As he moved, Langdon felt like he was trying to assemble a jigsaw puzzle in the dark. The newestaspect of this mystery was a deeply troubling one: The captain of the Judicial Police is trying toframe me for murder"Do you think," he whispered, "that maybe Fache wrote that message on the floor?"Sophie didn't even turn. "Impossible."Langdon wasn't so sure. "He seems pretty intent on making me look guilty. Maybe he thoughtwriting 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 mygrandfather."Langdon knew she was right. The symbolism of the clues meshed too perfectly—the pentacle, TheVitruvian 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. I'mcertain his message at the Louvre was his final effort to tell me something important, something hethought you could help me understand."Langdon frowned. O, Draconian devil! Oh, lame saint.! He wished he could comprehend themessage, both for Sophie's well-being and for his own. Things had definitely gotten worse since hefirst laid eyes on the cryptic words. His fake leap out the bathroom window was not going to helpLangdon's popularity with Fache one bit. Somehow he doubted the captain of the French policewould see the humor in chasing down and arresting a bar of soap.
"The doorway isn't much farther," Sophie said.
"Do you think there's a possibility that the numbers in your grandfather's message hold the key tounderstanding the other lines?" Langdon had once worked on a series of Baconian manuscripts thatcontained epigraphical ciphers in which certain lines of code were clues as to how to decipher theother lines.
"I've been thinking about the numbers all night. Sums, quotients, products. I don't see anything.
Mathematically, they're arranged at random. Cryptographic gibberish.""And yet they're all part of the Fibonacci sequence. That can't be coincidence.""It's not. Using Fibonacci numbers was my grandfather's way of waving another flag at me—likewriting the message in English, or arranging himself like my favorite piece of art, or drawing apentacle on himself. All of it was to catch my attention.""The pentacle has meaning to you?""Yes. I didn't get a chance to tell you, but the pentacle was a special symbol between mygrandfather and me when I was growing up. We used to play Tarot cards for fun, and my indicatorcard always turned out to be from the suit of pentacles. I'm sure he stacked the deck, but pentaclesgot to be our little joke."Langdon felt a chill. They played Tarot? The medieval Italian card game was so replete withhidden heretical symbolism that Langdon had dedicated an entire chapter in his new manuscript tothe Tarot. The game's twenty-two cards bore names like The Female Pope, The Empress, and TheStar. Originally, Tarot had been devised as a secret means to pass along ideologies banned by theChurch. 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 ifSaunière 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 alarmsounded. Only the doors to the outside were wired. Sophie led Langdon down a tight set ofswitchback 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, didhe 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 Iwas 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 Saunière's clues wereeven 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 thatLangdon 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.
1.618Langdon 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 isone 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 inart. 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 beautifulnumber 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 theFibonacci sequence—a progression famous not only because the sum of adjacent terms equaled thenext term, but because the quotients of adjacent terms possessed the astonishing property ofapproaching 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, andeven human beings all possessed dimensional properties that adhered with eerie exactitude to theratio of PHI to 1.
"PHI's ubiquity in nature," Langdon said, killing the lights, "clearly exceeds coincidence, and sothe 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 DivineProportion in nature.""No?" Langdon grinned. "Ever study the relationship between females and males in a honeybeecommunity?""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 malebees 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 shellto 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.
斯提勒笑着补充道："别把它跟PI（π）弄混了。我们搞数学的喜欢说：PHI 多一个H，却比PI 棒多了！"兰登大笑起来，其他人却不解其意。
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 growin 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 onplant 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 parchmentdisplaying Leonardo da Vinci's famous male nude—The Vitruvian Man—named for MarcusVitruvius, the brilliant Roman architect who praised the Divine Proportion in his text DeArchitectura.
"Nobody understood better than Da Vinci the divine structure of the human body. Da Vinciactually exhumed corpses to measure the exact proportions of human bone structure. He was thefirst to show that the human body is literally made of building blocks whose proportional ratiosalways 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 thedistance 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 thedistance from your shoulder to your fingertips, and then divide it by the distance from your elbowto your fingertips. PHI again. Another? Hip to floor divided by knee to floor. PHI again. Fingerjoints. Toes. Spinal divisions. PHI. PHI. PHI. My friends, each of you is a walking tribute to theDivine Proportion."Even in the darkness, Langdon could see they were all astounded. He felt a familiar warmth inside.
兰登关上教室里的灯，说道："PHI 在自然界中无处不在，这显然不是巧合，所以祖先们估计PHI 是造物主事先定下的。早期的科学家把1.618 称为黄金分割。""等一下。"一名坐在前排的女生说。"我是生物专业的学生，我从来没有在自然界中见到黄金分割。""没有吗？"兰登咧嘴笑了。"研究过一个蜂巢里的雄蜂和雌蜂吗？"
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 buildingblock 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-reveringreligions. Many of us celebrate nature the way the pagans did, and don't even know it. May Day isa 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. Manis simply playing by Nature's rules, and because art is man's attempt to imitate the beauty of theCreator's hand, you can imagine we might be seeing a lot of instances of the Divine Proportion inart this semester."Over the next half hour, Langdon showed them slides of artwork by Michelangelo, Albrecht Dürer,Da Vinci, and many others, demonstrating each artist's intentional and rigorous adherence to theDivine Proportion in the layout of his compositions. Langdon unveiled PHI in the architecturaldimensions of the Greek Parthenon, the pyramids of Egypt, and even the United Nations Buildingin New York. PHI appeared in the organizational structures of Mozart's sonatas, Beethoven's FifthSymphony, as well as the works of Bartók, Debussy, and Schubert. The number PHI, Langdon toldthem, was even used by Stradivarius to calculate the exact placement of the f-holes in theconstruction of his famous violins.
"In closing," Langdon said, walking to the chalkboard, "we return to symbols" He drew fiveintersecting lines that formed a five-pointed star. "This symbol is one of the most powerful imagesyou will see this term. Formally known as a pentagram—or pentacle, as the ancients called it—thissymbol is considered both divine and magical by many cultures. Can anyone tell me why thatmight be?"Stettner, the math major, raised his hand. "Because if you draw a pentagram, the linesautomatically 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 thegoddess 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 thissemester. 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 tributesto 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 ata 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 Saunière'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 beenpondering 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 onlyhave 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 hadbeen 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.
13-3-2-21-1-1-8-5O, 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 toapply 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 anewspaper?"Langdon could see the skepticism on Sophie's face and certainly understood. Few people realizedthat anagrams, despite being a trite modern amusement, had a rich history of sacred symbolism.
"就是PHI."兰登回答道。"正是1.618.想再看一个例子吗？量一下你肩膀到指尖的距离，然后用它除以肘关节到指尖的距离，又得到了PHI.用臀部到地面的距离除以膝盖到地面的距离，又可以得到PHI.再看看手指关节、脚趾、脊柱的分节，你都可以从中得到PHI.朋友们，我们每个人都是离不开黄金分割的生物。"虽然教室里的灯都关了，但兰登可以看得出大家都很震惊。一股暖流涌上他的心头，这正是他热爱教学的原因。"朋友们，正如你们所见，纷繁复杂的自然界隐藏着规则。当古人发现PHI 时，他们肯定自己已经偶然发现了上帝造物的大小比例，也正因为这一点他们对自然界充满了崇拜之情。上帝的杰作可以在自然界中找到印证，直至今日还存在着一个异教组织--大地母亲教。我们中的许多人也像异教徒一样赞颂着自然，只不过我们自己没有意识到。比如说我们庆祝五朔节就是一个很好的例证。五朔节是赞颂春天的节日，人们通过它来庆祝大地复苏，给予人类馈赠。从一开始，黄金分割的神秘特质就已经被确定了。人们只能按自然规则活动，而艺术又是人们试图模仿造物主创造之美的一种尝试，所以这学期我们将在艺术作品中看到许多黄金分割的实例。"在接下来的半个小时中，兰登给学生们播放了米开朗基罗、阿尔布莱希特。丢勒、达。芬奇和许多其他艺术家作品的幻灯片，这些艺术家在设计创作其作品时都有意识地、严格地遵循了黄金分割比率。兰登向大家揭示了希腊巴特农神殿、埃及金字塔甚至纽约联合国大楼在建筑设计中所运用的黄金分割率，并指出PHI 也被运用在莫扎特的奏鸣曲、贝多芬的《第五交响曲》以及巴托克、德彪西、舒伯特等音乐家的创作中。兰登还告诉大家，甚至斯特拉迪瓦里在制造他那有名的小提琴时也运用了黄金分割来确定f 形洞的确切位置。
The mystical teachings of the Kabbala drew heavily on anagrams—rearranging the letters ofHebrew words to derive new meanings. French kings throughout the Renaissance were soconvinced that anagrams held magic power that they appointed royal anagrammatists to help themmake better decisions by analyzing words in important documents. The Romans actually referredto 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 rightin 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 ineach line.
O, Draconian devil! Oh, lame saint!
was a perfect anagram of...
Leonardo da Vinci! The Mona Lisa!