2,500 years ago, a Greek, tired of arguing in the agora about justice, philosophy, politics and mathematics, decided that what was truly important was to measure the human body. This is how the canon of Polykleitos the Elder germinated: the obsession with finding perfect symmetry.
Roman copy of the Doryphorus (“spear bearer”) of Polykleitos, preserved in the National Archaeological Museum of Naples. Wikimedia Commons., CC BY
The most famous selfie in history
Twenty centuries later, Leonardo da Vinci drew the famous Vitruvian Man, based on the Roman canon of architecture, as a reflection of the order of nature. The result was that naked man trapped in a circle and a square. The message was – and continues to be – provocative: if we extend our arms, we are as wide as we are tall, with our navel at the geometric center of this universe of perfect beauty.
Da Vinci, ahead of his time in so many fields, turned human proportions into a viral diagram five centuries before Instagram and mass cosmetic surgery.
God’s number fever
Behind all this lurked the golden ratio (or divine proportion): 1.618…. This number seems to materialize for the first time on several Babylonian and Assyrian stelae 4,000 years ago, but also on seashells, on the Mona Lisa, on the pyramids, on the Greek and Roman temples and on the Eiffel Tower.
It also appears when climbing a staircase: our feet find a natural balance between the tread (horizontal part) and the riser (vertical part). Curiously, the ratio between the two is usually around 1.6, very close to the golden ratio. It is not because architects have sought it, but because the human body dictates comfortable measurements that end up bordering on divine proportion. Thus, just as with the 3.16 decimeter tiles that we walk on, mathematics sneaks into our daily lives almost without us realizing it.
Beauty recipe
This irrational number of infinite decimals was described in detail in the 13th century by Leonardo of Pisa, better known as Fibonacci. It all started with a seemingly harmless problem: how many pairs of rabbits can be born from a single pair in a year, if every month each pair matures and begins to reproduce? Unintentionally, it gave rise to one of the most beautiful stories in mathematics. The resulting sequence of natural numbers is the famous Fibonacci sequence:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…
Initially we have two ones, a rabbit and a doe, and each new term arises from adding the previous two: as if numbers also had their own mating instinct.
So far, nothing more than a nice progression. But if we divide each number by the previous one, the magic happens: 3/2 = 1.5; 5/3 = 1.66; 8/5 = 1.6… and so on until reaching the limit of infinity, God’s number: 1.6180339… It is as if Fibonacci’s rabbits, in addition to multiplying seductively and enigmatically, had invented an aesthetic canon.
And the Fibonacci sequence also seems to inhabit our body: the relationship between our height and the height up to the navel, between the distance from the shoulder to the fingers and the distance from the elbow to the fingers, between the height of the hip and the height of the knee, between the first bone of the fingers (metacarpal) and the first phalanx. And also the relationship between successive phalanges, between our smile and our jaw. A mathematical festival that some present as the “secret recipe” of beauty.
The Vitruvian Man, drawn by Leonardo da Vinci in 1492. Wikimedia Commons., CC BY
The cosmic echo of a human proportion
Some astrophysicists even show us that similar patterns appear in unexpected places: some spiral galaxies or the hidden vibrations of stars seem to resonate with the same mysterious number.
The golden ratio seems so ubiquitous that one begins to suspect cheating. Is it really in everything or do we simply look for it with the same faith with which some find their zodiac sign in the horoscope? How much truth and how much human necessity is there in reducing everything to simple relationships that we can understand?
The golden ratio is not a proven pattern in the structure of the cosmos, although it may appear as an approximation in multiple natural systems. Its divine force lies more in the metaphorical and symbolic: a bridge between the human scale (art, body, architecture) and the universe (galaxies, natural dynamics).
However, the long-standing debate persists between the desire for a perfect mathematical god who gives meaning to existence and the mathematical quantification of reality.
Measure yourself to understand everything
The Fibonacci number, applied to Don Quixote. Armando Ríos Almarza. Measure without a meter, Ávila City Council, 2006.
Calling mathematics “a universal language that connects the human being with the patterns of art, biology and the cosmos” does not mean that there is a single magic number governing everything. What really connects these dimensions is the tendency of nature and humans to generate proportions, symmetries and regularities that help us understand the world and predict the uncertain future. The golden ratio is just one of many possible formulas, perhaps the most famous for its elegance and for the times it seems to approximate natural phenomena and human creations.
The interesting question is not whether the golden ratio is really everywhere, but why we keep looking for it, why we are so attracted to the idea that a simple proportion can bridge our anatomy, Greek temples, and galactic spirals.
The question remains floating
Maybe everything is the result of our obstinacy in finding meaning where, perhaps, there is only chance. Do we really share a secret pattern with the stars, or do we invent it because we are fascinated by recognizing ourselves in everything that shines?
That answer, dear readers, would force us to deploy all the artillery of thought, philosophy, art, history, physics and, of course, mathematics. It would be necessary to write entire treatises, organize conferences and perhaps even invoke Polycletus and Fibonacci themselves to set the time for us. Difficult, right?
Although, if we think about it, it is even more difficult to resist continuing to measure our nose in the mirror in the hope of discovering the secrets of the universe in it.
This article was originally published on The Conversation.