I was just thinking, which I know can be very dangerous, about this. We have
a name for it, but in fact it does not exist. I mean we often quote PI, as
an infinite number. That is only so because we tie ourselves to values with
finite amounts, so to speak. In the end its a pointer toward the way the
universe works, which at its smallest level seems random and one can only
describe anything as a range of probabilities.
Ever wondered why the first attempts at digital audio sounded so bad? It
was because at the lowest volume level it could encode it then jumped to 0.
This sounds awful, makes sounds fuzzy. Modern digital recording added dither
and then levels are not defined as accurately, making them more real.

I remember when at school and we were taught about atoms and how most solids
are mostly empty space, but nobody could come up with a measure of that
space, since you could never tell where an electron was at a given moment.
The world refuses to be governed by numbers, but we simply use them to
approximate things so we get a level of accuracy we can work with, but in
reality, reality is not like that at all.
Brian

--

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Note this Signature is meaningless.!

Early digital sounded bad as the engineers were still learning how to
master for it, and also because even the best converters of the time
could only reliably manage 14 bits of resolution, no matter what it said
on the box. The analogue part of the ADC wasn't all that linear, either.

Modern converters, even in my portable recorders, can handle at least 24
bits, and the only time dithering is used is when I reduce the
resolution to 16 bits to burn the music to CD. My digital masters sound
better than anything I've ever been able to do using analogue formats.

On 08/01/2023 12:20, Brian Gaff wrote:
> I was just thinking, which I know can be very dangerous, about this. We have
> a name for it, but in fact it does not exist. I mean we often quote PI, as
> an infinite number. That is only so because we tie ourselves to values with
> finite amounts, so to speak. In the end its a pointer toward the way the
> universe works, which at its smallest level seems random and one can only
> describe anything as a range of probabilities.
> Ever wondered why the first attempts at digital audio sounded so bad? It
> was because at the lowest volume level it could encode it then jumped to 0.
> This sounds awful, makes sounds fuzzy. Modern digital recording added dither
> and then levels are not defined as accurately, making them more real.

--
Tciao for Now!

John.

On 2023-01-08, John Williamson <johnwilliamson@btinternet.com> wrote:
> Early digital sounded bad as the engineers were still learning how to
> master for it, and also because even the best converters of the time
> could only reliably manage 14 bits of resolution, no matter what it said
> on the box. The analogue part of the ADC wasn't all that linear, either.
>
> Modern converters, even in my portable recorders, can handle at least 24
> bits, and the only time dithering is used is when I reduce the
> resolution to 16 bits to burn the music to CD. My digital masters sound
> better than anything I've ever been able to do using analogue formats.
>
> On 08/01/2023 12:20, Brian Gaff wrote:
>> I was just thinking, which I know can be very dangerous, about this. We have
>> a name for it, but in fact it does not exist. I mean we often quote PI, as
>> an infinite number. That is only so because we tie ourselves to values with
>> finite amounts, so to speak. In the end its a pointer toward the way the
>> universe works, which at its smallest level seems random and one can only
>> describe anything as a range of probabilities.
>> Ever wondered why the first attempts at digital audio sounded so bad? It
>> was because at the lowest volume level it could encode it then jumped to 0.
>> This sounds awful, makes sounds fuzzy. Modern digital recording added dither
>> and then levels are not defined as accurately, making them more real.
>
>

When I used a lathe, and all that entails, I disliked digital measurers
that would tell me lengths in thousands of an inch {before metrics) It
is all bollix. Until you learned how to hold a calipers, it was hard to
get a hundered precision

--
greymausg@mail.com

Fe, Fi, Fo, Fum, I smell the stench of an Influencer.
Where is our money gone, Dude?

On Sun, 8 Jan 2023 12:20:36 -0000
"Brian Gaff" <brian1gaff@gmail.com> wrote:

> I was just thinking, which I know can be very dangerous, about this.

A fellow named Cantor drove himself mad thinking about infinity and
the fact that there's more than one distinct infinity.

--
Steve O'Hara-Smith
Odds and Ends at http://www.sohara.org/

In article <k1vu4vFifgkU1@mid.individual.net>, John Williamson
<johnwilliamson@btinternet.com> on Sun, 8 Jan 2023 at 13:18:22 awoke
Nicholas from his slumbers and wrote
>On 08/01/2023 12:20, Brian Gaff wrote:
>> I was just thinking, which I know can be very dangerous, about this. We have
>> a name for it, but in fact it does not exist. I mean we often quote PI, as
>> an infinite number.
>
[Pedant Mode ON]

As I remember it pi is an irrational number, in that its value cannot be
expressed as a fraction of two real integers. Pi has a value and
therefore cannot have an infinite value.

[Pedant Mode OFF]

OTOH this pedant could be wrong.
--
0sterc@tcher -

"Où sont les neiges d'antan?"

On 08/01/2023 17:19, Nicholas D. Richards wrote:
> In article <k1vu4vFifgkU1@mid.individual.net>, John Williamson
> <johnwilliamson@btinternet.com> on Sun, 8 Jan 2023 at 13:18:22 awoke
> Nicholas from his slumbers and wrote
>> On 08/01/2023 12:20, Brian Gaff wrote:
>>> I was just thinking, which I know can be very dangerous, about this. We have
>>> a name for it, but in fact it does not exist. I mean we often quote PI, as
>>> an infinite number.
>>
> [Pedant Mode ON]
>
> As I remember it pi is an irrational number, in that its value cannot be
> expressed as a fraction of two real integers. Pi has a value and
> therefore cannot have an infinite value.
>
> [Pedant Mode OFF]
>
> OTOH this pedant could be wrong.

(Homer Simpson mode ON)

H'mmmm, pi !

(Homer Simpson mode OFF)

Tone

On Sun, 8 Jan 2023 17:19:26 +0000
"Nicholas D. Richards" <nicholas@salmiron.com> wrote:

> As I remember it pi is an irrational number, in that its value cannot be
> expressed as a fraction of two real integers. Pi has a value and
> therefore cannot have an infinite value.

This is correct as far as it goes, pi is not just irrational
(cannot be expressed as a ratio of integers) but also transcendental,
it cannot be the solution of a polynomial with rational coefficients. I'm
not certain but I believe the last implies that it cannot be represented by
any finite collection of rational numbers which is the sense in which it
can be considered infinite - or at least requiring an infinite
representation.

Proving any of this is not for the faint hearted or mathematically
challenged.

--
Steve O'Hara-Smith
Odds and Ends at http://www.sohara.org/

On 08/01/2023 17:19, Nicholas D. Richards wrote:
> In article <k1vu4vFifgkU1@mid.individual.net>, John Williamson
> <johnwilliamson@btinternet.com> on Sun, 8 Jan 2023 at 13:18:22 awoke
> Nicholas from his slumbers and wrote
>> On 08/01/2023 12:20, Brian Gaff wrote:
>>> I was just thinking, which I know can be very dangerous, about this. We have
>>> a name for it, but in fact it does not exist. I mean we often quote PI, as
>>> an infinite number.
>>
> [Pedant Mode ON]
>
> As I remember it pi is an irrational number, in that its value cannot be
> expressed as a fraction of two real integers. Pi has a value and
> therefore cannot have an infinite value.
>
> [Pedant Mode OFF]
>
> OTOH this pedant could be wrong.

Doesn't 22/7 count as a ratio[1] of two integers then?

Chris
[1] Yes, I know you said fraction but..
--
The Deuchars BBB#40 COFF#14
Yamaha XV750SE & Suzuki GS550t
http://www.Deuchars.org.uk

Well, I do notice the differences between dithered and not dithered, but
then we are going to run into the problem of how well designed the d to a
was in the first place. I have aCD100 machine here, and I think it has a
tendency to blast ie one symptom of not getting the samples very
accurately, and muddling up the detail.
I notice that these days, digital recorders are floating point which means
as far as I can see that its almost impossible to overload or get into noise
issues in the digital part of the device. I only came across this since it
means blindies like me need not be too worried about levels and even things
up later on.
I have a cd here called Digital Magic, which shows up the effect about it
not being very linear at low levels, and sounding grainy.
Brian

--

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Blind user, so no pictures please
Note this Signature is meaningless.!
"John Williamson" <johnwilliamson@btinternet.com> wrote in message
news:k1vu4vFifgkU1@mid.individual.net...
> Early digital sounded bad as the engineers were still learning how to
> master for it, and also because even the best converters of the time could
> only reliably manage 14 bits of resolution, no matter what it said on the
> box. The analogue part of the ADC wasn't all that linear, either.
>
> Modern converters, even in my portable recorders, can handle at least 24
> bits, and the only time dithering is used is when I reduce the resolution
> to 16 bits to burn the music to CD. My digital masters sound better than
> anything I've ever been able to do using analogue formats.
>
> On 08/01/2023 12:20, Brian Gaff wrote:
>> I was just thinking, which I know can be very dangerous, about this. We
>> have
>> a name for it, but in fact it does not exist. I mean we often quote PI,
>> as
>> an infinite number. That is only so because we tie ourselves to values
>> with
>> finite amounts, so to speak. In the end its a pointer toward the way the
>> universe works, which at its smallest level seems random and one can
>> only
>> describe anything as a range of probabilities.
>> Ever wondered why the first attempts at digital audio sounded so bad? It
>> was because at the lowest volume level it could encode it then jumped to
>> 0.
>> This sounds awful, makes sounds fuzzy. Modern digital recording added
>> dither
>> and then levels are not defined as accurately, making them more real.
>
>
> --
> Tciao for Now!
>
> John.

Well, yes but you are in fact saying the same thing differently. It all
boils down to numbers. (Noting that Kate Bush has a song called PI) and yet
we still use it to calculate circles and stuff.
Brian

--

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Blind user, so no pictures please
Note this Signature is meaningless.!
"Tone" <tone@email.com> wrote in message
news:tpeuqp$3t55g$2@dont-email.me...
> On 08/01/2023 17:19, Nicholas D. Richards wrote:
>> In article <k1vu4vFifgkU1@mid.individual.net>, John Williamson
>> <johnwilliamson@btinternet.com> on Sun, 8 Jan 2023 at 13:18:22 awoke
>> Nicholas from his slumbers and wrote
>>> On 08/01/2023 12:20, Brian Gaff wrote:
>>>> I was just thinking, which I know can be very dangerous, about this. We
>>>> have
>>>> a name for it, but in fact it does not exist. I mean we often quote PI,
>>>> as
>>>> an infinite number.
>>>
>> [Pedant Mode ON]
>>
>> As I remember it pi is an irrational number, in that its value cannot be
>> expressed as a fraction of two real integers. Pi has a value and
>> therefore cannot have an infinite value.
>>
>> [Pedant Mode OFF]
>>
>> OTOH this pedant could be wrong.
>
>
> (Homer Simpson mode ON)
>
> H'mmmm, pi !
>
> (Homer Simpson mode OFF)
>
> Tone

No half way through the explanation at School, I stated to think of girls
instead of PI, now that might have been because it lost me or that I was of
a certain age.
Brian

--

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Blind user, so no pictures please
Note this Signature is meaningless.!
"Ahem A Rivet's Shot" <steveo@eircom.net> wrote in message
news:20230108194740.619657a3f12ba3607c71387f@eircom.net...
> On Sun, 8 Jan 2023 17:19:26 +0000
> "Nicholas D. Richards" <nicholas@salmiron.com> wrote:
>
>> As I remember it pi is an irrational number, in that its value cannot be
>> expressed as a fraction of two real integers. Pi has a value and
>> therefore cannot have an infinite value.
>
> This is correct as far as it goes, pi is not just irrational
> (cannot be expressed as a ratio of integers) but also transcendental,
> it cannot be the solution of a polynomial with rational coefficients. I'm
> not certain but I believe the last implies that it cannot be represented
> by
> any finite collection of rational numbers which is the sense in which it
> can be considered infinite - or at least requiring an infinite
> representation.
>
> Proving any of this is not for the faint hearted or mathematically
> challenged.
>
> --
> Steve O'Hara-Smith
> Odds and Ends at http://www.sohara.org/

Does this mean in fact that there an infinite number of infinities, or that
our current knowledge and methods of thinking simply will not allow us to
comprehend this, or maybe there is no infinity, other than a failure to be
able to define it.

Brian

--

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Note this Signature is meaningless.!
"Ahem A Rivet's Shot" <steveo@eircom.net> wrote in message
news:20230108161706.10e32f240b8eaf0198253d3a@eircom.net...
> On Sun, 8 Jan 2023 12:20:36 -0000
> "Brian Gaff" <brian1gaff@gmail.com> wrote:
>
>> I was just thinking, which I know can be very dangerous, about this.
>
> A fellow named Cantor drove himself mad thinking about infinity and
> the fact that there's more than one distinct infinity.
>
> --
> Steve O'Hara-Smith
> Odds and Ends at http://www.sohara.org/

On 09/01/2023 10:16, chrisnd @ukrm wrote:
> On 08/01/2023 17:19, Nicholas D. Richards wrote:
>> [Pedant Mode ON]
>>
>> As I remember it pi is an irrational number, in that its value cannot be
>> expressed as a fraction of two real integers. Pi has a value and
>> therefore cannot have an infinite value.
>>
>> [Pedant Mode OFF]
>>
>> OTOH this pedant could be wrong.
>
> Doesn't 22/7 count as a ratio[1] of two integers then?
>
It does, but 22/7 is not the exact value of Pi. It is near enough for
most purposes, as the error is fairy small, at around 0.04%, but the
error adds up when you go round the circle a few (Or even worse, a few
thousand or million) times. Before calculators, we had 4 digit log
tables, and slide rules of about the same accuracy, so we used Pi =
3.142. Then, at college, we got calculators, and PI magically became
3.1415927 overnight.

You can get arbitrarily close when calculating Pi and writing down the
value, but you can never be exact. The most accurate value of Pi is
known to 62,831,853,071,796 digits (Which, you have to admit, is pretty
precise) and has no repeating strings of digits. There is probably a
computer working on the next few million digits as I type.

--
Tciao for Now!

John.

On 09/01/2023 11:48, John Williamson wrote:
> On 09/01/2023 10:16, chrisnd @ukrm wrote:
>> On 08/01/2023 17:19, Nicholas D. Richards wrote:
>>> [Pedant Mode ON]
>>>
>>> As I remember it pi is an irrational number, in that its value cannot be
>>> expressed as a fraction of two real integers. Pi has a value and
>>> therefore cannot have an infinite value.
>>>
>>> [Pedant Mode OFF]
>>>
>>> OTOH this pedant could be wrong.
>>
>> Doesn't 22/7 count as a ratio[1] of two integers then?
>>
> It does, but 22/7 is not the exact value of Pi. It is near enough for
> most purposes, as the error is fairy small ...

And in the other direction
PI^2 is near enough to 10 to make no significant difference in most cases.

--
Nev
It causes me a great deal of regret and remorse
that so many people are unable to understand what I write.

On Mon, 9 Jan 2023 10:55:03 -0000
"Brian Gaff" <brian1gaff@gmail.com> wrote:

> Well, yes but you are in fact saying the same thing differently. It all
> boils down to numbers. (Noting that Kate Bush has a song called PI) and
> yet we still use it to calculate circles and stuff.

We have to, pi is defined as the ratio between the diameter
and circumference of a circle so it is rather fundamental to circles.
Whenever pi appears in mathematics there is a circle somewhere, when you
find it you achieve a deeper understanding of the mathematics involved.

--
Steve O'Hara-Smith
Odds and Ends at http://www.sohara.org/

On Mon, 9 Jan 2023 10:56:53 -0000
"Brian Gaff" <brian1gaff@gmail.com> wrote:

> No half way through the explanation at School, I stated to think of
> girls instead of PI, now that might have been because it lost me or that
> I was of a certain age.

I managed to do both and wound up with the girl who surprised
everyone by beating me in maths tests from time to time.

--
Steve O'Hara-Smith
Odds and Ends at http://www.sohara.org/

On Mon, 9 Jan 2023 10:50:45 -0000
"Brian Gaff" <brian1gaff@gmail.com> wrote:

> Well, I do notice the differences between dithered and not dithered, but
> then we are going to run into the problem of how well designed the d to a
> was in the first place.

Really good D/A is easy, really good A/D rather less so.

--
Steve O'Hara-Smith
Odds and Ends at http://www.sohara.org/

On Mon, 9 Jan 2023 11:00:45 -0000
"Brian Gaff" <brian1gaff@gmail.com> wrote:

> Does this mean in fact that there an infinite number of infinities, or

Yes it does, the infinities are enumerated by the transfinite
integers aleph-null, aleph-one ... which I think means that the order of
the set of infinities is the same as that of the set of integers, but I
can't prove it.

We covered this in the second year of maths at Cambridge with some
of the most wonderful lectures I have ever attended (John Conway is a
*fantastic* lecturer) - we were warned not to take notes because he kept
erasing parts of the board and redrawing them in different colours to
illustrate what he was saying. I certainly can't reproduce much of it now.

--
Steve O'Hara-Smith
Odds and Ends at http://www.sohara.org/

In article <tph0fc$5dgl$1@dont-email.me>, nev young <newsforpasiphae1953
@yahoo.co.uk> on Mon, 9 Jan 2023 at 12:14:36 awoke Nicholas from his
slumbers and wrote
>On 09/01/2023 11:48, John Williamson wrote:
>> On 09/01/2023 10:16, chrisnd @ukrm wrote:
>>> On 08/01/2023 17:19, Nicholas D. Richards wrote:
>>>> [Pedant Mode ON]
>>>>
>>>> As I remember it pi is an irrational number, in that its value cannot be
>>>> expressed as a fraction of two real integers. Pi has a value and
>>>> therefore cannot have an infinite value.
>>>>
>>>> [Pedant Mode OFF]
>>>>
>>>> OTOH this pedant could be wrong.
>>>
>>> Doesn't 22/7 count as a ratio[1] of two integers then?
>>>
>> It does, but 22/7 is not the exact value of Pi. It is near enough for
>> most purposes, as the error is fairy small ...
>
>And in the other direction
>PI^2 is near enough to 10 to make no significant difference in most cases.
>
>
QI but is that significant mathematically.

Is Pi raised to the power n (except where n is 1) for anything other
than that it is QI?
--
0sterc@tcher -

"Où sont les neiges d'antan?"

In article <20230109135953.662a3e2a44f2b2201d9b4feb@eircom.net>, Ahem A
Rivet's Shot <steveo@eircom.net> on Mon, 9 Jan 2023 at 13:59:53 awoke
Nicholas from his slumbers and wrote
>On Mon, 9 Jan 2023 11:00:45 -0000
>"Brian Gaff" <brian1gaff@gmail.com> wrote:
>
>> Does this mean in fact that there an infinite number of infinities, or
>
> Yes it does, the infinities are enumerated by the transfinite
>integers aleph-null, aleph-one ... which I think means that the order of
>the set of infinities is the same as that of the set of integers, but I
>can't prove it.
>
> We covered this in the second year of maths at Cambridge with some
>of the most wonderful lectures I have ever attended (John Conway is a
>*fantastic* lecturer) - we were warned not to take notes because he kept
>erasing parts of the board and redrawing them in different colours to
>illustrate what he was saying. I certainly can't reproduce much of it now.
>
Despite my grade 'A' in 'A' Level Maths (Pure and Applied) I am awfully
glad that I did not go onto read Mathematics. I thoroughly enjoyed that
A level but when I took a peak at the content of degree level Maths I
quickly came to the conclusion that I would not be able to hack it.
Thermodynamics was enough for me in Chemistry.

My brother read Mining Engineering and needed coaching beyond A level
Maths. Biology was more my choice although from what I can see (65+
years later) Biology seems to be moving in the same direction, away from
the tangible world.
--
0sterc@tcher -

"Où sont les neiges d'antan?"

On 09/01/2023 17:02, Nicholas D. Richards wrote:

> Despite my grade 'A' in 'A' Level Maths (Pure and Applied) I am awfully
> glad that I did not go onto read Mathematics. I thoroughly enjoyed that
> A level but when I took a peak at the content of degree level Maths I
> quickly came to the conclusion that I would not be able to hack it.
> Thermodynamics was enough for me in Chemistry.
>
Randall cracked it a while back.

https://xkcd.com/435/

--
Tciao for Now!

John.

On Mon, 9 Jan 2023 17:02:40 +0000
"Nicholas D. Richards" <nicholas@salmiron.com> wrote:

> In article <20230109135953.662a3e2a44f2b2201d9b4feb@eircom.net>, Ahem A
> Rivet's Shot <steveo@eircom.net> on Mon, 9 Jan 2023 at 13:59:53 awoke

> > We covered this in the second year of maths at Cambridge with some
> >of the most wonderful lectures I have ever attended (John Conway is a
> >*fantastic* lecturer) - we were warned not to take notes because he kept
> >erasing parts of the board and redrawing them in different colours to
> >illustrate what he was saying. I certainly can't reproduce much of it
> >now.
> >
> Despite my grade 'A' in 'A' Level Maths (Pure and Applied) I am awfully
> glad that I did not go onto read Mathematics. I thoroughly enjoyed that

Despite my effortless 'A's and distinctions in Maths and Further
Maths 'A' and 'S' levels I ran out of steam in second year probability and
sadistics which was twisted beyond belief (or at least beyond my capacity
for corkscrewing my brian). If it hadn't been for that I'd probably have
been OK (I loved the abstractions that algebra and analysis grew into
before all but merging) but I'll never know because I bailed to computer
science and a career in industry.

--
Steve O'Hara-Smith
Odds and Ends at http://www.sohara.org/

Ahem A Rivet's Shot <steveo@eircom.net> wrote in
news:20230109182343.f230ec40a8e543bb1251245e@eircom.net:

> On Mon, 9 Jan 2023 17:02:40 +0000
> "Nicholas D. Richards" <nicholas@salmiron.com> wrote:
>
>> In article <20230109135953.662a3e2a44f2b2201d9b4feb@eircom.net>, Ahem
>> A Rivet's Shot <steveo@eircom.net> on Mon, 9 Jan 2023 at 13:59:53
>> awoke
>
>> > We covered this in the second year of maths at Cambridge with
>> > some
>> >of the most wonderful lectures I have ever attended (John Conway is
>> >a *fantastic* lecturer) - we were warned not to take notes because
>> >he kept erasing parts of the board and redrawing them in different
>> >colours to illustrate what he was saying. I certainly can't
>> >reproduce much of it now.
>> >
>> Despite my grade 'A' in 'A' Level Maths (Pure and Applied) I am
>> awfully glad that I did not go onto read Mathematics. I thoroughly
>> enjoyed that
>
> Despite my effortless 'A's and distinctions in Maths and Further
> Maths 'A' and 'S' levels I ran out of steam in second year probability
> and sadistics which was twisted beyond belief (or at least beyond my
> capacity for corkscrewing my brian). If it hadn't been for that I'd
> probably have been OK (I loved the abstractions that algebra and
> analysis grew into before all but merging) but I'll never know because
> I bailed to computer science and a career in industry.
>

Similar here. I did rather well at A-level and I was allowed to skip the
first year of my BSc chemistry course. This was a mistake - I was plunged
straight into quantum theory and atomic orbitals with no understanding of
the subject. I failed, but managed to get a place on an Ocaeanography
course and that worked out very well for me.

--
Peter
-----

On 09/01/2023 17:02, Nicholas D. Richards wrote:

>>
> Despite my grade 'A' in 'A' Level Maths (Pure and Applied) I am awfully ...

(I'm not worthy)
I only managed a B and O at A level (pure and applied).
I was "burnt out" a few months before the exams. :-(
possibly caused by missing bits due to illness.

Since then I have come to view maths like some folk view golf.
I enjoy it. I'm just not all that good at it. :-)

Although I've got better (at maths) after 60 odd years practise.

--
Nev
It causes me a great deal of regret and remorse
that so many people are unable to understand what I write.

On 09/01/2023 17:54, John Williamson wrote:
> On 09/01/2023 17:02, Nicholas D. Richards wrote:
>
>> Despite my grade 'A' in 'A' Level Maths (Pure and Applied) I am awfully
>> glad that I did not go onto read Mathematics. I thoroughly enjoyed that
>> A level but when I took a peak at the content of degree level Maths I
>> quickly came to the conclusion that I would not be able to hack it.
>> Thermodynamics was enough for me in Chemistry.
>>
> Randall cracked it a while back.
>
> https://xkcd.com/435/
>
Hmm, all the others could exist without maths - they just wouldn't be as
good. So maths is just the icing on the cake - which is obviously
mainly physics!

HTH

Chris
--
The Deuchars BBB#40 COFF#14
Yamaha XV750SE & Suzuki GS550t
http://www.Deuchars.org.uk