Review of Divine Golden Ingenious: The Golden Ratio as a Theory of Everything?
Hirmer Publishers, Munich, Germany 2016
224 pp., illus. 115 colour. Paper, $35.00
This is a delightful publication with chapters that cover all aspects of the mysterious Golden Ratio. This so called Divine Proportion is mysterious indeed, and although the book’s lofty aim is to solve the enigma, unfortunately it remains unsolved. If anything, despite the scholarly, erudite essays, the Golden Ratio as a Divine feature of the universe remains as enigmatic as ever.
The book is beautifully produced and graphically rich, numerous illustrations in both colour and black & white lift the book above the ordinary. Perhaps this is also partly because the layout of the book is “...based on the golden ratio. The proportion of 1:1.618 defines all spacing and layout rules. The typography is also set in this ratio” (p. 224). There are 24 sections (chapters) with such intriguing titles as “Two offset Fibonacci sequences,” “Proportions in music as a temporal art,” “Grids and rules,” and “The golden ratio is basic vocabulary, an absolute must-have.” The chapters are followed by biographies of the contributors and a list of illustrations but have no index.
The quest to solve the mystery is frustrated by the amazing paradox that the answer to the question of the Define Proportion being in fact universal, hence possibly Divine, is empathically Yes and No! The reason the book is delightful is because it is a little like a conjuror’s performance. One chapter proves the Golden ratio is divine; the next disproves it. As an example back in 1876, Fechner, a founding father of psychology, carried out a test with different rectangles (of the same area) but different sizes. The majority of recipients preferred the rectangle of the Golden ratio, the minority preferred the square. “At this point, one could close this chapter with the universal law of aesthetics confirmed. But unfortunately it is not quite that simple” (p. 150). Höge repeated the experiment exactly in 2016 with diametrically opposed results: The minority preferred the Golden ratio and the majority the square. So much for a universal law?
The previous example shows the beauty of the scientific method. The next example is more anecdotal but still illuminating:
“Admittedly, the significance of the golden ratio today does not lie in real documentary evidence, but in the myth woven around this history over the last 150 years. In common with those searching for the Holy Grail or the treasure of the knights Templar, the golden ratio devotees weave together clues and allusions in history, mathematics and the natural science to create grand images which primarily prompt amazement and claim the existence of universal theory of everything.” (p. 24)
Further, adding weight to the myth, in type design the myth of the golden ratio abounds, however, unbiased investigation shows:
“The Trajan font (113 CE), the most famous and beautiful example of the capitalis monumentalis, was designed in accordance with the golden ratio,” is in fact not based on the golden ratio at all...but instead the square, circle and triangle.” (p. 99)
In the book section, “Workshop Report, Golden Pythagoras Trees: Fractals and self-similarity by Daniel Lordick” (pp. 164-169), his concluding remarks indicate that the use of the golden ratio as a design tool is arbitrary:
“No matter how surprising it is to discover frequent examples of the golden ratio in nature, exclusively using the golden ratio as a design tool clearly remains an arbitrary decision and one that is rarely successful.”
The idea, or desperate hope, that the golden ratio perhaps provides a Theory of Everything is clearly not true. However, without doubt the golden ratio may be observed often in nature. The Fibonacci series evident in the Nautilus shell is just one example. So, we have what may be described as a Divine Paradox. Evidence in nature of the Divine Proportion is astounding, and then the cultural “meme” replication myth, now growing out of all proportion (excuse pun) on the Internet will keep researchers puzzled for some time to come. This proliferation on the Internet has both serious and humorous content. As an example the very recent photos of American president Donald Trump’s hairstyle likened to, or complying with, the golden ratio!
This book full of intriguing puzzles (itself both serious and humorous) will become an important resource for future researchers and students of this illusive mystery.