The Golden Ratio

[Ant Sinclair]

I've read that some believe that Phidias, whose name was given to the Golden Ratio Phi, was the first to use the ratio in his sculptures, others say it goes further back in history to the Summerians.

It appears frequently in nature,but, what causes it's existence?

[studiot]

To save you getting bogged down in mysticism here is an extract from Ball: The Self-Made Tapestry with a solid reference to Ian Stewart's book at the end.

 

[Daecon]

It appears frequently in nature,but, what causes it's existence?

I would suggest it's an artefact (I think that's the right word) of the mathematical laws of reality.

Edited February 13, 2017 by Daecon

[Strange]

I've read that some believe that Phidias, whose name was given to the Golden Ratio Phi, was the first to use the ratio in his sculptures, others say it goes further back in history to the Summerians.

 

 

Thanks for that. I didn't know that Phi was named after Phidias. (I don't know if he is thought to be the first to use it, but was perhaps the first named/renowned person.)

 

 

 

It appears frequently in nature,but, what causes it's existence?

 

Organic growth often follows a Fibonacci series (which was, supposedly, first developed to illustrate the growth of rabbit populations). The ratio between terms in the Fibonacci series is (approximately) Phi. So the ratio is often seen in the natural world - in the shape of seashells, sunflower seeds, Romanesco broccoli, etc. That explains its (claimed) aesthetic appeal.

[DrKrettin]

 

 

Thanks for that. I didn't know that Phi was named after Phidias. (I don't know if he is thought to be the first to use it, but was perhaps the first named/renowned person.)

 

 

 

Not entirely - it was coined in 1914, partly Phidias and partly Fibonacci. Link. We don't know much about Phidias, but he was a very respected sculptor and they suspect that he used phi in connection with the construction of the Parthenon.

[Ant Sinclair]

Thanks for your replies gentlemen, I was wondering if the ratio has always been the same value, ie approximately 1.618, could this value possibly change over say time or some other variable changing?

Could it be possible to say check fossil records of shells from creatures just after the Cambrian Extinction, then say 280 million years ago and compare them to today's shells.

The change would be small, say 1.614 approximately 540 million years ago, then 1.616 approximately 280 million years back leading to today's value.

Does anybody know if any such checks have been carried out or if the values mentioned would be big enough changes to 'see'?

[Daecon]

Would that not imply that the laws of mathematics have changed over millions of years? I suspect some lifeforms approximate the golden ratio/Fibonacci sequence closer than others, but I don't believe the underlying mathematical sequence would change - in fact if we were to ever discover alien life, I believe that it too would show the same shapes and patterns.

[Ant Sinclair]

Would that not imply that the laws of mathematics have changed over millions of years? I suspect some lifeforms approximate the golden ratio/Fibonacci sequence closer than others, but I don't believe the underlying mathematical sequence would change - in fact if we were to ever discover alien life, I believe that it too would show the same shapes and patterns.

I see where you're coming from Daecon but it may just be a case of wedding dresses, it fit her when she was 21, but now at 42....

[Strange]

Thanks for your replies gentlemen, I was wondering if the ratio has always been the same value, ie approximately 1.618, could this value possibly change over say time or some other variable changing?

Could it be possible to say check fossil records of shells from creatures just after the Cambrian Extinction, then say 280 million years ago and compare them to today's shells.

The change would be small, say 1.614 approximately 540 million years ago, then 1.616 approximately 280 million years back leading to today's value.

Does anybody know if any such checks have been carried out or if the values mentioned would be big enough changes to 'see'?

 

 

The ratio itself cannot change as it is defined mathematically.

 

Where we see the ratio in nature, it is only ever very approximate. For example, the spirals of sunflower seeds may have numbers of seeds close to numbers in the fibonacci series, but not necessarily exact. And the ratio between numbers in the Fibonacci series only approximates Phi, anyway (it gets closer for larger numbers). Or you could look at spiral sheets, but the growth rates vary from year to year, so it only approximates a geometric spiral in the first place. These variations could lead to a wide range of measured values for the "golden ratio" (growth rate).

[Ant Sinclair]

Thanks for replying Strange, you mention that spirals in nature are in close approximation to the Fibonacci Sequence which again approximately fits to the Golden Ratio, even though nature seems to have it's little blurps when reproducing the spiral.

I have read that some Spiral Galaxies including our own Milkyway seem to conform to the Spiral, also even some hurricanes that form on earth.

If this is the case the cause of the Spiral isn't biological and it's root must lay somewhere that effects everything in the verse.

[Strange]

I have read that some Spiral Galaxies including our own Milkyway seem to conform to the Spiral, also even some hurricanes that form on earth.

If this is the case the cause of the Spiral isn't biological and it's root must lay somewhere that effects everything in the verse.

 

 

I have no idea if that is the case or not. But if it is, there are two possible explanations that I can think of:

 

1. It is a coincidence: some galaxy/hurricane spirals match that ratio, while others have ratios of 1.2, 1.2, 1.3, 1.4, 1.5, 1.7, 1.8, 1.9 ...

 

2. The underlying physics of density waves (in galaxies) or velocities (in hurricanes) cause them to approximate a logarithmic spiral.

 

Note that the underlying cause is not "biological" but is simply related to growth (see how the Fibonacci series is defined). So there could be some truth in possibility 2. I have no idea.

More here: http://goldenratiomyth.weebly.com/the-logarithmic-spiral.html

[Ant Sinclair]

Math Phi (1+√5)/2 = 1.618034....

 

Natures Phi = C/π × C/√π = 1.614048....

 

Math Phi = Designed Value of Phi

 

Nature's Phi = As-Built Value of Phi

 

The exponents on C/π × C/√π have been deliberately omitted, it is the mixing of the e-m waves that is the important factor!!!

[Raider5678]

Math Phi (1+√5)/2 = 1.618034....

 

Natures Phi = C/π × C/√π = 1.614048....

 

Math Phi = Designed Value of Phi

 

Nature's Phi = As-Built Value of Phi

 

The exponents on C/π × C/√π have been deliberately omitted, it is the mixing of the e-m waves that is the important factor!!!

Phi for all.

[Ant Sinclair]

Phi for all.

Thank you for your interesting and enlightening input

[Strange]

Math Phi (1+√5)/2 = 1.618034....

 

Natures Phi = C/π × C/√π = 1.614048....

 

Math Phi = Designed Value of Phi

 

Nature's Phi = As-Built Value of Phi

 

 

How can that be "nature's" Phi when you are using the arbitrary and man-made units of 10⁸ m/s?

 

You don't get an approximation to Phi with imperial (American) units or with furlongs/fortnight.

Edited April 8, 2017 by Strange

[Ant Sinclair]

How can that be "nature's" Phi when you are using the arbitrary and man-made units of 10⁸ m/s?

 

You don't get an approximation to Phi with imperial (American) units or with furlongs/fortnight.

Strange your post, it is empty!

[Bignose]

Strange your post, it is empty!

It is not empty. Apart from the obvious that you quoted some obviously non-empty text, he point is valid.

 

The numerical representation of c changes depending on what units you use. Hence whatever specific representation you used to find that [math]\frac{c^2}{\pi^{\frac{3}{2}}}[/math] to be equal to phi (and it is not really obvious what units you used for c to do this...) for a few decimal points is coincidence. Just dumb luck. In other words, meaningless.

 

Hence, Strange's post is exceedingly not-empty.

Edited April 8, 2017 by Bignose

[Ant Sinclair]

Again as Strange's post, your post Big Nose has little relevance to what Strange quoted against.

 

Why unless stated would C's Units not be metres per second, and considering the use of π why wouldn't Strange assume it's units to be in metres, I'm beginning to think Strange is AI, a program!

 

One more thing Big Nose, your little red/green stickers bear no relevance either, so you know where you can post them don't you???

Edited April 8, 2017 by Ant Sinclair

[DrKrettin]

Again as Strange's post, your post Big Nose has little relevance to what Strange quoted against.

 

 

 

I must be missing something because I thought that not only were the posts from Strange and Bignose relevant, they made a lot of sense.

 

Which is more than can be said for an approximate equal value of phi and the value of something which depends entirely on the units used - in this case, metres and seconds.

 

Try expressing c in units of furlongs per weekend, and see if you can find another fascinating equivalence!

[Ant Sinclair]

Dr Kretin,

 

"Try expressing c in units of furlongs per weekend, and see if you can find another fascinating equivalence!",

 

are you about to tell us some story about a race horse?

[DrKrettin]

Dr Kretin,

 

"Try expressing c in units of furlongs per weekend, and see if you can find another fascinating equivalence!",

 

are you about to tell us some story about a race horse?

 

Not at all - I'm just trying to point out that "Nature's phi" as you define it depends on the units of c. Why choose metres and seconds?

[Ant Sinclair]

Not at all - I'm just trying to point out that "Nature's phi" as you define it depends on the units of c. Why choose metres and seconds?

 

Maybe I have reasons for using the Units, I, as it seems wrongly, assumed the gentlemen reading would take for granted.

Maybe I wouldn't know how the thread would open up, I thought that what I stated would eventually(after the usual Strange interactions) lead to a 'split' from The Golden Ratio to a Scalar Waves Thread!

[DrKrettin]

Maybe I have reasons for using the Units,

 

This is a science forum, and it might be expected for you to take the trouble to state your reasons.

 

The obvious reason is that there is no coincidence between the "two phis" in other units, so what exactly is the point?

[Ant Sinclair]

"The obvious reason is that there is no coincidence between the "two phis" in other units, so what exactly is the point?"

 

I Agree 100%, There is No Coincidence!

 

"This is a science forum, and it might be expected for you to take the trouble to state your reasons."

 

Like The Multi-Verse Doc, I like to roll slow, I thought I would show you Nature's Phi and we would all get round to discussing it.

You in a rush?

Edited April 8, 2017 by Ant Sinclair

[Strange]

Again as Strange's post, your post Big Nose has little relevance to what Strange quoted against.

 

Why unless stated would C's Units not be metres per second, and considering the use of π why wouldn't Strange assume it's units to be in metres,

 

 

It might be the case that most people today would assume m/s (although not many people would assume 10⁸ m/s).

 

But a lot of people in the USA, and even more people in the past, would probably think first of miles per second.

 

And aliens on another planet might think of it as qwerkles per blonk.

 

So it isn't "natural" except to a proportion of humans at a particular time in history. It certainly has no universal meaning. Unlike the mathematical version, which is based on the way things grow in nature. And so aliens on another planet would almost certainly be aware of that as well.

Edited April 8, 2017 by Strange