[Supervolant (OP)]

Hello everyone,

I would like to start a topic about the Golden Number: 1.61803399...

What makes a single number so interesting that ancient Egypts, Greeks, Renaissance artists, a 17th century astronomer and a 21st century novelist all would use and write about it? It's a number that goes by many names. This “golden” number, 1.61803399..., represented by the Greek letter Phi (Φ), is known as the Golden Ratio, Golden Number, Golden Proportion, Golden Mean, Golden Section, Divine Proportion and Divine Section.

If you don't know what the Golden Number is I am here to give you a short introduction into this fascinating but still mysterious topic with the intention to start an interesting discussion on the why.

The Golden Number and Ratio is unique in its mathematical properties and pervasive in its appearance throughout natural reality. Most of you may be more interested in the appearances of Phi in nature, it's application to art, architecture and design, and its potential insights into the more spiritual aspects of life, but as we are the inside the nakedscients forum, let's begin with the purest of facts about Phi, which are found in mathematics.

Mathematics of the Golden Number

Most of you know about the number Pi (3,14...) but relatively few about Phi (1,618...), the Golden Ratio. Why is that? Phi, just as Pi is one of a few irrational numbers found inside mathematics. Meaning they have an infinite number of digits after the decimal point.

Phi is not only irrational but the very most irrational number. Watch this video for validation (I suggest watching it after reading trough the topic if this is your first encounter to Phi as it might be confusing):

Where Pi (3,14...) is the ratio of the circumference of a circle to its diameter, Phi (1,618...) is the Golden Ratio that results when a line is divided in the ratio of 1 : 1,618... .

Imagine a rope and you were asked to cut it somewhere. There's an infinite amount of places at which you could cut it. Each place of cut would result in different ratios for the length of the small piece to the large piece, and of the large piece to the entire rope. For example cut it in exact half and you get a ratio of 1 : 1 from small to large piece and 1 : 1/2 from any of the two pieces to the original length of the rope.
There is this one unique point, at which the ratio of the large piece to the smaller piece is exactly the same as the ratio of the whole rope to the larger piece, and at this point the golden ratio of both is 1 : 1,618... , or Phi.


golden ratio line.gif (4.08 kB . 600x347 - viewed 7146 times)

What makes this so much more than an exercise in mathematics is that this proportion appears throughout creation and extensively in the human face and body. It's found in the proportions of animals, in plants, the solar system and even in the seemingly chaotic movements of stock markets. And that's why it's so appealing to mathematicians, doctors, naturalists, artists, inventors, mystics or anyone else having the slightest ammount curiosity for the reality we are living in.

The Fibonacci Sequence

The Fibonacci sequence, also a plot element in "The Da Vinci Code", provides yet another way to derive Phi mathematically. The series is quite simple and elegant. Start with 0 and add 1 to get 1. Then repeat the process adding each two numbers in series to determine the next one: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233...


FibonacciRow.gif (28.89 kB . 600x500 - viewed 7020 times)

The relationship between the Fibonacci numbers to the Golden Ratio or Phi is found by dividing each number by the one before. The further you go in the series, the closer the result gets to Phi. For example:

1/1 = 1
2/1 = 2
3/2 = 1,5
5/3 = 1,666
13/8 = 1,625
21/13 = 1,615

Furthermore in the series and you'll find that 233/144 = 1,61805 is a very close approximation of Phi, which to den decimal places is 1,6180339887.

Geometry of the Golden Ratio

The Golden ratio is also found in geometry, appearing in basic construction of an equilateral triangle, square and pentagon placed inside a circle, as well as in more complex three-dimensional solids such as dodecahedrons and many more.


golden spiral.jpg (18.24 kB . 575x349 - viewed 7037 times)

*Insert pictures of golden geometry examples*

Johannes Kepler (1571 - 1630) - key figure in the 17th-century scientific revolution and best know for his discovery of the true elliptical nature of the orbits of the planets inside our solar system described it as such: "Geometry has two great treasures: one is the Theorem of Pxythagoras; the other, the division of a line into the extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel."

Nature and Life

There are many other fascinating mathematical relationships and oddities in both Phi and the Fibonacci series that can be explored but now I would like to venture with you into the nature, where Phi and the Fibonacci sequence manifest themselves pervasively, tough not universally.

Fibonacci numbers are always the number of petals in a flower or the number of branches splitting from one point in vegetation.
Funfact: That's why a four-leaved clover is regarded as rare, since 4 isn't a fibonacci number. The positions and proportions of the key dimension on animals are based on Phi. Examples include the body sections of insects, dimensions of bird wings, the spiral of sea shells and the position of the dorsal fins on dolphin, to name a very few. The library of Phi on living and moving things seems to reach into infinity just as it's irrational nature is. Every living being is a projection of Phi meaning if you happen to find something alive (or moving) you are certain to find Golden Proportions.


Nautilus_Cutaway_with_Logarithmic_Spiral.jpg (44.84 kB . 886x670 - viewed 6968 times)

*Insert pictures of golden ratios in the nature*

Even more intriguing is the extensive appearance of Phi throughout the human body. Extremities, the face, teeth, organ positioning the ratio at which our heart beats, we breath and even the spiral of the Human DNA are based on the Golden Proportions. This has a direct impact on our perceptions of (human-) beauty. Some would argue that beauty is in the eye of the beholder, but there is evidence to support that our perception of beauty in women and men is based on how closely the proportion of facial and body dimensions come to Phi. It seems that Phi is hard-wired into our consciousness as a guide to beauty. For this reason models and stars most often show of Golden Ratios throughout their body which also lead to facial plastic surgery and cosmetic dentistry as a guide to achieve the most "natural" and beautiful results in facial features and appearance. As Phi is deeply imbedded we even find golden proportions at geometries carved inside caves from 10.000 years ago or from a child drawing seemingly abstract lines on paper.


1507244255279.png (42.7 kB . 848x444 - viewed 8129 times)

*Insert pictures of golden ratios in the human body*

Art, Architecture and Design

With all the unique mathematical properties of Phi and its appearance throughout creations, it's of little wonder that mankind would not only take notice of this number and the Golden Ratio it creates, but also use it to capture the beauty and harmony of nature in our own creations in art, architecture and other areas of design. In some cases, mankind application of Phi is undeniable. In other cases, it is still the subject of debate. The Great Pyramid of Egypt appears to embody the Golden Ratio in the ratios of base, height and hypotenuse, tough there are no record of the ancient Egyptians mentioning Phi. The Greeks knew of Phi at the time of building the Pantheon. While the Pantheon overall dimensions only approximate the golden ratio, there appear to be Golden Ratios everywhere throughout the design elements and columns. De divina proportione (translated from Italian: the divine proportions) a book from 1500 on mathematics and geometry written by Luca Pacioli was illustrated by none other than the great Leonardo Da Vinci. Himself using the golden ratio extensively in famous paintings such as the Mona Lisa and Salvator Mundi. The dimensions of Stradivarius violins is built around Phi proportions and of course good sounding music and acoustical note proportions involve many examples of golden ratios.
More modern applications of the Golden Ratio in architecture can be seen in the Notre Dame in Paris, the United Nations Headquarters Secretariat building in New York (UN) and in the blueprint of whole Washington DC. It's very commonly used in the design of products and logos by many major corporations such as google and apple. It has been used in high fashion clothing design and the basis for "the fashion code", a style guide to dressing.
Various studies have validated that the golden rectangle is the most pleasing to the human eye.


monalisa.jpg (33.7 kB . 453x640 - viewed 7050 times)

*Insert pictures of golden ratios in art, architecture and design*

The Solar System and Universe

Curiously enough, we even find golden ratio relationships in the solar system and universe. The diameters of the Earth and Moon form a triangle whose dimensions are based on the mathematical characteristics of phi. The rings of Saturn are very close in dimension to the golden ratio of the planets diameter. Even the position of the great know bodies inside our solar system seem to be directly linked to the Golden ratio.


PhiSolarSystem.jpg (45.8 kB . 800x800 - viewed 14885 times)



 [ Invalid Attachment ]


spiralinggalaxies.jpg (43.3 kB . 564x701 - viewed 6993 times)

*Insert pictures of golden ratio:
- Moon to earth
- Saturn and it's rings
- whole solar system *

New Discoveries involving the Golden Ratio

The golden ratio continuous to open new doors in our understanding of life and the universe. As we have entered the 21st century Phi seems to having a rebirth in integrating knowledge across a wide variety of fields of study, including time, light and quantum physics.

Trying to get things written down as straight as possible. Please feel free to ask for more examples (Feel free to ask, as these topics are amazing as well but very complex in nature I will skip them for now)



*Insert picture of mathematical light speed angular momentum g-factor ratio of electron to proton*

Spiritual Aspects

The description of this golden proportion as the divine proportion is perhaps fitting because is seen by many as a door to a deeper understanding of beauty and spirituality in life, unveiling a hidden harmony or connectedness in so much of what we see and are. If you came down all the way to here you might find it difficult to deny the importance this single number plays inside the reality we perceive.

Phi does not explicitly appear in the Bible. Still you can find it in most volumes page ratios or the dimensions given by God to Noah for the Ark which reflect a 5 to 3 proportion. Both Fibonacci numbers with a ratio of 1,666..., a reasonably close approximation to Phi. The Kaaba, the most sacred site of Islam in Mecca, is located very close to the golden ratio of the distance between the Earths north and south poles. Even the symbol for Phi, a circle with a line drawn trough it, can be tough to represent a zero, or void, divided by one, or unity, to create beauty, or live. Analogous to God creating the universe from nothing.

*purposefully have chosen examples of the major religions in order to not start world war three...


The Discovery

The whole is the sum of it's parts...


phi-limit.gif (1.88 kB . 224x55 - viewed 6799 times)

All of this led me to a path of self discovery, passion, invention and riches in various ways.

I tried my best to keep things short and concise. Any of these topics has potential to be highly exaggerated but I wanted to keep this into the further communications inside this topic.

To me the golden ratio represents the highest amount of efficiency inside a system. Phi can play a larger role inside invention, as efficiency is something we clearly crave for.

A wonderful example of this is seen in this video by the inventor Jay Harman and his water mixing apparatus which is being designed around Phi:

"The path of least resistance" - Jay Harman

If you happen to like what you saw in the above mentioned video go ahead and watch this as well. The video is a very good addition to this topic as he is not only describing his invention but starting with a good explanation of Phi I mostly agree with.

Phi might be the very foundation of making living things possible. As we see in our solar system  and it's high organization around Phi including Earth and all of it's live.
In my research, so far, other planetary systems we found have no direct link of Phi to their solar midpoints. (We have found thousands, I might not have searched trough the right ones we know of) On our search on habitable planets and extraterrestrial live forms we might should try involve Phi as a central filter.

I as a human without any religious following and feet grounded into science (facts rather then believes) am starting to ask myself: "Is the golden ratio the fingerprint of a creator, who appears to love math? Is it a code hidden in plain sight?"
Can all of this really be a huge coincidence? This isn't chaos, this is order by design and by analogy every design should have a designer, right?

I believe science and the golden ratio have a long way to go and we should seriously start spreading the knowledge. The golden proportion of live is pervasive around us and it's shocking how such a big number is known to such a little number of fellow humans (after my observation of talking to many).

So why?

I am very thankful about having access to the internet as without that I would've had it difficult to acquire the knowledge on topics such as the golden ratio.
Also I would like to Gary B. Meisner who is about to publish a book on the Golden Ratio I already have preordered. It's called "The Golden Ratio: The Divine Beauty of Mathematics" This thread is heavily inspired by his work and I have used to some extend text and pictures of his website. He deserves Applaus!

It's wonderful to be able to share the knowledge around the Golden Ratio now with everyone.

Together we might start with a library of Phi, involving all the observable golden ratios as all these observations are what Phi is leading to and ultimately will also lead us to the why of things.

Thanks you for reading trough, looking forward to further communicate,
- Robert

[Bored chemist]

Well, the stuff about colours is bullshit.

[Supervolant (OP)]

Well, the stuff about colours is bullshit.

You think so? A pity that the only thing you see in my post is something negative. Here's more proof as this is the only way to show folks like you.


Colors02.jpg (44.34 kB . 1250x384 - viewed 6728 times)

[Supervolant (OP)]

@Everyone I am only allowed to insert 12 images at a time. Even tough I count 11 in the starterpost, I can't insert any more. Thats why I just spread the visual knowledge further down here but first of another fact about time. And to the one saying the color thing is incorrect, tell me isn't color the byproduct of light? Isn't light the constant everything is measured after, since light in turn is directly linked to time, the speed of light?

Mathematically, the electron g-factor is approximately:

gfactore = -2 / sin (Ř)

and the proton g-factor is approximately:

gfactorp = 2Ř / sin (1/Ř)

 Thus it appears that the Golden Ratio, or Phi, is a constant produced by time.

The National Institute of Standards and Technology (NIST) states these gfactor constants as per the table below.


timeg-factor.png (54.4 kB . 832x434 - viewed 6794 times)

[Supervolant (OP)]

EiffelTower.jpg (21.37 kB . 330x509 - viewed 6683 times)


TajMahal.jpg (24.89 kB . 320x292 - viewed 6700 times)


TajmahalClose.jpg (26.81 kB . 275x321 - viewed 6692 times)


NotreDame.jpg (19.65 kB . 171x295 - viewed 6614 times)



Pyramid.jpg (10.02 kB . 300x240 - viewed 6656 times)


5f553896fc23f57ca024860c3dd72108.jpg (150.43 kB . 1514x1097 - viewed 6810 times)


Golden-Planets-Five.jpg (459.95 kB . 1220x754 - viewed 7443 times)


africa.jpg (31.21 kB . 359x400 - viewed 6689 times)

[Bored chemist]

"folks like me" will not be convinced by you pulling numbers out of your hat. We also won't be convinced by you simply doing the same thing again.
If you say the numbers are "approximate" why give them to three places of decimals?
Like I said- it's bullshit.
BTW, the middle of the "optical spectrum"- the peak of the human eye 's sensitivity is about 555nm

[Supervolant (OP)]

"folks like me" will not be convinced by you pulling numbers out of your hat. We also won't be convinced by you simply doing the same thing again.
If you say the numbers are "approximate" why give them to three places of decimals?
Like I said- it's bullshit.
BTW, the middle of the "optical spectrum"- the peak of the human eye 's sensitivity is about 555nm

Go to: https://www.artofclaytaylor.com/single-post/2016/08/22/The-Magnetic-Spectrum-of-Inertial-Polarization

Ask the author @claytaylor why he put an approx. in front of the numbers.

[Bored chemist]

@Everyone I am only allowed to insert 12 images at a time. Even tough I count 11 in the starterpost, I can't insert any more. Thats why I just spread the visual knowledge further down here but first of another fact about time. And to the one saying the color thing is incorrect, tell me isn't color the byproduct of light? Isn't light the constant everything is measured after, since light in turn is directly linked to time, the speed of light?

Mathematically, the electron g-factor is approximately:

gfactore = -2 / sin (Ř)

and the proton g-factor is approximately:

gfactorp = 2Ř / sin (1/Ř)

 Thus it appears that the Golden Ratio, or Phi, is a constant produced by time.

The National Institute of Standards and Technology (NIST) states these gfactor constants as per the table below.


timeg-factor.png (54.4 kB . 832x434 - viewed 6794 times)

OK, so the correct values are
   −2.00231930436182
give or take
0.00000000000052
and
+5.585694702
give or take
0.000000017

So your calculated values are wrong.

That's it.
End of discussion.
You have the wrong numbers.

[Supervolant (OP)]

@Everyone I am only allowed to insert 12 images at a time. Even tough I count 11 in the starterpost, I can't insert any more. Thats why I just spread the visual knowledge further down here but first of another fact about time. And to the one saying the color thing is incorrect, tell me isn't color the byproduct of light? Isn't light the constant everything is measured after, since light in turn is directly linked to time, the speed of light?

Mathematically, the electron g-factor is approximately:

gfactore = -2 / sin (Ř)

and the proton g-factor is approximately:

gfactorp = 2Ř / sin (1/Ř)

 Thus it appears that the Golden Ratio, or Phi, is a constant produced by time.

The National Institute of Standards and Technology (NIST) states these gfactor constants as per the table below.


timeg-factor.png (54.4 kB . 832x434 - viewed 6794 times)

OK, so the correct values are
   −2.00231930436182
give or take
0.00000000000052
and
+5.585694702
give or take
0.000000017

So your calculated values are wrong.

That's it.
End of discussion.
You have the wrong numbers.

End of discussion? Is this how folks like you discover? Don't think so..

While the phi-based approach is not exactly equal to the NIST constant, with quantum level constants, there will always be a difference between theoretical work and empirical work.  This can be due to the irregularities in the metal of the test equipment, stray background radiations, or a host of other minute causes. The results of any empirical measurement always show some degree of statistical spread as a consequence.

Such constants are adjusted as new measuring techniques and better materials become available. So any theoretical value that is within one part in a thousand has scientific value.  Even if the degree of accuracy of a constant is believed to be accurate to within one part in a billion this is true. The accuracy of one part in a billion could mean that a stable condition for a specific experiment configuration has been achieved, but that particular configuration could still be influencing the measurement to a small degree.

[Bored chemist]

Ask the author @claytaylor why he put an approx. in front of the numbers.

He isn't posting here, you are.
So it's you who need to go and ask him (or you can accept that you are wrong)
He has used numbers that fit the answer he was after, rather than answers that have aby sensible basis.
The "green" light at 547.533 nm has an amusing property.
The frequency corresponding to that wavelength has a value of 547.533 THz

But don't get excited about that having any real significance. It only works with metres and seconds. If we used inches or feet (or minutes) we would get a different "magical" number.

So, he has taken a meaningless coincidence and pretended that it supports his idea.
Incidentally, the middle of the red part of the spectrum is nearer to 690nm
And for blue light it would be about 470 to 475 nm
https://en.wikipedia.org/wiki/Visible_spectrum#Spectral_colors

So, he's wrong on all three counts and has started with a meaningless arbitrary point.
Are you still saying this isn't bullshit?

[Bored chemist]

While the phi-based approach is not exactly equal to the NIST constant, with quantum level constants, there will always be a difference between theoretical work and empirical work.

Yes.
That's why I included it in the post. (It's 0.00000000000052 for the electron which is about a ten millionth of teh error in your calculation)
You, on the other hand, did not.

So, perhaps you can re-appraise your views on " Is this how folks like you discover? Don't think so.."

Do you understand that when you say"  This can be due to the irregularities in the metal of the test equipment, stray background radiations, or a host of other minute causes. The results of any empirical measurement always show some degree of statistical spread as a consequence." the obvious answer is that we measured those things...
And they are still add up to vastly less than your method's wrongness.

You got the wrong answer.
That really is the end of it.

[Supervolant (OP)]

Ask the author @claytaylor why he put an approx. in front of the numbers.

He isn't posting here, you are.
So it's you who need to go and ask him (or you can accept that you are wrong)
He has used numbers that fit the answer he was after, rather than answers that have aby sensible basis.
The "green" light at 547.533 nm has an amusing property.
The frequency corresponding to that wavelength has a value of 547.533 THz

But don't get excited about that having any real significance. It only works with metres and seconds. If we used inches or feet (or minutes) we would get a different "magical" number.

So, he has taken a meaningless coincidence and pretended that it supports his idea.
Incidentally, the middle of the red part of the spectrum is nearer to 690nm
And for blue light it would be about 470 to 475 nm
https://en.wikipedia.org/wiki/Visible_spectrum#Spectral_colors

So, he's wrong on all three counts and has started with a meaningless arbitrary point.
Are you still saying this isn't bullshit?

After going trough the numbers again I give you this one. Seems I got too much into wishful thinking there and tricked by my own fandom. Still the numbers are close and you can't deny that, I guess the original author was aware of that and thats why he put up the approx in front of the numbers. Thanks for the correction. I ll go ahead and delete the picture out of the original post.

[Bored chemist]

OK, the numbers for the electron g-factor and proton g-factor are simply wrong.
When do you plan to accept that?

[Bored chemist]

This sort of hokum is called "numerology" and it's well known bullshit
https://en.wikipedia.org/wiki/Numerology

The fact that the Eiffel Tower (etc) matches is simple- the designer chose to make it that way.
The planets work fine- until you realise that nearly half of them are missing. Only 5 of the 9 actually fit.

Doesn't that look fishy to you?

And the spiral over Africa is just plain silly.

[Supervolant (OP)]

This sort of hokum is called "numerology" and it's well known bullshit
https://en.wikipedia.org/wiki/Numerology

The fact that the Eiffel Tower (etc) matches is simple- the designer chose to make it that way.
The planets work fine- until you realise that nearly half of them are missing. Only 5 of the 9 actually fit.

Doesn't that look fishy to you?

And the spiral over Africa is just plain silly.

You seem uninspired. If you read it all trough (I bet you did) and this look like hokum to you, then sorry I have no room for respect. As I said, you are one of "these" folks I would not spend a minute around in real life as your negativity drags down. Go change, see the wonder and be inspired... I am not here to fight but to answer why there is this pervasive proportion, you wanna help on that? Go ahead! I am looking forward to it if not, I will kindly ignore all your further answers.

Have a wonderful day and good luck. 

Edit: Anyone else in here?

[Bored chemist]

I am not here to fight but to answer why there is this pervasive proportion, you wanna help on that? Go ahead!

No problem.
https://en.wikipedia.org/wiki/Confirmation_bias

[Supervolant (OP)]

I am not here to fight but to answer why there is this pervasive proportion, you wanna help on that? Go ahead!

No problem.
https://en.wikipedia.org/wiki/Confirmation_bias

Thanks again, already knew about confirmation_bias. The fact that I accepted your answer to the light spectrum denies that I am the victim of any cognitive bias. Since I am a life long learner having no respect for someone does not mean I won't learn from this someone.
In fact I learned a lot from you. For example how I, as a human being, don't wan't to become and being viewed from the outside world.

And If what you wan't to say is that "Phi is hokum" then please go ahead and read the article yourself.
Oh and I can also most warmly recommend to you this topic.
https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect

[Bored chemist]

And If what you wan't to say is that "Phi is hokum"

Except, I didn't say that, did I?
Now here's an interesting idea.
Read this
https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect
You will see that the people who suffer from this are the ones who are not well enough informed to recognise that they are wrong.
They keep on saying they are right- even when that's not what the evidence shows.

So, that would be you saying this

You think so? A pity that the only thing you see in my post is something negative. Here's more proof as this is the only way to show folks like you.

and this

Go to: https://www.artofclaytaylor.com/single-post/2016/08/22/The-Magnetic-Spectrum-of-Inertial-Polarization [nofollow]

Ask the author @claytaylor why he put an approx. in front of the numbers.

and this

End of discussion? Is this how folks like you discover? Don't think so..

While the phi-based approach is not exactly equal to the NIST constant, with quantum level constants, there will always be a difference between theoretical work and empirical work

When I pointed out that the numbers were quite simply not right, you carried on saying they were.
How do you distinguish that from this?
 https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect

[evan_au]

Is 1,618... the golden number?

I agree that Phi has some interesting mathematical properties - I've used some of them in software that I've written, stretching back many years.
- And the seed patterns on sunflowers and pinecones is a rational (ie ratio of integers) approximation to Phi, related to Fibonnacci sequences
- I'll even agree that some nice architecture could have been designed with this ratio in mind.

But when you look for Phi everywhere, you are likely to see it places that it isn't.

Dunning Kruger effect

I would be careful of this yourself...

Mr Chemist knows a lot about light because he has done a lot of ... chemistry!

[Bored chemist]

Pi is one of a few irrational numbers found inside mathematics.

There are an infinite number of irrational numbers.
So you are infinitely wrong.
That's sort of impressive.