I constantly get annoyed by various “golden ratio in art/nature!” articles. Outside of a very small number of artists who deliberately used the ratio, it doesn’t even show up in art and architecture, and there are plenty of spirals in nature, but “a spiral” is not the same as the golden spiral. (Leonardo da Vinci did a work or two using it, realized it looked weird and stopped, for instance.) But people can mis-measure and play mathematical tricks - or just plain ignore the reality - to make the numbers fit if they want to. I notice religious folk like to repeat the idea, as if the notion that the golden ratio/golden spiral repeating in nature was evidence of God’s hand making the universe.
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This is offered by the article to prove the ratio does not apply to the Parthenon.
This is offered to prove it does.
Guess it depends on who draws the lines where.
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Back in architecture school, they definitely force fed us the “Golden ratio” bullshit. If you have a bad design at the final review, you can say that you were trying to fit a Golden Ratio in, and they would forgive you for putting a solitary toilet in the middle of a museum. It’s an instant half-grade boost, it doesn’t even have to measure up.
Anyway, most designers don’t really understand the golden ratio (phi). I heard many say it is 2:3 or 1:1.6 ratio. They just post the spiral and call it “art inspired by nature”. Alternatively, the Vitruvian Man is used when you do circle or square. (Like “Put a bird on it” in Portlandia.)
The truth is, it has to do with the space between the human eyes. In a flat surface, a ratio near 1.6 is nice to look at for most people. In very large, very tiny, or something with depth and moving parts, the golden ratio does not necessarily apply.
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I know, right?! It’s like the Bible Code. If you want to see it, you will see it.
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I don’t think anyone really says that the ‘golden ratio’ is pervasive or everywhere. It’s more part of the general ‘math is everywhere’ appreciation of art and math. Like the way seeds spiral out of sunflowers or symmetry, or crystal shapes, or even fractals and chaos and randomness. The golden spiral is just cool because a nautilus shell looks really neat.
Now lets all go watch some Vi Hart videos 
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Look at the dome on that dude! Just look at it!
Wait, does it conform to the Golden Ratio, is that why it is so irresistible?
As a graphic design student I remember a bit of “look hard enough and you’ll find them everywhere”, but that has always seemed to me to be more telling about our human love for pattern recognition, cognitive biases and other artifacts of perception than anything.
There are, however, at least a few actual real world uses for golden rations among the ‘canons of page construction’ in book design.
The Discordians had it right with the Law of Fives.
All things happen in fives, or are divisible by or are multiples of five, or are somehow directly or indirectly appropriate to 5.
“I find the Law of Fives to be more and more manifest the harder I look.”
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The Golden Ratio is “bullshit”:
Depending upon how it’s applied it can be. However, the respected mathematician Arthur T. Benjamin would disagree with you that it’s not an interesting fact when it shows up in nature:
The ratio as it’s applied within nature is often an approximation that’s not meant to be taken --literally–. It’s just noting similarities in patterns that anyone (including laypersons) can observe and there’s nothing wrong with doing that.
People recognize “fractal” patterns in nature all the time and find some significance in that (spiritual, metaphysical, philosophical and/or scientific observations).
It makes some feel “connected”. Kind of like what can be experienced on shrooms/acid, etc. (for some).
Are fractals “bullshit”?
Like almost anything, it can be utilized to prop up pseudo-science, etc. – but to refer to the entire concept as “bullshit” is a bit extreme, in my opinion.
Suggested reading:
Some call certain science “magical” not due to ignorance, but as a respectful nod towards the vast complexities involved that we still don’t know (and perhaps never will) that surround the complex “nature” of science:
If you haven’t already read it, I think this is a pretty interesting take on it (in a sense):
http://www.amazon.com/New-Kind-Science-Stephen-Wolfram/dp/1579550088
Series of followups 10 years later:
As Wolfram mentions in the above link, there’s the applied NKS academic literature with hundreds of new models:
Hair patterns in mice. Shapes of human molars. Collective butterfly motion. Evolution of soil thicknesses. Interactions of trading strategies (interesting one that is, 
). Clustering of red blood cells in capillaries. Patterns of worm appendages. Shapes of galaxies. Effects of fires on ecosystems. Structure of stromatolites. Patterns of leaf stomata operation. Spatial spread of influenza in hospitals. Pedestrian traffic flow. Skin cancer development. Size distributions of companies. Microscopic origins of friction. And many, many more.
Our little lives get complicated
It’s a simple thing
Simple as a flower
And that’s a complicated thing
– “No New Tale To Tell”, Love and Rockets
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The Antikythera mechanism comes pretty close…
I bet it was not the first of its line either. While the cycles for predicting the the motion of the planets and the solar eclipses were known to the Babylonians, I find it hard to believe you would predict the motion of the planets using forth or fifty epicycles as Ptolomey wrote without some Alexandrian or Syracusan gear-maker wanting to actually build the sucker.
The golden ratio or the rule of three is good only as a note that a many people are happy seeing things laid out roughly thus, perhaps because it has been around a long time and we are used to it. Any more than that is woo.
Most of the golden rato/Fibonacci debunking traces back to a pleasantly acerbic article by George Markowsky in The College Mathematics Journal, Vol. 23, No. 1 (Jan., 1992), pp. 2-19. The text from which we teach our “math for liberal arts” survey course repeats the false statements (even though it also cites the Livio book!), so I assign this article by Markowsky as a counterpoint.
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That’s the nice thing about classical architecture - it’s got all these different elements, so if you pick a couple (totally) arbitrary points to start with, you’ll end up with some of your subsequent dividing lines roughly aligning with something on the building. Likewise with photographs - with enough elements, those lines will seem to correspond with something (and just ignore everything they don’t correspond with).
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This might have already been said above, but there is a large difference between talking about the golden ratio and fractals, etc in nature: the latter comes from models. Fractals naturally arise from simple models which involve branching. Certain evolved structures, like lungs, effectively have no other choice but to be fractal-like.
Most of the golden ratio examples are more like: “I think it’s about 1.6” But there are lots of numbers near 1.6. Why would it be (1+sqrt(5))/2 in particular?
I think you missed the points of my post. I can only suggest re-reading my post and perusing the links I provided.
Ok. I see what you are going for now. Still, without an underlying model, going from the fact that several quantities turn out near 1.6 to the claim that we are seeing the golden ratio is more than a little suspect. The claims that the golden ratio gives the most attractive rectangle are so subjective as to be non-falsifiable; not even wrong. I think that calling it BS is pretty fair.
Sure, I would agree with you in that context. Unfortunately, pseudoscience can latch onto just about any concept like unwanted barnacles. 
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It is a well known fact that we only use the golden ratio of our brains. The library and music hall guy said so.
