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interests / talk.origins / The Golden Ratio

SubjectAuthor
* The Golden Ratiodgb (David)
+* Re: The Golden RatioJ. J. Lodder
|+* Re: The Golden Ratiodgb (David)
||`- Re: The Golden RatioChris
|+* Re: The Golden RatioRichmond
||`* Re: The Golden RatioJ. J. Lodder
|| +- Re: The Golden RatioRichmond
|| `* Re: The Golden RatioBurkhard
||  `* Re: The Golden RatioJ. J. Lodder
||   `* Re: The Golden Ratioerik simpson
||    +- Re: The Golden RatioJ. J. Lodder
||    `* Re: The Golden RatioBurkhard
||     +- Re: The Golden RatioJ. J. Lodder
||     `* Re: The Golden RatioBurkhard
||      `- Re: The Golden RatioJ. J. Lodder
|`* Re: The Golden Ratioerik simpson
| `* Re: The Golden RatioBob Casanova
|  `* Re: The Golden Ratioerik simpson
|   `- Re: The Golden RatioBob Casanova
+* Re: The Golden Ratiodgb (David)
|`* Re: The Golden RatioT i m
| +- Re: The Golden RatioBob Casanova
| `- Re: The Golden Ratiojillery
+* Re:The Golden RatioKalkidas
|+- Re: Re:The Golden Ratioerik simpson
|+- Re:The Golden Ratiodgb (David)
|`* Re: The Golden RatioJ. J. Lodder
| `* Re: The Golden Ratiodgb (David)
|  +* Re: The Golden RatioMark Isaak
|  |`* Re: The Golden RatioRichmond
|  | `* Re: The Golden Ratiodgb (David)
|  |  `* Re: The Golden RatioFromTheRafters
|  |   `- Re: The Golden RatioBob Casanova
|  `* Re: The Golden RatioJ. J. Lodder
|   `* Re: The Golden Ratiodgb (David)
|    +* Re: The Golden RatioBob Casanova
|    |+* Re: The Golden RatioAthel Cornish-Bowden
|    ||+- Re: The Golden RatioBob Casanova
|    ||`* Re: The Golden RatioJ. J. Lodder
|    || `* Re: The Golden RatioBob Casanova
|    ||  `* Re: The Golden RatioJ. J. Lodder
|    ||   `* Re: The Golden RatioBob Casanova
|    ||    +* Re: The Golden RatioJ. J. Lodder
|    ||    |+* Re: The Golden RatioBob Casanova
|    ||    ||`* Re: The Golden RatioJ. J. Lodder
|    ||    || `* Re: The Golden Ratioerik simpson
|    ||    ||  `* Re: The Golden RatioJ. J. Lodder
|    ||    ||   `* Re: The Golden Ratioerik simpson
|    ||    ||    `- Re: The Golden RatioJ. J. Lodder
|    ||    |`- Re: The Golden RatioRichmond
|    ||    `* Re: The Golden Ratioerik simpson
|    ||     +* Re: The Golden RatioJ. J. Lodder
|    ||     |`* Re: The Golden Ratioerik simpson
|    ||     | `- Re: The Golden RatioJ. J. Lodder
|    ||     `* Re: The Golden RatioBob Casanova
|    ||      `* Re: The Golden RatioJ. J. Lodder
|    ||       `* Re: The Golden RatioBob Casanova
|    ||        `- Re: The Golden RatioJ. J. Lodder
|    |`* Re: The Golden RatioJ. J. Lodder
|    | `* Re: The Golden RatioBob Casanova
|    |  `- Re: The Golden RatioJ. J. Lodder
|    `* Re: The Golden RatioJ. J. Lodder
|     `* Re: The Golden Ratiodgb (David)
|      `* Re: The Golden RatioJ. J. Lodder
|       `* Re: The Golden Ratiodgb (David)
|        `- Re: The Golden RatioT i m
`- Re: The Golden Ratiojillery

Pages:123
The Golden Ratio

<l4lh5qFs93hU1@mid.individual.net>

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From: dav...@nomail.afraid.org (dgb (David))
Newsgroups: alt.computer.workshop,talk.origins
Subject: The Golden Ratio
Date: 4 Mar 2024 09:04:58 GMT
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 by: dgb (David) - Mon, 4 Mar 2024 09:04 UTC

Does this occur by accident?

https://en.wikipedia.org/wiki/Golden_ratio

Or by design?

Re: The Golden Ratio

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From: nos...@de-ster.demon.nl (J. J. Lodder)
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Subject: Re: The Golden Ratio
Date: Mon, 4 Mar 2024 10:34:11 +0100
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 by: J. J. Lodder - Mon, 4 Mar 2024 09:34 UTC

dgb <david@nomail.afraid.org> wrote:

> Does this occur by accident?
>
> https://en.wikipedia.org/wiki/Golden_ratio
>
> Or by design?

Mathematics doesn't occur.
It is.

Jan

Re: The Golden Ratio

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From: dav...@nomail.afraid.org (dgb (David))
Newsgroups: alt.computer.workshop,talk.origins
Subject: Re: The Golden Ratio
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 by: dgb (David) - Mon, 4 Mar 2024 10:31 UTC

On 4 Mar 2024 at 09:34:11 GMT, "J. J. Lodder" <J. J. Lodder> wrote:

> dgb <david@nomail.afraid.org> wrote:
>
>> Does this occur by accident?
>>
>> https://en.wikipedia.org/wiki/Golden_ratio
>>
>> Or by design?
>
> Mathematics doesn't occur.
> It is.
>
> Jan

Rather like this:- https://en.wikipedia.org/wiki/I_am_(biblical_term)

David

Re: The Golden Ratio

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From: dav...@nomail.afraid.org (dgb (David))
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Subject: Re: The Golden Ratio
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 by: dgb (David) - Mon, 4 Mar 2024 10:33 UTC

On 4 Mar 2024 at 09:37:53 GMT, "FromTheRafters" <FTR@nomail.afraid.org> wrote:

> dgb (David) presented the following explanation :
>> Does this occur by accident?
>>
>> https://en.wikipedia.org/wiki/Golden_ratio
>>
>> Or by design?
>
> Happenstance, like Pi.

I don't believe that.

Re: The Golden Ratio

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 by: Richmond - Mon, 4 Mar 2024 10:42 UTC

nospam@de-ster.demon.nl (J. J. Lodder) writes:

> dgb <david@nomail.afraid.org> wrote:
>
>> Does this occur by accident?
>>
>> https://en.wikipedia.org/wiki/Golden_ratio
>>
>> Or by design?
>
> Mathematics doesn't occur.
> It is.
>

If it didn't occur then it is, and always was. But was it so before the
beginning of the universe? or maybe the universe didn't begin, because
time and space are not fundamental properties of nature.

Re: The Golden Ratio

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From: nos...@de-ster.demon.nl (J. J. Lodder)
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Subject: Re: The Golden Ratio
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 by: J. J. Lodder - Mon, 4 Mar 2024 13:43 UTC

Richmond <dnomhcir@gmx.com> wrote:

> nospam@de-ster.demon.nl (J. J. Lodder) writes:
>
> > dgb <david@nomail.afraid.org> wrote:
> >
> >> Does this occur by accident?
> >>
> >> https://en.wikipedia.org/wiki/Golden_ratio
> >>
> >> Or by design?
> >
> > Mathematics doesn't occur.
> > It is.
> >
>
> If it didn't occur then it is, and always was. But was it so before the
> beginning of the universe? or maybe the universe didn't begin, because
> time and space are not fundamental properties of nature.

The universe, whatever it is, or was, or may be
is irrelevant for mathematics,

Jan

Re: The Golden Ratio

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Subject: Re: The Golden Ratio
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 by: Richmond - Mon, 4 Mar 2024 15:24 UTC

nospam@de-ster.demon.nl (J. J. Lodder) writes:

> Richmond <dnomhcir@gmx.com> wrote:
>
>> nospam@de-ster.demon.nl (J. J. Lodder) writes:
>>
>> > dgb <david@nomail.afraid.org> wrote:
>> >
>> >> Does this occur by accident?
>> >>
>> >> https://en.wikipedia.org/wiki/Golden_ratio
>> >>
>> >> Or by design?
>> >
>> > Mathematics doesn't occur. It is.
>> >
>>
>> If it didn't occur then it is, and always was. But was it so before
>> the beginning of the universe? or maybe the universe didn't begin,
>> because time and space are not fundamental properties of nature.
>
> The universe, whatever it is, or was, or may be is irrelevant for
> mathematics,
>

A bold statement. But what is the meaning of geometry without the
physical world from which it was derived?

And what do you know about physics, other than that which is expressed
by the standard model, which is a mathematical model?

Re: The Golden Ratio

<us4r8d$37m3l$1@dont-email.me>

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From: eter...@spaced.me.uk (T i m)
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Subject: Re: The Golden Ratio
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 by: T i m - Mon, 4 Mar 2024 16:01 UTC

On 04/03/2024 10:33, dgb (David) wrote:
> On 4 Mar 2024 at 09:37:53 GMT, "FromTheRafters" <FTR@nomail.afraid.org> wrote:
>
>> dgb (David) presented the following explanation :
>>> Does this occur by accident?
>>>
>>> https://en.wikipedia.org/wiki/Golden_ratio
>>>
>>> Or by design?
>>
>> Happenstance, like Pi.
>
> I don't believe that.
>
I have (and wear) one of these:

https://www.geeksoutfit.com/products/science-doesnt-care-what-you-believe-t-shirt

Cheers, T i m

Re: The Golden Ratio

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Subject: Re: The Golden Ratio
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 by: Bob Casanova - Mon, 4 Mar 2024 16:30 UTC

On Mon, 4 Mar 2024 16:01:15 +0000, the following appeared in
talk.origins, posted by T i m <eternal@spaced.me.uk>:

<Snip irrelevant site>

>On 04/03/2024 10:33, dgb (David) wrote:
>> On 4 Mar 2024 at 09:37:53 GMT, "FromTheRafters" <FTR@nomail.afraid.org> wrote:
>>
>>> dgb (David) presented the following explanation :
>>>> Does this occur by accident?
>>>>
>>>> https://en.wikipedia.org/wiki/Golden_ratio
>>>>
>>>> Or by design?
>>>
>>> Happenstance, like Pi.
>>
>> I don't believe that.
>>
>I have (and wear) one of these:
>
>https://www.geeksoutfit.com/products/science-doesnt-care-what-you-believe-t-shirt
>
Too restrictive; the *universe* doesn't care what anyone
believes.
>
--

Bob C.

"The most exciting phrase to hear in science,
the one that heralds new discoveries, is not
'Eureka!' but 'That's funny...'"

- Isaac Asimov

Re: The Golden Ratio

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Subject: Re: The Golden Ratio
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 by: Chris - Mon, 4 Mar 2024 18:21 UTC

dgb (David) <david@nomail.afraid.org> wrote:
> On 4 Mar 2024 at 09:34:11 GMT, "J. J. Lodder" <J. J. Lodder> wrote:
>
>> dgb <david@nomail.afraid.org> wrote:
>>
>>> Does this occur by accident?
>>>
>>> https://en.wikipedia.org/wiki/Golden_ratio
>>>
>>> Or by design?
>>
>> Mathematics doesn't occur.
>> It is.
>>
>> Jan
>
> Rather like this:- https://en.wikipedia.org/wiki/I_am_(biblical_term)

Nothing like.

Re: The Golden Ratio

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From: eastside...@gmail.com (erik simpson)
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Subject: Re: The Golden Ratio
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 by: erik simpson - Mon, 4 Mar 2024 18:38 UTC

On 3/4/24 1:34 AM, J. J. Lodder wrote:
> dgb <david@nomail.afraid.org> wrote:
>
>> Does this occur by accident?
>>
>> https://en.wikipedia.org/wiki/Golden_ratio
>>
>> Or by design?
>
> Mathematics doesn't occur.
> It is.
>
> Jan
>
>
Not sure about "occur". This may be a philosophical quibble, but I have
always regarded mathematics as a form of language, based primarily on
counting. And yes, humans aren't the only animals capable of that. That
said, if there are things to count and creatures to count them, there
will be numbers. We (humans) are capable of finding interesting kinds
of numbers (irrational, transcendental). So far as I know, there is no
such thing as an "accidental" number.

Re: The Golden Ratio

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 by: Bob Casanova - Mon, 4 Mar 2024 23:51 UTC

On Mon, 4 Mar 2024 10:38:14 -0800, the following appeared in
talk.origins, posted by erik simpson
<eastside.erik@gmail.com>:

>On 3/4/24 1:34 AM, J. J. Lodder wrote:
>> dgb <david@nomail.afraid.org> wrote:
>>
>>> Does this occur by accident?
>>>
>>> https://en.wikipedia.org/wiki/Golden_ratio
>>>
>>> Or by design?
>>
>> Mathematics doesn't occur.
>> It is.
>>
>> Jan
>>
>>
>Not sure about "occur". This may be a philosophical quibble, but I have
>always regarded mathematics as a form of language, based primarily on
>counting. And yes, humans aren't the only animals capable of that. That
>said, if there are things to count and creatures to count them, there
>will be numbers. We (humans) are capable of finding interesting kinds
>of numbers (irrational, transcendental). So far as I know, there is no
>such thing as an "accidental" number.
>
I believe his point is the math expresses existing
relationships which existed prior to the invention of math,
just like everything in nature.
>
--

Bob C.

"The most exciting phrase to hear in science,
the one that heralds new discoveries, is not
'Eureka!' but 'That's funny...'"

- Isaac Asimov

Re: The Golden Ratio

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From: eastside...@gmail.com (erik simpson)
Newsgroups: alt.computer.workshop,talk.origins
Subject: Re: The Golden Ratio
Date: Mon, 4 Mar 2024 16:38:27 -0800
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 by: erik simpson - Tue, 5 Mar 2024 00:38 UTC

On 3/4/24 3:51 PM, Bob Casanova wrote:
> On Mon, 4 Mar 2024 10:38:14 -0800, the following appeared in
> talk.origins, posted by erik simpson
> <eastside.erik@gmail.com>:
>
>> On 3/4/24 1:34 AM, J. J. Lodder wrote:
>>> dgb <david@nomail.afraid.org> wrote:
>>>
>>>> Does this occur by accident?
>>>>
>>>> https://en.wikipedia.org/wiki/Golden_ratio
>>>>
>>>> Or by design?
>>>
>>> Mathematics doesn't occur.
>>> It is.
>>>
>>> Jan
>>>
>>>
>> Not sure about "occur". This may be a philosophical quibble, but I have
>> always regarded mathematics as a form of language, based primarily on
>> counting. And yes, humans aren't the only animals capable of that. That
>> said, if there are things to count and creatures to count them, there
>> will be numbers. We (humans) are capable of finding interesting kinds
>> of numbers (irrational, transcendental). So far as I know, there is no
>> such thing as an "accidental" number.
>>
> I believe his point is the math expresses existing
> relationships which existed prior to the invention of math,
> just like everything in nature.
>>
That's it. In particular, the "Golden Ratio" isn't an accident or a
design. It's just a definition. Now if there were a universe that
contained nothing, or maybe just one thing, there wouldn't be any math.

Re: The Golden Ratio

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From: nos...@buzz.off (Bob Casanova)
Newsgroups: alt.computer.workshop,talk.origins
Subject: Re: The Golden Ratio
Date: Mon, 04 Mar 2024 22:56:34 -0700
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 by: Bob Casanova - Tue, 5 Mar 2024 05:56 UTC

On Mon, 4 Mar 2024 16:38:27 -0800, the following appeared in
talk.origins, posted by erik simpson
<eastside.erik@gmail.com>:

>On 3/4/24 3:51 PM, Bob Casanova wrote:
>> On Mon, 4 Mar 2024 10:38:14 -0800, the following appeared in
>> talk.origins, posted by erik simpson
>> <eastside.erik@gmail.com>:
>>
>>> On 3/4/24 1:34 AM, J. J. Lodder wrote:
>>>> dgb <david@nomail.afraid.org> wrote:
>>>>
>>>>> Does this occur by accident?
>>>>>
>>>>> https://en.wikipedia.org/wiki/Golden_ratio
>>>>>
>>>>> Or by design?
>>>>
>>>> Mathematics doesn't occur.
>>>> It is.
>>>>
>>>> Jan
>>>>
>>>>
>>> Not sure about "occur". This may be a philosophical quibble, but I have
>>> always regarded mathematics as a form of language, based primarily on
>>> counting. And yes, humans aren't the only animals capable of that. That
>>> said, if there are things to count and creatures to count them, there
>>> will be numbers. We (humans) are capable of finding interesting kinds
>>> of numbers (irrational, transcendental). So far as I know, there is no
>>> such thing as an "accidental" number.
>>>
>> I believe his point is the math expresses existing
>> relationships which existed prior to the invention of math,
>> just like everything in nature.
>>>
>That's it. In particular, the "Golden Ratio" isn't an accident or a
>design. It's just a definition. Now if there were a universe that
>contained nothing, or maybe just one thing, there wouldn't be any math.
>
Pretty much the way I see it; the math results from the
physical relationships.
>
--

Bob C.

"The most exciting phrase to hear in science,
the one that heralds new discoveries, is not
'Eureka!' but 'That's funny...'"

- Isaac Asimov

Re: The Golden Ratio

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Subject: Re: The Golden Ratio
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 by: jillery - Tue, 5 Mar 2024 11:58 UTC

On Mon, 4 Mar 2024 16:01:15 +0000, T i m <eternal@spaced.me.uk> wrote:

>On 04/03/2024 10:33, dgb (David) wrote:
>> On 4 Mar 2024 at 09:37:53 GMT, "FromTheRafters" <FTR@nomail.afraid.org> wrote:
>>
>>> dgb (David) presented the following explanation :
>>>> Does this occur by accident?
>>>>
>>>> https://en.wikipedia.org/wiki/Golden_ratio
>>>>
>>>> Or by design?
>>>
>>> Happenstance, like Pi.
>>
>> I don't believe that.
>>
>I have (and wear) one of these:
>
>https://www.geeksoutfit.com/products/science-doesnt-care-what-you-believe-t-shirt
>
>Cheers, T i m

I like this one:

“The good thing about science is that it's true whether or not you
believe in it.”

--
To know less than we don't know is the nature of most knowledge

Re:The Golden Ratio

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From: eat...@joes.pub (Kalkidas)
Newsgroups: alt.computer.workshop,talk.origins
Subject: Re:The Golden Ratio
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 by: Kalkidas - Thu, 7 Mar 2024 01:34 UTC

dgb (David) <david@nomail.afraid.org> Wrote in message:r
> Does this occur by accident?https://en.wikipedia.org/wiki/Golden_ratioOr by design?

It will never be known.
--

----Android NewsGroup Reader----
https://piaohong.s3-us-west-2.amazonaws.com/usenet/index.html

Re: Re:The Golden Ratio

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From: eastside...@gmail.com (erik simpson)
Newsgroups: alt.computer.workshop,talk.origins
Subject: Re: Re:The Golden Ratio
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 by: erik simpson - Thu, 7 Mar 2024 01:50 UTC

On 3/6/24 5:34 PM, Kalkidas wrote:
> dgb (David) <david@nomail.afraid.org> Wrote in message:r
>> Does this occur by accident?https://en.wikipedia.org/wiki/Golden_ratioOr by design?
>
> It will never be known.
Nonsense. It's a definition.

Re: The Golden Ratio

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 by: jillery - Thu, 7 Mar 2024 04:07 UTC

On 4 Mar 2024 09:04:58 GMT, dgb (David) <david@nomail.afraid.org>
wrote:

>Does this occur by accident?
>
>https://en.wikipedia.org/wiki/Golden_ratio
>
>Or by design?

Yes to both. It's not either/or.

--
To know less than we don't know is the nature of most knowledge

Re:The Golden Ratio

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Subject: Re:The Golden Ratio
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 by: dgb (David) - Thu, 7 Mar 2024 08:03 UTC

On 7 Mar 2024 at 01:34:10 GMT, "Kalkidas" <eat@joes.pub> wrote:

> dgb (David) <david@nomail.afraid.org> Wrote in message:r
>> Does this occur by accident?https://en.wikipedia.org/wiki/Golden_ratio
>> Or by design?
>
> It will never be known.

Have you ever studied, REALLY studied, nature?

See:-
https://upload.wikimedia.org/wikipedia/commons/8/86/Mother_and_daughter.jpg

Then look here:-
https://upload.wikimedia.org/wikipedia/commons/5/5a/FibonacciChamomile.PNG

The "nature" section here tells you more:-
https://en.wikipedia.org/wiki/Fibonacci_sequence

=

I KNOW it's not just an 'accident'! ;-)

Re: The Golden Ratio

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 by: J. J. Lodder - Thu, 7 Mar 2024 09:38 UTC

Kalkidas <eat@joes.pub> wrote:

> dgb (David) <david@nomail.afraid.org> Wrote in message:r
> > Does this occur by accident?https://en.wikipedia.org/wiki/Golden_ratioOr by
design?
>
> It will never be known.

There is nothing to know there,

Jan

Re: The Golden Ratio

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 by: dgb (David) - Thu, 7 Mar 2024 10:13 UTC

On 7 Mar 2024 at 09:38:23 GMT, "J. J. Lodder" <J. J. Lodder> wrote:

> Kalkidas <eat@joes.pub> wrote:
>
>> dgb (David) <david@nomail.afraid.org> Wrote in message:r
>>> Does this occur by accident?https://en.wikipedia.org/wiki/Golden_ratio
>>> Or by design?
>>
>> It will never be known.
>
> There is nothing to know there,
>
> Jan

The thing to know, Jan, is that it hasn't all happened by accident! :-D

In my opinion, of course!

--
David

Re: The Golden Ratio

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 by: Mark Isaak - Thu, 7 Mar 2024 15:55 UTC

On 3/7/24 2:13 AM, dgb (David) wrote:
> On 7 Mar 2024 at 09:38:23 GMT, "J. J. Lodder" <J. J. Lodder> wrote:
>
>> Kalkidas <eat@joes.pub> wrote:
>>
>>> dgb (David) <david@nomail.afraid.org> Wrote in message:r
>>>> Does this occur by accident?https://en.wikipedia.org/wiki/Golden_ratio
>>>> Or by design?
>>>
>>> It will never be known.
>>
>> There is nothing to know there,
>>
>> Jan
>
> The thing to know, Jan, is that it hasn't all happened by accident! :-D
>
> In my opinion, of course!

And how about the number 72287 & 9/11ths? Did it happen by accident?

--
Mark Isaak
"Wisdom begins when you discover the difference between 'That
doesn't make sense' and 'I don't understand.'" - Mary Doria Russell

Re: The Golden Ratio

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 by: Richmond - Thu, 7 Mar 2024 16:36 UTC

Mark Isaak <specimenNOSPAM@curioustaxon.omy.net> writes:

> On 3/7/24 2:13 AM, dgb (David) wrote:
>> On 7 Mar 2024 at 09:38:23 GMT, "J. J. Lodder" <J. J. Lodder> wrote:
>>
>>> Kalkidas <eat@joes.pub> wrote:
>>>
>>>> dgb (David) <david@nomail.afraid.org> Wrote in message:r
>>>>> Does this occur by accident?https://en.wikipedia.org/wiki/Golden_ratio
>>>>> Or by design?
>>>>
>>>> It will never be known.
>>>
>>> There is nothing to know there,
>>>
>>> Jan
>> The thing to know, Jan, is that it hasn't all happened by accident!
>> :-D
>> In my opinion, of course!
>
> And how about the number 72287 & 9/11ths? Did it happen by accident?

One might ask if a rectange has four sides by accident. How could it be
otherwise and still be a rectangle?

Re: The Golden Ratio

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From: nos...@de-ster.demon.nl (J. J. Lodder)
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Subject: Re: The Golden Ratio
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 by: J. J. Lodder - Thu, 7 Mar 2024 17:41 UTC

dgb <david@nomail.afraid.org> wrote:

> On 7 Mar 2024 at 09:38:23 GMT, "J. J. Lodder" <J. J. Lodder> wrote:
>
> > Kalkidas <eat@joes.pub> wrote:
> >
> >> dgb (David) <david@nomail.afraid.org> Wrote in message:r
> >>> Does this occur by accident?https://en.wikipedia.org/wiki/Golden_ratio
> >>> Or by design?
> >>
> >> It will never be known.
> >
> > There is nothing to know there,
> >
> > Jan
>
> The thing to know, Jan, is that it hasn't all happened by accident! :-D

It hasn't happened at all.

> In my opinion, of course!

Opinions are worthless,
(yours in particular)

Jan

Re: The Golden Ratio

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Subject: Re: The Golden Ratio
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 by: dgb (David) - Thu, 7 Mar 2024 17:51 UTC

On 7 Mar 2024 at 17:41:02 GMT, "J. J. Lodder" <J. J. Lodder> wrote:

> dgb <david@nomail.afraid.org> wrote:
>
>> On 7 Mar 2024 at 09:38:23 GMT, "J. J. Lodder" <J. J. Lodder> wrote:
>>
>>> Kalkidas <eat@joes.pub> wrote:
>>>
>>>> dgb (David) <david@nomail.afraid.org> Wrote in message:r
>>>>> Does this occur by accident?https://en.wikipedia.org/wiki/Golden_ratio
>>>>> Or by design?
>>>>
>>>> It will never be known.
>>>
>>> There is nothing to know there,
>>>
>>> Jan
>>
>> The thing to know, Jan, is that it hasn't all happened by accident! :-D
>
> It hasn't happened at all.

You are, of course, mistaken.

>> In my opinion, of course!
>
> Opinions are worthless,
> (yours in particular)
>
> Jan

You'd do well to watch and listen here:-

https://www.youtube.com/watch?v=uGHQcplhpYY

--
David


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