This is an excerpt from Master Fibonacci: The Man Who Changed Math. All citations are catalogued on the Citations page. (Previous Section: Fibonacci in Applied Arts)
Mike Spinak argues that most of the evidence presented for proof that the Golden Ratio is ubiquitous in art and nature is weak and misguided. He presents many detailed explanations for why this focus upon the use of the Golden Ratio is not beneficial for either artists, art, or patrons. He makes a case against what he says is known in academic circles as “the Golden Section hypothesis” or “the Golden Section theory.”
The Golden Section theory is “a prevalent belief about composition among photographers and other visual artists” which leads to discrimination against photographers (and others) who do not follow its prescriptions. Spinak believes “the Golden Section hypothesis has been elevated to established orthodoxy,” and it is unfortunate because artists and their works which do not conform to contemporary societal expectations for symmetry and compositional harmony are being discriminated against in the professional arts industry (Spinak).
“Any competent mathematician could easily derive a Golden Mean construct to match absolutely any subject placement within a frame” and interpretation is purely subjective. Unfortunately, subjective interpretation can be prejudiced (Spinak). Prejudice, of course, can be significantly detrimental to the financial health of those who are its victims, but it also harms society; for, “by accepting a flawed and rigid model as the accepted ‘basis for beauty,’ the biological basis for genuine beauty is replaced, and the results are unnatural” (Salingaros “Applications”).
Mathematician and polymath Nikos Salingaros confirms that “the Golden Mean does indeed arise in architectural design, as a method for ensuring that a structure possesses a natural and balanced hierarchy of scales.” This is the same “experimentally verified role found in a wide variety of structures in nature that exhibit hierarchical scaling” (Salingaros, “Applications”). However, researchers have also refuted claims that the Golden Mean was incorporated into design structure with paradigmatic case studies, two of which are introduced here.
Salingaros joins Spinak in refuting the traditional “evidence” that the Parthenon was purposely designed or built using golden proportions. According to Salingaros, claims by artists and architects that people prefer “rectangles having
aspect ratio 1.618:1 approximating the Golden Mean” are “false and are chiefly due to failing to measure things accurately.” He uses perjorative terminology when he describes these as “embarrassing errors … perpetuated by a kind of cult mysticism” (Salingaros, “Applications”).
Geometrical analysis accounting for curvature of the Parthenon in 1980 determined that the design shows no evidence of use of the Golden Mean. The building was designed “based on a module of 85.76 cm” (Salingaros, “Applications”).
The Parthenon’s dimensions:
|Eastern Width||101 ft. 3.5 in|
|Western Width||101 ft. 3.9 in|
|North Length||228 ft. 0.8 in|
|South Length||228 ft. 0.7 in|
|Length to Width ratio||1:2.25|
|Height to Length ratio||1:3.56|
|Height to Width ratio||1:1.58|
“The ancient Greeks would have built it much closer to the Golden Ratio, if they were trying to do that,” Spinak asserts; after all, “they got the length on the North side of the Parthenon within about a tenth of an inch of the length on the South side” (Spinak). He also disparages the way some “Golden numberists” arbitrarily superimpose Golden Rectangles on photos of landmark buildings in order to demonstrate the presence of Golden Mean proportions.
Golden “numberists” (as Spinak calls them) and adherents to the Golden Section hypothesis invariably use paintings by Leonardo Da Vinci to validate claims that Renaissance artists purposefully incorporated the Golden Mean into their works of art. However, Pacioli did not prescribe the Golden Ratio as the determinate proportion for all works of art as some allege; instead, “when dealing with design and proportion, he specifically advocates the Vitruvian system, which is based on simple (rational) ratios.” It appears that French mathematicians Jean Etienne Montucla and Jerome de Lalande were the first to falsely claim Pacioli preferred and dictated the Golden Ratio for proportion (Livio 134-5).
“Vitruvian Man’s navel height / full height ratio is .604, not .618” which is a difference of “a little more than two and a quarter percent.” Spinak argues Leonardo would have placed the man’s navel slightly higher if he had intended to maintain golden proportion. According to Spinak, another of da Vinci’s iconic works is misrepresented as having been imbued with golden proportions: the Mona Lisa. Just as they do with the Parthenon, people place overlays of Golden Sections and Golden Rectangles atop the image and arbitrarily exclude part of her face or body to support their claims (Spinak). For example, some purport that a rectangle drawn around Mona Lisa’s face would have Golden Ratio dimensions; yet, Mario Livio charges, “in the absence of any clear (and documented) indication of where precisely such a rectangle should be drawn, this idea represents just another opportunity for number juggling” (162).
In conclusion, not everyone considers the Golden Mean as something to be celebrated, used, or obeyed religiously; nor are these detractors compelled to seek Fibonacci everywhere. While the idea of an amazing, mysterious, ubiquitous but purposeful pattern is appealing to some, others hold that such beliefs have no basis in reality and are “nothing more than superstition and hoax. They are not scientific observation based on evidence; they are mystical beliefs in numerology” and there is no need to embellish the magnificent splendor of nature or, for that matter, art (Spinak).
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Paperback: 128 pages
Author: Shelley Allen, M.A.Ed.
Publisher: Fibonacci Inc.; 1st edition (2019)