Author Topic: The golden ratio is still BS  (Read 1693 times)

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Offline jt512

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Re: The golden ratio is still BS
« Reply #15 on: August 13, 2019, 02:57:09 PM »
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...


Actually, as the embedded quote above shows, you were arguing that it is impossible to make a golden rectangle as a consequence of the golden ratio being irrational.


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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.


That's probably true.




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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.


Is it?  It would be simple enough to design a study to test whether it is true or not. 


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There is no biological basis for why the golden ratio should apply to the length of your arm or torso.


At least, no known biological basis for it.

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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.


It appears to me, too, that the spiral was arbitrarily fitted to the picture, with essentially infinite degrees of freedom.
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Offline John Albert

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Re: The golden ratio is still BS
« Reply #16 on: August 13, 2019, 03:16:13 PM »
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,

Come on, man. The space between the right edge of Clint's mustache and beard is not the center of attention in that shot. The viewer is obviously intended to focus on his eyes, and possibly also the movement of the cigar between his teeth.

I'll give you the golden ratio with his nose as the rough centerline of the composition though.

But do you really think Leone intentionally set the shot up to utilize the Golden Ratio? If so, what mechanism did he use to measure the position of the nose when setting up the shot? Did he bring a tiny ruler to stick in front of the eyepiece of his Arriflex IIc?

It seems far more likely it was a happy accident, perhaps guided by blind intuition at best. Leone was a master.
« Last Edit: August 13, 2019, 03:32:58 PM by John Albert »

Offline Shibboleth

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Re: The golden ratio is still BS
« Reply #17 on: August 13, 2019, 03:46:05 PM »
The lower left cheek is the window into a person's soul.
common mistake that people make when trying to design something completely foolproof is to underestimate the ingenuity of complete fools.

Offline Alex Simmons

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Re: The golden ratio is still BS
« Reply #18 on: August 13, 2019, 06:15:39 PM »
Other areas we are seeing Golden ratios embedded include quantum mechanics (eignenvalue probabilities), ratios of atomic hydrogen radii in some molecular structures, black holes physics, natural Quasicrystals and in theories on Quantum Gravity (given the black holes stuff I guess this isn't surprising).

Offline Sawyer

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Re: The golden ratio is still BS
« Reply #19 on: August 13, 2019, 07:33:55 PM »
Other areas we are seeing Golden ratios embedded include quantum mechanics (eignenvalue probabilities), ratios of atomic hydrogen radii in some molecular structures, black holes physics, natural Quasicrystals and in theories on Quantum Gravity (given the black holes stuff I guess this isn't surprising).

Assuming for a moment that these are valid examples, this still kind of showcases how the Golden Ratio is just a godawful teaching tool to learn about science.


WHY is the golden ratio showing up in these situations?  In the previous post you claimed it was the optimal ratio for staggering leaves in plants.  Really?  Has someone calculated the overall number of photons of light that are incident on leaf surfaces based on the geographic location and growing season, adjusted for the efficiency of chlorophyll and other photoactive compounds, estimated energy expenditures for either the formation of buds or the overall growth of a leaf, and then proved that setting (L1+L2)/L2 = L2/L1 maximizes overall energy intake?  Based on those factors I listed, I'd bet that whenever you get something close to the golden ratio it is a coincidence rather than a fundamental organizational structure.  I could (maybe) write out some differential equations and boundary conditions where the golden ratio really *does* represent some sort of min or max, but I doubt they'll correspond to any realistic situation that we encounter in biology or physics.  We should also consider the fact that just because a particular design is optimal does not mean there is an evolutionary pathway to get there or maintain it.  Perhaps a lot of classes of plants reach ~1.5/1 distances between leaves but then hit a kind of barrier where there's no way to further increase without drastically altering their morphology.

This is what bugs me so much about this topic - instead of inspiring people to think about the why or the how, the Golden Ratio is just thrown out there like it's some sort of mythical force that automatically explains everything.  If it's not immediately intuitive why it's so special, or if there's doubt about it's significance, it's up to people that tout its utility to do actually do the math and prove their thesis.  Or even those that tout the aesthetics - come up with something beyond Psych 101 explanations of why people find it pleasing. 

Sorry to be a dick, but if you can't tell is dislike 99% of talk about this topic, both for and against.

Offline amysrevenge

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Re: The golden ratio is still BS
« Reply #20 on: August 13, 2019, 07:45:10 PM »
I just remember being pleased with myself in high school when I worked out for myself that it was the solution to x^2-x-1=0, x=0.5+sqrt(1.25)
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Offline Captain Video

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Re: The golden ratio is still BS
« Reply #21 on: August 13, 2019, 07:49:55 PM »
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.

I have to disagree, it was thought out in advance regardless of what John Albert thinks

Did anyone watch the video I posted above?  You will see how the G R is used to frame the shot, it was absolutely done intentionally and nobody had to draw any curves. Those lines are available the same as if he was using the rule of thirds, the cinematographer knows where they are in the frame based on the aspect they are shooting.  The line is right there on Clints nose where he placed the center of his shot, if using the rule of thirds it would be farther to the left. 

The red lines are rule of thirds the blue vertical line (and its opposite on the other side not shown like with Clint) are Golden ratio.


Offline Sawyer

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Re: The golden ratio is still BS
« Reply #22 on: August 13, 2019, 10:33:22 PM »
But look at how many objects/lines/arcs that the spiral and rectangles do not pass through.  And how many lines are kind of close to focal points on the image, but not quite.  The whole point of superdave's original post (which I still disagree with parts of) is that there is nothing special about the exactness of the Golden Ratio.  Images are often pleasing when they have symmetry, and when symmetry is not appropriate, they'll still look good when they have objects that scale somewhere in the range of ~4:3 to ~2:1.  Doesn't it make way more sense that your eyes and your brain have adapting to seeing anything within this range, and that maybe the 1.618 value is just an arbitrary value that's kind of close to the average?

It may help if you think of extreme examples - what if some awful artist or photographer tried creating an image that followed a 1:10 ratio (and wanted it to be a "natural" scene that's enjoyable to look at).  It wouldn't work.  The scale at which our minds can process images quickly and make sense of them is relatively narrow, and the golden ratio happens to fall into that range.  Not because it's special - it's just a convenient goalpost that falls somewhere between symmetry and order of magnitude size changes.

Offline arthwollipot

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Re: The golden ratio is still BS
« Reply #23 on: August 13, 2019, 10:39:50 PM »
I'm going to go out on a limb here and suggest that there are very good reasons why artists, photographers and cinematographers use the golden ratio in their work, but many of the claims about it - and I have seen some astoundingly woo-filled claims - are BS.
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Offline Alex Simmons

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Re: The golden ratio is still BS
« Reply #24 on: August 13, 2019, 11:01:25 PM »
In the previous post you claimed it was the optimal ratio for staggering leaves in plants.  Really?

No, not really.

I never claimed it was THE optimal ratio. I said it and other ratios like it were often or commonly found in nature, not that it was universal or unique.

Please read what I wrote and don't put words into my keyboard...

This is what I actually wrote:
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.

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.

Offline Sawyer

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Re: The golden ratio is still BS
« Reply #25 on: August 14, 2019, 12:26:55 AM »
So I know I could simply google it to find out for myself, but I would really like to see a mathematical explanation of why the Golden Ratio (or some other specific irrational ratio besides pi or e) is an actual solution to any optimization process in nature.  I accept that there are situations where the solution to a problem in nature will not automatically be an integer or fraction, but most of them will be akin to "your car engine is maximally efficient at 63.26828629 miles per hour".  But there's nothing inherently special about that number, it's just a combination of a dozen different equations that do not all have integer solutions.

Sorry if I was being rude Alex.  I really do feel like this is a topic that hardly anyone ever bothers to really get down to the basics before they make up their mind about it.  It's also something that middle school science teachers tend to overstate or botch the explanation of, and I'm no longer satisfied with discussion that is not enforced by hard numbers.

Offline CarbShark

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Re: The golden ratio is still BS
« Reply #26 on: August 14, 2019, 01:06:18 AM »
The lower left cheek is the window into a person's soul.
It’s his lower right cheek.


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Offline Alex Simmons

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Re: The golden ratio is still BS
« Reply #27 on: August 14, 2019, 05:42:15 AM »
So I know I could simply google it to find out for myself, but I would really like to see a mathematical explanation of why the Golden Ratio (or some other specific irrational ratio besides pi or e) is an actual solution to any optimization process in nature.

One of the reasons the GR is a good one for optimisation is it is the ratio which takes the longest to settle into a fractional approximation. That can be shown mathematically - will leave it to you to read up why.

It's a packing optimisation problem when considering a growth scenario (i.e. how to optimise as a plant grows). There have been various mathematical analyses of such things but some key work was by a pair of French physicists Douady and Couder, e.g.:
https://www.sciencedirect.com/science/article/pii/S0022519396900247
I don't have full text link.
edit, I think this is full text:
http://www.johnboccio.com/courses/Physics120_2008/docs/douady.pdf

This paper covers their work amongst other mathematical investigations but like all science it also expresses the limitations and unanswered questions:
http://cs.smith.edu/~cgole/PHYLLOH/NSFcritiques/propose1.pdf

Here's another paper on the topic which discusses the biological, physical and mathematical considerations examining and expanding further on the work by Douady and Couder:
https://www.math.arizona.edu/~anewell/publications/Plants_and_Fibonacci.pdf

But by all means do some searching and reading on the topic. It's fascinating. I don't propose to go deeper, I've no real need or desire to. Reality is such things do occur in nature, are not confined to one specific example and so there will be good reasons for it. In nature and in physics (esp energy), optimisation is everywhere.
« Last Edit: August 14, 2019, 05:49:48 AM by Alex Simmons »

Offline fuzzyMarmot

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Re: The golden ratio is still BS
« Reply #28 on: August 14, 2019, 06:30:51 AM »
Haven't read the whole thread yet, but let's be clear: phi is the limiting ratio of the Fib seq, and hence there is a mechanistic reason why it emerges in the results of many simple growth processes. Unfortunately, people have used this as a motivation to find it in a variety of goofy places.

Offline Guillermo

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Re: The golden ratio is still BS
« Reply #29 on: August 14, 2019, 08:31:30 AM »
I've seen research done with modern art in which blinded subjects rate paintings from modern artists and similar but random splashes of paint and color. And the results do find the artists work more pleasing, so saying "Even a child can do that" requieres a gifted child.

I would be surprise if a similar experiment cannot be perform using ratios like this, to definitely test if they are more pleasing.

I do think that people find non-symmetrical images more pleasing, but I don't by that the golden ratio is better than any other ratio.

Also:



In this example the golden ratio is forced on the image as it doesn't really fit in the image and is cut off on the top by the letterbox.
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