On 15/07/2021 23:39, Owen Rees wrote:
> On Thu, 15 Jul 2021 12:03:21 +0100, Roderick Stewart
> <rjfs@escapetime.myzen.co.uk> wrote in
> <qg40fglmuueuovoh3hsq69njpble39sr0s@4ax.com>:
>
>> It's possible to derive the value of pi (not by me but by somebody
>> clever enough) without reference to geometry at all. The same can be
>> said of a great many other mathematical properties and relationships,
>> because they can exist in pure thoughtspace and so are unaffected by
>> any aspect of physical reality.
>
> Euler's formula - e^(i*pi) = -1 - is an example that relates three of
> the important numbers in mathematics. From what I remember, there is no
> geometry involved in that.
>

Its actually Euler's identity rather than Euler's formula.....

https://en.wikipedia.org/wiki/Euler%27s_identity

On 16/07/2021 07:38, SH wrote:
> On 15/07/2021 23:39, Owen Rees wrote:
>> On Thu, 15 Jul 2021 12:03:21 +0100, Roderick Stewart
>> <rjfs@escapetime.myzen.co.uk> wrote in
>> <qg40fglmuueuovoh3hsq69njpble39sr0s@4ax.com>:
>>
>>> It's possible to derive the value of pi (not by me but by somebody
>>> clever enough) without reference to geometry at all. The same can be
>>> said of a great many other mathematical properties and relationships,
>>> because they can exist in pure thoughtspace and so are unaffected by
>>> any aspect of physical reality.
>>
>> Euler's formula - e^(i*pi) = -1 - is an example that relates three of
>> the important numbers in mathematics. From what I remember, there is no
>> geometry involved in that.
>>
>
> Its actually Euler's identity rather than Euler's formula.....
>
> https://en.wikipedia.org/wiki/Euler%27s_identity

Euler's identity is a special case of Euler's formula for where x = pi

https://en.wikipedia.org/wiki/Euler%27s_formula

In article <scmjm2$quc$1@dont-email.me>, gareth evans
<headstone255@yahoo.com> wrote:
> On 12/07/2021 09:59, Jim Lesurf wrote:
> > ... Those at the top have not paid in any way for the damage they did
> > to *hundreds* of other people. Instead, they carry on as people 'at
> > the top'.

> Especially noticeable in the higher echelons of the NHS chumocracy where
> spectacular failure is rewarded by even more remunerative moves to other
> jobs.

Add the way leeches are now back in fashion - in the forms of
'outsourcings' of many different types - sucking the vitality and cash from
the NHS. Loads of private revenue streams wearing a cover-badge.

Fortunately, as in other areas like social housing, Scotland hasn't made
all the same changes that England has been saddled with in this respect.
But the people who fund the Tory party get their rewards quite nicely from
the 'NHS'.

Jim

--
Please use the address on the audiomisc page if you wish to email me.
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Audio Misc http://www.audiomisc.co.uk/index.html

On 15/07/2021 23:39, Owen Rees wrote:
> On Thu, 15 Jul 2021 12:03:21 +0100, Roderick Stewart
> <rjfs@escapetime.myzen.co.uk> wrote in
> <qg40fglmuueuovoh3hsq69njpble39sr0s@4ax.com>:
>
>> It's possible to derive the value of pi (not by me but by somebody
>> clever enough) without reference to geometry at all. The same can be
>> said of a great many other mathematical properties and relationships,
>> because they can exist in pure thoughtspace and so are unaffected by
>> any aspect of physical reality.
>
> Euler's formula - e^(i*pi) = -1 - is an example that relates three of
> the important numbers in mathematics. From what I remember, there is no
> geometry involved in that.
>

If you present it in a slightly different format, it relates
FOUR important numbers ...

e^(i*PI) + 1 = 0

.... the zero, AKA cipher was a latecomer to arithmetic!

On 15/07/2021 23:51, Owen Rees wrote:
> On Thu, 15 Jul 2021 11:31:16 +0000 (UTC),
> MrSpud__6_Empu@_wcx8qng2806nrkb65.co.uk wrote in
> <scp6a4$ns5$1@gioia.aioe.org>:
>
>> Also mathametics cannot describe reality accuractly as witnessed
>> by pi being an irrational number.
>
> Pi is transcendental rather than just irrational (this has been known
> since the 19th Century). There are whole branches of mathematics that
> deal with things that cannot be expressed in the number system we use in
> normal life. The difficulty in describing reality is not a weakness in
> mathematics.
>

Reminds me of the 1960s hippy who refused anaesthetic at the dental
surgery because ...

He wanted to transcend dental medicaiton.

"gareth evans" <headstone255@yahoo.com> wrote in message
news:scrrko$tba$1@dont-email.me...
> On 15/07/2021 23:39, Owen Rees wrote:
>> On Thu, 15 Jul 2021 12:03:21 +0100, Roderick Stewart
>> <rjfs@escapetime.myzen.co.uk> wrote in
>> <qg40fglmuueuovoh3hsq69njpble39sr0s@4ax.com>:
>>
>>> It's possible to derive the value of pi (not by me but by somebody
>>> clever enough) without reference to geometry at all. The same can be
>>> said of a great many other mathematical properties and relationships,
>>> because they can exist in pure thoughtspace and so are unaffected by
>>> any aspect of physical reality.
>>
>> Euler's formula - e^(i*pi) = -1 - is an example that relates three of
>> the important numbers in mathematics. From what I remember, there is no
>> geometry involved in that.
>>
>
> If you present it in a slightly different format, it relates
> FOUR important numbers ...
>
> e^(i*PI) + 1 = 0
>
> ... the zero, AKA cipher was a latecomer to arithmetic!

Reminds me of a crossword clue I saw in an engineering magazine somewhere. I
forget the exact wording but it gave that formula and the answer was "OILER"
(which is the way that the name Euler is pronounced in his native Germany).

Almost as good as "sounds as if this bony mother is kept in reserve" -
osteospermum ;-)

On 16/07/2021 13:12, NY wrote:
> "gareth evans" <headstone255@yahoo.com> wrote in message
> news:scrrko$tba$1@dont-email.me...
>> On 15/07/2021 23:39, Owen Rees wrote:
>>> On Thu, 15 Jul 2021 12:03:21 +0100, Roderick Stewart
>>> <rjfs@escapetime.myzen.co.uk> wrote in
>>> <qg40fglmuueuovoh3hsq69njpble39sr0s@4ax.com>:
>>>
>>>> It's possible to derive the value of pi (not by me but by somebody
>>>> clever enough) without reference to geometry at all. The same can be
>>>> said of a great many other mathematical properties and relationships,
>>>> because they can exist in pure thoughtspace and so are unaffected by
>>>> any aspect of physical reality.
>>>
>>> Euler's formula - e^(i*pi) = -1 - is an example that relates three of
>>> the important numbers in mathematics. From what I remember, there is no
>>> geometry involved in that.
>>>
>>
>> If you present it in a slightly different format, it relates
>> FOUR important numbers ...
>>
>> e^(i*PI) + 1 = 0
>>
>> ... the zero, AKA cipher was a latecomer to arithmetic!
>
> Reminds me of a crossword clue I saw in an engineering magazine
> somewhere. I forget the exact wording but it gave that formula and the
> answer was "OILER" (which is the way that the name Euler is pronounced
> in his native Germany).
>
> Almost as good as "sounds as if this bony mother is kept in reserve" -
> osteospermum ;-)

Then I recommend that Asian newspaper, The "Delhi" Telegraph :-) and
its two cryptic crosswords, the easy one on the back page and the
Toughie in the middle.

Oddly enough, I am attuned to the way of the clues in the Telegraph,
but I find The Times' cryptic crossword well nigh impossible!

On 16/07/2021 12:47, gareth evans wrote:
> On 15/07/2021 23:39, Owen Rees wrote:
>> On Thu, 15 Jul 2021 12:03:21 +0100, Roderick Stewart
>> <rjfs@escapetime.myzen.co.uk> wrote in
>> <qg40fglmuueuovoh3hsq69njpble39sr0s@4ax.com>:
>>
>>> It's possible to derive the value of pi (not by me but by somebody
>>> clever enough) without reference to geometry at all. The same can be
>>> said of a great many other mathematical properties and relationships,
>>> because they can exist in pure thoughtspace and so are unaffected by
>>> any aspect of physical reality.
>>
>> Euler's formula - e^(i*pi) = -1 - is an example that relates three of
>> the important numbers in mathematics. From what I remember, there is no
>> geometry involved in that.
>>
>
> If you present it in a slightly different format, it relates
> FOUR important numbers ...
>
> e^(i*PI) + 1 = 0
>
> ... the zero, AKA cipher was a latecomer to arithmetic!

If you're into mathematical formulae, you might be amused by this old SF
story by Alfred Bester.
<https://www.gutenberg.org/files/61551/61551-h/61551-h.htm>

--

Jeff

"Jeff Layman" <jmlayman@invalid.invalid> wrote in message
news:scrtqp$sq7$1@dont-email.me...
> On 16/07/2021 12:47, gareth evans wrote:
>> On 15/07/2021 23:39, Owen Rees wrote:
>>> On Thu, 15 Jul 2021 12:03:21 +0100, Roderick Stewart
>>> <rjfs@escapetime.myzen.co.uk> wrote in
>>> <qg40fglmuueuovoh3hsq69njpble39sr0s@4ax.com>:
>>>
>>>> It's possible to derive the value of pi (not by me but by somebody
>>>> clever enough) without reference to geometry at all. The same can be
>>>> said of a great many other mathematical properties and relationships,
>>>> because they can exist in pure thoughtspace and so are unaffected by
>>>> any aspect of physical reality.
>>>
>>> Euler's formula - e^(i*pi) = -1 - is an example that relates three of
>>> the important numbers in mathematics. From what I remember, there is no
>>> geometry involved in that.
>>>
>>
>> If you present it in a slightly different format, it relates
>> FOUR important numbers ...
>>
>> e^(i*PI) + 1 = 0
>>
>> ... the zero, AKA cipher was a latecomer to arithmetic!
>
> If you're into mathematical formulae, you might be amused by this old SF
> story by Alfred Bester.
> <https://www.gutenberg.org/files/61551/61551-h/61551-h.htm>

This story of "Impure Mathematics" has been around for years. I remember
seeing it at university in the 1980s and I'm sure it was old even then.

https://www-users.cs.york.ac.uk/susan/joke/polly.htm

On 16/07/2021 14:20, NY wrote:
> "Jeff Layman" <jmlayman@invalid.invalid> wrote in message
> news:scrtqp$sq7$1@dont-email.me...
>> On 16/07/2021 12:47, gareth evans wrote:
>>> On 15/07/2021 23:39, Owen Rees wrote:
>>>> On Thu, 15 Jul 2021 12:03:21 +0100, Roderick Stewart
>>>> <rjfs@escapetime.myzen.co.uk> wrote in
>>>> <qg40fglmuueuovoh3hsq69njpble39sr0s@4ax.com>:
>>>>
>>>>> It's possible to derive the value of pi (not by me but by somebody
>>>>> clever enough) without reference to geometry at all. The same can be
>>>>> said of a great many other mathematical properties and relationships,
>>>>> because they can exist in pure thoughtspace and so are unaffected by
>>>>> any aspect of physical reality.
>>>>
>>>> Euler's formula - e^(i*pi) = -1 - is an example that relates three of
>>>> the important numbers in mathematics. From what I remember, there is no
>>>> geometry involved in that.
>>>>
>>>
>>> If you present it in a slightly different format, it relates
>>> FOUR important numbers ...
>>>
>>> e^(i*PI) + 1 = 0
>>>
>>> ... the zero, AKA cipher was a latecomer to arithmetic!
>>
>> If you're into mathematical formulae, you might be amused by this old SF
>> story by Alfred Bester.
>> <https://www.gutenberg.org/files/61551/61551-h/61551-h.htm>
>
> This story of "Impure Mathematics" has been around for years. I remember
> seeing it at university in the 1980s and I'm sure it was old even then.
>
> https://www-users.cs.york.ac.uk/susan/joke/polly.htm

Very clever. More puns and malapropisms (or are they? I thought
malapropisms were accidental, and these are intentional) than I've seen
in a long time!

--

Jeff

In message <scrrko$tba$1@dont-email.me>, gareth evans
<headstone255@yahoo.com> writes
>On 15/07/2021 23:39, Owen Rees wrote:
>> On Thu, 15 Jul 2021 12:03:21 +0100, Roderick Stewart
>> <rjfs@escapetime.myzen.co.uk> wrote in
>> <qg40fglmuueuovoh3hsq69njpble39sr0s@4ax.com>:
>>
>>> It's possible to derive the value of pi (not by me but by somebody
>>> clever enough) without reference to geometry at all. The same can be
>>> said of a great many other mathematical properties and relationships,
>>> because they can exist in pure thoughtspace and so are unaffected by
>>> any aspect of physical reality.
>>
>> Euler's formula - e^(i*pi) = -1 - is an example that relates three of
>> the important numbers in mathematics. From what I remember, there is no
>> geometry involved in that.
>>
>
>If you present it in a slightly different format, it relates
>FOUR important numbers ...
>
>e^(i*PI) + 1 = 0
>
>... the zero, AKA cipher was a latecomer to arithmetic!
>

The most beautiful equation in mathematics. It's astounding that two
irrational numbers and an imaginary number can be related in such a
simple way.
--
John Hall "Hard work often pays off after time, but laziness always
pays off now." Anon

In article <scp23h$qfd$1@dont-email.me>, gareth evans
<headstone255@yahoo.com> wrote:
> > That is incorrect. General Relativity tells us that the geometry of
> > space-time alters with the distribution of mass/energy/stress. The
> > standard definition of pi assumes a 'flat' space. Which in general is
> > just a good approximation.

> Not so much a flat spce, but taken in the plane of the circle, so even
> when the circle is drawn on a ball, the plane of the circle through the
> ball defines PI.

It defines the value *in a flat space*. (In your case, one cutting though
the 'ball'.) Not the value(s) in actual reality.

Jim

--
Please use the address on the audiomisc page if you wish to email me.
Electronics https://www.st-andrews.ac.uk/~www_pa/Scots_Guide/intro/electron.htm
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Audio Misc http://www.audiomisc.co.uk/index.html

In article <k200fgpjr22uar8fbfispooohf3p7cpmq3@4ax.com>, Roderick Stewart
<rjfs@escapetime.myzen.co.uk> wrote:
> On Wed, 14 Jul 2021 10:30:16 +0100, Jim Lesurf <noise@audiomisc.co.uk>
> wrote:

> >In article <fb9oeg12itvnbcgi8herphha0f0d9c015k@4ax.com>, Roderick
> >Stewart <rjfs@escapetime.myzen.co.uk> wrote:
> >> Maybe I'm not making myself clear. If you draw a circle on a ball in
> >> order to measure the value of pi, you're not drawing it on a flat
> >> surface. The value of pi is *defined* on a flat surface.
> >
> >By "is" you mean that this is what you and many textbooks assume.

> I mean that as far as I know it's the universally agreed definition. The
> textbooks don't "assume" it; they tell us what it is; it can be worked
> out.

> The ratio of circumference to diameter may be different on a curved
> surface, but it's not pi,

If you choose to define the mathematical abstraction 'pi' *only* in terms
of a flat space, then you can set the value you focus upon. But reality
doesn't actually care about your narrow determination to ignore it. In the
real world the value will vary.

> Thus pi, like every other mathematical truth, relationship or value, is
> an example of something which could not have been "created" in the sense
> of somebody (or something) deciding how it should be.

Erm You 'created' it by virture of having invented a 'flat space' as the
way you defined it. The 'flat space' is a mathematical construct.

> It may be made to look different depending on the language or notaion
> you choose, but its numerical value cannot be anything other than what
> it is, and even a god could not change it.

If there *is* a God, then the actual value be in accord with the geometry
they gave reality - and which varies with the local geometry.

We don't know for sure the geometry averaged over the entire universe. It
seems likely not to be 'flat'. But either way, we can know it varies from
place to place 'locally'. e.g. near any mass concentrations where space
isn't flat.

Jim

--
Please use the address on the audiomisc page if you wish to email me.
Electronics https://www.st-andrews.ac.uk/~www_pa/Scots_Guide/intro/electron.htm
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Audio Misc http://www.audiomisc.co.uk/index.html

In article <scp34g$9so$1@dont-email.me>, NY <me@privacy.invalid> wrote:
> "gareth evans" <headstone255@yahoo.com> wrote in message
> news:scp2ca$vp9$1@dont-email.me...
> > Irrespectiive of the nature of the curvature of the surface, if all
> > parts of what you draw are not coplanar, then what you haven't got is
> > a circle!
> >
> > eg, were you to have a circle drawn on a flat piece of paper, and then
> > that paper were to be wrapped around some other curved object, then
> > the resultant shape will have some other geometric definition other
> > than a circle.

> What's the geometric definition of wrinkles and creases? ;-)

Fractal? 8-]

Jim

--
Please use the address on the audiomisc page if you wish to email me.
Electronics https://www.st-andrews.ac.uk/~www_pa/Scots_Guide/intro/electron.htm
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Audio Misc http://www.audiomisc.co.uk/index.html

In article <dtg5shxpqq.ln2@threeformcow.myzen.co.uk>, #Paul
<news20k.noreply@threeformcow.myzen.co.uk> wrote:
> Jim Lesurf <noise@audiomisc.co.uk> wrote:
> > Will General Relativity do? It is usually defined in terms of 4D
> > geometric form. And can be used to specify how the measured value of
> > pi will vary in accord with local mass/etc distributions, etc.

> An important point here is that any "measured value of pi" is *not* the
> value of the mathematical constant pi, because the value of the
> mathematical constant is defined mathematically.

Yes. And the value you then get depends on your choice for the behaviour of
the space you assume.

> Also, in any region of constant curvature, the "measured value of pi"
> will depend on the size of the circle used; e.g. for fixed curvature,
> as a circle shrinks, the flatter the space appears, and so that circle,
> if ideally measured, will produce a measured value of pi ever closer to
> the mathematically defined value.

Yes. Assuming no discontinuities of fractality. Beware of naked kernels!
8-]

Jim

--
Please use the address on the audiomisc page if you wish to email me.
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In article <7ud1fgdefg6f1hhtc62halm5ufo630on4h@4ax.com>, Owen Rees
<orees@hotmail.com> wrote:
> On Thu, 15 Jul 2021 12:03:21 +0100, Roderick Stewart
> <rjfs@escapetime.myzen.co.uk> wrote in
> <qg40fglmuueuovoh3hsq69njpble39sr0s@4ax.com>:

> >It's possible to derive the value of pi (not by me but by somebody
> >clever enough) without reference to geometry at all. The same can be
> >said of a great many other mathematical properties and relationships,
> >because they can exist in pure thoughtspace and so are unaffected by
> >any aspect of physical reality.

> Euler's formula - e^(i*pi) = -1 - is an example that relates three of
> the important numbers in mathematics. From what I remember, there is no
> geometry involved in that.

Golden Rectangle? ... in a flat space, of course. 8-]

Also, by adopting complex numbers you also assume a 2D plane that is linear
and uniform - i.e. flat plane.

It's a lovely equation, though.

Jim

--
Please use the address on the audiomisc page if you wish to email me.
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On Fri, 16 Jul 2021 10:15:04 +0100, Jim Lesurf <noise@audiomisc.co.uk>
wrote:

>> The ratio of circumference to diameter may be different on a curved
>> surface, but it's not pi,
>
>If you choose to define the mathematical abstraction 'pi' *only* in terms
>of a flat space, then you can set the value you focus upon. But reality
>doesn't actually care about your narrow determination to ignore it. In the
>real world the value will vary.

I've always understood that pi is defined in terms of a flat space.
Even if you regard the commonly understood value to be just a special
case when the surface is flat, it has a fixed value that could not
have been the result of anybody's creative decision, because it is a
numerical property of the situation in which it is defined. It simply
is what it has to be. It makes no difference whether you call the
non-flat cases by the same name or a different one. Playing with words
doesn't change the fact that pi on a flat surface, like many other
mathematical constants, is a fixed value that could not be anything
different from what it must be.

We might like to imagine alternative universes in which the physical
constants are different (because for the time being we can't rule this
out as impossible because we don't know what, if anything, the
physical constants depend on), but there exist plenty of mathematical
constants that are absolute and unchangeable.

Rod.

On Fri, 16 Jul 2021 12:50:26 +0100
gareth evans <headstone255@yahoo.com> wrote:
>On 15/07/2021 23:51, Owen Rees wrote:
>> On Thu, 15 Jul 2021 11:31:16 +0000 (UTC),
>> MrSpud__6_Empu@_wcx8qng2806nrkb65.co.uk wrote in
>> <scp6a4$ns5$1@gioia.aioe.org>:
>>
>>> Also mathametics cannot describe reality accuractly as witnessed
>>> by pi being an irrational number.
>>
>> Pi is transcendental rather than just irrational (this has been known
>> since the 19th Century). There are whole branches of mathematics that
>> deal with things that cannot be expressed in the number system we use in
>> normal life. The difficulty in describing reality is not a weakness in
>> mathematics.

No, but it does show that mathematics cannot be a full description of reality
so any theories of reality sitting on a mathematical foundation are doomed to
eventually fail.

On Fri, 16 Jul 2021 16:07:44 +0100
John Hall <john_nospam@jhall.co.uk> wrote:
>In message <scrrko$tba$1@dont-email.me>, gareth evans
>>If you present it in a slightly different format, it relates
>>FOUR important numbers ...
>>
>>e^(i*PI) + 1 = 0
>>
>>... the zero, AKA cipher was a latecomer to arithmetic!
>>
>
>The most beautiful equation in mathematics. It's astounding that two
>irrational numbers and an imaginary number can be related in such a
>simple way.

Imaginary numbers are simply a hack to make the maths humans have invented
work properly. You won't find them in nature.

On Fri, 16 Jul 2021 10:09:33 +0100, Jim Lesurf <noise@audiomisc.co.uk>
wrote:

>In article <scp23h$qfd$1@dont-email.me>, gareth evans
><headstone255@yahoo.com> wrote:
>> > That is incorrect. General Relativity tells us that the geometry of
>> > space-time alters with the distribution of mass/energy/stress. The
>> > standard definition of pi assumes a 'flat' space. Which in general is
>> > just a good approximation.
>
>> Not so much a flat spce, but taken in the plane of the circle, so even
>> when the circle is drawn on a ball, the plane of the circle through the
>> ball defines PI.
>
>It defines the value *in a flat space*. (In your case, one cutting though
>the 'ball'.) Not the value(s) in actual reality.
>

pi is a CONSTANT defined in Euclidean goemetry, then the ratio of
cicumference to diameter in any geometry OTHER than Euclidean in not
pi, no matter what you call it.

--
brightside s9

On Sat, 17 Jul 2021 15:20:18 +0000 (UTC), MrSpud_t6y0f5o@k_0xu_t.org
wrote in <scusfi$1dsj$1@gioia.aioe.org>:

>On Fri, 16 Jul 2021 12:50:26 +0100
>gareth evans <headstone255@yahoo.com> wrote:
>>On 15/07/2021 23:51, Owen Rees wrote:
>>> On Thu, 15 Jul 2021 11:31:16 +0000 (UTC),
>>> MrSpud__6_Empu@_wcx8qng2806nrkb65.co.uk wrote in
>>> <scp6a4$ns5$1@gioia.aioe.org>:
>>>
>>>> Also mathametics cannot describe reality accuractly as witnessed
>>>> by pi being an irrational number.
>>>
>>> Pi is transcendental rather than just irrational (this has been known
>>> since the 19th Century). There are whole branches of mathematics that
>>> deal with things that cannot be expressed in the number system we use in
>>> normal life. The difficulty in describing reality is not a weakness in
>>> mathematics.
>
>No, but it does show that mathematics cannot be a full description of reality
>so any theories of reality sitting on a mathematical foundation are doomed to
>eventually fail.

Not so much fail as be replaced by something that builds on the previous
work and covers cases that were not handled well by earlier models.

We know the limitations of some of the older and simpler formulae and
that they are still good enough if the deviation from the newer more
complete model is negligible for the case in question.

We do not need the most up to date models of gravity and motion to
predict where a ball fired from a cannon will land. The old models with
all their imperfections give answers good enough that the margins of
error in other factors will dominate in any deviation from the
calculated result.

On Fri, 16 Jul 2021 10:17:57 +0100, Jim Lesurf <noise@audiomisc.co.uk>
wrote in <594cdc2f3bnoise@audiomisc.co.uk>:

>In article <dtg5shxpqq.ln2@threeformcow.myzen.co.uk>, #Paul
><news20k.noreply@threeformcow.myzen.co.uk> wrote:
>> Jim Lesurf <noise@audiomisc.co.uk> wrote:
>> > Will General Relativity do? It is usually defined in terms of 4D
>> > geometric form. And can be used to specify how the measured value of
>> > pi will vary in accord with local mass/etc distributions, etc.
>
>> An important point here is that any "measured value of pi" is *not* the
>> value of the mathematical constant pi, because the value of the
>> mathematical constant is defined mathematically.
>
>Yes. And the value you then get depends on your choice for the behaviour of
>the space you assume.
>

The formula for the relationship between circumference and diameter may
well vary depending on what those terms mean in whatever geometry you
are considering, the value of pi does not change.

On Sat, 17 Jul 2021 23:13:26 +0100, Owen Rees <orees@hotmail.com>
wrote:

>On Fri, 16 Jul 2021 10:17:57 +0100, Jim Lesurf <noise@audiomisc.co.uk>
>wrote in <594cdc2f3bnoise@audiomisc.co.uk>:
>
>>In article <dtg5shxpqq.ln2@threeformcow.myzen.co.uk>, #Paul
>><news20k.noreply@threeformcow.myzen.co.uk> wrote:
>>> Jim Lesurf <noise@audiomisc.co.uk> wrote:
>>> > Will General Relativity do? It is usually defined in terms of 4D
>>> > geometric form. And can be used to specify how the measured value of
>>> > pi will vary in accord with local mass/etc distributions, etc.
>>
>>> An important point here is that any "measured value of pi" is *not* the
>>> value of the mathematical constant pi, because the value of the
>>> mathematical constant is defined mathematically.
>>
>>Yes. And the value you then get depends on your choice for the behaviour of
>>the space you assume.
>>
>
>The formula for the relationship between circumference and diameter may
>well vary depending on what those terms mean in whatever geometry you
>are considering, the value of pi does not change.

The universal adoption of agreed definitions is vital here, otherwise
we're just arguing about words and not the actual concept. I can think
of two ways we could deal with the concept of the circle ratio-

1. pi=C/D for all surfaces. If the curvature of the surfaces varies,
then so does C/D and therefore pi varies with it because it is defined
in terms of C/D and nothing else. The values are linked. The value of
C/D and therefore pi for a flat surface is just a special case.

2. pi=C/D for a flat surface. If the curvature of the surface varies,
then C/D varies, but pi doesn't. pi and C/D can differ from each
other, and there is only one special case where they are the same. The
values are not linked. The value of pi remains the same because it is
defined for a particular curvature.

Either of the above would be a perfectly valid way of defining pi, as
long as everybody agreed which one we should use. However, as far as I
know, definition No 2 is the one that has always been regarded as the
correct one. It would be the more logical description anyway if we
call pi a constant - which we do - because it wouldn't be much of a
constant if we adopted a scheme in which it varied.

Rod.

On Sun, 18 Jul 2021 08:58:31 +0100, Roderick Stewart
<rjfs@escapetime.myzen.co.uk> wrote:

>On Sat, 17 Jul 2021 23:13:26 +0100, Owen Rees <orees@hotmail.com>
>wrote:
>
>>On Fri, 16 Jul 2021 10:17:57 +0100, Jim Lesurf <noise@audiomisc.co.uk>
>>wrote in <594cdc2f3bnoise@audiomisc.co.uk>:
>>
>>>In article <dtg5shxpqq.ln2@threeformcow.myzen.co.uk>, #Paul
>>><news20k.noreply@threeformcow.myzen.co.uk> wrote:
>>>> Jim Lesurf <noise@audiomisc.co.uk> wrote:
>>>> > Will General Relativity do? It is usually defined in terms of 4D
>>>> > geometric form. And can be used to specify how the measured value of
>>>> > pi will vary in accord with local mass/etc distributions, etc.
>>>
>>>> An important point here is that any "measured value of pi" is *not* the
>>>> value of the mathematical constant pi, because the value of the
>>>> mathematical constant is defined mathematically.
>>>
>>>Yes. And the value you then get depends on your choice for the behaviour of
>>>the space you assume.
>>>
>>
>>The formula for the relationship between circumference and diameter may
>>well vary depending on what those terms mean in whatever geometry you
>>are considering, the value of pi does not change.
>
>The universal adoption of agreed definitions is vital here, otherwise
>we're just arguing about words and not the actual concept. I can think
>of two ways we could deal with the concept of the circle ratio-
>
>1. pi=C/D for all surfaces. If the curvature of the surfaces varies,
>then so does C/D and therefore pi varies with it because it is defined
>in terms of C/D and nothing else. The values are linked. The value of
>C/D and therefore pi for a flat surface is just a special case.
>
>2. pi=C/D for a flat surface. If the curvature of the surface varies,
>then C/D varies, but pi doesn't. pi and C/D can differ from each
>other, and there is only one special case where they are the same. The
>values are not linked. The value of pi remains the same because it is
>defined for a particular curvature.
>
>Either of the above would be a perfectly valid way of defining pi, as
>long as everybody agreed which one we should use. However, as far as I
>know, definition No 2 is the one that has always been regarded as the
>correct one. It would be the more logical description anyway if we
>call pi a constant - which we do - because it wouldn't be much of a
>constant if we adopted a scheme in which it varied.

For example there is a particularly objectionable article published
on a US university site. The text clearly shows that the author did
not know the definition of pi.
https://physics.illinois.edu/news/article/10665

--
brightside S8

On Sat, 17 Jul 2021 22:59:03 +0100
Owen Rees <orees@hotmail.com> wrote:
>On Sat, 17 Jul 2021 15:20:18 +0000 (UTC), MrSpud_t6y0f5o@k_0xu_t.org
>wrote in <scusfi$1dsj$1@gioia.aioe.org>:
>>No, but it does show that mathematics cannot be a full description of reality
>>so any theories of reality sitting on a mathematical foundation are doomed to
>>eventually fail.
>
>Not so much fail as be replaced by something that builds on the previous
>work and covers cases that were not handled well by earlier models.
>
>We know the limitations of some of the older and simpler formulae and
>that they are still good enough if the deviation from the newer more
>complete model is negligible for the case in question.
>
>We do not need the most up to date models of gravity and motion to
>predict where a ball fired from a cannon will land. The old models with
>all their imperfections give answers good enough that the margins of
>error in other factors will dominate in any deviation from the
>calculated result.

I'm not talking about mathematics that does a good enough job of predicting
how various laws of physics pan out over time, I'm talking about the fundamental
underpinnings of reality itself. If mathematics is incomplete as Godel showed
it was and it needs various hacks such as complex numbers to work plus
oddities such as pi being transcendental when it describes a real physical
ratio, reality itself cannot be based on mathematics as we know it.