CHAPTER 20
Emerging from the shadows, Langdon and Sophie moved stealthily up the deserted Grand Gallery
+ \2 ~ N; r) Z V' z! |! Ycorridor toward the emergency exit stairwell.
- K5 h8 ]' k2 u7 R7 qAs he moved, Langdon felt like he was trying to assemble a jigsaw puzzle in the dark. The newest
: v7 [ T" v# a8 o+ Laspect of this mystery was a deeply troubling one: The captain of the Judicial Police is trying to
% m) C3 `% H' }& X. l8 sframe me for murder
0 t; y& S% h7 j3 _+ k) \3 Q"Do you think," he whispered, "that maybe Fache wrote that message on the floor?"9 Q/ t) P8 y$ n+ H
Sophie didn't even turn. "Impossible." Z& Q6 | n5 F- j6 N! M
Langdon wasn't so sure. "He seems pretty intent on making me look guilty. Maybe he thought O$ M9 F; B7 R- c+ f
writing my name on the floor would help his case?"
( R% b8 R, ?$ Z+ M"The Fibonacci sequence? The P.S.? All the Da Vinci and goddess symbolism? That had to be my
6 g' u3 L. S3 O$ @; T% g) ]grandfather."! L+ M' {( m( k( s: O# t, Z
Langdon knew she was right. The symbolism of the clues meshed too perfectly—the pentacle, The ( n, k% c U4 Q5 t$ E& W
Vitruvian Man, Da Vinci, the goddess, and even the Fibonacci sequence. A coherent symbolic set, . e$ A/ F" `! L) W- Y
as iconographers would call it. All inextricably tied.
0 O' a! B9 @( f: x9 s. \, f"And his phone call to me this afternoon," Sophie added. "He said he had to tell me something. I'm
$ B& p1 _. o" Q4 K7 O4 Scertain his message at the Louvre was his final effort to tell me something important, something he
3 }5 j7 ?4 g& r9 O/ u2 nthought you could help me understand."
) W! u* Y) E* [Langdon frowned. O, Draconian devil! Oh, lame saint.! He wished he could comprehend the " K* T5 z# P8 q b+ u7 l
message, both for Sophie's well-being and for his own. Things had definitely gotten worse since he
# ]% z7 k2 k6 Ifirst laid eyes on the cryptic words. His fake leap out the bathroom window was not going to help 9 x- g7 c- t7 n5 K$ X$ |
Langdon's popularity with Fache one bit. Somehow he doubted the captain of the French police 5 S% c o( n5 u- W; @
would see the humor in chasing down and arresting a bar of soap.# g3 Z( c0 S+ I& g2 i: J
"The doorway isn't much farther," Sophie said.( h) O7 [5 v" z' {
"Do you think there's a possibility that the numbers in your grandfather's message hold the key to
0 y6 \3 s7 f! wunderstanding the other lines?" Langdon had once worked on a series of Baconian manuscripts that 8 @+ M$ K3 L, H9 W; k
contained epigraphical ciphers in which certain lines of code were clues as to how to decipher the ! s7 _8 K' ^, B4 I: |6 f. J! W
7 j( r1 T, S+ i$ q5 X7 ^' O: j& V% vother lines.
* O4 A' U- I9 n) Q( @" a# S1 ]+ @"I've been thinking about the numbers all night. Sums, quotients, products. I don't see anything.
% j8 w# e6 l3 {8 `0 S2 \* s# aMathematically, they're arranged at random. Cryptographic gibberish."
+ L% G9 e4 U! i6 E8 S# ^3 k"And yet they're all part of the Fibonacci sequence. That can't be coincidence."( |9 H/ v3 m& L5 } K
"It's not. Using Fibonacci numbers was my grandfather's way of waving another flag at me—like
( k0 A! K; s& A; x" [writing the message in English, or arranging himself like my favorite piece of art, or drawing a
9 P+ B" ]6 P( B, B2 M9 [pentacle on himself. All of it was to catch my attention."
" j# [! n, O9 J- D4 [6 M* k0 g"The pentacle has meaning to you?"
8 K! R& I) V: a1 C"Yes. I didn't get a chance to tell you, but the pentacle was a special symbol between my ( G/ u4 A2 R+ L7 S% b y
grandfather and me when I was growing up. We used to play Tarot cards for fun, and my indicator 8 S$ v& y3 K' J G
card always turned out to be from the suit of pentacles. I'm sure he stacked the deck, but pentacles Y1 R1 C2 j4 e$ N3 T
got to be our little joke."/ F8 n4 P/ B% X/ t" Z K! n
Langdon felt a chill. They played Tarot? The medieval Italian card game was so replete with 3 t( X+ f7 a" Y. P
hidden heretical symbolism that Langdon had dedicated an entire chapter in his new manuscript to ]5 J7 R/ a: L! o8 y9 b1 e4 p" J
the Tarot. The game's twenty-two cards bore names like The Female Pope, The Empress, and The
& f+ y' G6 I* w0 }! RStar. Originally, Tarot had been devised as a secret means to pass along ideologies banned by the V" \2 f" K" l' N- f4 J/ f
Church. Now, Tarot's mystical qualities were passed on by modern fortune-tellers.+ J1 J+ e4 {$ ]8 c1 k l5 L: v
The Tarot indicator suit for feminine divinity is pentacles, Langdon thought, realizing that if
) ^$ W. k5 B1 Q, ASaunière had been stacking his granddaughter's deck for fun, pentacles was an apropos inside joke.
( B+ v% }+ T$ x- @# a4 {They arrived at the emergency stairwell, and Sophie carefully pulled open the door. No alarm 1 b) z, ~: u* g" o; p {7 X/ p2 o
sounded. Only the doors to the outside were wired. Sophie led Langdon down a tight set of # P9 ` F- m7 n0 O' k2 k
switchback stairs toward the ground level, picking up speed as they went.
" l: B8 E9 B8 c0 C% r"Your grandfather," Langdon said, hurrying behind her, "when he told you about the pentacle, did
) V% p( a) T0 b/ K( P/ a% Vhe mention goddess worship or any resentment of the Catholic Church?"
0 j. S% e5 A( P) FSophie shook her head. "I was more interested in the mathematics of it—the Divine Proportion, ; K9 g) q! M2 g% p: H% Q9 j
PHI, Fibonacci sequences, that sort of thing."8 ]8 T& o/ U& J3 s8 ^6 n8 }. L
Langdon was surprised. "Your grandfather taught you about the number PHI?"
5 W* W p1 m; }6 ^+ a" o$ C"Of course. The Divine Proportion." Her expression turned sheepish. "In fact, he used to joke that I ) N: M) ]$ W& ]! Y/ j: V
was half divine... you know, because of the letters in my name."
- V& R% o! _0 E9 u* m4 kLangdon considered it a moment and then groaned.
, v) f, D. R" [& C1 H7 H: c/ B8 L% Y t, V/ m; [
s-o-PHI-e.& O& E$ d; o$ ?5 g0 E- f+ }
Still descending, Langdon refocused on PHI. He was starting to realize that Saunière's clues were ' c4 |/ R* e b" s
even more consistent than he had first imagined.0 Y1 I& ]( p, w3 o9 r% x, ^
Da Vinci... Fibonacci numbers... the pentacle.- ]1 w4 |. I3 D9 q5 U5 ^
Incredibly, all of these things were connected by a single concept so fundamental to art history that
+ R+ t& h! z& q2 z! O0 \& ], zLangdon often spent several class periods on the topic.
, C' F/ `' q* n. A# zPHI.
+ a6 r' d& ]' H* x6 s: D% CHe felt himself suddenly reeling back to Harvard, standing in front of his "Symbolism in Art" class,
* ` r: ]( A/ {! r- u" ]7 x, Zwriting his favorite number on the chalkboard.
7 |2 u7 w+ V+ A1.618! ?- S# [) G3 P0 a& O2 Z
Langdon turned to face his sea of eager students. "Who can tell me what this number is?"
& J9 o: s- r* O+ q. S3 T4 \3 XA long-legged math major in back raised his hand. "That's the number PHI." He pronounced it fee.: A. E( \7 h2 r6 p
"Nice job, Stettner," Langdon said. "Everyone, meet PHI."7 C/ W9 ]3 F( L$ \
"Not to be confused with PI," Stettner added, grinning. "As we mathematicians like to say: PHI is v* Q& E( L }$ I3 N
one H of a lot cooler than PI!"
8 F0 q, |) o: x9 Z nLangdon laughed, but nobody else seemed to get the joke.8 A7 r% D1 w8 L5 Z P# _# S
Stettner slumped.- p. }6 D! z6 O- q% C M
"This number PHI," Langdon continued, "one-point-six-one-eight, is a very important number in ) p+ Z) A* j/ T9 S% @* C4 W
art. Who can tell me why?"* v1 J2 ?5 Q3 I: o% y4 ~7 E
Stettner tried to redeem himself. "Because it's so pretty?"9 v7 Z% u; o- s0 z, q4 \
Everyone laughed.
& J* h6 q# n1 [5 d/ P$ r"Actually," Langdon said, "Stettner's right again. PHI is generally considered the most beautiful 1 e! v. O2 n% G4 ~, m
number in the universe." B( l: X5 `6 I5 z+ v1 b: ^* A. F
The laughter abruptly stopped, and Stettner gloated.( E/ H' r/ A) O+ a
0 p- h8 ]% b6 N' H S& G- N' oAs Langdon loaded his slide projector, he explained that the number PHI was derived from the ( n8 V; ^2 n' p- |2 g
Fibonacci sequence—a progression famous not only because the sum of adjacent terms equaled the
0 w! i4 s4 r4 k L$ Wnext term, but because the quotients of adjacent terms possessed the astonishing property of 5 i$ T4 |, o' m f) [) F
approaching the number 1.618—PHI!
1 b' r7 L/ k/ q$ PDespite PHI's seemingly mystical mathematical origins, Langdon explained, the truly mind-
! _! u) C* A2 A+ `$ kboggling aspect of PHI was its role as a fundamental building block in nature. Plants, animals, and 5 R( f2 x) L, d, M/ r- a: R4 W
even human beings all possessed dimensional properties that adhered with eerie exactitude to the
) _* z, r' u6 {ratio of PHI to 1.. f/ O+ V2 w# _% K$ f* j# q+ A' A
"PHI's ubiquity in nature," Langdon said, killing the lights, "clearly exceeds coincidence, and so
9 u" O; n2 B2 E. F: e% Hthe ancients assumed the number PHI must have been preordained by the Creator of the universe. : y0 O- A. q+ q7 y0 S
Early scientists heralded one-point-six-one-eight as the Divine Proportion."
* Y7 Q: w- O1 X, z* g"Hold on," said a young woman in the front row. "I'm a bio major and I've never seen this Divine $ |/ ^- ~3 ~6 E t
Proportion in nature."# L8 f& t# F. B$ m0 _' ]+ O
"No?" Langdon grinned. "Ever study the relationship between females and males in a honeybee
, v8 s; S6 N4 O/ Dcommunity?"
$ k2 h* B% S2 y: U"Sure. The female bees always outnumber the male bees."
( l) }* E- Q( G0 l"Correct. And did you know that if you divide the number of female bees by the number of male " j `8 [9 v, [( S' j
bees in any beehive in the world, you always get the same number?"
% T0 n! p9 x' l4 H1 x0 r# y"You do?"
) A6 c, h# Z: v" a"Yup. PHI."% V) I: Q- |1 G- U! B, s K
The girl gaped. "NO WAY!"
. o0 e2 j& z- _"Way!" Langdon fired back, smiling as he projected a slide of a spiral seashell. "Recognize this?"# [( r8 r v9 e3 u1 Y q3 q
"It's a nautilus," the bio major said. "A cephalopod mollusk that pumps gas into its chambered shell 1 @" ^, ~* O6 a
to adjust its buoyancy.": C$ I1 m6 Y, G' R* R
"Correct. And can you guess what the ratio is of each spiral's diameter to the next?"1 I% @ j5 D6 x& l
The girl looked uncertain as she eyed the concentric arcs of the nautilus spiral.' L8 _# J6 G+ C+ n" S n( d2 x
Langdon nodded. "PHI. The Divine Proportion. One-point-six-one-eight to one."
" R9 w" i- L- |' Z1 YThe girl looked amazed.: t% C3 l# w3 r2 d) _2 j
+ R7 w$ ~. m5 l
Langdon advanced to the next slide—a close-up of a sunflower's seed head. "Sunflower seeds grow ; ]( q% N- C* z b- J' z* g
in opposing spirals. Can you guess the ratio of each rotation's diameter to the next?" G e H& `) A P. W( H
"PHI?" everyone said.
, A# E8 h) e9 ?"Bingo." Langdon began racing through slides now—spiraled pinecone petals, leaf arrangement on ; c% W! F8 Q7 V- H8 ^
plant stalks, insect segmentation—all displaying astonishing obedience to the Divine Proportion.
7 u% M6 E* O# p$ |0 q"This is amazing!" someone cried out.
) {2 Y1 j1 o6 X+ C, b0 e0 z" k1 F"Yeah," someone else said, "but what does it have to do with art?"# b: }. y3 C! t$ a. ~8 b
"Aha!" Langdon said. "Glad you asked." He pulled up another slide—a pale yellow parchment ! K9 V9 T; c N/ ^. R0 {$ o5 r
displaying Leonardo da Vinci's famous male nude—The Vitruvian Man—named for Marcus ( m. J$ | m0 j. @/ k( A
Vitruvius, the brilliant Roman architect who praised the Divine Proportion in his text De 6 i2 ?& i7 ~; v
Architectura.7 Q- i3 S8 k3 i* b w
"Nobody understood better than Da Vinci the divine structure of the human body. Da Vinci
4 `% @+ W$ {8 I5 K2 {9 Cactually exhumed corpses to measure the exact proportions of human bone structure. He was the - {8 L6 `5 G. }+ N! B
first to show that the human body is literally made of building blocks whose proportional ratios . V0 X2 K$ @4 `" B7 z
always equal PHI."
( i& M4 |' v- h9 ]4 I, K. \Everyone in class gave him a dubious look./ S, U# s8 a9 g3 |
"Don't believe me?" Langdon challenged. "Next time you're in the shower, take a tape measure."
" W# \1 v' T c) YA couple of football players snickered.0 D3 P$ Z6 ~0 W( `# o( ^3 d
"Not just you insecure jocks," Langdon prompted. "All of you. Guys and girls. Try it. Measure the
' B5 I% |: Z" zdistance from the tip of your head to the floor. Then divide that by the distance from your belly
0 L8 Y. f' z) {' O" n5 q. t1 f) cbutton to the floor. Guess what number you get."# [. p% f3 d& _/ g7 a" r
"Not PHI!" one of the jocks blurted out in disbelief.
# d3 J& L. b: z0 F- L7 P; h"Yes, PHI," Langdon replied. "One-point-six-one-eight. Want another example? Measure the
8 X- }( @- P$ ^6 F7 }. W* Y; Gdistance from your shoulder to your fingertips, and then divide it by the distance from your elbow
G2 K3 U( ~8 j& Vto your fingertips. PHI again. Another? Hip to floor divided by knee to floor. PHI again. Finger
; K" h3 g3 F' h* k& p0 @* ]joints. Toes. Spinal divisions. PHI. PHI. PHI. My friends, each of you is a walking tribute to the + @. k0 j1 `/ Z" \
Divine Proportion."7 N S5 \! v& {" }
Even in the darkness, Langdon could see they were all astounded. He felt a familiar warmth inside.
! H# N) r H; v; E. G& x* PThis is why he taught. "My friends, as you can see, the chaos of the world has an underlying order. ( c$ j2 Z( v: K9 G& K' { X# w0 E
When the ancients discovered PHI, they were certain they had stumbled across God's building
( c1 o. @ d J2 S8 Q3 i6 L* r8 S1 q& [+ T C, T
block for the world, and they worshipped Nature because of that. And one can understand why. 3 {+ r1 } E9 `6 N) r
God's hand is evident in Nature, and even to this day there exist pagan, Mother Earth-revering
0 H) k% e( z; }5 l7 oreligions. Many of us celebrate nature the way the pagans did, and don't even know it. May Day is
6 i( d2 h9 c! f# Y" A" La perfect example, the celebration of spring... the earth coming back to life to produce her bounty.
9 |: U0 ]' p" H) y. ^6 H$ s+ GThe mysterious magic inherent in the Divine Proportion was written at the beginning of time. Man 3 g/ E, I: i; l& A7 o" B
is simply playing by Nature's rules, and because art is man's attempt to imitate the beauty of the 1 B" d: n3 i6 \4 Y% C, K
Creator's hand, you can imagine we might be seeing a lot of instances of the Divine Proportion in 1 a3 s8 N* A% M7 y$ |
art this semester."
# x- U) `, [4 P) m6 d z" [Over the next half hour, Langdon showed them slides of artwork by Michelangelo, Albrecht Dürer, " s% k: [0 W* `/ B/ t2 ?$ y
Da Vinci, and many others, demonstrating each artist's intentional and rigorous adherence to the : Q7 H0 q3 _+ H/ a: z+ H
Divine Proportion in the layout of his compositions. Langdon unveiled PHI in the architectural
# H7 k# z" O& @6 C+ @3 q; Kdimensions of the Greek Parthenon, the pyramids of Egypt, and even the United Nations Building ' {9 N; z9 w1 X! @3 \! {6 i- m
in New York. PHI appeared in the organizational structures of Mozart's sonatas, Beethoven's Fifth
, Y: f+ A; U5 A6 X- ZSymphony, as well as the works of Bartók, Debussy, and Schubert. The number PHI, Langdon told
$ g0 X- V9 N" U! J+ }- y ithem, was even used by Stradivarius to calculate the exact placement of the f-holes in the
; ^5 {: h& O4 Pconstruction of his famous violins.1 _5 |5 |1 k+ N8 n7 ~& X1 @
"In closing," Langdon said, walking to the chalkboard, "we return to symbols" He drew five & ^2 [5 i& N) [+ e6 q6 k! l
intersecting lines that formed a five-pointed star. "This symbol is one of the most powerful images 6 x# r( `' X: _- Y; v9 N6 P
you will see this term. Formally known as a pentagram—or pentacle, as the ancients called it—this
( ]) A# Q7 A2 K) A# ]: |symbol is considered both divine and magical by many cultures. Can anyone tell me why that
; ~7 c1 n+ [1 m) J9 y- |( ~might be?"
7 k5 B* e/ C& i* R* M( XStettner, the math major, raised his hand. "Because if you draw a pentagram, the lines
3 J% V$ M+ c6 O6 j* v- t* X- C. Uautomatically divide themselves into segments according to the Divine Proportion."
7 F H8 K0 `* ^6 [Langdon gave the kid a proud nod. "Nice job. Yes, the ratios of line segments in a pentacle all
) p8 g( d- o3 s. \! S. w( N1 Tequal PHI, making this symbol the ultimate expression of the Divine Proportion. For this reason, 5 `& Q, U' d1 L" p5 J/ F
the five-pointed star has always been the symbol for beauty and perfection associated with the
, D' T& u' K, b5 dgoddess and the sacred feminine."
1 H. e Q$ q- h3 `' a+ X! jThe girls in class beamed.! H. Y0 U7 |3 n; |+ H/ `6 s, E
"One note, folks. We've only touched on Da Vinci today, but we'll be seeing a lot more of him this
. h! A0 W, u5 T. Gsemester. Leonardo was a well-documented devotee of the ancient ways of the goddess.
( e# l8 O( w$ k# M+ R3 PTomorrow, I'll show you his fresco The Last Supper, which is one of the most astonishing tributes . ^4 Q6 a$ \5 f0 f B2 r
to the sacred feminine you will ever see."
$ `/ r1 [; `* b: L( S) k" g"You're kidding, right?" somebody said. "I thought The Last Supper was about Jesus!"5 v: y( `/ h% b) f% R" l/ U
Langdon winked. "There are symbols hidden in places you would never imagine."
) H3 O/ D5 c+ G$ p6 ?8 x+ K) Z& }$ \! M8 ~7 P
8 }2 p* \3 e% t8 D* G
"Come on," Sophie whispered. "What's wrong? We're almost there. Hurry!"
" w& `" I! w5 y6 B! g& X+ K: k- iLangdon glanced up, feeling himself return from faraway thoughts. He realized he was standing at
9 J* T& e" w/ s$ T6 Ga dead stop on the stairs, paralyzed by sudden revelation.
7 p, @& L d; I; j: S5 Z h, fO, Draconian devil! Oh, lame saint!/ v% i+ R4 u7 J9 U" {& X7 R
Sophie was looking back at him.
+ u: n) E6 E, uIt can't be that simple, Langdon thought.
& t* Z3 i9 N$ O wBut he knew of course that it was.
5 A5 D3 @) T6 k8 WThere in the bowels of the Louvre... with images of PHI and Da Vinci swirling through his mind, # Y1 o, X' I% A
Robert Langdon suddenly and unexpectedly deciphered Saunière's code.
& U& T0 i$ H ~( q9 B2 }"O, Draconian devil!" he said. "Oh, lame saint! It's the simplest kind of code!"
" W2 m6 l6 Y! g3 i" |) _
) _1 q; E4 o: L/ T! K% J7 w$ ESophie was stopped on the stairs below him, staring up in confusion. A code? She had been
. l4 s x" A& Tpondering the words all night and had not seen a code. Especially a simple one.1 H( ^& ]' m" w* q& I U
"You said it yourself." Langdon's voice reverberated with excitement. "Fibonacci numbers only
% s1 \6 m& o1 Ehave meaning in their proper order. Otherwise they're mathematical gibberish."; w: W* ]) r- m
Sophie had no idea what he was talking about. The Fibonacci numbers? She was certain they had / i, g ~0 {! x" [/ n
been intended as nothing more than a means to get the Cryptography Department involved tonight. ; R2 }) ?: f' e$ l/ _
They have another purpose? She plunged her hand into her pocket and pulled out the printout,
4 j- B. j& c) U H. mstudying her grandfather's message again.; H' i! B: @/ f X: K9 `
13-3-2-21-1-1-8-5
/ W0 j4 O+ a( {8 P; }3 @5 EO, Draconian devil!- |, F- x3 d& @& N" y* V
Oh, lame saint!
/ g. b8 ] i5 L, M4 M& H* Z* E 2 V2 `: q6 }# m* B/ o* P6 Y7 T6 L
What about the numbers?. b! i0 H2 Q) ~# O( O
"The scrambled Fibonacci sequence is a clue," Langdon said, taking the printout. "The numbers are
4 K# w% v9 _& ^9 M ga hint as to how to decipher the rest of the message. He wrote the sequence out of order to tell us to ( E0 [6 |" | t. V b' _
apply the same concept to the text. O, Draconian devil? Oh, lame saint? Those lines mean nothing.
+ a9 x0 T9 u a
7 S, F- ]7 `5 d/ l WThey are simply letters written out of order."
) X; z4 P7 Y% X) i# ?Sophie needed only an instant to process Langdon's implication, and it seemed laughably simple. $ k" a3 ?0 Y4 J% G" B8 m" L: W( W6 S) m
"You think this message is... une anagramme?" She stared at him. "Like a word jumble from a 5 ]2 X+ u1 y: a+ ~
newspaper?"1 S2 `; l: T: o
Langdon could see the skepticism on Sophie's face and certainly understood. Few people realized
2 S0 x. ]6 ]' T) h, vthat anagrams, despite being a trite modern amusement, had a rich history of sacred symbolism.
N+ H! k' q: v# M0 B! IThe mystical teachings of the Kabbala drew heavily on anagrams—rearranging the letters of
J9 L% ? n+ k% v, K+ rHebrew words to derive new meanings. French kings throughout the Renaissance were so
1 `& C. y, t2 G$ gconvinced that anagrams held magic power that they appointed royal anagrammatists to help them
) x. A; S n9 Z- ~7 ]$ fmake better decisions by analyzing words in important documents. The Romans actually referred
0 f; g! \2 s5 n6 U2 g% Ito the study of anagrams as ars magna—"the great art."
Y+ W ]9 t6 j0 H9 j- h4 K5 v _Langdon looked up at Sophie, locking eyes with her now. "Your grandfather's meaning was right " j( B# q2 ^* w3 ^
in front of us all along, and he left us more than enough clues to see it."4 P$ Z5 t3 T, ~( \1 J- b
Without another word, Langdon pulled a pen from his jacket pocket and rearranged the letters in 1 M0 U s( d8 ]$ e' Z; `" D m
each line." M# [# D# U" z
O, Draconian devil! Oh, lame saint!
) F% g( {+ h% ~( S" Z7 j Qwas a perfect anagram of...' g" U1 z& N- u
Leonardo da Vinci! The Mona Lisa!