In article <7ot5fgpp6h4l29qi6kiiivg5920s2eg35l@4ax.com>, BrightsideS9
<reply_to_address_is_not@invalid.invalid> wrote:

> 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.

Which Papal Decree are you quoting? 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 <val6fgp2sar3sufvm5muh67vfm6jmmi2s5@4ax.com>, 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.

Depends on how you've chosen to define pi. :-)

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 <p2m7fg1ccejak4kllvgq6hg1aj7c73hffa@4ax.com>, Roderick Stewart
<rjfs@escapetime.myzen.co.uk> wrote:
> he 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.

With you up to the "always". :-)

The significant point to add is that we have now known for some time that
space-time isn't 'flat' everywhere. And non-flat geometries have been
studied for a long time. Hence your absolute use of "always" ran out some
time ago.

For the purpose of a specific mathematical argument you can set the
definition that suits and work out the consequences *in that framework*.

However mere physicsts and engineers have to deal with the real world. So
have the complication that their chosen framework also needs to fit the
reality. Hence pi becomes a value which varies in mere reality as distinct
from 'looking the other way' assumptions for the purpose of a nice
theoretical framework in the abstract.

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

On Sun, 18 Jul 2021 10:02:38 +0100, Jim Lesurf <noise@audiomisc.co.uk>
wrote:

>> 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.
>
>Depends on how you've chosen to define pi. :-)

I think we're going round in circles here. (Pun not intended unless
you think it's amusing or clever).

Nobody is disputing that the ratio C/D varies with curvature of the
surface. That's an immutable mathematical fact. What *can* vary is, as
you say, how we've chosen to define pi, because that's just a matter
of a human decision about the choice of terminology. It doesn't alter
any absolute universal facts. I think most people understand and
accept the same definition and the same numerical value.

Rod.

On 19/07/2021 09:13, MrSpud_Fbyeq@ov00mymhsmu.eu wrote:
>
> 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.

If we accept that the human frame is an incomplete sensory vehicle, eg,
we cannot see anything in UV or infra-red, then we can accept that we
cannot experience all of reality.

Taking exponentiation as an example, we can understand 10^2 as 100
and 10^3 as 1000, but we cannot come to grips with 10^0.3010(approx)
although it does exist as the integer 2.

By the same token, we understand intrinsically integer arithmetic
and their square roots, but have difficulty with complex numbers
even though they are part of a wider reality.

Think of complex numbers as the UV or infra-red of aritmetic,
there, and physically real, but not within our immediate
sensory capabilities.

On 19/07/2021 10:58, Roderick Stewart wrote:
> On Sun, 18 Jul 2021 10:02:38 +0100, Jim Lesurf <noise@audiomisc.co.uk>
> wrote:
>
>>> 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.
>>
>> Depends on how you've chosen to define pi. :-)
>
> I think we're going round in circles here. (Pun not intended unless
> you think it's amusing or clever).
>
> Nobody is disputing that the ratio C/D varies with curvature of the
> surface. That's an immutable mathematical fact. What *can* vary is, as
> you say, how we've chosen to define pi, because that's just a matter
> of a human decision about the choice of terminology. It doesn't alter
> any absolute universal facts. I think most people understand and
> accept the same definition and the same numerical value.

I'm not an expert on 3-D geometry, although I did study the conic
sections circle, ellipse, parabola and hyperbola in 'A' Level
mathematics just over 50 years ago, but I am confident that with
circles drawn on the surface of a sphere that there will be a formula
giving the ratio of C to D that will involve the conventional PI
together with correctional factors relating to the radius of the
sphere upon which the circle is drawn.

As an aside, when it comes to 3-D geometry I am amazed at the skill
of ship-bulders before the easy days of computers who could create the
intricately curved steel sheeting to be included in a ship's hull where
the pre-drilled holes for the rivets are exactly correctly positioned
to mate with the holes in the adjacent sheet steel!

What a trivially easy mathematical job we have nowadays in comparison!

On 18/07/2021 10:01, Jim Lesurf wrote:
> In article <7ot5fgpp6h4l29qi6kiiivg5920s2eg35l@4ax.com>, BrightsideS9
> <reply_to_address_is_not@invalid.invalid> wrote:
>
>> 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.
>
> Which Papal Decree are you quoting? 8-]

Are you implying BULL?

On Mon, 19 Jul 2021 12:33:15 +0100
gareth evans <headstone255@yahoo.com> wrote:
>On 19/07/2021 09:13, MrSpud_Fbyeq@ov00mymhsmu.eu wrote:
>> 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.
>
>If we accept that the human frame is an incomplete sensory vehicle, eg,
>we cannot see anything in UV or infra-red, then we can accept that we
>cannot experience all of reality.

No doubt and I suspect if an ultra intelligent alien race came along and showed
us the wiring under the board our monkey brains wouldn't understand it anyway.
I suspect for any significantly deeper delves into the depths of reality will
require some kind of AI assistance.

>By the same token, we understand intrinsically integer arithmetic
>and their square roots, but have difficulty with complex numbers
>even though they are part of a wider reality.

No they're not. Either the square root of -1 doesn't exist in which case
complex numbers are simply a hack to get over the mathematical equivalent of
an energy barrier, or sqr(-1) does exist and the whole basis of our
mathematics is wrong. You can't have it both ways.

On Sun, 18 Jul 2021 10:08:47 +0100, Jim Lesurf <noise@audiomisc.co.uk>
wrote:

>In article <p2m7fg1ccejak4kllvgq6hg1aj7c73hffa@4ax.com>, Roderick Stewart
><rjfs@escapetime.myzen.co.uk> wrote:
>> he 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.
>
>With you up to the "always". :-)
>
>The significant point to add is that we have now known for some time that
>space-time isn't 'flat' everywhere. And non-flat geometries have been
>studied for a long time. Hence your absolute use of "always" ran out some
>time ago.
>
>For the purpose of a specific mathematical argument you can set the
>definition that suits and work out the consequences *in that framework*.
>
>However mere physicsts and engineers have to deal with the real world. So
>have the complication that their chosen framework also needs to fit the
>reality. Hence pi becomes a value which varies in mere reality as distinct
>from 'looking the other way' assumptions for the purpose of a nice
>theoretical framework in the abstract.

Give in Jim you lost!

--,
brightside S9

In message <sd452s$p9r$1@gioia.aioe.org>, MrSpud_k9@j5ei2on7o.org writes
>Either the square root of -1 doesn't exist in which case complex
>numbers are simply a hack to get over the mathematical equivalent of an
>energy barrier, or sqr(-1) does exist and the whole basis of our
>mathematics is wrong. You can't have it both ways.

I think first you have to define what you mean by "exist". I suspect we
might be straying into Bertrand Russell territory here.
--
John Hall "Hard work often pays off after time, but laziness always
pays off now." Anon

On Mon, 19 Jul 2021 16:54:43 +0100
John Hall <john_nospam@jhall.co.uk> wrote:
>In message <sd452s$p9r$1@gioia.aioe.org>, MrSpud_k9@j5ei2on7o.org writes
>>Either the square root of -1 doesn't exist in which case complex
>>numbers are simply a hack to get over the mathematical equivalent of an
>>energy barrier, or sqr(-1) does exist and the whole basis of our
>>mathematics is wrong. You can't have it both ways.
>
>I think first you have to define what you mean by "exist". I suspect we
>might be straying into Bertrand Russell territory here.

You can't have 1 part of a mathematical framework saying "this number can't
exist" while another part says "yes it does exist and we use it" and still
claim that framework is consistent. And if its not consistent how can it be
expected to answer deep questions about reality?

On 19/07/2021 16:17, MrSpud_k9@j5ei2on7o.org wrote:
>
> No they're not. Either the square root of -1 doesn't exist in which case
> complex numbers are simply a hack to get over the mathematical equivalent of
> an energy barrier, or sqr(-1) does exist and the whole basis of our
> mathematics is wrong. You can't have it both ways.

The difficulty is in trying to understand something as an integer
when it is not an integer, it is an operator that when applied
twice changes +1 into -1

YMMV

It again is part of our limited sensory perception, for the
real number system that we experience is a subset of
the complete number system of complex numbers, a
2-dimensional thing, that we cannot experience.

Another way of looking at i (or j to the electrical engineer)
is to think of it as akin to a chemical catalyst, in that
it is something we inject to solve our equations which
we then take out, unchanged, at the end.

Further examples of our lack of sensory appreciation is
when we move from 3-D to multiple-D in the field
of tensor arithmetic

On Mon, 19 Jul 2021 08:13:26 -0000 (UTC), MrSpud_Fbyeq@ov00mymhsmu.eu
wrote in <sd3c76$1du$1@gioia.aioe.org>:

>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.

Did anybody suggest that reality is based on mathematics?

All of mathematics is artificial, created as a tool to help people to
write down and reason about various things.

Even the "natural numbers" are an invented concept that does not occur
in nature. They may be one of the oldest concepts used to write down and
reason about collections of things but even there it is necessary to
create a model that is simpler than reality in order to use them.

As for pi, since the concept of a circle, its circumference and its
radius or diameter do not occur in nature there is no reason why
anything about it should be expected to occur in nature. There are
physical things for which a circle is a useful model, good enough for
the purpose at hand, but they are never a true circle.

As for Gödel, he proved that there are true statements that cannot be
proved within a formal system and that any sufficiently powerful
consistent theory cannot prove its own consistency. Since that is all
about formal systems with computable sets of axioms, it does not address
the question of the relationship of mathematics with reality.

On Mon, 19 Jul 2021 16:07:02 -0000 (UTC), MrSpud_w7q7n3vj@8vbmgz.com
wrote in <sd47v6$ag9$1@gioia.aioe.org>:

>On Mon, 19 Jul 2021 16:54:43 +0100
>John Hall <john_nospam@jhall.co.uk> wrote:
>>In message <sd452s$p9r$1@gioia.aioe.org>, MrSpud_k9@j5ei2on7o.org writes
>>>Either the square root of -1 doesn't exist in which case complex
>>>numbers are simply a hack to get over the mathematical equivalent of an
>>>energy barrier, or sqr(-1) does exist and the whole basis of our
>>>mathematics is wrong. You can't have it both ways.
>>
>>I think first you have to define what you mean by "exist". I suspect we
>>might be straying into Bertrand Russell territory here.
>
>You can't have 1 part of a mathematical framework saying "this number can't
>exist" while another part says "yes it does exist and we use it" and still
>claim that framework is consistent. And if its not consistent how can it be
>expected to answer deep questions about reality?

Which mathematical framework do you mean? -1 is an Integer but not a
Natural Number, i is neither an Integer not a Natural Number but it is
an algebraic number.

Mathematics is a tool that has been used and developed over centuries to
help people create models that can be used to predict various things in
the universe. If you are concerned about the difference between the
universe and the current best available models then mathematics will not
be the limiting factor in the exploration of that issue. If you are
concerned about the relationship between the universe as we observe it
and 'reality' then it is not obvious what tools would help with that.

On Mon, 19 Jul 2021 17:36:50 +0100
gareth evans <headstone255@yahoo.com> wrote:
>On 19/07/2021 16:17, MrSpud_k9@j5ei2on7o.org wrote:
>>
>> No they're not. Either the square root of -1 doesn't exist in which case
>> complex numbers are simply a hack to get over the mathematical equivalent of
>> an energy barrier, or sqr(-1) does exist and the whole basis of our
>> mathematics is wrong. You can't have it both ways.
>
>The difficulty is in trying to understand something as an integer
>when it is not an integer, it is an operator that when applied
>twice changes +1 into -1
>
>YMMV
>
>It again is part of our limited sensory perception, for the
>real number system that we experience is a subset of
>the complete number system of complex numbers, a
>2-dimensional thing, that we cannot experience.

Because they don't exist, they're an invention, a hack to get other bits of
maths to work.

>is to think of it as akin to a chemical catalyst, in that
>it is something we inject to solve our equations which
>we then take out, unchanged, at the end.

See above.

On Mon, 19 Jul 2021 22:10:49 +0100
Owen Rees <orees@hotmail.com> wrote:
>On Mon, 19 Jul 2021 08:13:26 -0000 (UTC), MrSpud_Fbyeq@ov00mymhsmu.eu
>wrote in <sd3c76$1du$1@gioia.aioe.org>:
>>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.
>
>Did anybody suggest that reality is based on mathematics?

Yes, plenty of current thinking in physics is that reality is based on some
sort of information reliant on mathematical laws.

>All of mathematics is artificial, created as a tool to help people to
>write down and reason about various things.

Agreed.

In article <qhp7fghv8vvt0bfeh5hg70v5nvstf97tki@4ax.com>, BrightsideS9
<reply_to_address_is_not@invalid.invalid> wrote:

> 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

Your reaction reminds me of something the military say: "If you can't take
a joke, you should never have signed up!" 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
biog http://jcgl.orpheusweb.co.uk/history/ups_and_downs.html
Audio Misc http://www.audiomisc.co.uk/index.html

On Tue, 20 Jul 2021 07:46:10 -0000 (UTC),
MrSpud_vfO_e@bx6eilxvg4u5tdk53dvc6at.net wrote:

>On Mon, 19 Jul 2021 22:10:49 +0100
>Owen Rees <orees@hotmail.com> wrote:
>>On Mon, 19 Jul 2021 08:13:26 -0000 (UTC), MrSpud_Fbyeq@ov00mymhsmu.eu
>>wrote in <sd3c76$1du$1@gioia.aioe.org>:
>>>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.
>>
>>Did anybody suggest that reality is based on mathematics?
>
>Yes, plenty of current thinking in physics is that reality is based on some
>sort of information reliant on mathematical laws.
>
>>All of mathematics is artificial, created as a tool to help people to
>>write down and reason about various things.
>
>Agreed.
>

We may have invented mathematical notation as a means of understanding
numbers, but we did not invent their properties. The squares, primes,
logarithms and all the other numerical relationships that we use are
the same ones that an alien species on the other side of the universe
would have to use. Even if we regard the square root of minus one as a
notational bodge that we use to perform certain tasks, if those aliens
want to perform the same tasks they'll have to invent the same bodge,
because it's the one that works. Then if they investigate its
relationship with the exponential constant and the circle constant
they'll discover the same thing that Euler discovered, because it's a
discovery not an invention. It must be the same anywhere in the
universe because being an abstract concept it doesn't depend on the
physical universe at all, and nobody could make it different.

Rod.

On 20/07/2021 08:43, MrSpud_z8iO1@3v77bw.tv wrote:
>
> Because they don't exist, they're an invention, a hack to get other bits of
> maths to work.

But all of mathematics is an abstract invention.

Let's take something that you seem to be happy about, the
natural numbers used for counting.

You can have two fingers, two apples, two of anything
but two, by itself, on its own, does not exist!

OK, you might say, what about "two", "2" or "II" (as in Roman)?
.... and I will say to you that they are just different ways of
describing something, but are not the thing itself.

So, "the other bits of maths" don't work either!

On Tue, 20 Jul 2021 10:45:10 +0100, gareth evans
<headstone255@yahoo.com> wrote:

>On 20/07/2021 08:43, MrSpud_z8iO1@3v77bw.tv wrote:
>>
>> Because they don't exist, they're an invention, a hack to get other bits of
>> maths to work.
>
>But all of mathematics is an abstract invention.
>
>Let's take something that you seem to be happy about, the
>natural numbers used for counting.
>
>You can have two fingers, two apples, two of anything
>but two, by itself, on its own, does not exist!
>
>OK, you might say, what about "two", "2" or "II" (as in Roman)?
>... and I will say to you that they are just different ways of
>describing something, but are not the thing itself.
>
>So, "the other bits of maths" don't work either!

True. If a Roman had II sheep and someody gave him another III, then
he'd have V, just the same as today. Whether he put all those sheep
including the newly acquired ones together in the same pen, or just
left them where they were and considered their totality in the
abstract as a single concept because they were now subject to the same
ownership, there would still be the same number whatever he called it.

I remember a playground conundrum concerning sheep that wouldn't work
at all in Roman but only when spoken aloud in English. "If you had
XXVI sheep and one died, how many would you have?" The only way it can
be made to work is by deliberately creating confusion between the
pronunciation of "twenty six sheep" and "twenty sick sheep", so that
whichever answer is given can be declared wrong, but that's just
playing with the notation rather than any fundamental concept, or in
other words, it's cheating.

Yan, tan, tethera, methera, pip... The numbers are the same.

Rod.

On 19/07/2021 16:54, John Hall wrote:
> In message <sd452s$p9r$1@gioia.aioe.org>, MrSpud_k9@j5ei2on7o.org writes

>> Either the square root of -1 doesn't exist in which case complex
>> numbers are simply a hack to get over the mathematical equivalent of
>> an energy barrier, or sqr(-1) does exist and the whole basis of our
>> mathematics is wrong. You can't have it both ways.
>
> I think first you have to define what you mean by "exist". I suspect we
> might be straying into Bertrand Russell territory here.

He wrote a book trying to prove that 1+1=2 and failed...

--
Max Demian

On 20/07/2021 08:43, MrSpud_z8iO1@3v77bw.tv wrote:
> On Mon, 19 Jul 2021 17:36:50 +0100
> gareth evans <headstone255@yahoo.com> wrote:
>> On 19/07/2021 16:17, MrSpud_k9@j5ei2on7o.org wrote:
>>>
>>> No they're not. Either the square root of -1 doesn't exist in which case
>>> complex numbers are simply a hack to get over the mathematical equivalent of
>>> an energy barrier, or sqr(-1) does exist and the whole basis of our
>>> mathematics is wrong. You can't have it both ways.
>>
>> The difficulty is in trying to understand something as an integer
>> when it is not an integer, it is an operator that when applied
>> twice changes +1 into -1
>>
>> YMMV
>>
>> It again is part of our limited sensory perception, for the
>> real number system that we experience is a subset of
>> the complete number system of complex numbers, a
>> 2-dimensional thing, that we cannot experience.
>
> Because they don't exist, they're an invention, a hack to get other bits of
> maths to work.
0! = 1 is another "hack".

--
Max Demian

On Tue, 20 Jul 2021 11:22:19 +0100, Max Demian
<max_demian@bigfoot.com> wrote:

>On 20/07/2021 08:43, MrSpud_z8iO1@3v77bw.tv wrote:
>> On Mon, 19 Jul 2021 17:36:50 +0100
>> gareth evans <headstone255@yahoo.com> wrote:
>>> On 19/07/2021 16:17, MrSpud_k9@j5ei2on7o.org wrote:
>>>>
>>>> No they're not. Either the square root of -1 doesn't exist in which case
>>>> complex numbers are simply a hack to get over the mathematical equivalent of
>>>> an energy barrier, or sqr(-1) does exist and the whole basis of our
>>>> mathematics is wrong. You can't have it both ways.
>>>
>>> The difficulty is in trying to understand something as an integer
>>> when it is not an integer, it is an operator that when applied
>>> twice changes +1 into -1
>>>
>>> YMMV
>>>
>>> It again is part of our limited sensory perception, for the
>>> real number system that we experience is a subset of
>>> the complete number system of complex numbers, a
>>> 2-dimensional thing, that we cannot experience.
>>
>> Because they don't exist, they're an invention, a hack to get other bits of
>> maths to work.
>0! = 1 is another "hack".

The most annoying one for me is 1+2+3+4+5...(to infinity) = -1/12.

At least you can imagine that a number like i or a fractional power
might exist even if our normal notation doesn't allow us to see it
directly so we have to approach it from a different direction, but all
the positive whole numbers adding up to a negative fraction just flies
in the face of reason. At least with a verbal paradox like "This
statement is false" we can admit that that's what it is, but some seem
to treat a numerical paradox like this more seriously, perhaps just
because the notation can be made to work.

Rod.

On 20/07/2021 11:18, Roderick Stewart wrote:
> On Tue, 20 Jul 2021 10:45:10 +0100, gareth evans
> <headstone255@yahoo.com> wrote:
>
>> On 20/07/2021 08:43, MrSpud_z8iO1@3v77bw.tv wrote:
>>>
>>> Because they don't exist, they're an invention, a hack to get other bits of
>>> maths to work.
>>
>> But all of mathematics is an abstract invention.
>>
>> Let's take something that you seem to be happy about, the
>> natural numbers used for counting.
>>
>> You can have two fingers, two apples, two of anything
>> but two, by itself, on its own, does not exist!
>>
>> OK, you might say, what about "two", "2" or "II" (as in Roman)?
>> ... and I will say to you that they are just different ways of
>> describing something, but are not the thing itself.
>>
>> So, "the other bits of maths" don't work either!
>
> True. If a Roman had II sheep and someody gave him another III, then
> he'd have V, just the same as today. Whether he put all those sheep
> including the newly acquired ones together in the same pen, or just
> left them where they were and considered their totality in the
> abstract as a single concept because they were now subject to the same
> ownership, there would still be the same number whatever he called it.
>
> I remember a playground conundrum concerning sheep that wouldn't work
> at all in Roman but only when spoken aloud in English. "If you had
> XXVI sheep and one died, how many would you have?" The only way it can
> be made to work is by deliberately creating confusion between the
> pronunciation of "twenty six sheep" and "twenty sick sheep", so that
> whichever answer is given can be declared wrong, but that's just
> playing with the notation rather than any fundamental concept, or in
> other words, it's cheating.
>
> Yan, tan, tethera, methera, pip... The numbers are the same.
>
> Rod.
>

There are 10 types of people. Those that understand binary and those
that dont understand binary.....

I can do binary arithmetic in my head:

1 + 1 = 10

10 + 10 = 100

10 x 10 = 100

100 + 100 = 1000

100 x 100 = 10000

:-)

On 20/07/2021 11:18, Roderick Stewart wrote:
> On Tue, 20 Jul 2021 10:45:10 +0100, gareth evans
> <headstone255@yahoo.com> wrote:
>
>> On 20/07/2021 08:43, MrSpud_z8iO1@3v77bw.tv wrote:
>>>
>>> Because they don't exist, they're an invention, a hack to get other bits of
>>> maths to work.
>>
>> But all of mathematics is an abstract invention.
>>
>> Let's take something that you seem to be happy about, the
>> natural numbers used for counting.
>>
>> You can have two fingers, two apples, two of anything
>> but two, by itself, on its own, does not exist!
>>
>> OK, you might say, what about "two", "2" or "II" (as in Roman)?
>> ... and I will say to you that they are just different ways of
>> describing something, but are not the thing itself.
>>
>> So, "the other bits of maths" don't work either!
>
> True. If a Roman had II sheep and someody gave him another III, then
> he'd have V, just the same as today. Whether he put all those sheep
> including the newly acquired ones together in the same pen, or just
> left them where they were and considered their totality in the
> abstract as a single concept because they were now subject to the same
> ownership, there would still be the same number whatever he called it.
>
> I remember a playground conundrum concerning sheep that wouldn't work
> at all in Roman but only when spoken aloud in English. "If you had
> XXVI sheep and one died, how many would you have?" The only way it can
> be made to work is by deliberately creating confusion between the
> pronunciation of "twenty six sheep" and "twenty sick sheep", so that
> whichever answer is given can be declared wrong, but that's just
> playing with the notation rather than any fundamental concept, or in
> other words, it's cheating.
>
> Yan, tan, tethera, methera, pip... The numbers are the same.

Reminds me of the price you have to pay for seafood that is not
in the best of health ...

Six Quid