The golden ratio is still BS

[superdave]

https://www.fastcompany.com/3044877/the-golden-ratio-designs-biggest-myth

I posted this because the brand new math curriculum I am using this year perpetuates this myth on what is supposed to be the opening lesson of the year...But now I think this could be a good chance to talk some skepticism.  We can talk about why the myth persists and how it could be tested.


The myth says that all kinds of art and nature follow the ratio of about 1.1618... to 1, and that we are inclined to find that ratio pleasing.  There is one obvious problem which is that the first number in the ratio is irrational, which means the whole proportion is irrational, which means it is literally impossible for any object to follow that proportion.  But bigger problem is that all the typical examples used to describe how the proportion are used in art or architecture make their rectangles in entirely arbitrary ways just to fit the picture into the ratio.

[Sawyer]

There is one obvious problem which is that the first number in the ratio is irrational, which means the whole proportion is irrational, which means it is literally impossible for any object to follow that proportion. 

The golden ratio is probably nonsense, but this isn't true either.

E is irrational.  It shows up in nature all the time.  I'm pretty sure there are chemical bonds whose angle measurements that are irrational in both radians and degrees.  I don't see what's special about physical proportions that they cannot repeatedly follow the same irrational ratio.

[arthwollipot]

There is one obvious problem which is that the first number in the ratio is irrational, which means the whole proportion is irrational, which means it is literally impossible for any object to follow that proportion. 

The golden ratio is probably nonsense, but this isn't true either.

E is irrational.  It shows up in nature all the time.  I'm pretty sure there are chemical bonds whose angle measurements that are irrational in both radians and degrees.  I don't see what's special about physical proportions that they cannot repeatedly follow the same irrational ratio.

Indeed. The ratio of a circle's circumference to its radius is also irrational, and yet circles exist.

[jt512]

There is one obvious problem which is that the first number in the ratio is irrational, which means the whole proportion is irrational, which means it is literally impossible for any object to follow that proportion. 

The golden ratio is probably nonsense, but this isn't true either.

E is irrational.  It shows up in nature all the time.  I'm pretty sure there are chemical bonds whose angle measurements that are irrational in both radians and degrees.  I don't see what's special about physical proportions that they cannot repeatedly follow the same irrational ratio.

You beat me to it.

[Captain Video]

This was not an accident nor BS



This video does an interesting comparison to using the Golden ratio vs the rule of thirds in cinematography.



It doesn't exactly work with all aspect ratios we use in film so you have to cheat it in but I do think it makes some shots much better.   He says when he stretches the curve that it no longer works mathematically but its still close enough to the same curve that becomes pleasing to the eye.

on a side note Its interesting that he uses a Wes Anderson film to demonstrate film aspect ratios at the beginning of the video when Anderson does not use the rule of thirds nor the golden ratio. Not too many people can get away with that, the other two framing styles are almost always used.

[Alex Simmons]

Golden ratios or similar (there are a family of such ratios, it's not confined to just the Golden ratio) appear in nature often because of evolutionary selection pressure. Distribution of leaves around a stem, or flowers petals, or seeds are often optimised when the pattern used follows such irrational ratios.

e.g. if you want to maximise the light collected from one stem, then rotating the placement of leaves around the stem using such an irrational ratio will do this, or if you want to maximise the packing of seeds in a flower, then it represents a optimal design strategy.

If you think nature doesn't do irrational numbers, then you'll probably not want to know about how often fractals appear in nature as well. Just look at a fern leaf. Classic fractal pattern. Indeed, fractals are a brilliantly efficient way to encode a method of replication (which is why computer graphics use them all the time). The simplest of algorithms can lead to very complex and intricate patterns, as well as lead to optimal outcomes.

Then there are the appearance of prime numbers in nature as well, e.g. the number of years between when a species of cicadas appears in season is often a prime number of years (2,3,5,7,11,13,17). This evolved over millennia to be a very efficient survival strategy as it minimises the chances that two or more species emerge in the same season.

Another "natural" irrational number of course is ∏. ∏ appears everywhere in the natural world since spherical and related forms are a consequence of physics (e.g. gravity). The meandering ratio of rivers is a function of ∏. Biological processes are ultimately the consequence of physical laws, and is why ∏ appears in various places in nature. e.g. the patterns of spots and stripes on many animals has ∏ encoded within them. It's a key value in many periodic biological processes.

[Alex Simmons]

There is one obvious problem which is that the first number in the ratio is irrational, which means the whole proportion is irrational, which means it is literally impossible for any object to follow that proportion.

Irrational ratios appear in nature all over the place. The Golden ratio is but one and it's certainly not ubiquitous. There are others.

It is most certainly not impossible to create them. Indeed it's a consequence of minimising energy states (physics) and optimising outcomes (evolutionary pressure) that leads to the common appearance of such irrational ratios in the natural world.

[Alex Simmons]

and that we are inclined to find that ratio pleasing. 
<snip>
But bigger problem is that all the typical examples used to describe how the proportion are used in art or architecture make their rectangles in entirely arbitrary ways just to fit the picture into the ratio.

Well the first is subjective, so any claim as to how pleasing such forms are is probably just because nature using these forms is often pleasing the look at.

As to overlaying such ratios onto art and architecture yeah sometimes that looks a bit arbitrary and a case of post hoc rationalisation, when really one should examine the planning and design stage to see if use of such a ratio was a deliberate intent.

You can make a paper rectangle in the Golden ratio by simply performing a series of paper folds. It's just a consequence of trigonometry.

[Ah.hell]

My thoughts:
A.  Repeat the stuff folks have said about irrational numbers, nature, and repeating. 
B1.  I'm pretty sure some Greek came up with the notion that the golden ratio is pleasing to the eye and thus had some special properties.
B2.  Western artists have been aping the greeks ever since, so I'm also pretty sure the golden ratio is often featured in western art and architecture as a result.
B3.  This could easily be the case whether or not the golden ratio is pleasing to the eye and westerners may well be conditioned to think the golden ratio is pleasing thus it is. 



 I'd be curious if there is anything similar in eastern art.  I'm sure there is though.  No fours if nothing else. 

[seamas]

I recall first learning about the Golden Ratio./Golden Mean some 25 years ago when I was very active in oil painting.
What is interesting is the whole thing was barely (if ever) discussed much during time earlier when I was getting my BFA in painting.
I think it was slightly touched on in my freshman 2-D design course, but overall other proportions were far more illustrated in Art History and design analysis.

Anyway, upon learning about the ratio I stretched a couple canvases that conformed to the ratio, marked the ratio within the rectangle and set out to compose within the "ideal".
Meh.
Your mileage may vary, but I didn't get much liftoff at all.

There is a certain truth to a composition having a little more interest--or dynamics-- if the central interest point of the composition is somewhere kinda close to that point of the ratio, but it is not in any way exact or a tell-tale formula.
Put the central focal point dead in the center, (say something like Leonardo's Last supper, or any number of Renaissance Madonnas) and the dynamic becomes more calm, still, serene balanced. Have it off the center--more or less where the golden mean would describe and the eye is more free to wander the composition. Have it too far to one edge and the composition will usually look cropped, unbalanced or otherwise weak.

of course this part of a pictoral composition is but one of many interrelated elements that an artist or designer will exploit to accomplish their aim.

[seamas]

This was not an accident nor BS

Because what really captures that compositions's importance is Clint's lower cheek, which we all know is the most important part of a person's face.

[superdave]

OK I admit I might have been really sleepy when I wrote some of this,  the golden ratio being an irrational number doesn't disprove anything...but it does have consequences.

Because the number is irrational, any real life application has to be an approximation, but most of the examples you read about take that approximation to the extreme, justifying anything remotely close to 1.618 as being a golden ratio.  I think many of the other examples are just post hoc rationalizations.  Letterbox format is close to the golden ratio but the traditional TV standard before that was 4:3, which isn't close.   

The number is of course real, and there are going to be rectangles that come close to fitting it's proportions that exist in nature by virtue of the fact that there's just a lot of rectangular things out there. 


https://www.iflscience.com/plants-and-animals/why-is-the-golden-ratio-seem-to-be-everywhere-in-nature/


The real myth is that the golden ratio is tied to human perception in some way.  That doesn't seem true and the article in the OP explains why.

[Captain Video]

This was not an accident nor BS

Because what really captures that compositions's importance is Clint's lower cheek, which we all know is the most important part of a person's face.

in that shot it certainly was

the phi gridline is on his nose anyway,

[jt512]

Because the number is irrational, any real life application has to be an approximation...

Any real-life realization of any geometric object will be an approximation, wether the dimensions are rational or irrelational.  IRL, you can't construct a perfect square any more or less than you can a perfect circle or a perfect golden rectangle.  However, for any of these objects, you can come arbitrarily close to perfect, or at least as close as your construction technique permits.  With a compass you can construct an approximately perfect circle, even though the ratio of the circumference to the radius is irrational.  The error in the real-world circle does not stem from irrationality, but rather from limitations of precision of the real-world construction materials.  Similarly, with a compass and a straight edge, you can construct an approximately perfect goden rectangle.  The error, likewise, has nothing to do with the irrationality of the ratio of the sides.

[superdave]

Because the number is irrational, any real life application has to be an approximation...

Any real-life realization of any geometric object will be an approximation, wether the dimensions are rational or irrelational.  IRL, you can't construct a perfect square any more or less than you can a perfect circle or a perfect golden rectangle.  However, for any of these objects, you can come arbitrarily close to perfect, or at least as close as your construction technique permits.  With a compass you can construct an approximately perfect circle, even though the ratio of the circumference to the radius is irrational.  The error in the real-world circle does not stem from irrationality, but rather from limitations of precision of the real-world construction materials.  Similarly, with a compass and a straight edge, you can construct an approximately perfect goden rectangle.  The error, likewise, has nothing to do with the irrationality of the ratio of the sides.

No one is arguing that it's impossible to make a golden rectangle, I just did a few minutes ago with a compass and a straight edge.  The argument is that the golden rectangle and the golden ratio don't actually show up in many of the places that it is claimed.  For example, you can find people who argue that the ratio of certain lengths of body parts converge on the golden ratio, but this is just cherry picking.  There is no biological basis for why the golden ratio should apply to the length of your arm or torso.

or the above example from the movie.  A piece of the curve is cut completely off!  Clearly saying the golden ratio applies to that frame is opinion only.