Thursday, January 17, 2013

Part 3: How the golden mean caught on with artists

After considering the Parthenon and Leonardo Da Vinci, let's see if we can continue taking a rational look at the claims about "phi," (or the "golden mean" or "golden ratio") that has been so popular with artists.

The story gets more complex in the nineteenth and twentieth centuries as artists begin to consciously adopt it in their work, and so it gets harder to separate fact from fiction. Let's start with what we know for sure.

One of the nineteenth century champions of the golden mean was German psychologist Adolf Zeising (1810-1876) who found the golden mean in nature, especially in branching patterns, leaves, and seed patterns. These manifestations of the ratio are acknowledged by even the most skeptical scientists.

Over the years scientists have found other places where the golden mean turns up. In 2010, the journal Science published a paper about how these numerical patterns appear in crystals at the atomic scale.

The golden mean appears most often in terms of numerical relations, such as the Fibonacci numbers that appear in flowerheads, seeds, and shells.

Zeisler promoted the idea that the golden mean could be found in the Parthenon and the works of Leonardo. He made broad claims that the golden ratio was: 
"the universal law in which is contained the ground-principle of all formative striving for beauty and completeness in the realms of both nature and art, and which permeates, as a paramount spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical; which finds its fullest realization, however, in the human form." 
Whether or not Zeisler's ideas had a solid grounding in observable fact, they caught on with artists and mystics. 

A group of painters led by Jacques Villon and called "Section d’Or," (French: “Golden Section”) held exhibitions in Paris between 1912 and 1914. They included Juan Gris, Robert Delaunay and Giro Severini and several others, though not all used the mathematical principles. Later artists such as Salvador Dali also claimed to use golden mean principles. 

In the 1920s, Jay Hambidge, a student of William Merritt Chase, published a book called Dynamic Symmetry  which presented a grid system based on the golden mean. The system was picked up by artists such as Maxfield Parrish, whose preliminary drawing for the famous painting "Daybreak" is above. Here's one person's analysis of the structure behind Daybreak. 

Above: Architects' Data (German: Bauentwurfslehre) First published in 1936 by Ernst Neufert,

Golden mean principles were adopted in extremely different aesthetic quarters in the twentieth century. Many readers of this blog have encountered golden mean principles in the context of contemporary realist ateliers.

The methods were also embraced by the Bauhaus school (literally "House of Construction"), founded by Walter Gropius in Germany between World War I and II, and run by influential architects such as Ludwig Mies van der Rohe. 

The Swiss architect Le Corbusier, who championed the international style of building design, used the golden ratio and the Fibonacci series as a central tenet of his work and teaching. He described the patterns as:
 "rhythms apparent to the eye and clear in their relations with one another. And these rhythms are at the very root of human activities. They resound in man by an organic inevitability, the same fine inevitability which causes the tracing out of the Golden Section by children, old men, savages and the learned."
Many Bauhaus teachers emigrated to America, where their ideas about the golden section became incorporated in university art educations, where they are taught to this day. 


Anonymous said...

So it really begins in the early 20th century, the very era of the birth of art dubiousness? The spiral as an art compositional device, at least, is looking more and more like a cheap gimmick peddled by art instructors to make an extra buck. Fascinating series, James; thank you.

Carol said...

Watch Vi Hart explain Fibonacci numbers:

J. Bustamante said...

I'll be honest, I never really understood how or why the golden ratio was used to make a composition. Nor did i ever understand how the parthenon in any way breaks up into a spiral, I still don't see it.

This series of posts is making me feel less like a dunce. Thank you.

nystudios said...

I think much could be said in the defense of Caravaggio using it at least in the piece "The Card Sharps".

Unknown said...

This blog series on the Golden Ratio is very well written and presents some very good information, but some of its research is incomplete, which is leading to incorrect conclusions and "facts" as it progresses. To know if Leonardo used the golden ratio in his paintings then survey his more complex paintings, not just illustrations of Vitruvian Man, a rhombicuboctahedron and a single, simple portrait of the Mona Lisa. His other paintings, most notably “The Last Supper,” show some rather clear applications of the golden ratio. Michelango’s “The Creation of Adam” from 1512 has the finger tips of God and Adam touching at the golden ratio point of the width of the painting. It is simply wrong to dismiss artistic application of the golden ratio prior to the late 19th century and consider it to be only a modern invention. As we await tomorrow’s article on whether the golden mean really does appear in the human figure, I hope that James and the readers will do more complete research before coming to their conclusions. Test it using a golden ratio design app such as PhiMatrix and see examples at and related pages on the golden ratio in the human form that site. Thank you for the discussion.

P-S said...
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Leonardo Zavala Cuevas said...

james you are the most amazing person ever! your whole blog is pure gold for us self taught artist that wish to get more knowledge into our heads, i dont know how much time it will take me but i wish to learn all of your lessons and look for ways to apply theese concepts in my everyday work, the latter will take a while but in themean time reading its just a pleasure, please never stop sir!