THE GOLDEN RATIO OR GOLDEN MEAN
The post titled “The Evolution of Adagio: A Therapeutic Motion Machine” by guest blogger James Wilson, has quickly become the most viewed on Art and Zen Today during the past 90 days. A comment on that article from Charlie from Mass. raised some interesting questions about validity of some of the theoretical foundations used by James in the evolution of his “machine”. Specifically, the validity of the “golden mean” or “golden ratio” was questioned. (Click here to read “The Evolution of Adagio: A therapeutic Motion Machine.”)
THE GOLDEN GINGERBREAD BOY
This got me thinking about the place of “truth” and “faith” in the artistic and spiritual systems we use to guide our practices. James later penned a response to Charlie’s comment but it could not be posted because I have placed a time limit on comments in order to cut down on the “robo-spam” sent to the blogsite.
So today’s post consists of: 1) Charlie’s comment on “The Evolution of Adagio”; 2) James’ response; 3) some additional material intended to help the reader follow along, and finally; 4) some comments by me on how I see the discussion relating to the practices of art and Zen. Because this post consists of ideas expressed by several different people, I have physically separated each authors contributions to make it easier to follow. I’d like to thank Charlie and James for inspiring me to sit down and think about all of this.
First is the comment by Charles that was published soon after the post on Adagio by appeared in Art and Zen Today. In his post, James had written about the use of the “golden ratio” in the development of his invention.
“The golden ratio is like religion—it’s an old theory which doesn’t hold up under scientific scrutiny. I googled “skeptic ‘golden ratio” and came up with a nice quote from a comment by Phil in Australia:
“Beauty like love is one of life’s greatest mysteries. Numbers can’t explain it.”
Comment by Phil, Sydney Australia, from the following link:
SENT IN BY CHARLIE
The comment by Phil, referred to above by Charles, was in response to an article titled “The Golden Ratio” published on the website Skeptoid:Critical analysis of Pop Phenomena . Below is one paragraph from the original article that prompted Phil’s comment. I include it here to help put Phil’s comment into some context.
φ, the golden ratio, and the Fibonacci series are mathematically interesting and do have natural manifestations. That doesn’t mean everything, or even anything else, is based on them. The popularity and “big name” of the “divine proportion” has been the real driver of its pseudoscientific assignment to just about anything and everything. Those whose brains’ pattern-matching software is in overdrive have probably heard of the golden ratio, and so it’s the one they think of whenever they see a rectangle, or a great work of art (like the Mona Lisa, which is not based on the golden ratio), or patterns in the stock market (which don’t exist at all, let alone at the golden ratio), or in the numerology of the Bible (unless any other number is allowed to be considered just as significant). Not every claim about the golden ratio is the result of hyperactive pattern matching, but most are. At a minimum, such a claim is always a good tipoff that you should be skeptical.
The entire article and comments, including the one referenced by Charlie, can be seen at:
In this section, I have copied James’ response to the comment made by Charlie. This was not previously published on Art and Zen Today.
I agree that discussions around the “Golden Mean” can sometimes lapse into a matter of “faith”. From what I can tell, science has neither proven anything about it (except it has some pretty amazing mathematical properties), but it hasn’t really dis-proven anything either.
The way I think of it, and use it, is that when starting a creative project, like a piece of music or painting, it is helpful to the composer or artist or designer to create some kind of “limits”; otherwise the possibilities are infinite and can result in artistic paralysis. Take 12 tone compositions for example. Here’s a definition:
Twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition—is a method of musical composition devised by Austrian composer Arnold Schoenberg (1874–1951). The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any one note through the use of tone rows, an ordering of the 12 pitches. All 12 notes are thus given more or less equal importance, and the music avoids being in a key. The technique was influential on composers in the mid-20th century.
To me, Twelve-tone is basically a lot of BS, and it really doesn’t “avoid being in a key”, which was its primary purpose in life. However, it did get a lot of people to write a lot of music (some good, some not) simply because it gave them a “system” to work within. I.e., it got them to initiate the creative process!
And, if nothing else, this is the magic of using the Golden Means, or any other system for that matter, particularly in the arts, where, as I said above, the possibilities are basically infinite. It imposes enough limits that the artist/musician can get his/her hand/head around it.
If in fact artists and/or architects have and do use these ratios in their work, it is probably for this reason more than any other. It’s almost like; in absence of any other confining system, why NOT use it? Yes, it may just be BS, but, then again, it might not!
Ok. Now it is my turn to chime in as Editor of Art and Zen Today.
It is pretty well known that artist’s of all kind often impose systems on their practice that challenge them to go beyond their usual boundaries and possibly attain to highly creative results. I covered this topic in some detail in the post titled “Buddha as a Performance Artist?” I believe that it is possible to say that these artistic or spiritual systems may be said to foster “mindful creativity” as the term is used by Langer (see “On Becoming Mindful” ) But, the “mindfully creative artist is able to use the restrictions imposed by whatever system they are using to foster new ways of imagining that inevitably go beyond that system.
Often the “systems” evoked for such purpose, whether artistic or spiritual, do not really “make sense” to others and if the system is touted by the user as some sort of “truth”, the chances are that someone will find way to poke holes in it. I think that this is along the lines of what James is saying in his comment above.
About a year ago I did some googling around the internet looking for artists who explicitly used the Golden Mean concept in their work. I found one painter who made a big deal of his dedication to the Golden mean ratios in constructing his painting. It was my impression that he was consciously trying to appeal to buyers who were into new agey “sacred geometry”. I found his work to be rather boring, predictable and not very creative. This, I think, speaks to the problem of any “systems” that we impose upon ourselves. As Jim seems to say in his comment, “systems” that impose restrictions can lead to greater creativity but not when followed slavishly (i.e. without mindfulness).
The quote from Phil that Charlie included in his reply is actually the last line of a quite long comment response to the article debunking the use of the Golden Mean. In the next segment,I have included all of Phils’ comment because it seems to me that he provides an example that reinforces my notion that genuine creativity is not found in the “truth” of the system but rather in how an artist uses this system (see insert below).
Here I have copied the full comment made by Phil in his response to the article debunking the use of the Golden Mean. Charlie referred only to the last line of this comment, but the rest of it seems to provide an example of my main point.
I had a violin maker friend who made every instrument in accordance with golden section proportions. This included sound post positioning, the ratio of string length above and below the bridge, neck length, and the actual proportions of the body themselves.
He had a great deal of success and believed that the proportions were common in some historical violin making.
He also considered the setting of the violin to be very critical and that most violinists hadn’t a clue how to do it. One major difference between a Strad and a cheaper violin, he said, is that if you pay millions of dollars for an instrument, you just might be keen to set it up properly – sound post position, bridge positioning and shape etc
Whether or not Golden proportions help – he was convinced they did – the real magic was in the hands of the maker who completed the task and the final adjustments. I am sure that applies equally to everything from architecture to furniture. Sometimes I think that in attributing success to the golden section the creator of a masterpiece is perhaps a little too modest – or his critic a little too coldly scientific
Beauty like love is one of life’s greatest mysteries. Numbers can’t explain it.
Phil, Sydney Australia
August 22, 2013 11:15pm
Ok, this is me again.
Ellen Langer’s Book On Becoming an Artist consistently prompts the reader to question any existing artistic systems that they encounter as they embark on their creative journey.( see ELLEN LANGER ON THE “TALENT MYTH” ). Especially when we are beginners in any realm, we tend to look for some “system” that provides us guidelines for how to proceed. There is nothing wrong with this, but to the extent that we get “stuck” in the system, our creativity will suffer. I think that this also applies to artists who have been creative enough to evolve their own “systems”, so to speak, of making art. When they are no longer mindful and begin automatically doing what has been successful for them in the past, there is no creative growth. The ability to push beyond even self- imposed boundaries is why artists like Picasso, Miles Davis and Bob Dylan, to name a few, are acknowledged as creative geniuses. And, so it goes, I would suggest, in the realm of the spirit. This brings me to Zen, and most forms of Buddhism generally.
Buddhist thought and practices inevitably entail boundaries or limitations. Furthermore, they often don’t make rational sense and I have heard myself and fellow Zen students refer to various teachings as “B.S.” The non-rational aspects of the teaching require that the student develop a degree of “faith”, to use the term that Jim seems to use derogatively. I would suggest that “faith” is only problematic when it stifles mindfulness. It is important to point out that Buddhist practice does not demand “blind faith”. Rather it requires a willingness (i.e. “necessary “faith”) to try out a certain viewpoint and set of practices to see whether or how they work in one’s own life. Buddha famously said something along the lines of the quote below (I don’t have “faith” that Buddha actually said everything attributed to him):
“Do not believe in anything simply because you have heard it. Do not believe in anything simply because it is spoken and rumored by many. Do not believe in anything simply because it is found written in your religious books. Do not believe in anything merely on the authority of your teachers and elders. Do not believe in traditions because they have been handed down for many generations. But after observation and analysis, when you find that anything agrees with reason and is conducive to the good and benefit of one and all, then accept it and live up to it.”
The Zen literature is especially contradictory and difficult to make sense of because it points out again and again, that Zen is simply a system, and that if you use the system wisely you end up transcending the system itself. This does not seem “rational”, at least to most beginners. It requires some degree of “faith” to continue with Buddhist practice until one can develop an understanding of how this works. Eventually, the student sees that there is no set view which is considered to be true and there is no end to discovering this; that is, as you discover new ways of seeing your life, you find that you can not rely (i.e. have “faith in” ) on that viewpoint forever.
To the extent that Buddhist practice leads to a constant re-visioning of one’s self and reality, it could be seen as the ultimate creative practice. Dale Wright makes this point in his recent book, The Six Perfections. Interestingly, Wright uses language that is consistent with Langer’s where “mindfulness” and “creativity” are equated. Wright’s book examines the various conventions and guidelines for attaining enlightened “Wisdom” as they have been passed down in Buddhist literature. However, Wright makes a point of reminding the reader over and over that blind conformity to these strictures is not what the journey is all about. “Wisdom” says Wright “is the ability to recognized what is and what is not an appropriate guide for dealing with situations skillfully.” (pg. 233).
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