half divine… you know, because of the letters in my name.”
Langdon considered it a moment and then groaned.
Still descending, Langdon refocused on
Incredibly, all of these things were connected by a single concept so fundamental to art history that Langdon often spent several class periods on the topic.
He felt himself suddenly reeling back to Harvard, standing in front of his “Symbolism in Art” class, writing his favorite number on the chalkboard.
1.618
Langdon turned to face his sea of eager students. “Who can tell me what this number is?”
A long-legged math major in back raised his hand. “That's the number PHI.” He pronounced it
“Nice job, Stettner,” Langdon said. “Everyone, meet PHI.”
“Not to be confused with PI,” Stettner added, grinning. “As we mathematicians like to say: PHI is one
Langdon laughed, but nobody else seemed to get the joke.
Stettner slumped.
“This number PHI,” Langdon continued, “one-point-six-one-eight, is a very important number in art. Who can tell me why?”
Stettner tried to redeem himself. “Because it's so pretty?”
Everyone laughed.
“Actually,” Langdon said, “Stettner's right again. PHI is generally considered the most beautiful number in the universe.”
The laughter abruptly stopped, and Stettner gloated.
As Langdon loaded his slide projector, he explained that the number PHI was derived from the Fibonacci sequence—a progression famous not only because the sum of adjacent terms equaled the next term, but because the
Despite PHI's seemingly mystical mathematical origins, Langdon explained, the truly mind-boggling aspect of PHI was its role as a fundamental building block in nature. Plants, animals, and even human beings all possessed dimensional properties that adhered with eerie exactitude to the ratio of PHI to 1.
“PHI's ubiquity in nature,” Langdon said, killing the lights, “clearly exceeds coincidence, and so the ancients assumed the number PHI must have been preordained by the Creator of the universe. Early scientists heralded one-point-six-one-eight as the
“Hold on,” said a young woman in the front row. “I'm a bio major and I've never seen this Divine Proportion in nature.”
“No?” Langdon grinned. “Ever study the relationship between females and males in a honeybee community?”
“Sure. The female bees always outnumber the male bees.”
“Correct. And did you know that if you divide the number of female bees by the number of male bees in any beehive in the world, you always get the same number?”
“You do?”
“Yup. PHI.”
The girl gaped. “NO WAY!”
“Way!” Langdon fired back, smiling as he projected a slide of a spiral seashell. “Recognize this?”
“It's a nautilus,” the bio major said. “A cephalopod mollusk that pumps gas into its chambered shell to adjust its buoyancy.”
“Correct. And can you guess what the ratio is of each spiral's diameter to the next?”
The girl looked uncertain as she eyed the concentric arcs of the nautilus spiral.
Langdon nodded. “PHI. The Divine Proportion. One-point-six-one-eight to one.”
The girl looked amazed.
Langdon advanced to the next slide—a close-up of a sunflower's seed head. “Sunflower seeds grow in opposing spirals. Can you guess the ratio of each rotation's diameter to the next?”
“PHI?” everyone said.
“Bingo.” Langdon began racing through slides now—spiraled pinecone petals, leaf arrangement on plant stalks, insect segmentation—all displaying astonishing obedience to the Divine Proportion.
“This is amazing!” someone cried out.
“Yeah,” someone else said, “but what does it have to do with
“Aha!” Langdon said. “Glad you asked.” He pulled up another slide—a pale yellow parchment displaying Leonardo da Vinci's famous male nude—
“Nobody understood better than Da Vinci the divine structure of the human body. Da Vinci actually
Everyone in class gave him a dubious look.
“Don't believe me?” Langdon challenged. “Next time you're in the shower, take a tape measure.”
A couple of football players snickered.
“Not just you insecure jocks,” Langdon prompted.
“Not PHI!” one of the jocks blurted out in disbelief.
“Yes, PHI,” Langdon replied. “One-point-six-one-eight. Want another example? Measure the distance from your shoulder to your fingertips, and then divide it by the distance from your elbow to your fingertips. PHI again. Another? Hip to floor divided by knee to floor. PHI again. Finger joints. Toes. Spinal divisions. PHI. PHI. PHI. My friends, each of you is a walking tribute to the Divine Proportion.”
Even in the darkness, Langdon could see they were all astounded. He felt a familiar warmth inside. This is why he taught. “My friends, as you can see, the chaos of the world has an underlying order. When the ancients discovered PHI, they were certain they had stumbled across God's building block for the world, and they worshipped Nature because of that. And one can understand why. God's hand is evident in Nature, and even to this day there exist pagan, Mother Earth-revering religions. Many of us celebrate nature the way the pagans did, and don't even know it. May Day is a perfect example, the celebration of spring… the earth coming back to life to produce her bounty. The mysterious magic inherent in the Divine Proportion was written at the beginning of time. Man is simply playing by Nature's rules, and because
Over the next half hour, Langdon showed them slides of artwork by Michelangelo, Albrecht Dьrer, Da Vinci, and many others, demonstrating each artist's intentional and rigorous adherence to the Divine Proportion in the layout of his compositions. Langdon unveiled PHI in the architectural dimensions of the Greek Parthenon, the pyramids of Egypt, and even the United Nations Building in New York. PHI appeared in the organizational structures of Mozart's sonatas, Beethoven's Fifth Symphony, as well as the works of Bartуk, Debussy, and Schubert. The number PHI, Langdon told them, was even used by Stradivarius to calculate the exact placement of the f-holes in
