Re: The Golden Ratio

On 3/14/24 2:40 PM, J. J. Lodder wrote:

erik simpson <eastside.erik@gmail.com> wrote:
 

On 3/14/24 9:56 AM, Bob Casanova wrote:

On Thu, 14 Mar 2024 13:58:30 +0100, the following appeared
in talk.origins, posted by nospam@de-ster.demon.nl (J. J.
Lodder):
>

Bob Casanova <nospam@buzz.off> wrote:
>

On Wed, 13 Mar 2024 13:39:38 +0100, the following appeared
in talk.origins, posted by nospam@de-ster.demon.nl (J. J.
Lodder):
>

Athel Cornish-Bowden <me@yahoo.com> wrote:
>

On 2024-03-07 22:31:27 +0000, Bob Casanova said:
>

On 7 Mar 2024 17:51:40 GMT, the following appeared in
talk.origins, posted by dgb (David)
<david@nomail.afraid.org>:
>

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_

ra

tio

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!

>
It hasn't happened at all.

>
You are, of course, mistaken.
>

Wrong. Nothing "happened"; the so-called Golden Ratio, like
all mathematical relationships which describe observed
phenomena, is a property of physical

>
mathematical
>

   reality, no more. And,
of course, no less.

>
You are wasting your breath. Bob is an incurable materialist,
incapable of abstraction and idealisation,
>

Ummm, I didn't say that there are no parts of math which are
abstract, only that all math relationships WHICH DESCRIBE
PHYSICAL PHENOMENA are properties of those phenomena.

>
So the integers are a property of your football scores?
"No more, and no less", like you say,
>

Overgeneralizations and "football scores" aside...
>
If I understand you, the mathematical relationships which
describe observed physical relationships do *not* describe
those relationships? OK. Maybe the word "properties" is
what's causing you grief? Or maybe it's the phrase "no more
and no less; if that's the case consider it removed,
leaving:
>
"...the so-called Golden Ratio, like all mathematical
relationships which describe observed phenomena, is a
property of physical reality in the sense that it precisely
describes such physical relationship."
>
Better? Clumsy, of course, but since hyperbole and/or
imprecision in general discussion is apparently verboten...

>
The golden ratio a/b == (a+b)/a.  Observed phenomena may approximate
that number, but the mathematical interest since antiquity has little to
do with that.  In mathematics it appears in all kinds of surprising
contexts.  Wikipedia presents many of them.

 And it is not really a ratio of anything.
It is traditionally called a ratio because to the ancient Greeks
all numbers except the integers could only be represented as ratios.
It is just a number.
Best defined, as a number, purely arithmetically,
as the simplest possible continued fraction.
(just my preference)
No need to invoked more complicated concepts,
like square roots, solving quadratic equations, etc.,
or even number systems to some base,
 Jan
 

The Pythagoreans did better than that by proving that there exit irrational numbers (such as the golden ratio).  The continued fraction representation is indeed very elegant, but it also implies an irrational value.