The Golden Section Revisited — Magic Or Myth?

Posted: 02 Jun 2014 05:30 AM PDT

The golden section is commonly found in nature and has been used since antiquity in both art and architecture. Or has it? It depends who you ask. You can find information suggesting it’s the most magical ratio in the universe or that it’s complete nonsense. Which is it? Perhaps, as is often the case, the truth lies somewhere in between.

A little more than a month ago I received a comment on a post I wrote a few years ago about the golden section and design. Since the comment was from a first time commenter, it needed to be approved before anyone other than me could see it. Intended or not, the comment came across as rude and I decided not to approve it.

Beyond the rudeness the comment said the golden section was complete nonsense and pointed me to a video that claimed to prove as much. While I decided not to post the comment, I did think the points made were valid and I thought it worthwhile to watch the video and take another look at the golden ratio.

This post represents my initial reaction to a reaction. I’d like to look deeper into the golden section and all proportions more when I have the time, but for the moment here are my thoughts.

According to Salvador he used the golden section in “The Sacrament of the Last Supper,” above.
© This artwork may be protected by copyright. It’s being posted in accordance with fair use principles.

The Golden Section and Some Context

As I said, the post in question was one I wrote a few years ago about the golden section or divine proportion or however you want to refer to it. If you’re not familiar with the golden section and want details, you can read the older post, but here’s a quick summary.

The golden section or golden ratio comes from the fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, 34, 55…) Take any number in the sequence and divide it by the number before it and the result approaches 1.618 (the value of φ) as you move further along in the sequence. The ratio (1:1.618) is the golden ratio.

None of the above is controversial. Where it it gets controversial is whether or not the golden ratio contains some intrinsic aesthetic beauty. You can find a lot online that suggests it does and you can find a lot that says it doesn’t

The comment I received pointed me to a video by Dr. Keith Devlin at Stanford University, expressing the latter. I’ll get to the video in a moment, but let me first offer a bit more context about my post.

My understanding of design when I wrote the post was less at the time than it is now. I started my research for it in some design books I have and grabbed additional information online.

As you’re no doubt aware lots of things on the internet aren’t true. Shocking, I know. Things get said and then get repeated over and over. What originally isn’t presented as fact often gets reported as fact in the repetition. The more something is said, the more it appears to be true, regardless of whether or not it’s actually true. It’s not just the internet, but the internet has a way of making things happen faster and spread further.

If I were to change anything in that previous post, it would be to remove some absolute language and replace it with something less absolute. Something to make clear that there’s disagreement about the golden ratio and that some of the examples in the post have been called into question.

I’m certain many posts written in recent years about the golden section are less factually accurate than they should be and I’ll include my post among them. I did my best to find the truth, but I was so much older then. I’m younger than that now.

The Video and the “Myths”

Here’s the 11 and half minute video, Debunking 10 Golden Ratio Myths. You might want to watch it before finishing this post or at least give it a watch after. It’s worth viewing to understand why some consider the golden ratio a myth.

I’m not sure it proved anything to me, though I did agree with much of what was said. While I certainly understand the point being made, something was lacking in the presentation.

The video follows a pattern of presenting a “myth” such as the Greeks used the golden ratio in their architecture and then says it’s nonsense before moving on to the next myth. The entire video follows this pattern.

Here’s what people say
It’s nonsense
Here’s what people say
It’s nonsense

In fairness to Dr. Devlin it shouldn’t be his responsibility to prove what’s said about the golden ratio is a myth. The burden of proof should be on the people claiming the golden ratio holds intrinsic beauty.

However, I do expect more than saying something isn’t so if you want to debunk it. The same way repeating something over and over doesn’t make it true, repeating over and over that it’s not true doesn’t mean it isn’t.

In the video Dr. Devlin says there’s no documented proof the Greeks used the Golden ratio. Here’s a quote from the book Geometry of Design by Kimberly Elam that says otherwise.

…documented evidence is found in the writing, art, and architecture of the ancient Greeks in the 5th century B.C.

The quote above isn’t exactly proof of anything either. It’s a statement you’re expected to accept at face value. What we have is a literal he said, she said situation. What is there to convince you one or the other is right?

There was also a bit too much “This isn’t true except for those occasions where it is” in the video. To say it’s nonsense that artists use the golden section in their work and then list a few who tell you they did, seems a little disingenuous.

I’d also argue that’s what “true” to a mathematician or scientist and what’s “true” to an artist or designer are sometimes different things. All might be seeking the truth, but they seek it in different ways. The former seek objective truth, while the latter are often concerned with subjective truth.

I’m not disagreeing with Dr. Devlin by the way. Just thinking there might be a little more going on than what’s on the surface. Like I said, the burden of proof isn’t on him, but rather those that claim there is something magical about the golden ratio.

Debunking the Debunking

Some of the debunking strikes me as easy to debunk itself. I think much of what the video claims as proof is less about the golden ratio and more about the ease of publishing on the web and how quickly anything published spreads. Think how quickly rumor becomes fact on tech blogs.

The video mentions how most posts on the golden section include an image of a nautilus shell that isn’t actually governed by the golden ratio. Let’s face it bloggers are often lazier than we should be. We know an image will improve the packaging of a post and we find one to use. Maybe the image isn’t as accurate as it should be, but we use it because it works well in the design of the post.

I don’t think a poor choice in an image is proof the rest of a post isn’t accurate. Rather it says something about bloggers and how we should put a little more effort into fact checking if we want to pass something off as fact.

Another point in the video is that the phrase golden ratio or it’s variants (golden section, divine proportion) weren’t mentioned until the mid 19th century. That doesn’t mean that actual ratio wasn’t used. It just means the expression was coined later. Language changes over time and it’s not too hard to find mentions of the divine proportion prior to the 19th century.

I don’t think anyone is questioning whether the fibonacci sequence and the ratio φ were known in antiquity. There’s really no question that the ratio exists, has been known about for a long time, and has even been used in works of art and architecture. It does occur in nature as well.

The issue is ultimately whether the golden ratio contains some kind of intrinsic aesthetic beauty. After this second look I think it does, but not in the way it usually gets talked about. It’s unlikely there’s magic in the golden section, but it is a geometric ratio and I think there’s beauty in math, geometry, and ratios in general.

The Intrinsic Beauty of Ratios

Beauty is in the eye of the beholder. Aesthetics can be meaningful, but they’re also subjective. I’ve gone as far as saying all design is subjective. If a human being is involved so is subjectivity. It’s kind of the definition.

I think mathematical ratios are beautiful. I’m not the only one. I’ve said on numerous occasions that designing for the web is about proportion and I think any and all ratios are fair game when it comes to aesthetic exploration.

Proportion is what gives us harmony and rhythm. There is no music without ratios. Musicians use their ears more than their calculators to determine those ratios, but the ratios are there.

The golden ratio is simply one ratio among many that you can use. You can create a modular scale to make your type more meaningful. You can use its proportions to create rectangles and spirals or anything else you want to create.

Artists and designers can use anything we want in an attempt to create beauty. There are no absolute rules. Mathematical ratios have been used to create beauty for a long time. It probably startd a few moments after someone first noticed there was such a thing as a ratio. Human beings seek patterns. A ratio expresses a pattern. We like them. We use them in art and design.

In the end the golden section a geometric ratio. It’s one of many that can be used to create proportion in your work and it can be used in both art and design as a way to add aesthetic beauty.

Summary

The power of the golden section to create harmony arises from its unique capacity to unite different parts of a whole so that each preserves its own identity and yet blends into the greater pattern of a single whole.
— György Dóczi, The Power of Limits

The quote above is one I used at the start of my previous post on the golden section. I still don’t see anything that causes me to disagree with it. The golden section is a ratio based on the fibonacci sequence. Ratios and proportion create harmony and, used well, human beings find these things aesthetically pleasing.

Its specific qualities are that it can unite different parts of the whole. The smaller is to the larger as the larger is to the sum. That’s an interesting ratio and one worthy of exploration in works of art and in design aesthetics.

It may not be any more special than any other ratio you might use, but it, like all proportion, has intrinsic beauty in my eyes. My opinion on that hasn’t changed and I feel safe in saying I’m not alone in that opinion.

The golden ratio is not nonsense. It may not be as important as some, myself included, may have said outright or implied, but it’s hardly nonsense. It’s a ratio worthy of consideration in aesthetics, the same as a perfect 4th in music, or π, or any ratio you want to derive from anything you want to derive it from.

When you look deeper at the golden ratio, it’s pretty clear people exaggerate it’s significance and assign it magical properties it doesn’t have. At the same time people debunking it shouldn’t imply it’s utter nonsense and anyone who talks about it is a fool. Like most things, the truth lies somewhere in between.

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