“The good, of course, is always beautiful, and the beautiful never lacks proportion.”  ~ Plato

“Without mathematics there is no art.”  ~ Luca Pacioli

Contemplating the Divine Proportion (Ryoanji)

The Rev. Kawakami, on our private tour of the Shunkō Buddhist temple where we were staying and had taken our first Zen meditation session, continued, “When you examine the ratio of the sides of the garden, you find….”

“The divine proportion!” I eagerly interrupted.

Buddhist Temple Rock Garden

Pausing while turning to look at me, the Reverend smiled, “Yes, the golden ratio.  It is also here in this room, and in within the three rooms combined overlooking the garden.”

Golden Spirals are rampant in nature.

Another unlikely connection, but this one not as surprising.  At the time I was re-reading a book I decided to drag along with us to Okinawa entitled Divine Proportion:  PHI in Art, Nature, and Science, by Priya Hemingway, which I highly recommend.  As someone schooled in the hard math and sciences, but also as an inquisitive soul constantly searching for deeper meaning and the spirituality of life, I am astonished at the manifest interconnectedness between math, nature, and aesthetics.

Golden Rectangles of the Parthenon

The golden ratio has fascinated intellectuals of science and philosophy for millennia.  Some of the greatest minds of the ages, from the Greeks Pythagoras and Euclid to the Italians Leonardo of Pisa and Fibonacci, have poured their hearts and minds into this simple ratio with the most complex of properties.  Plato considered it the most binding of all mathematical relations and as the key to the cosmos.  It is exactly because of ratio’s inescapable ubiquity that this fascination endures; modern biologists, artists, musicians, historians, and architects alike continue to ponder its relevance and appeal.

The Artist Hokusai meets the Fibonacci series….

And, of course, the Japanese have their own understanding of the “true” divine proportion…which they call Absolute Territory.  Unsurprisingly, even this sexually obscure, anime-based ratio of 1.6 approaches closely that of Phi.

A truly Japanese take on the Divine Proportion. It too approaches closes Phi.

The ancient Egyptians, while leaving no real record of Phi’s knowledge, used it in the construction of the great pyramids and in the design of hieroglyphs found on tomb walls.  In another time, across thousands of miles of globe and gulfs of culture, the ancients of Mexico encompassed the ratio while building the Sun Pyramid at Teotihuacan.  While some may claim that we today find the ratio where we want to and well after the fact, I remain convinced that even without direct knowledge, and whether by design or unsophisticated intuition, even the ancients could not escape the universality of such a proportion.

Golden Ratios calcified in our Bodies!

Initially the “Golden Ratio” was first studied because of its frequent appearance in mathematical geometry, particularly in the creation of “regular” pentagrams and pentagons.  It has a relatively straightforward definition, which is best graphically represented (see below):   when a line is cut just so, as the whole line is to the greater segment, so is the greater segment to the lesser.

It’s odd that I couldn’t find any analyses of Japanese gardens or temple architecture in terms of the Divine Proportion.  It is, however, easily found all around us, from the spirals of galaxies and seashells, to the symmetry of architecture and the human body, to the beauty in art and the human face.  The Rev. Kawakami was clearly versed on his own temple’s basis of design.

The Divine Proportion of the Mona Lisa. Doesn’t explain the attitude.

The idea that Phi appears to be fixed in nature has led to another designation:  that of the “Hand of God.”  However, like all else we contemplate around us, the Golden Ratio is simply an interpretation, even after being run through the aged filters and lenses of our collective human condition.  But it is in this very elucidation that this humble mathematical ratio becomes one of Divine Proportion.  It can be seen as the very essence of the harmony and beauty found throughout the cosmos.  In this way, WE have come to endow this symbol with a wholly spiritual presence.

Proportion is not just for nature or art.

And it can be found in the simplest of gardens in a remote corner of Japan, tended in part by the Hand of Buddha (or the god of your choice).

What is your experience with Divine Proportion?