## Rationalizing Phi: The Golden Ratio as a Western Phenomenon

**"There is no doubt that anybody who grew up in a western or mideastern civilization is a pupil of the ancient Greeks, when it comes to mathematics, science, philosophy, art, and literature." -Mario Livio, The Golden Ratio: The Story of Phi, the World's Most Astonishing Number.**

## Phi in the West: The Ancient Spark

As discussed earlier, the discovery and subsequent fascination with the golden ratio arose with the ancient Greeks. Since Western civilization is mostly a product of the Enlightenment, which was a product of the Renaissance, which was a product of ancient Greece and Rome, it is highly probable that the fascination with the golden ratio is an exclusively Western phenomenon.

Livio notes that "one clear source of the mystical attitude toward whole numbers was the manifestation of such numbers in human and animal bodies and in the cosmos, as perceived by the early cultures" (22). Indeed, the number two, for example, is found in many places on the human body: two eyes, two ears, two arms, two legs, et cetera. There are four seasons, three tenses of time (past, present, and future), seven days of the week, the list goes on. Early societies were filled with whole numbers, and it is precisely for this reason that the golden ratio, which is derived from whole numbers, shocked people with its irrationality, as discussed earlier. Clearly the world has yet to recover.

History also shows that early cultures were fascinated with numerology. The Jews, Muslims, and Greeks all hd systems in which numbers could be translated to words by assigning numerical combinations to letters. This is still done today on the back of children's cereal boxes occasionally. Also, the number 666 has captivated Christians as the "number of the Beast." "Amusingly, in 1994, a relation was 'discovered' (and appeared in the

*Journal of Recreational Mathematics*) even between the 'number of the Beast' and the Golden Ratio" (Livio "Story," 23): the sine of 666 degrees plus the cosine of six cubed (six times six times six) is a good approximation of negative phi. Is this an eerie connection, or just a coincidence resulting from residual fascination in numerology?Plato himself was fascinated with numbers and geometry. In his

*Laws*, he argues that the optimal number of citizens in a state is 5,040, because it has some rather peculiar arithmetical properties (like that it has 59 divisors, including all the whole numbers from 1 to 12, that its twelfth part can be evenly divided by 12, etc.). In*Timaeus*, Plato attempts to explain matter using what are now known as the Platonic solids: "the only existing solids in which all the faces are identical and equilateral, and each of the solids can be circumscribed by a sphere" (Livio "Story," 67). The golden ratio can be observed in the dimensions and symmetry of some Platonic solids. Since it is nearly impossible for any American college student to graduate without reading some of Plato's works, and because of Plato's revered status as one of history's greatest philosophers, the concept of the golden ratio as an ideal still continues.In our earlier discussion of the history of phi, we mentioned Luca Pacioli, who really brought about a revival of the ideal of the golden ratio and its subsequent rechristening as the Divine Proportion. Pacioli r

## The Golden Ratio in Other Cultures

In a 1969 study, psychologist D.E. Berlyne conducted a study in which twenty Canadian subjects were shown examples of Western art from the 18th through 20th centuries as well as Chinese, Indian, and Japanese pieces. Participants were asked to locate the major subdivision of each work. The mean of modal divisions was 0.390, very close to one minus phi, but Berlyne ultimately concluded that there was no evidence for the golden ratio having a "privileged status" (Green 955). Berlyne believed that the golden ratio was a cultural matter instead of a psychological one, and so performed a study to compare preferences of 33 Canadian high-school girls and 44 Japanese high-school girls. On average, the Asian students preferred rectangles close to squares, but the subjects' first choices tell a different story. In both groups, the square was selected as their first choice for the most pleasing rectangle, but the Canadian girls' preferences dropped markedly after that, peaking again only after the 1.5:1 rectangle, exactly where the Japanese subjects' preferences dropped off (Green 955).