Emerging from the shadows, Langdon and Sophie moved stealthily up the deserted Grand Gallery corridor toward the emergency exit stairwell.
As he moved, Langdon felt like he was trying to assemble a jigsaw puzzle in the dark. The newest aspect of this mystery was a deeply troubling one: The captain of the Judicial Police is trying to frame me for murder
Do you think, he whispered, that maybe Fache wrote that message on the floor?
Sophie didnt even turn. Impossible.
Langdon wasnt so sure. He seems pretty intent on making me look guilty. Maybe he thought writing my name on the floor would help his case?
The Fibonacci sequence? The P.S. ? All the Da Vinci and goddess symbolism? That had to be my grandfather.
Langdon knew she was right. The symbolism of the clues meshed too perfectlythe pentacle, The Vitruvian Man, Da Vinci, the goddess, and even the Fibonacci sequence. A coherent symbolic set, as iconographers would call it. All inextricably tied.
And his phone call to me this afternoon, Sophie added. He said he had to tell me something. Im certain his message at the Louvre was his final effort to tell me something important, something he thought you could help me understand.
Langdon frowned. O, Draconian devil! Oh, lame saint. ! He wished he could comprehend the message, both for Sophies well‑being and for his own. Things had definitely gotten worse since he first laid eyes on the cryptic words. His fake leap out the bathroom window was not going to help Langdons popularity with Fache one bit. Somehow he doubted the captain of the French police would see the humor in chasing down and arresting a bar of soap.
The doorway isnt much farther, Sophie said.
Do you think theres a possibility that the numbers in your grandfathers message hold the key to understanding the other lines? Langdon had once worked on a series of Baconian manuscripts that contained epigraphical ciphers in which certain lines of code were clues as to how to decipher the other lines.
Ive been thinking about the numbers all night. Sums, quotients, products. I dont see anything. Mathematically, theyre arranged at random. Cryptographic gibberish.
And yet theyre all part of the Fibonacci sequence. That cant be coincidence.
Its not. Using Fibonacci numbers was my grandfathers way of waving another flag at melike writing the message in English, or arranging himself like my favorite piece of art, or drawing a pentacle on himself. All of it was to catch my attention.
The pentacle has meaning to you?
Yes. I didnt get a chance to tell you, but the pentacle was a special symbol between my grandfather and me when I was growing up. We used to play Tarot cards for fun, and my indicator card always turned out to be from the suit of pentacles. Im sure he stacked the deck, but pentacles got to be our little joke.
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 games 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, Tarots 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 granddaughters 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 itthe 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 Saunieres 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. Thats 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.
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 its so pretty?
Actually, Langdon said, Stettners 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 sequencea 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 1.618PHI!
Despite PHIs 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.
PHIs 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. Im a bio major and Ive 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?
The girl gaped. NO WAY!
Way! Langdon fired back, smiling as he projected a slide of a spiral seashell. Recognize this?
Its 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 spirals 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 slidea close‑up of a sunflowers seed head. Sunflower seeds grow in opposing spirals. Can you guess the ratio of each rotations diameter to the next?
PHI? everyone said.
Bingo. Langdon began racing through slides nowspiraled pinecone petals, leaf arrangement on plant stalks, insect segmentationall 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 slidea pale yellow parchment displaying Leonardo da Vincis famous male nudeThe Vitruvian Mannamed 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.
Dont believe me? Langdon challenged. Next time youre 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 belly button 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 Gods building block for the world, and they worshipped Nature because of that. And one can understand why. Gods 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 dont 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 Natures rules, and because art is mans attempt to imitate the beauty of the Creators 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 Dьrer, Da Vinci, and many others, demonstrating each artists 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 Mozarts sonatas, Beethovens 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 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 pentagramor pentacle, as the ancients called itthis 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 all equal 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. Weve only touched on Da Vinci today, but well be seeing a lot more of him this semester. Leonardo was a well‑documented devotee of the ancient ways of the goddess. Tomorrow, Ill show you his fresco The Last Supper, which is one of the most astonishing tributes to the sacred feminine you will ever see.
Youre 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. Whats wrong? Were 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 cant 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 Saunieres code.
O, Draconian devil! he said. Oh, lame saint! Its 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. Langdons voice reverberated with excitement. Fibonacci numbers only have meaning in their proper order. Otherwise theyre 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 grandfathers 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 are a 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 Langdons 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 Sophies 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 anagramsrearranging 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 magnathe great art.
Langdon looked up at Sophie, locking eyes with her now. Your grandfathers 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!