Date of Award
Bachelor of Science
William M. Mace
The Golden Proportion is the place where a line is divided in such a way that the ratio of the length of the shorter segment to the longer segment is equal to the ratio of the longer segment to the length of the whole line. It has been claimed by artists, architects, and aestheticians that the Golden Section is the most aesthetically pleasing division of a line, and that the Golden Rectangle is the most aesthetically pleasing of all rectangles. Although there is experimental support for these claims, it is not unequivocal. Many studies have been on preference for the Golden Rectangle. It is possible to recognize something and not prefer it, so one could still be sensitive to the Golden Proportion without preferring it in comparisons. The aim of the current study was to test how good people were at recognizing a Golden Rectangle (as opposed to preferring a Golden Rectangle). Jay Hambidge’s (1920) writings focused on the Greek design of the Golden Section that was included in art and architecture. From this, McCulloch (1923) became interested in whether such a division of an area was pleasant. He wrote his masters thesis in 1923 in which his experiments were “designed to discover whether a basic preference exists for dynamic (characteristic of organic life) and the intermediate symmetries, how this preference is affected by the ability to discover symmetry, by the repetition of the act of judging, and by the optical illusions involved (p. 3).” McCulloch (1965) asserted, “I happen to have spent two years in measuring man’s ability to set an adjustable oblong to a preferred shape, because I did not believe that he did prefer the golden section or that he could recognize it. He does and he can! On repeated settings for the most pleasing form he comes to prefer it and can set for it. The same man who can only detect a difference of a twentieth in length, area, or volume sets it at 1 to 1.618 (McCulloch, 1965, p. 395-96).” The current study’s purpose was to investigate this claim. The current study reported data on ten observers who participated in four experimental conditions. This study was designed to see if, with little training, people could naturally pick out Golden Rectangles. In the first experimental condition, the observers were shown a series of 33 rectangles of different widths. There were eight rectangles smaller than a Golden Rectangle, the smallest being 217 by 144 pixels, and 24 rectangles larger than a Golden Rectangle, the largest being 281 by 144 pixels. The Golden Rectangle presented was 233 by 144 pixels. The observers were asked if in each instance the presented rectangle was wider than a Golden Rectangle. In the second condition, to test for directional symmetry, the rectangles varied vertically and observers were asked if each instance was taller than a Golden Rectangle. As a baseline control, observers were given the same tasks but were asked to judge rectangles according to how they compared to a square. The results showed that the task of judging the rectangles, and even the squares, was fairly difficult. Some observers performed systematically, whereas others did not. Responding to the square conditions was much more systematic and less variable than the Golden Rectangle conditions. It was discovered that the scale of two pixels and as well as the task were very hard, but not impossible because Subject 2 and Subject 8 were able to do complete the task relatively well. Some participants showed very systematic results across all the different sized rectangles, and some did not. Most conditions for the majority of the observers were non-monotonic but once the data were binned into larger groups, many of the subjects showed smooth curves. This study failed to support McCulloch’s claim that people can recognize the Golden Rectangle.
Eydt, Rebecca A., "How Good is Gold? Recognition of The Golden Rectangle". Senior Theses, Trinity College, Hartford, CT 2013.
Trinity College Digital Repository, https://digitalrepository.trincoll.edu/theses/320