A New Da Vinci Code? Divine Proportion Found in Human Skulls

Johns Hopkins study finds The Golden Ratio (divine proportion) in human skulls.

Posted Oct 04, 2019

 Modified by Rafael Tamargo
Leonardo’s Vitruvian Man with Golden ratios highlighted.
Source: Credit: Modified by Rafael Tamargo

Over 500 years ago, Leonardo da Vinci created illustrations for a book, On the Divine Proportion (De Divina Proportione), which was composed in 1498 and first published in 1509. This seminal manuscript explores seemingly "mystical" mathematical proportions that are commonly referred to in modern times as the "Golden Ratio."

The Golden Ratio (Phi, or Φ ≈ 1.618) is omnipresent in nature and is frequently applied to visual arts and sculpture, as well as architecture; the Golden Ratio creates structurally sound and aesthetically pleasing buildings.

Earlier this week, two neurosurgeons affiliated with Johns Hopkins University School of Medicine reported (Tamargo & Pindrik, 2019) that the Golden Ratio (Φ) is observable in the architecture of human skulls but (surprisingly) is not present in the skull proportions of other mammals. These findings were published in the September issue of the Journal of Craniofacial Surgery.

 Rafael Tamargo & Jonathan Pindrik/Journal of Craniofacial Surgery. (Open Access)
The Golden Ratio characterizes a unique relationship in the study of integers, a branch of mathematics called Number Theory. Numerically, Φ can be calculated as a ratio within the Fibonacci series as the series approaches infinity.
Source: Rafael Tamargo & Jonathan Pindrik/Journal of Craniofacial Surgery. (Open Access)

For this study, Rafael Tamargo and Jonathan Pindrik fastidiously measured the proportions of 100 human skulls and 70 skulls from six other mammalian species. Then, they calculated the proportion and ratio between distinct regions.

Notably, the authors found that, in humans, two important ratios approximate the Golden Ratio. However, in the other six mammalian species, both these ratios did not reflect so called "divine proportions" or Φ.

Source: Pixabay

According to Tamargo and Pindrik, "The difference between the ratios showed a trend toward convergence on Φ correlating with species complexity." The skulls of species such as dogs, two kinds of monkeys, rabbits, as well as lions and tigers, diverged from the Golden Ratio.

"The other mammals we surveyed actually have unique ratios that approach the Golden Ratio with increased species sophistication," Rafael Tamargo, who is a professor of neurosurgery at JHUSM, said in a Johns Hopkins news release. "We believe that this finding may have important anthropological and evolutionary implications."

As Tamargo and Pindrik write in the paper's conclusion, "We hypothesize that the Golden Ratio principle, which has been documented in other biological and natural systems, may be present in the architecture and evolution of the human skull as well."

Rafael Tamargo has a lifelong passion for exploring the intersection of art and neuroanatomy. In 2010, he published a paper, "Concealed Neuroanatomy in Michelangelo's Separation of Light From Darkness in the Sistine Chapel," in the journal Neurosurgery.

For this study, Tamargo and Ian Suk, who is a medical illustrator, identified anatomically correct depictions of the human spinal cord and brain stem in the Creation of Adam painting on the central panel of the Sistine Chapel ceiling. Scientific American published a fascinating article (with lots of photos) by R. Douglas Fields about this discovery.

Viking/Public Domain
Source: Viking/Public Domain

The Golden Ratio, Divine Proportions, and The Fabric of Mind

My father, Richard Bergland (1932-2007), was a late-20th-century neurosurgeon who was trained by Bronson Ray, a protegé of Harvey Cushing (1869-1939). Cushing was a pioneering early-20th century brain surgeon at Johns Hopkins who is considered by many the "father" of modern neurosurgery.

As you can see from this dust jacket image, my dad wrote The Fabric of Mind. I love the composition of this book cover. That said, back in the 1980s, he had to push hard to convince his publisher to put this graphic brain image on a book cover geared for general readership.

When the layout for Dad's book cover was being designed, folks in the marketing department expressed concern that this sagittal slice of a human brain was a bit too "postmortem-ish" and wouldn't appeal to a mass audience. Maybe they were right; the book wasn't a bestseller. Nevertheless, my father thought is was a beautiful image and accurately displayed the exquisite proportions and architecture of a Homo sapiens brain.

While reading the lengthy new study by Rafael Tamargo this morning, I got nostalgic remembering the in-depth conversations my father and I would have about neuroscience. I wish Dad was here to explain the historical significance of this recent Φ discovery over coffee, using layperson terms.

Coincidentally, much like Rafael Tamargo, my father was fascinated with the intersection of art and neuroanatomy. As a hobby, Dad would make brain sculptures out of clay. As an amateur sculptor and brain scientist, my father idolized both Michelango and Leonardo da Vinci.

For reasons that I've never completely understood, my father was fanatically obsessed with Leonardo's sketches from Divina Proportione. The degree of his intrigue with the Golden Ratio always seemed kind of "out there" to me. Dad went so far as to have da Vinci illustrations of divine proportion printed on over-sized poster board and hung them in his office.

Whenever my father wanted to bring neuroscience to life or romanticize the history of brain science, he'd tell stories about how Leonardo da Vinci was a Renaissance-era neuroanatomy pioneer who was ahead of his time.

Anecdotally, Dad would say things like: "In 1504, Leonardo da Vinci made wax casting of the human brain and coined the term cerebellum (Latin for "litte brain") after he observed two small, kumquat-shaped hemispheres neatly tucked under the much larger cerebral hemispheres."

Unfortunately, I've had very little luck corroborating my dad's anecdotal stories about Leonardo da Vinci using Google Scholar, which is frustrating. Therefore, ever since my father died in 2007, I've been on the lookout for any neuroscience-related scholarly literature that references Leonardo da Vinci.

Yesterday afternoon, when my phone dinged with a Google Alert about this new study, I almost fell off my chair. On a personal note, I think it's fantastic that 21st-century neurosurgeons at Johns Hopkins are still pushing the envelope in such unique and interesting ways. Harvey Cushing's spirit lives on through their work.


Rafael Tamargo and Jonathan Pindrik. “Mammalian Skull Dimensions and the Golden Ratio (Φ)" The Journal of Craniofacial Surgery  (First published: September 2019) DOI: 10.1097/SCS.0000000000005610