Langdon felt a chill. They played Tarot? The medieval Italian card game was so replete with hidden heretical symbolism that Langdon had dedicated an entire chapter in his new manuscript to the Tarot. The game's twenty-two cards bore names like The Female Pope, The Empress, and The Star.Originally, Tarot had been devised as a secret means to pass along ideologies banned by the Church. Now, Tarot's mystical qualities were passed on by modern fortune-tellers.
The Tarot indicator suit for feminine divinity is pentacles, Langdon thought, realizing that if Sauniere had been stacking his granddaughter's deck for fun, pentacles was an apropos inside joke.
They arrived at the emergency stairwell, and Sophie carefully pulled open the door. No alarm sounded. Only the doors to the outside were wired. Sophie led Langdon down a tight set of switchback stairs toward the ground level, picking up speed as they went.
"Your grandfather," Langdon said, hurrying behind her," when he told you about the pentacle, did he mention goddess worship or any resentment of the Catholic Church?"
Sophie shook her head. "I was more interested in the mathematics of it - the Divine Proportion, PHI, Fibonacci sequences, that sort of thing."
Langdon was surprised. "Your grandfather taught you about the number PHI?"
"Of course. The Divine Proportion." Her expression turned sheepish. "In fact, he used to joke that I was half divine... you know, because of the letters in my name." Langdon considered it a moment and then groaned.
Still descending, Langdon refocused on PHI.He was starting to realize that Sauniere's clues were even more consistent than he had first imagined.
Da Vinci... Fibonacci numbers... the pentacle.
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.
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 fee.
"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 H of a lot cooler than PI!"
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 quotients of adjacent terms possessed the astonishing property of approaching the number 1. 618 - PHI!
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 Divine Proportion."
"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 art?"
"Aha!" Langdon said. "Glad you asked." He pulled up another slide - a pale yellow parchment displaying Leonardo Da Vinci's famous male nude - The Vitruvian Man - named for Marcus Vitruvius, the brilliant Roman architect who praised the Divine Proportion in his text De Architectura.
"Nobody understood better than Da Vinci the divine structure of the human body. Da Vinci actually exhumed corpses to measure the exact proportions of human bone structure. He was the first to show that the human body is literally made of building blocks whose proportional ratios always equal PHI."
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. "All of you. Guys and girls. Try it. Measure the distance from the tip of your head to the floor. Then divide that by the distance from your bellybutton to the floor. Guess what number you get."
"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 art is man's attempt to imitate the beauty of the Creator's hand, you can imagine we might be seeing a lot of instances of the Divine Proportion in art this semester."
Over the next half hour, Langdon showed them slides of artwork by Michelangelo, Albrecht Durer, 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 Bartok, Debussy, and Schubert. The number PHI, Langdon told them, was even used by Stradivarius to calculate the exact placement of the f-holes in the construction of his famous violins.
"In closing," Langdon said, walking to the chalkboard," we return to symbols" He drew five intersecting lines that formed a five-pointed star. "This symbol is one of the most powerful images you will see this term. Formally known as a pentagram - or pentacle, as the ancients called it - this symbol is considered both divine and magical by many cultures. Can anyone tell me why that might be?"
Stettner, the math major, raised his hand. "Because if you draw a pentagram, the lines automatically divide themselves into segments according to the Divine Proportion."
Langdon gave the kid a proud nod. "Nice job. Yes, the ratios of line segments in a pentacle allequal PHI, making this symbol the ultimate expression of the Divine Proportion. For this reason, the five-pointed star has always been the symbol for beauty and perfection associated with the goddess and the sacred feminine."
The girls in class beamed.
"One note, folks. We've only touched on Da Vinci today, but we'll be seeing a lot more of him this semester. Leonardo was a well-documented devotee of the ancient ways of the goddess. Tomorrow, I'll show you his fresco The Last Supper, which is one of the most astonishing tributes to the sacred feminine you will ever see."
"You're kidding, right?" somebody said. "I thought The Last Supper was about Jesus!" Langdon winked. "There are symbols hidden in places you would never imagine."
"Come on," Sophie whispered. "What's wrong? We're almost there. Hurry!"
Langdon glanced up, feeling himself return from faraway thoughts. He realized he was standing at a dead stop on the stairs, paralyzed by sudden revelation.
O, Draconian devil! Oh, lame saint!
Sophie was looking back at him.
It can't be that simple, Langdon thought. But he knew of course that it was. There in the bowels of the Louvre... with images of PHI and Da Vinci swirling through his mind, Robert Langdon suddenly and unexpectedly deciphered Sauniere's code.
"O, Draconian devil!" he said. "Oh, lame saint! It's the simplest kind of code!"
Sophie was stopped on the stairs below him, staring up in confusion. A code? She had been pondering the words all night and had not seen a code. Especially a simple one.
"You said it yourself." Langdon's voice reverberated with excitement. "Fibonacci numbers only have meaning in their proper order. Otherwise they're mathematical gibberish."
Sophie had no idea what he was talking about. The Fibonacci numbers? She was certain they had been intended as nothing more than a means to get the Cryptography Department involved tonight. They have another purpose? She plunged her hand into her pocket and pulled out the printout, studying her grandfather's message again.
O, Draconian devil!
Oh, lame saint!
What about the numbers?
"The scrambled Fibonacci sequence is a clue," Langdon said, taking the printout. "The numbers area hint as to how to decipher the rest of the message. He wrote the sequence out of order to tell us to apply the same concept to the text. O, Draconian devil? Oh, lame saint? Those lines mean nothing.
They are simply letters written out of order."
Sophie needed only an instant to process Langdon's implication, and it seemed laughably simple. "You think this message is... une anagramme?" She stared at him. "Like a word jumble from a newspaper?"
Langdon could see the skepticism on Sophie's face and certainly understood. Few people realized that anagrams, despite being a trite modern amusement, had a rich history of sacred symbolism.
The mystical teachings of the Kabbala drew heavily on anagrams - rearranging the letters of Hebrew words to derive new meanings. French kings throughout the Renaissance were so convinced that anagrams held magic power that they appointed royal anagrammatists to help them make better decisions by analyzing words in important documents. The Romans actually referred to the study of anagrams as ars magna - "the great art."
Langdon looked up at Sophie, locking eyes with her now. "Your grandfather's meaning was right in front of us all along, and he left us more than enough clues to see it."
Without another word, Langdon pulled a pen from his jacket pocket and rearranged the letters in each line.
O, Draconian devil! Oh, lame saint! was a perfect anagram of... Leonardo Da Vinci! The Mona Lisa!