt, and one that hasn't halted yet, then Turing Machines could be used
> to prove hypotheses.
>
> If you are currently waiting for the halt decider to decide, but
> actually KNOW that it will at some point, you know you just need to
> crank on that computation longer (or get a faster computation engine) to
> get the answer, and it WILL eventually arrive.
>
> Thus we know the problem to be at least theoretically solved (but don't
> know the answer yet).
>
> You still have the practical problem that it might be that doing the
> computation is totally out of the ability of ANYTHING we might be able
> to actually do (like it needs more storage than could exist in the
> universe) but that is just the line between theory and practice.
>
> Once something is shown possible, it seems often even if the first
> solution was impractical, better methods are found and many thing that
> were impractical become practical. The big step is showing it is possible.
>
Showing that something is either possible or inherently impossible is a
big step.
But with the "dog recognition problem" for example it is red herring.
The problem is finite, so there must exist a machine which can classify
images into dogs and non-dogs correctly. But the set has (2^24)^(512*512)
members. Clearly humans can't be using a lookup table algorithm.

On 7/15/22 8:00 AM, Malcolm McLean wrote:
> On Friday, 15 July 2022 at 12:34:30 UTC+1, richar...@gmail.com wrote:
>> On 7/15/22 6:13 AM, Malcolm McLean wrote:
>>> On Thursday, 14 July 2022 at 00:17:00 UTC+1, Ben Bacarisse wrote:
>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>>
>>>>> On Wednesday, 13 July 2022 at 02:29:13 UTC+1, Ben Bacarisse wrote:
>>>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>>
>>>>>>> However you can convert any parallel algorithm to a single-threaded
>>>>>>> algorithm. It has been proposed that the reason that computers can't
>>>>>>> match human cognitive abilities is that the algorithms are not
>>>>>>> parallel enough. Whilst theoretically this is nothing to do with
>>>>>>> hardware, in practice of course it is, because you can't be hanging
>>>>>>> around for the results.
>>>>>>
>>>>>> There's no "hanging around" with a TM.
>>>>>>
>>>>> Of course there is. You build it, and set it running, and some time later it
>>>>> comes back with the results. Or never stops. Time is inherent in the
>>>>> model.
>>>> No. I can't imagine how you can think this, but it seems there is no
>>>> common ground for this discussion.
>>>>
>>> You can't distinguish, in the general case, a TM that doesn't halt from
>>> one that you can't hang round for. That's a fundamental characteristic of
>>> the model and means that TMs cannot be used to prove hypotheses in
>>> number theory. You can't get away from the fact that, to know the configuration
>>> at step three, which is wholly determined by the configuration at step one,
>>> you absolutely have to calculate the configuration at step two (in the
>>> general case again). That's how the model works. Time is inherent to it.
>>>
>> Which is precisely the effect of the Halting Theorem.
>>
>> If we COULD tell the diference between a machine that just won't EVER
>> halt, and one that hasn't halted yet, then Turing Machines could be used
>> to prove hypotheses.
>>
>> If you are currently waiting for the halt decider to decide, but
>> actually KNOW that it will at some point, you know you just need to
>> crank on that computation longer (or get a faster computation engine) to
>> get the answer, and it WILL eventually arrive.
>>
>> Thus we know the problem to be at least theoretically solved (but don't
>> know the answer yet).
>>
>> You still have the practical problem that it might be that doing the
>> computation is totally out of the ability of ANYTHING we might be able
>> to actually do (like it needs more storage than could exist in the
>> universe) but that is just the line between theory and practice.
>>
>> Once something is shown possible, it seems often even if the first
>> solution was impractical, better methods are found and many thing that
>> were impractical become practical. The big step is showing it is possible.
>>
> Showing that something is either possible or inherently impossible is a
> big step.
> But with the "dog recognition problem" for example it is red herring.
> The problem is finite, so there must exist a machine which can classify
> images into dogs and non-dogs correctly. But the set has (2^24)^(512*512)
> members. Clearly humans can't be using a lookup table algorithm.

The "recognition" problem is actually an very interesting to look at. At
first glance, it seems it must be at least theoretically possible, as
there are a finite number of pictures, and you can say that every
picture either has a dog or it doesn't, so you must be able to build a
table.

But, when we think more about it, we realize that the act of taking a
picture has lost information. Two different scenes, one with a Dog in
it, and another with something else there might give the same picture.
Maybe the dog is so far away that it becomes too small to actually be
distinct enough to tell. Also, what is a "Dog", is a wolf dog like
enough to count, or do we need to be able to distinguish between the
different species, and a lot of pictures of a dog might not be distinct
enough to actually tell them apart if we define that as part of the problem.

This means that perfect recognition is actually an unsolvable problem in
general (sort of like the halting problem), but may have many practical
solutions of varying quality, and the interesting thing is defining how
good we can actually get.

This is actually something that is part of my work, how to get an image
that allows the recognition and/or identification of things in it. There
are defined standards that define various parameters that allow you to
define how "hard" your recognition task is (dog vs rock, dog vs cat, dog
vs wolf, etc) and image quality (size, contrast, etc) and come up with
measure of how likely a typical trained human will be able to do that
recognition.

On Friday, 15 July 2022 at 13:22:46 UTC+1, richar...@gmail.com wrote:
> On 7/15/22 8:00 AM, Malcolm McLean wrote:
> > On Friday, 15 July 2022 at 12:34:30 UTC+1, richar...@gmail.com wrote:
> >> On 7/15/22 6:13 AM, Malcolm McLean wrote:
> >>> On Thursday, 14 July 2022 at 00:17:00 UTC+1, Ben Bacarisse wrote:
> >>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
> >>>>
> >>>>> On Wednesday, 13 July 2022 at 02:29:13 UTC+1, Ben Bacarisse wrote:
> >>>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
> >>>>
> >>>>>>> However you can convert any parallel algorithm to a single-threaded
> >>>>>>> algorithm. It has been proposed that the reason that computers can't
> >>>>>>> match human cognitive abilities is that the algorithms are not
> >>>>>>> parallel enough. Whilst theoretically this is nothing to do with
> >>>>>>> hardware, in practice of course it is, because you can't be hanging
> >>>>>>> around for the results.
> >>>>>>
> >>>>>> There's no "hanging around" with a TM.
> >>>>>>
> >>>>> Of course there is. You build it, and set it running, and some time later it
> >>>>> comes back with the results. Or never stops. Time is inherent in the
> >>>>> model.
> >>>> No. I can't imagine how you can think this, but it seems there is no
> >>>> common ground for this discussion.
> >>>>
> >>> You can't distinguish, in the general case, a TM that doesn't halt from
> >>> one that you can't hang round for. That's a fundamental characteristic of
> >>> the model and means that TMs cannot be used to prove hypotheses in
> >>> number theory. You can't get away from the fact that, to know the configuration
> >>> at step three, which is wholly determined by the configuration at step one,
> >>> you absolutely have to calculate the configuration at step two (in the
> >>> general case again). That's how the model works. Time is inherent to it.
> >>>
> >> Which is precisely the effect of the Halting Theorem.
> >>
> >> If we COULD tell the diference between a machine that just won't EVER
> >> halt, and one that hasn't halted yet, then Turing Machines could be used
> >> to prove hypotheses.
> >>
> >> If you are currently waiting for the halt decider to decide, but
> >> actually KNOW that it will at some point, you know you just need to
> >> crank on that computation longer (or get a faster computation engine) to
> >> get the answer, and it WILL eventually arrive.
> >>
> >> Thus we know the problem to be at least theoretically solved (but don't
> >> know the answer yet).
> >>
> >> You still have the practical problem that it might be that doing the
> >> computation is totally out of the ability of ANYTHING we might be able
> >> to actually do (like it needs more storage than could exist in the
> >> universe) but that is just the line between theory and practice.
> >>
> >> Once something is shown possible, it seems often even if the first
> >> solution was impractical, better methods are found and many thing that
> >> were impractical become practical. The big step is showing it is possible.
> >>
> > Showing that something is either possible or inherently impossible is a
> > big step.
> > But with the "dog recognition problem" for example it is red herring.
> > The problem is finite, so there must exist a machine which can classify
> > images into dogs and non-dogs correctly. But the set has (2^24)^(512*512)
> > members. Clearly humans can't be using a lookup table algorithm.
> The "recognition" problem is actually an very interesting to look at. At
> first glance, it seems it must be at least theoretically possible, as
> there are a finite number of pictures, and you can say that every
> picture either has a dog or it doesn't, so you must be able to build a
> table.
>
> But, when we think more about it, we realize that the act of taking a
> picture has lost information. Two different scenes, one with a Dog in
> it, and another with something else there might give the same picture.
> Maybe the dog is so far away that it becomes too small to actually be
> distinct enough to tell. Also, what is a "Dog", is a wolf dog like
> enough to count, or do we need to be able to distinguish between the
> different species, and a lot of pictures of a dog might not be distinct
> enough to actually tell them apart if we define that as part of the problem.
>
> This means that perfect recognition is actually an unsolvable problem in
> general (sort of like the halting problem), but may have many practical
> solutions of varying quality, and the interesting thing is defining how
> good we can actually get.
>
> This is actually something that is part of my work, how to get an image
> that allows the recognition and/or identification of things in it. There
> are defined standards that define various parameters that allow you to
> define how "hard" your recognition task is (dog vs rock, dog vs cat, dog
> vs wolf, etc) and image quality (size, contrast, etc) and come up with
> measure of how likely a typical trained human will be able to do that
> recognition.
>
Yes, you've got marginal cases. A wolf isn't a dog, but it is a canine. Then you've
got very small or poorly lit images which may be dogs but it's hard to be sure.
Then there are other wild cards, such as Snoopy, or a hot dog.

Fuzzy logic assigns a "membership value" or 0.0 - 1.0 to the image. S if it
clearly has nothing to do with dogs it's an 0,0, if it's clearly a dog it's 1.0,
and if it's a marginal it's an intermediate value. However the question is how to
assign values to the intermediate cases.

Humans do dog recognition all the time. With a high but not perfect degree of
accuracy. And it's easy for us. You don't have to be trained. You don't even need
to be formally taught what a dog is. A child will be told "pat the doggie" and will
generalise to the set.

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

> On Thursday, 14 July 2022 at 00:17:00 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>> > On Wednesday, 13 July 2022 at 02:29:13 UTC+1, Ben Bacarisse wrote:
>> >> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>> >> > However you can convert any parallel algorithm to a single-threaded
>> >> > algorithm. It has been proposed that the reason that computers can't
>> >> > match human cognitive abilities is that the algorithms are not
>> >> > parallel enough. Whilst theoretically this is nothing to do with
>> >> > hardware, in practice of course it is, because you can't be hanging
>> >> > around for the results.
>> >>
>> >> There's no "hanging around" with a TM.
>> >>
>> > Of course there is. You build it, and set it running, and some time later it
>> > comes back with the results. Or never stops. Time is inherent in the
>> > model.
>> No. I can't imagine how you can think this, but it seems there is no
>> common ground for this discussion.
>>
> You can't distinguish, in the general case, a TM that doesn't halt from
> one that you can't hang round for.

What's the point of continuing the discussion when there is this
fundamental mis-match in the use of terms? You've just talked about
hanging around again, but there is no hanging around with TMs.

> That's a fundamental characteristic of
> the model and means that TMs cannot be used to prove hypotheses in
> number theory.

No, it's not the hanging around that's fundamental, it's the
undecidabilty.

This distinction matters because your original argument was about the
hanging around, not the undecidabilty.

> You can't get away from the fact that, to know the configuration
> at step three, which is wholly determined by the configuration at step one,
> you absolutely have to calculate the configuration at step two (in the
> general case again). That's how the model works. Time is inherent to
> it.

Nonsense. There is a sequence. Time has nothing to do with it. If we
apply an iterative function, say f(n) = n/2, f^1000(1) does not "take
longer" than f^2(1). A TM is just an iterated function.

--
Ben.