On 16/08/2021 09:06, mickspud@downthefarm.com wrote:

> Even some animals can understand simple integers.
>
>
The dog under my desk can indicate that it wants a second sausage.

Bill

On 16/08/2021 09:06, mickspud@downthefarm.com wrote:
> On Sat, 14 Aug 2021 22:21:06 +0100
> Owen Rees <orees@hotmail.com> wrote:
>> On Sat, 14 Aug 2021 15:11:42 -0000 (UTC), mickspud@downthefarm.com wrote

>> in <sf8mfe$a9s$1@gioia.aioe.org>:
>>> 2 is not an abstraction in the sense I can show you two of something. Show me
>>> 'i' of something.
>>>
>>
>> 2 is a much older abstraction but the idea that you can consider things
>> to be sufficiently like each other to be able to count them is still
>> creating a model then manipulating the model rather than the things
>> themselves.
>
> Having 2 of something is not an abstraction. The only abstract part about it
> is what name you give it and what written figure you use to represent it with.
> Even some animals can understand simple integers.

Sometimes it is said that some animals can count small numbers, but they
generally don't distinguish counting from estimating numbers of objects
by just looking at them, which is easy enough for numbers up to five or
six (depending on how the objects are arranged), and approximations can
be made for larger numbers: but this isn't really "counting", which, I
would have thought, has to involve a sequence of symbols, whether verbal
or mental.

(Of course there was Clever Hans, the horse who could do arithmetic, but
we know now how he did it.)

--
Max Demian

On Mon, 16 Aug 2021 10:55:44 +0000 (UTC)
richard@cogsci.ed.ac.uk (Richard Tobin) wrote:
>In article <sfd62r$1d77$1@gioia.aioe.org>, <mickspud@downthefarm.com> wrote:
>
>>>>2 is not an abstraction in the sense I can show you two of something. Show
>me
>>>>'i' of something.
>
>>>Show me 2,473,845,582,972,592,398,117,937,832,969,322,411 of something.
>
>>Go to a beach and start counting the grains of sand.
>
>There aren't that many.
>
>There are estimated to be only 10^80 baryons in the universe. Do you
>believe in numbers bigger than that?

Your response nicely demonstrates you have no valid argument.

On Mon, 16 Aug 2021 10:58:36 +0000 (UTC)
richard@cogsci.ed.ac.uk (Richard Tobin) wrote:
>In article <sfd69d$1g7m$1@gioia.aioe.org>, <mickspud@downthefarm.com> wrote:
>
>>Having 2 of something is not an abstraction.
>
>Of course it is. That you see something in common between 2 cows and
>2 pigs requires abstracting away from the animals themselves. It's
>just an abstraction you're familiar with.

If counting is an abstraction purely because its a way of refereing the
real world then everything is an abstraction - eg , whats a cow? Its just a
collection of atoms after all and atoms are just quarks. Which rather renders
the whole term meaningless and this argument moot.

On 16/08/2021 14:42, Max Demian wrote:

> Sometimes it is said that some animals can count small numbers, but they
> generally don't distinguish counting from estimating numbers of objects
> by just looking at them,

Humans as well. I have nine hens and I can tell immediately if one is
AWOL. I don't need to count them.

Bill

In article <TuOdnSYAb-Kh9of8nZ2dnUU78T3NnZ2d@brightview.co.uk>,
Max Demian <max_demian@bigfoot.com> wrote:
>Sometimes it is said that some animals can count small numbers, but they
>generally don't distinguish counting from estimating numbers of objects
>by just looking at them, which is easy enough for numbers up to five or
>six (depending on how the objects are arranged), and approximations can
>be made for larger numbers: but this isn't really "counting", which, I
>would have thought, has to involve a sequence of symbols, whether verbal
>or mental.

Various birds appear to be able to count up to about 6. One
experiment involves hiding a number of pieces of food under boxes; the
birds stop turning over boxes once they have found the number of items
they saw hidden.

-- Richard

On 16/08/2021 09:04, mickspud@downthefarm.com wrote:

> Break a stick in 2 - you have 2 halves.

Alternatively, break a stick in half and you have two smaller sticks.

Jim

On Mon, 16 Aug 2021 08:04:27 -0000 (UTC), mickspud@downthefarm.com wrote
in <sfd66b$1f2e$1@gioia.aioe.org>:

>On Sat, 14 Aug 2021 22:03:38 +0100
>Owen Rees <orees@hotmail.com> wrote:
>>On Sat, 14 Aug 2021 15:08:52 -0000 (UTC), mickspud@downthefarm.com wrote
>>in <sf8ma4$7vn$1@gioia.aioe.org>:
>>
>>>On Fri, 13 Aug 2021 21:14:23 +0100
>>>Owen Rees <orees@hotmail.com> wrote:
>>
>>>>It is the simplest thing to add to the real numbers in order to
>>>>construct the algebraic numbers. Having created complex numbers they
>>>>turn out to be useful to scientists and engineers in modelling things
>>>>they are interested in.
>>>
>>>I never said otherwise. I simply said they're a hack. Hacks usually work but
>>>they're also ugly and often there's a better way of doing things.
>>
>>In what way are complex numbers ugly? If you have a simpler way to
>
>Using a value that cannot exist can hardly be said to be elegant.

On the contrary. The usefulness of complex numbers has already been
discussed. Defining complex numbers by introducing one constant is very
elegant.

>
>>define the set of numbers needed to contain the zeros of all polynomials
>>with rational coefficients than the construction using i that has been
>>around for centuries then you should write it up - mathematicians love
>>simplicity and if you can produce something simpler than is currently
>>used then you could be a candidate for the Fields Medal.
>
>As I've already said twice - though apparently being able to read properly is
>optional on this group - the human brain probably isn't up to that task.

Human brains have created a simple and elegant way to construct the
complex numbers by introducing a single constant. Repeating the
assertion that that construction is in some way unsatisfactory does not
strengthen the argument.

>
>>>Fractions are needed to represent fractional parts of things. No need to get
>>>carried away with some convoluted explanation.
>>>
>>
>>What do you mean by a fractional part of something? Do you expect to be
>>able to do arithmetic with fractions? If so, how does that work?
>
>Break a stick in 2 - you have 2 halves. Is that too complex for you?
>Pun intended.

In that example you have two shorter sticks and, for a real stick, the
pieces will not be identical. You do not need the concept of 'half'
unless you want to describe or reason about what could be or has been
done to the stick. Even if you have the concept of "half a stick" you do
not necessarily have the more general concept of "half" that can be
applied to other things.

On Mon, 16 Aug 2021 08:02:13 -0000 (UTC), mickspud@downthefarm.com wrote
in <sfd625$1d5r$1@gioia.aioe.org>:

>On Sat, 14 Aug 2021 19:17:20 +0100
>Norman Wells <hex@unseen.ac.am> wrote:
>>On 14/08/2021 16:11, mickspud@downthefarm.com wrote:
>>> On Sat, 14 Aug 2021 12:46:28 +0000 (UTC)
>>> richard@cogsci.ed.ac.uk (Richard Tobin) wrote:
>>>> In article <sf61dp$1rb2$1@gioia.aioe.org>, <mickspud@downthefarm.com>
>>wrote:
>>>>
>>>>>>>>> Whats its value? sqrt(-1) isn't a value, its an operation.
>>>>
>>>>>>>> You're just making up terms. You could call square root an operation,
>>>>>>>> but sqrt(-1) certainly isn't.
>>>>
>>>>>>> Whats its value?
>>>>
>>>>>> i.
>>>>
>>>>> You're about 3 posts too late for that joke.
>>>>
>>>> It's not a joke. "i" is a name for the square root of -1, just as
>>>> "2" is a name for 1+1.
>>>>
>>>> 2 and i are both abstractions, but for some reason you seem happy
>>>> with one but not the other.
>>>
>>> 2 is not an abstraction in the sense I can show you two of something. Show me
>>
>>> 'i' of something.
>>
>>Can you show me minus three bananas?
>
>I can show you minus 3 feet - dig a hole.

People had been diging holes quite successfully for a long time before
the idea of negative numbers emerged. You can get along quite well with
positive numbers measured in a different direction, you do not need the
general concept of a negative number (they just make the formulae
simpler).

On Mon, 16 Aug 2021 14:25:11 -0000 (UTC), mickspud@downthefarm.com wrote
in <sfdsg7$20q$1@gioia.aioe.org>:

>On Mon, 16 Aug 2021 10:58:36 +0000 (UTC)
>richard@cogsci.ed.ac.uk (Richard Tobin) wrote:
>>In article <sfd69d$1g7m$1@gioia.aioe.org>, <mickspud@downthefarm.com> wrote:
>>
>>>Having 2 of something is not an abstraction.
>>
>>Of course it is. That you see something in common between 2 cows and
>>2 pigs requires abstracting away from the animals themselves. It's
>>just an abstraction you're familiar with.
>
>If counting is an abstraction purely because its a way of refereing the
>real world then everything is an abstraction - eg , whats a cow? Its just a
>collection of atoms after all and atoms are just quarks. Which rather renders
>the whole term meaningless and this argument moot.

The concept 'cow' is an abstraction, a specific actual cow is not. We
could not discuss cows in general if that were not the case.

As for numbers, why do we use the same sequence of numbers for counting
different kinds of things? There are significant advantages in doing so
but it is not fundamentally necessary.

On 17/08/2021 00:12, Owen Rees wrote:

>
> As for numbers, why do we use the same sequence of numbers for counting
> different kinds of things? There are significant advantages in doing so
> but it is not fundamentally necessary.
>
For example Yan tan tethera etc for counting sheep

Jim

On Mon, 16 Aug 2021 23:19:11 +0100
Owen Rees <orees@hotmail.com> wrote:
>On Mon, 16 Aug 2021 08:04:27 -0000 (UTC), mickspud@downthefarm.com wrote
>in <sfd66b$1f2e$1@gioia.aioe.org>:
>>>In what way are complex numbers ugly? If you have a simpler way to
>>
>>Using a value that cannot exist can hardly be said to be elegant.
>
>On the contrary. The usefulness of complex numbers has already been
>discussed. Defining complex numbers by introducing one constant is very
>elegant.

You think they're elegant? I guess thats just personal taste. I happen to
think they're a pig ugly hack.

>>As I've already said twice - though apparently being able to read properly is
>>optional on this group - the human brain probably isn't up to that task.
>
>Human brains have created a simple and elegant way to construct the
>complex numbers by introducing a single constant. Repeating the
>assertion that that construction is in some way unsatisfactory does not
>strengthen the argument.

See above.

>>Break a stick in 2 - you have 2 halves. Is that too complex for you?
>>Pun intended.
>
>In that example you have two shorter sticks and, for a real stick, the
>pieces will not be identical. You do not need the concept of 'half'
>unless you want to describe or reason about what could be or has been
>done to the stick. Even if you have the concept of "half a stick" you do
>not necessarily have the more general concept of "half" that can be
>applied to other things.

You're just playing with semantics in order to try and win the point. It
doesn't change anything - I could give you half a stick, half a banana or
half cake. Its still a half.

On Mon, 16 Aug 2021 23:29:20 +0100
Owen Rees <orees@hotmail.com> wrote:
>On Mon, 16 Aug 2021 08:02:13 -0000 (UTC), mickspud@downthefarm.com wrote
>in <sfd625$1d5r$1@gioia.aioe.org>:
>>I can show you minus 3 feet - dig a hole.
>
>People had been diging holes quite successfully for a long time before
>the idea of negative numbers emerged. You can get along quite well with
>positive numbers measured in a different direction, you do not need the

Numbers going in a different direction is all negative numbers are.

On Tue, 17 Aug 2021 00:12:43 +0100
Owen Rees <orees@hotmail.com> wrote:
>On Mon, 16 Aug 2021 14:25:11 -0000 (UTC), mickspud@downthefarm.com wrote
>in <sfdsg7$20q$1@gioia.aioe.org>:
>
>>On Mon, 16 Aug 2021 10:58:36 +0000 (UTC)
>>richard@cogsci.ed.ac.uk (Richard Tobin) wrote:
>>>In article <sfd69d$1g7m$1@gioia.aioe.org>, <mickspud@downthefarm.com> wrote:
>
>>>
>>>>Having 2 of something is not an abstraction.
>>>
>>>Of course it is. That you see something in common between 2 cows and
>>>2 pigs requires abstracting away from the animals themselves. It's
>>>just an abstraction you're familiar with.
>>
>>If counting is an abstraction purely because its a way of refereing the
>>real world then everything is an abstraction - eg , whats a cow? Its just a
>>collection of atoms after all and atoms are just quarks. Which rather renders
>>the whole term meaningless and this argument moot.
>
>The concept 'cow' is an abstraction, a specific actual cow is not. We

Neither is having 2 cows an abstraction. And so we go in a circle.

>As for numbers, why do we use the same sequence of numbers for counting
>different kinds of things? There are significant advantages in doing so
>but it is not fundamentally necessary.

What?

On 17/08/2021 09:17, mickspud@downthefarm.com wrote:
> On Mon, 16 Aug 2021 23:29:20 +0100
> Owen Rees <orees@hotmail.com> wrote:
>> On Mon, 16 Aug 2021 08:02:13 -0000 (UTC), mickspud@downthefarm.com wrote
>> in <sfd625$1d5r$1@gioia.aioe.org>:
>>> I can show you minus 3 feet - dig a hole.
>>
>> People had been diging holes quite successfully for a long time before
>> the idea of negative numbers emerged. You can get along quite well with
>> positive numbers measured in a different direction, you do not need the
>
> Numbers going in a different direction is all negative numbers are.

It's still very flat-earthy, blinkered and linear.

Complex numbers are just utilising another of the available dimensions.

On Tue, 17 Aug 2021 09:37:39 +0100
Norman Wells <hex@unseen.ac.am> wrote:
>On 17/08/2021 09:17, mickspud@downthefarm.com wrote:
>> On Mon, 16 Aug 2021 23:29:20 +0100
>> Owen Rees <orees@hotmail.com> wrote:
>>> On Mon, 16 Aug 2021 08:02:13 -0000 (UTC), mickspud@downthefarm.com wrote
>>> in <sfd625$1d5r$1@gioia.aioe.org>:
>>>> I can show you minus 3 feet - dig a hole.
>>>
>>> People had been diging holes quite successfully for a long time before
>>> the idea of negative numbers emerged. You can get along quite well with
>>> positive numbers measured in a different direction, you do not need the
>>
>> Numbers going in a different direction is all negative numbers are.
>
>It's still very flat-earthy, blinkered and linear.

Not really. Its exactly what they are.

>Complex numbers are just utilising another of the available dimensions.

Those other dimensions only exist in the human mind.

On 17/08/2021 09:19, mickspud@downthefarm.com wrote:
> On Tue, 17 Aug 2021 00:12:43 +0100
> Owen Rees<orees@hotmail.com> wrote:

>> The concept 'cow' is an abstraction, a specific actual cow is not. We
>
> Neither is having 2 cows an abstraction. And so we go in a circle.
>
>> As for numbers, why do we use the same sequence of numbers for counting
>> different kinds of things? There are significant advantages in doing so
>> but it is not fundamentally necessary.
>
> What?
>
https://en.wikipedia.org/wiki/Yan_tan_tethera

<mickspud@downthefarm.com> wrote in message
news:sffu9m$13s6$1@gioia.aioe.org...
> On Tue, 17 Aug 2021 09:37:39 +0100
> Norman Wells <hex@unseen.ac.am> wrote:
>>Complex numbers are just utilising another of the available dimensions.
>
> Those other dimensions only exist in the human mind.

Where I worked in my first job, the head of department was called Bill
Taylor but people referred to him as j-omega. Then I saw his initials J W T
and it dawned on me: the universal j-omega-t term used in many electronic
engineering equations - they use j rather than i for sqrt(-1), because i
tends to be used for instantaneous current. I think he must have become an
electronic engineer by nominative determinism ;-)

On Tue, 17 Aug 2021 10:49:13 +0100
Indy Jess John <bathwatchdog@OMITTHISgooglemail.com> wrote:
>On 17/08/2021 09:19, mickspud@downthefarm.com wrote:
>> On Tue, 17 Aug 2021 00:12:43 +0100
>> Owen Rees<orees@hotmail.com> wrote:
>
>>> The concept 'cow' is an abstraction, a specific actual cow is not. We
>>
>> Neither is having 2 cows an abstraction. And so we go in a circle.
>>
>>> As for numbers, why do we use the same sequence of numbers for counting
>>> different kinds of things? There are significant advantages in doing so
>>> but it is not fundamentally necessary.
>>
>> What?
>>
>https://en.wikipedia.org/wiki/Yan_tan_tethera

Hows that any different from someone saying "lots" or "many" in answer to a
question of how many sheep are there?

"Indy Jess John" <bathwatchdog@OMITTHISgooglemail.com> wrote in message
news:sfg0mq$ifc$1@dont-email.me...
> On 17/08/2021 09:19, mickspud@downthefarm.com wrote:
>> On Tue, 17 Aug 2021 00:12:43 +0100
>> Owen Rees<orees@hotmail.com> wrote:
>
>>> The concept 'cow' is an abstraction, a specific actual cow is not. We
>>
>> Neither is having 2 cows an abstraction. And so we go in a circle.
>>
>>> As for numbers, why do we use the same sequence of numbers for counting
>>> different kinds of things? There are significant advantages in doing so
>>> but it is not fundamentally necessary.
>>
>> What?
>>
> https://en.wikipedia.org/wiki/Yan_tan_tethera

It's interesting that the sheep-counting numbering system uses a lot of
multi-syllable words for 1-10, whereas we only have one word seven that has
two syllables. By the time you get to 20 you have a *lot* of syllables to
express a number. Though French takes the piss with contortions such as
quatre-vignts-dix-sept.

I wonder why Celtic-based numbering systems tended to be base 20 rather than
base 10. Did they go around barefoot and therefore could additionally use
their toes as well as their fingers/thumbs to count?

What is interesting is to see how different cultures use their fingers to
denote numbers. Starting with all my digits folded into my palm, I would
tend to hold up:

index finger = 1
index+middle = 2
index+middle+ring = 3
index+middle+ring+little = 4
index+middle+ring+little+thumb = 5

But some cultures start with the thumb

thumb = 1
thumb+index = 2
thumb+index+middle = 3
etc

And some (I believe Japan is one) start with all the fingers visible and
fold them back to the palm in succession to denote increasing numbers - a
sort of 1's complement of the system I'd use.

On Tue, 17 Aug 2021 11:21:13 +0100
"NY" <me@privacy.invalid> wrote:
>"Indy Jess John" <bathwatchdog@OMITTHISgooglemail.com> wrote in message
>news:sfg0mq$ifc$1@dont-email.me...
>> On 17/08/2021 09:19, mickspud@downthefarm.com wrote:
>>> On Tue, 17 Aug 2021 00:12:43 +0100
>>> Owen Rees<orees@hotmail.com> wrote:
>>
>>>> The concept 'cow' is an abstraction, a specific actual cow is not. We
>>>
>>> Neither is having 2 cows an abstraction. And so we go in a circle.
>>>
>>>> As for numbers, why do we use the same sequence of numbers for counting
>>>> different kinds of things? There are significant advantages in doing so
>>>> but it is not fundamentally necessary.
>>>
>>> What?
>>>
>> https://en.wikipedia.org/wiki/Yan_tan_tethera
>
>It's interesting that the sheep-counting numbering system uses a lot of
>multi-syllable words for 1-10, whereas we only have one word seven that has
>two syllables. By the time you get to 20 you have a *lot* of syllables to
>express a number. Though French takes the piss with contortions such as
>quatre-vignts-dix-sept.

Some parts of the francophone world saw sense and use octante instead of
quatre vingt.

On 17/08/2021 11:19, mickspud@downthefarm.com wrote:
> On Tue, 17 Aug 2021 10:49:13 +0100
> Indy Jess John<bathwatchdog@OMITTHISgooglemail.com> wrote:
>> On 17/08/2021 09:19, mickspud@downthefarm.com wrote:
>>> On Tue, 17 Aug 2021 00:12:43 +0100
>>> Owen Rees<orees@hotmail.com> wrote:
>>
>>>> The concept 'cow' is an abstraction, a specific actual cow is not. We
>>>
>>> Neither is having 2 cows an abstraction. And so we go in a circle.
>>>
>>>> As for numbers, why do we use the same sequence of numbers for counting
>>>> different kinds of things? There are significant advantages in doing so
>>>> but it is not fundamentally necessary.
>>>
>>> What?
>>>
>> https://en.wikipedia.org/wiki/Yan_tan_tethera
>
> Hows that any different from someone saying "lots" or "many" in answer to a
> question of how many sheep are there?
>
It is a method of counting in regular use that doesn't use the 1 2 3
notation. It gives an exact number though, not "lots".

Jim

On 17/08/2021 11:26, mickspud@downthefarm.com wrote:
> On Tue, 17 Aug 2021 11:21:13 +0100
> "NY"<me@privacy.invalid> wrote:
>> "Indy Jess John"<bathwatchdog@OMITTHISgooglemail.com> wrote in message
>> news:sfg0mq$ifc$1@dont-email.me...
>>> On 17/08/2021 09:19, mickspud@downthefarm.com wrote:
>>>> On Tue, 17 Aug 2021 00:12:43 +0100
>>>> Owen Rees<orees@hotmail.com> wrote:
>>>
>>>>> The concept 'cow' is an abstraction, a specific actual cow is not. We
>>>>
>>>> Neither is having 2 cows an abstraction. And so we go in a circle.
>>>>
>>>>> As for numbers, why do we use the same sequence of numbers for counting
>>>>> different kinds of things? There are significant advantages in doing so
>>>>> but it is not fundamentally necessary.
>>>>
>>>> What?
>>>>
>>> https://en.wikipedia.org/wiki/Yan_tan_tethera
>>
>> It's interesting that the sheep-counting numbering system uses a lot of
>> multi-syllable words for 1-10, whereas we only have one word seven that has
>> two syllables. By the time you get to 20 you have a *lot* of syllables to
>> express a number. Though French takes the piss with contortions such as
>> quatre-vignts-dix-sept.
>
> Some parts of the francophone world saw sense and use octante instead of
> quatre vingt.
>
>
And nonante instead of quatre vingt dix

Jim

On Mon, 19 Jul 2021 08:13:26 -0000 (UTC), MrSpud_Fbyeq@ov00mymhsmu.eu
wrote:

>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.

To take just one example, the minimum distance there can be between
physical particles depends on the geometry of spheres, which does
depend on properties of mathematics. Whether it's oranges in a box or
atoms in a crystal lattice, there is a maximum packing density that
depends on mathematical rules. Physics is subservient to mathematics.

Rod.

<mickspud@downthefarm.com> wrote in message
news:sfg2rt$16r9$1@gioia.aioe.org...
> On Tue, 17 Aug 2021 11:21:13 +0100
> "NY" <me@privacy.invalid> wrote:
>>"Indy Jess John" <bathwatchdog@OMITTHISgooglemail.com> wrote in message
>>news:sfg0mq$ifc$1@dont-email.me...
>>> On 17/08/2021 09:19, mickspud@downthefarm.com wrote:
>>>> On Tue, 17 Aug 2021 00:12:43 +0100
>>>> Owen Rees<orees@hotmail.com> wrote:
>>>
>>>>> The concept 'cow' is an abstraction, a specific actual cow is not. We
>>>>
>>>> Neither is having 2 cows an abstraction. And so we go in a circle.
>>>>
>>>>> As for numbers, why do we use the same sequence of numbers for
>>>>> counting
>>>>> different kinds of things? There are significant advantages in doing
>>>>> so
>>>>> but it is not fundamentally necessary.
>>>>
>>>> What?
>>>>
>>> https://en.wikipedia.org/wiki/Yan_tan_tethera
>>
>>It's interesting that the sheep-counting numbering system uses a lot of
>>multi-syllable words for 1-10, whereas we only have one word seven that
>>has
>>two syllables. By the time you get to 20 you have a *lot* of syllables to
>>express a number. Though French takes the piss with contortions such as
>>quatre-vignts-dix-sept.
>
> Some parts of the francophone world saw sense and use octante instead of
> quatre vingt.

Exactly: septante, huitante and nonante (some/all used in Belgium,
Luxembourg and Switzerland) would seem far simpler and more logical. I
wonder why mainstream France has never adopted these improvements and has
stuck with (the equivalent of) four-twenties seventeen that than ninety
seven.

I read of a German spy (or maybe a British resistance worker) who was
unmasked in Belgium because he mistakenly used the French four-twenties
seventeen notation instead of the ninety seven notation, blowing his cover
as a Belgian. One of those "oh shit" moments like in the film "Went the Day
Well" when the German invaders, masquerading as British soldiers, were
unmasked when one gave a child a bar of chocolate with the word Schokolade
(the German spelling) embossed on it.