Yarbus and the GR Spiral Armature

The nineteenth and twentieth centuries saw many instances of the merging of the Golden Ratio (GR), the Fibonacci sequence, mysticism, and art. Pareidolia and the GR gave birth to elaborate geometrical armatures for pictorial composition that persist to this day. Like Pythagoras, many believed that the numbers related to these geometries held special powers, or at the very least–some aesthetic advantage for the artist.

Several artists published books that aimed to demonstrate that the irrational number that may have once led a bunch of cranky mathematicians to drown a man at sea, held a “secret” formula for beauty. One such book, The Elements of Dynamic Symmetry, was written by a Canadian-born American artist named Jay Hambidge in 1920.

One of the largest contributors to the marriage of the Golden Ratio and art was German psychologist, Adolf Zeising (24 September 1810 – 27 April 1876). Zeising’s work in this area began with a series of publications (described by mathematician Mario Livio as “crankish”) including an 1854 work titled A New Theory of the proportions of the human body, developed from a basic morphological law which stayed hitherto unknown, and which permeates the whole nature and art, accompanied by a complete summary of the prevailing systems. (yes, that is all one title). After Zeising’s death, this and other publications would be combined into a large book titled Der Goldne Schnitt (The Golden Section). In his writings, Zeising claimed that in the Golden Section “is contained the fundamental principle of all formation striving to beauty and totality in the realm of nature and in the field of the pictorial arts, and that it, from the very first beginning was the highest aim and ideal of all figurations and formal relations, whether cosmic or individualizing, organic or inorganic, acoustic or optical, which had found its most perfect realization however only in the human figure.” Of Zeising’s work, Mario Livio writes, “In these works, Zeising combined his own interpretation of Pythagorean and Vitruvian ideas to argue that “the partition of the human body, the structure of many animals which are characterized by well-developed building, the fundamental types of many forms of plants,…the harmonics of the most satisfying musical accords, and the proportionality of the most beautiful works in architecture and sculpture” are all based on the Golden Ratio. To him, therefore, the Golden Ratio offered the key to the understanding of all proportions in “the most refined forms of nature and art”.

So what is the effect of this “key to the understanding of all proportions in the most refined forms of nature and art” at the earliest stages of our interaction with a complex stimulus (like a piece of visual art?)

Here we took one of the Golden Ration armatures (The Golden Spiral) and layed it over the eye-tracking images used for the research of Russian psychologist Alfred Yarbus. As you can see, there is absolutely no discernible correlation between the armature and the eye patterns/fixations recorded by Yarbus. We even included the more widely accepted “Rule-of-Thirds” to see of there was any correlation between points of intersection (argued “ideal” focal areas) and eye fixation and still found nothing.

While this discrepancy alone is not sufficient to thoroughly debunk the claims of aesthetic influence inherent to such compositional armatures, it at least goes quite a long way to demonstrating no significant influence at the earliest levels of engagement (eye fixations) with a piece of visual art.


I have to read this tonight…just caught my eye but extremely valuable!!!