On Sunday, 21 August 2022 at 20:42:52 UTC+2, richar...@gmail.com wrote:
> So, you really have zero knowledge in your system.
>
> Thats for confirming it.
You needed confirmation?

There is no knowledge in Mathematics. It's just make-believe.

On Sunday, 21 August 2022 at 20:58:11 UTC+2, Jeff Barnett wrote:
> And the idea of sets is prior to set theory.
I know. I pointed that fact out!

I explicitly said THAT sets are NOT defined anywhere in Mathematics.

But some assholes just want to "be right".

On Sunday, 21 August 2022 at 20:58:11 UTC+2, Jeff Barnett wrote:
> And the idea of sets is prior to set theory. Now go in your corner, have
> a good cry and take a nap. When your head clears you can wake up and go
> be nasty to the big boys again. (Does your mommy know you've been bad?)
Of course, the idea of sets is a bit stupid, don't you think? A collection of things!

Who the hell thought I can't have two of the same thing in my collection ?!?!

Skep Dick <skepdick22@gmail.com> writes:

> On Sunday, 21 August 2022 at 16:32:31 UTC+2, Ben Bacarisse wrote:
>> > What is 'Provable Theorems', definition man!
>> As usual I'm curious about the meta question... Why would you ask this?
>> Do you think that people who study formal theories have not defined what
>> a provable theorem is? And if you know that they have, but have some
>> issue with that definition, why not ask about what's bothering you about
>> it? Are you asking for RD to copy and paste two chapters from a
>> textbook like Shoenfield's, Mendelson's or Kleene's?
>
> I guess the disagreement is (as always) about acceptable
> standards/criteria of "definition" and "proof".

What makes you think you have any insight into why Wij would ask that
question?

> Copy/pasting chapters out of the Bible is no definition/proof of
> anything.

Indeed. I doubt anyone here thinks of any Bible (there is no "the
Bible") as a quality textbook on any topic.

--
Ben.

On 8/21/22 3:01 PM, Skep Dick wrote:
> On Sunday, 21 August 2022 at 20:42:52 UTC+2, richar...@gmail.com wrote:
>> So, you really have zero knowledge in your system.
>>
>> Thats for confirming it.
> You needed confirmation?
>
> There is no knowledge in Mathematics. It's just make-believe.

So we can safely ignore everything you say, as you admit you are just a
dumb dick.

On Sunday, 21 August 2022 at 21:15:33 UTC+2, Ben Bacarisse wrote:
> > I guess the disagreement is (as always) about acceptable
> > standards/criteria of "definition" and "proof".
> What makes you think you have any insight into why Wij would ask that
> question?
Nothing makes me think that. Hence me starting my sentence with "I guess".

> Indeed. I doubt anyone here thinks of any Bible (there is no "the
> Bible") as a quality textbook on any topic.
In so far as the subject matter is all made up - I figure the quality of the bible compares to the quality of Maths textbooks.

wij <wyniijj2@gmail.com> writes:

> On Sunday, 21 August 2022 at 22:32:31 UTC+8, Ben Bacarisse wrote:
>> wij <wyni...@gmail.com> writes:
>>
>> > On Sunday, 21 August 2022 at 20:19:01 UTC+8, richar...@gmail.com wrote:
>>
>> >> The number of Provable Theorems in the real number system is, I beleive,
>> >> infinte (not sure if it is a countable or an uncountable infinity, I
>> >> think countable).
>> >
>> > What is 'Provable Theorems', definition man!
>> As usual I'm curious about the meta question... Why would you ask this?
>> Do you think that people who study formal theories have not defined what
>> a provable theorem is? And if you know that they have, but have some
>> issue with that definition, why not ask about what's bothering you about
>> it? Are you asking for RD to copy and paste two chapters from a
>> textbook like Shoenfield's, Mendelson's or Kleene's?
>
> 'P' and 'T' are capitalized and 'theorem' is 'defined' for proved statement.
> RD likes to say things he don't really understand.

Ah, I see. I don't think either the capitalisation or the pleonasm
suggest that Richard intended anything but the usual meanings. The best
discussions happen when we are generous in interpreting what people say
and when we ask probing questions to get to the real substantive
disagreements.

--
Ben.

On Sunday, 21 August 2022 at 18:46:06 UTC+1, Skep Dick wrote:
> On Sunday, 21 August 2022 at 19:36:33 UTC+2, malcolm.ar...@gmail.com wrote:
> > That's another potential ambiguity.
> > Is the lowest number we can represent one or zero?
> > However in the case of a light, normally you'd have an "off" state which would be represented by zero,
> > because zero current is flowing.
> Again. I have no idea what you are aven asking; or saying. Numbers don't exist.
>
> When we are talking about light/physics we are dealing with quantities, not numbers.
>
> We use the symbols we call numbers to represent quantities.
>
Typically a light in a display would have a natural lower limit of light it can emit, which
is none, and which is achieved by setting the current to zero. There will be an engineered
upper limit, which you could maybe override by fiddling with the electronics, but not
in normal operation, and is achieved by setting the current to the maximum engineered
level. Since current is analogue, there are also intermediate levels.
Since the light is attached to a digital computer, the desired level is represented within the
computer symbolically, and there isn't necessarily any natural or straightforwards mapping
from the symbols to the light level. However the symbols are ultimately fed into a digital to
analogue converter, and that device defines the conversion, or the "meaning" of the
symbols.

On 8/21/2022 1:04 PM, Skep Dick wrote:
> On Sunday, 21 August 2022 at 20:58:11 UTC+2, Jeff Barnett wrote:
>> And the idea of sets is prior to set theory.
> I know. I pointed that fact out!
>
> I explicitly said THAT sets are NOT defined anywhere in Mathematics.
>
> But some assholes just want to "be right".
Go take your nap and calm down. You said and snipped:

"Computation is conceptually prior to set theory.
Computation is prior to any theory - even a theory of computation!"

Which is very likely false. Primitive animals and man where aware of
categories of things - food, enemies, etc. - long before they knew how
to count or represent these concepts. Recognition of "class" or
"sameness" is much easier. Further, if you would go read some high
school math books you'll certainly learn that sets are defined. If you
continue on to texts for real analysis or set theory you learn how to
"better" define sets. There was an approximately 30 year war in the
mathematically and philosophical communities about 100 years ago on
trying to find a set theory (which has exactly one purpose - to define
sets) that met intuitions.

I merely pointed out that you omitted that sets were concepts before
sets were defined.
--
Jeff Barnett

On 8/21/22 3:49 PM, Ben Bacarisse wrote:
> wij <wyniijj2@gmail.com> writes:
>
>> On Sunday, 21 August 2022 at 22:32:31 UTC+8, Ben Bacarisse wrote:
>>> wij <wyni...@gmail.com> writes:
>>>
>>>> On Sunday, 21 August 2022 at 20:19:01 UTC+8, richar...@gmail.com wrote:
>>>
>>>>> The number of Provable Theorems in the real number system is, I beleive,
>>>>> infinte (not sure if it is a countable or an uncountable infinity, I
>>>>> think countable).
>>>>
>>>> What is 'Provable Theorems', definition man!
>>> As usual I'm curious about the meta question... Why would you ask this?
>>> Do you think that people who study formal theories have not defined what
>>> a provable theorem is? And if you know that they have, but have some
>>> issue with that definition, why not ask about what's bothering you about
>>> it? Are you asking for RD to copy and paste two chapters from a
>>> textbook like Shoenfield's, Mendelson's or Kleene's?
>>
>> 'P' and 'T' are capitalized and 'theorem' is 'defined' for proved statement.
>> RD likes to say things he don't really understand.
>
> Ah, I see. I don't think either the capitalisation or the pleonasm
> suggest that Richard intended anything but the usual meanings. The best
> discussions happen when we are generous in interpreting what people say
> and when we ask probing questions to get to the real substantive
> disagreements.
>

I tack "Provable" to Theorem, because we have people playing word games,
and might try to define a theorem as something that isn't actually
provable, and actually just a conjecture.

After all, if a theorem is just a "program", can we have a buggy program
create in "Theorem" that can't be correctly proved?

Also, I will admit that I then to somewhat randomly capitalize words for
emphasis that it is a word with a specific definition.

The key point is the number of "facts" (aka theorems) we can generate
about the Real Numbers is unbounded, and thus no "Computation" can
enumerate them in finite time.

This says that the Dicks concept of just making the Real Number System
be the output of a "Program" just doesn't work.

Just as many of the Real Numbers can not be represented as a finite
string, and thus can't be the results of a "Program".

One reason the Classical Computation Theory doesn't deal with Real Numbers.

Richard Damon <Richard@Damon-Family.org> writes:

> Just as many of the Real Numbers can not be represented as a finite
> string, and thus can't be the results of a "Program".
>
> One reason the Classical Computation Theory doesn't deal with Real
> Numbers.

I'm not sure exactly what your point it, but there's an irony here.
Turing's original paper is surely part of "classical computation theory"
and that is about computable numbers, specifically numbers whose
representation is not finite.

--
Ben.

On 8/21/22 8:33 PM, Ben Bacarisse wrote:
> Richard Damon <Richard@Damon-Family.org> writes:
>
>> Just as many of the Real Numbers can not be represented as a finite
>> string, and thus can't be the results of a "Program".
>>
>> One reason the Classical Computation Theory doesn't deal with Real
>> Numbers.
>
> I'm not sure exactly what your point it, but there's an irony here.
> Turing's original paper is surely part of "classical computation theory"
> and that is about computable numbers, specifically numbers whose
> representation is not finite.
>

Maybe I wasn't exposed to the right parts of the theory then, as I was
taught that the computation engines were finite symbol manipulators, and
of course, such a machine can not handle a non-finite representable
number. You could handle repeating digit numbers with appropriate marks.

Skep Dick <skepdick22@gmail.com> writes:

> On Sunday, 21 August 2022 at 21:15:33 UTC+2, Ben Bacarisse wrote:
>> > I guess the disagreement is (as always) about acceptable
>> > standards/criteria of "definition" and "proof".
>> What makes you think you have any insight into why Wij would ask that
>> question?
>
> Nothing makes me think that. Hence me starting my sentence with "I
> guess".

I should have thought that you would not let a lack of insight inhibit
your writing.

>> Indeed. I doubt anyone here thinks of any Bible (there is no "the
>> Bible") as a quality textbook on any topic.
>
> In so far as the subject matter is all made up - I figure the quality
> of the bible compares to the quality of Maths textbooks.

Then you are very much mistaken. Writing well about a made-up subject
like mathematics is not easy, but some authors do it well with clarity,
wit and erudition. There will be a logical structure, a good index and
a bibliography of sources. All lacking from the bibles I've seen.
Chalk and cheese, frankly.

And, if I step away from textbooks for the moment, there is, in my
opinion, little to compare with the feats of human imagination that
mathematics encompasses. I doubt there is anything in any religious
text that compares with Cantor or Leibniz.

--
Ben.

On Monday, 22 August 2022 at 02:21:16 UTC+1, Ben Bacarisse wrote:
> Skep Dick <skepd...@gmail.com> writes:
>
> > On Sunday, 21 August 2022 at 21:15:33 UTC+2, Ben Bacarisse wrote:
> >> > I guess the disagreement is (as always) about acceptable
> >> > standards/criteria of "definition" and "proof".
> >> What makes you think you have any insight into why Wij would ask that
> >> question?
> >
> > Nothing makes me think that. Hence me starting my sentence with "I
> > guess".
> I should have thought that you would not let a lack of insight inhibit
> your writing.
> >> Indeed. I doubt anyone here thinks of any Bible (there is no "the
> >> Bible") as a quality textbook on any topic.
> >
> > In so far as the subject matter is all made up - I figure the quality
> > of the bible compares to the quality of Maths textbooks.
> Then you are very much mistaken. Writing well about a made-up subject
> like mathematics is not easy, but some authors do it well with clarity,
> wit and erudition. There will be a logical structure, a good index and
> a bibliography of sources. All lacking from the bibles I've seen.
> Chalk and cheese, frankly.
>
> And, if I step away from textbooks for the moment, there is, in my
> opinion, little to compare with the feats of human imagination that
> mathematics encompasses. I doubt there is anything in any religious
> text that compares with Cantor or Leibniz.
>
You have to remember that when the first chapter of Genesis was composed,
the priests were likely located in the capital city of one of the most sophisticated
states of the time. And in that culture, it was believed that the world had been
created when the god Marduk cut the dragon Tiamat in two.
So in fact it's quite a remarkable approach to the truth. It's demythologised.
God says, and it is.

Richard Damon <Richard@Damon-Family.org> writes:

> On 8/21/22 8:33 PM, Ben Bacarisse wrote:
>> Richard Damon <Richard@Damon-Family.org> writes:
>>
>>> Just as many of the Real Numbers can not be represented as a finite
>>> string, and thus can't be the results of a "Program".
>>>
>>> One reason the Classical Computation Theory doesn't deal with Real
>>> Numbers.
>> I'm not sure exactly what your point it, but there's an irony here.
>> Turing's original paper is surely part of "classical computation theory"
>> and that is about computable numbers, specifically numbers whose
>> representation is not finite.
>>
>
> Maybe I wasn't exposed to the right parts of the theory then, as I was
> taught that the computation engines were finite symbol manipulators,
> and of course, such a machine can not handle a non-finite
> representable number. You could handle repeating digit numbers with
> appropriate marks.

"Handle" is too broad a term. A TM the generates the digits of some
number "handles" that number in some sense. But there are reals that
can't be "handled" even in this sense. For example, Chaitin's Omega.

--
Ben.

Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:
> On Monday, 22 August 2022 at 02:21:16 UTC+1, Ben Bacarisse wrote:
>> Skep Dick <skepd...@gmail.com> writes:
>>
>> > On Sunday, 21 August 2022 at 21:15:33 UTC+2, Ben Bacarisse wrote:
>> >> > I guess the disagreement is (as always) about acceptable
>> >> > standards/criteria of "definition" and "proof".
>> >> What makes you think you have any insight into why Wij would ask that
>> >> question?
>> >
>> > Nothing makes me think that. Hence me starting my sentence with "I
>> > guess".
>> I should have thought that you would not let a lack of insight inhibit
>> your writing.
>> >> Indeed. I doubt anyone here thinks of any Bible (there is no "the
>> >> Bible") as a quality textbook on any topic.
>> >
>> > In so far as the subject matter is all made up - I figure the quality
>> > of the bible compares to the quality of Maths textbooks.
>> Then you are very much mistaken. Writing well about a made-up subject
>> like mathematics is not easy, but some authors do it well with clarity,
>> wit and erudition. There will be a logical structure, a good index and
>> a bibliography of sources. All lacking from the bibles I've seen.
>> Chalk and cheese, frankly.
>>
>> And, if I step away from textbooks for the moment, there is, in my
>> opinion, little to compare with the feats of human imagination that
>> mathematics encompasses. I doubt there is anything in any religious
>> text that compares with Cantor or Leibniz.
>>
> You have to remember that when the first chapter of Genesis was composed,
> the priests were likely located in the capital city of one of the most sophisticated
> states of the time. And in that culture, it was believed that the world had been
> created when the god Marduk cut the dragon Tiamat in two.
> So in fact it's quite a remarkable approach to the truth. It's demythologised.
> God says, and it is.

Yes, by all means, let's argue about the Bible here in comp.theory.
It will increase the already impressively high signal-to-noise ratio.

(Should I redirect followups to comp.sarcasm?)

--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Philips
void Void(void) { Void(); } /* The recursive call of the void */

On 8/21/22 9:35 PM, Ben Bacarisse wrote:
> Richard Damon <Richard@Damon-Family.org> writes:
>
>> On 8/21/22 8:33 PM, Ben Bacarisse wrote:
>>> Richard Damon <Richard@Damon-Family.org> writes:
>>>
>>>> Just as many of the Real Numbers can not be represented as a finite
>>>> string, and thus can't be the results of a "Program".
>>>>
>>>> One reason the Classical Computation Theory doesn't deal with Real
>>>> Numbers.
>>> I'm not sure exactly what your point it, but there's an irony here.
>>> Turing's original paper is surely part of "classical computation theory"
>>> and that is about computable numbers, specifically numbers whose
>>> representation is not finite.
>>>
>>
>> Maybe I wasn't exposed to the right parts of the theory then, as I was
>> taught that the computation engines were finite symbol manipulators,
>> and of course, such a machine can not handle a non-finite
>> representable number. You could handle repeating digit numbers with
>> appropriate marks.
>
> "Handle" is too broad a term. A TM the generates the digits of some
> number "handles" that number in some sense. But there are reals that
> can't be "handled" even in this sense. For example, Chaitin's Omega.
>

So is this defining that if we can computation of number to an arbitrary
accuracy can be done in finite time it has been consieded computable?

Sort of like how the Limit Theorem works?

On Monday, 22 August 2022 at 05:33:00 UTC+2, richar...@gmail.com wrote:
> So is this defining that if we can computation of number to an arbitrary
> accuracy can be done in finite time it has been consieded computable?
>
> Sort of like how the Limit Theorem works?
Have you bothered to read the paper?

"computable number" doesn't mean you get the whole number at once. You get one digit at a time.
Which digit? The n-th digit.

But I am not really sure what the 0th digit of pi is defined as.

On Monday, 22 August 2022 at 03:42:52 UTC+2, Keith Thompson wrote:
> Yes, by all means, let's argue about the Bible here in comp.theory.
> It will increase the already impressively high signal-to-noise ratio.
>
> (Should I redirect followups to comp.sarcasm?)

Well, why not? We are already discussing one religion - Mathematics.

What do you have against all others?

On Monday, 22 August 2022 at 03:21:16 UTC+2, Ben Bacarisse wrote:
> I should have thought that you would not let a lack of insight inhibit
> your writing.
Hahahahaha.

What makes you think you have any insiight into my "lack of" insight?

> >> Indeed. I doubt anyone here thinks of any Bible (there is no "the
> >> Bible") as a quality textbook on any topic.
> >
> > In so far as the subject matter is all made up - I figure the quality
> > of the bible compares to the quality of Maths textbooks.
> Then you are very much mistaken. Writing well about a made-up subject
> like mathematics is not easy, but some authors do it well with clarity,
> wit and erudition. There will be a logical structure, a good index and
> a bibliography of sources. All lacking from the bibles I've seen.
> Chalk and cheese, frankly.
>
> And, if I step away from textbooks for the moment, there is, in my
> opinion, little to compare with the feats of human imagination that
> mathematics encompasses. I doubt there is anything in any religious
> text that compares with Cantor or Leibniz.
>
> --
> Ben.

On Monday, 22 August 2022 at 02:53:44 UTC+2, richar...@gmail.com wrote:
> Maybe I wasn't exposed to the right parts of the theory then, as I was
> taught that the computation engines were finite symbol manipulators, and
> of course, such a machine can not handle a non-finite representable
> number. You could handle repeating digit numbers with appropriate marks.
Infinite structures are representable as finite strings. That's literally what it means to "define" something.
It's in the actual word. Turning the infinite into finite -> DEFINE.

Some infinite objects admit exhaustive searches in finite time.

https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.127.3062

Richard Damon <Richard@Damon-Family.org> writes:

> On 8/21/22 9:35 PM, Ben Bacarisse wrote:
>> Richard Damon <Richard@Damon-Family.org> writes:
>>
>>> On 8/21/22 8:33 PM, Ben Bacarisse wrote:
>>>> Richard Damon <Richard@Damon-Family.org> writes:
>>>>
>>>>> Just as many of the Real Numbers can not be represented as a finite
>>>>> string, and thus can't be the results of a "Program".
>>>>>
>>>>> One reason the Classical Computation Theory doesn't deal with Real
>>>>> Numbers.
>>>> I'm not sure exactly what your point it, but there's an irony here.
>>>> Turing's original paper is surely part of "classical computation theory"
>>>> and that is about computable numbers, specifically numbers whose
>>>> representation is not finite.
>>>>
>>>
>>> Maybe I wasn't exposed to the right parts of the theory then, as I was
>>> taught that the computation engines were finite symbol manipulators,
>>> and of course, such a machine can not handle a non-finite
>>> representable number. You could handle repeating digit numbers with
>>> appropriate marks.
>>
>> "Handle" is too broad a term. A TM the generates the digits of some
>> number "handles" that number in some sense. But there are reals that
>> can't be "handled" even in this sense. For example, Chaitin's Omega.
>
> So is this defining that if we can computation of number to an
> arbitrary accuracy can be done in finite time it has been consieded
> computable?

That is equivalent to Turing's definition. His computable numbers are
those reals whose fractional binary digits are generated by some
non-halting TM which he calls, rather confusingly to the modern reader,
"circle-free machines". In Turing's terminology, all halting machines,
and some non-halting machines are "circular".

> Sort of like how the Limit Theorem works?

Do you mean the usual definition of a limit? If so, yes, it's closely
related. Turing's original model has many peculiarities, so it's not
usually helpful to go into the technical details.

--
Ben.

On Monday, 22 August 2022 at 03:35:15 UTC+2, Ben Bacarisse wrote:
> "Handle" is too broad a term. A TM the generates the digits of some
> number "handles" that number in some sense. But there are reals that
> can't be "handled" even in this sense. For example, Chaitin's Omega.
Does there ever come a point where you recognize that the limiting factor in your thinking is the very medium you are using to think about abstract objects?

You can't "handle" Chaitin's Omega using symbols on an infinitely long tape.
Can you "handle" Chaitin's Omega using color-coded symbols on an infinitely long tape?

Colors... prefixes. What's the difference?

Skep Dick <skepdick22@gmail.com> writes:

> On Monday, 22 August 2022 at 03:35:15 UTC+2, Ben Bacarisse wrote:
>> "Handle" is too broad a term. A TM the generates the digits of some
>> number "handles" that number in some sense. But there are reals that
>> can't be "handled" even in this sense. For example, Chaitin's Omega.
>
> Does there ever come a point where you recognize that the limiting
> factor in your thinking is the very medium you are using to think
> about abstract objects?

All the time. You?

> You can't "handle" Chaitin's Omega using symbols on an infinitely long
> tape. Can you "handle" Chaitin's Omega using color-coded symbols on
> an infinitely long tape?
>
> Colors... prefixes. What's the difference?

Indeed. What's your point? Do you have a point, or are you just
looking to chat using technical-sounding terms?

--
Ben.

On Monday, 22 August 2022 at 17:37:04 UTC+2, Ben Bacarisse wrote:
> > Does there ever come a point where you recognize that the limiting
> > factor in your thinking is the very medium you are using to think
> > about abstract objects?
> All the time. You?

It sure doesn't seem like it. In all your content there's zero mention of dynamic symbols/mediums.

> > Colors... prefixes. What's the difference?
> Indeed. What's your point? Do you have a point, or are you just
> looking to chat using technical-sounding terms?
Does this attack vector actually work for you?

You were the one mumbling about probabilities, Chaitin constants, real numbers and other technical mumbo-jumbo. There's really no need to use such big words to make yoursefl appear smart. It's just a color encoding for your symbols.

If you can't explain it to a 5 year old you probably don't understand it.....