The Institute for Mathematical Behavioral Sciences Colloquium Series presents
“Fibonacci, The Golden Mean, and Natural Law in Vision (and Language)”
with Tom Bever, University of Arizona
Thursday, May 1, 2014
Social Science Plaza A, Room 2112
In several classical schools, artists made their own picture frames: it is striking that these schools systematically used an average rectangular ratio of 1.62 for landscapes,and smaller ones for interior scenes. This ratio, The Golden Mean (“Phi”), is also the ratio preferred by everyone as the ‘best rectangle’ and has played a role in art and architecture for millennia. Traditional explanations for the preference for Phi are usually based on (a) Phi’s unique mathematical properties and (b) Phi’s simplifying role in repeating selfembedded shapes in nature and human artefacts, as the limit of the Fibonacci series.
Bever introduces a new explanation for how phi, accounts for the preference for Phi ratio frames, based in modern perceptual science, on which an early stage of visual perception is automatic reduction of complex figures into simpler ones; this combines with the two Aristotelian aesthetic theories to explain the aesthetic preference for phi rectangles: a) traditional conflict-creation-and-resolution theory of aesthetic preferences; b) Ideal level of complexity. In his analysis, (a) a two-dimensional Phi-rectangle creates a mental representational conflict in the early stages of its perception: this conflict is resolved by accessing a third dimension; (b) The recursive analysis into embedded squares combines with size permanence to create the illusion of “holes” in the space. Thus, on both aesthetic explanations for its preference, Phi stimulates a sequence of perceptual activities that involve the illusion of depth.
This explanation makes a novel prediction: Phi rectangles should enhance the perception of spatial depth for scenes they frame. He will report several converging studies that show that this prediction is correct. This in turn offers an explanation for why certain schools of art have chosen Phi ratio frames for landscapes and for the repeated use of phi in art and architecture.
Since the phi ratio automatically interacts with the principles of visual reduction, no new brain mechanisms have to be postulated to account both for its preference and its enhancement of depth perception. The special effects of phi simply follow from (mathematically transparent) laws of nature in combination with principles of decomposition in normal vision.
This result for vision can be related to recent investigations of the role of phi in constraining hierarchical structures in language. In particular, the primary kernel of phrase structure, XBar internal and external merge, also follows the same polynomial as phi. This (very tentatively) suggests a common (uniquely human?) process of hierarchical decomposition that is constrained by the same physical/mathematical laws.
(Collaborator: David Medeiros)
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