The Da Vinci Code: Its anagrams, coded messages and other references to mathematics

1
The Da Vinci CodeIts anagrams coded messages
and other references to mathematics

• Library Literature Lecture Series
• Gary Britton
• Emeritus Professor of Mathematics
• UW-Washington County
• April 20 2006

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Example of commercial products inspired by the
novel
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More products related to The Da Vinci Code

• Cryptex security boxes at http//www.cryptex.org/h
  _gallery.htm.
• The Da Vinci Quest board game The Movie Game
  Inc. www.triviainatrunk.com.
• Cracking the Da Vinci Code Day Calendar 2006
  Barnes Nobel 2005. (material from Cracking
  the Da Vinci Code by Simon Cox. See excerpts on
  the followingand severals at the end
  of the presentation.)

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Samples from Cracking the Da Vinci Code Day
Calendar 2006

• The Golden Rectangle is one in which the sides
  are in proportion of the Golden Ratio in other
  words the longer side is 1.618 times longer than
  the shorter side. Aesthetically pleasing it is
  found throughout world art and culture. Leonardo
  da Vincis drawing of the Vitruvian Man has the
  outlines of a Golden Rectangle based on the head
  one on the torso and another over the legs.
  April 14

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Todays entry from Cracking the Da Vinci Code Day
Calendar 2006

• The mortally wounded Louvre curator Jacques
  Sauniere scribbles the puzzling reference on the
  floor of the Grand Gallery to a Draconian
  devil. This briefly brings to Langdons mind
  the Athenian legislator Draco remembered for his
  harsh law code of 621 BCE which imposed the
  death penalty for relatively trivial crimes. In
  this contest the word draconian describes
  harsh or repressive legal measures. April 20

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Another example from the commercial marketplace.

• A Borders Books web site search on The Da Vinci
  Code yielded
• 86 responses on 12/27/05
• and 103 items including the following on
  4/18/06.
• 29.The Diet Code Revolutionary Weight Loss
  Secrets from Da Vinci and the Golden Ratio
  Lanzalotta Stephen Compact Disc April 2006
  In PrintList Price 24.98

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Key characters

• Robert Langdon Professor of Religious Symbology
  Harvard University
• Sophie Neveu Cryptographer Direction Centrale
  Police Judiciare (DCPJ) (approximately the
  French equivalent of the FBI)
• Jacques Sauniere Curator The Louvre Museum
  (and Sophie Neveus grandfather)
• Andre Vernet president of the Paris branch of
  the Depository Bank of Zurich
• Sir Leigh Teabing British religious historian
  living near Versailles France

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Overview of tonights talk

• Introductory remarks and key characters
• Clues from the opening murder scene
• Fibonacci sequence
• Golden ratio
• Anagram messages
• Passwords and the Fundamental Principle of
  Counting
• Mirror messages
• Cryptology and coded messages
• Websites and references

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Clues found at the opening murder scene of the
novel

• Jacques Sauniere had removed his clothes placed
  his body like a snow angel drawn circular arcs
  with his arms and traced in blood a pentacle
  (see next) centered on his navel.
• The following message was written on the floor
  beside the body.
• 13-3-2-21-1-1-8-5O Draconian Devil!Oh lame
  saint!

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• To try to determine if this message has any coded
  meaning first consider just the numbers.
• 13-3-2-21-1-1-8-5
• As a start lets arrange them numerically.

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2
21
1
1
8
5
13
3
13
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of female ancestors in each generation for a
male sweat bee.

• FMFFMFMFFMFFMFMFFMFMF 13
• F MF F MF MF F MF F M 8
• F M F F M F M F 5
• F M F F M 3
• F M F 2
• F M 1
• F 1
• M

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of female ancestors in each generation for a
female sweat bee.

• FMFFMFMFFMFFMFMFFMFMF 13
• F MF F MF MF F MF F M 8
• F M F F M F M F 5
• F M F F M 3
• F M F 2
• F M 1
• F

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Ratio of female to male ancestors in each
generation for sweat bees
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Fibonacci sequence appears in other places.

• Construct a spiral based on inscribing
  quarter-circle arcs in squares of size
  11235813
• This spiral appears in the shell of the chambered
  nautilus (mollusk of the So. Pacific Ocean)
  placement of leaves on some plants the hexagonal
  scales of a pineapple and the seeds in the head
  of a sunflower.

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Seeds in the head of a sunflower
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Divine Proportion

• Divide a line so the ratio of the line to the
  longer segment equals the ratio of the longer
  segment to the shorter. In the line above C
  divides AB in such segments. The number is
  called the Golden Ratio and is 1.618033989. or
  approximately 1.62 as in the diagram.

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F

• The divine proportion is denoted by the Greek
  letter phi. (though Dan Brown chooses not to use
  the symbol for any of his frequent references to
  the number)
• The exact value is (1v5)/2.
• Also called the golden ratio or golden section.
• The ratio of successive numbers in the Fibonacci
  sequence approaches F.

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F (continued)

• Dan Brown has Langdon recall his lecture about
  PHI for his Symbolism in Art class pp. 93-97
  where he references many appearances of the
  golden ratio in art architecture music and in
  the pentagram. (Recall the pentagram that
  Sauniere traced on his body. See next.)
• In Technical Analysis of stock and commodity
  prices F -1 and (F-1)2 are used to determine
  potential support resistance and price levels.
  Ross p. 63

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Rectangles with (almost) golden ratio dimensions.
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13-3-2-21-1-1-8-51-1-2-3-5-8-13-21O Draconian
Devil!Oh lame saint!

• Assuming the text lines are also anagrams lets
  try to rearrange the letters into a meaningful
  message for Langdon and Neveu one line at a time.

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O
D
R
A
C
O
N
I
A
N
D
E
V
I
L
When decrypting a message we usually delete all
spaces and punctuation.
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O
D
R
A
C
O
N
I
A
N
D
E
V
I
L
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Partially decoded message on museum floor

• 1-1-2-3-5-8-13-21
• LEONARDO DA VINCI
• OH LAME SAINT!

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O
H
L
A
M
E
S
A
I
N
T
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Complete decoded message from Jacques Sauniere.

• 1-1-2-3-5-8-13-21
• LEONARDO DA VINCI
• THE MONA LISA

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SO DARK THE CON OF MAN

• Message written by Sauniere on the glass of the
  Mona Lisa.

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S
O
D
A
R
K
T
H
E
C
N
O
F
M
A
N
O
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Decoded message written on the glass of the Mona
Lisa.

• Madonna of the Rocks

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Madonna of the Rocks leads to

• Gold electronic key with 24 Rue Haxo written on
  it.
• Escape from the Louvre.
• Wild chase through Paris.
• Paris branch of Depository Bank of Zurich. (see
  web site on next)
• Saunieres deposit box.

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Fundamental Principle of Counting

• Vernet says every key is electronically paired
  with a ten-digit account number that functions as
  a password. (p. 184)
• Sophie calculates the cryptographic odds to be
  ten billion possible choices.
• The Fundamental Principle of Counting is a
  procedure for counting total possible outcomes in
  multistage processes. The number of ways that
  the entire process can be done is the product of
  the number of ways each stage can be done.
• Each digit of the password has 10 possibilities
  so the password has (10)(10)(10)(10)1010
  possibilities.

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Predicting the password

• Notice that Saunieres message
  13-3-2-21-1-1-8-5 has 10 digits.
• Sophie enters 1332211185 and realizes she only
  has one chance to get it right.
• She says Its too random. he would have
  chosen a number that he could easily remember
  something that appeared random but was not.
• So she enters 1123581321.

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Success! The password worked.

• Rosewood box obtained from the vault at
  Depository Bank of Zurich.
• Cryptex is found inside the box.
• Langdon and Neveu escape bank and go to Sir Leigh
  Teabings estate.
• Langdon discovers a coded message written
  underneath an inlaid rose in the top of the box.
  It leads to opening the cryptex.

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Description of cryptex

• A cylinder approximately the dimensions of a
  tennis ball can.
• Five lettered dials that rotate like a bicycle
  lock. (though on p. 198 it mentions 6)
• The inside is hollow to contain a message.
• It opens at the end when all the dials are
  properly set.
• 265 11881376 possible settings.
• May look similar to the following picture.

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Coded verse written in the lid of the rosewood
box
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Remembering her Grandfathers teachings Sophie
determines the code.
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• an ancient word of wisdom frees this scroll
• and helps us keep her scatterd family whole
• a headstone praised by templars is the key
• and atbash will reveal the truth to thee
• Sauniere had written this iambic pentameter
  verse using a mirrored script the same as
  Leonardo Da Vinci used in his notebook now known
  as Codex Leicester and owned by Bill Gates.

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Cipher disk (see model)

• Two concentric disks with the alphabet on one
  disk and symbols or a mixed reversed or standard
  alphabet on the other.
• Invented in Italy before 1470.
• First large scale use in the U.S. during Civil
  War.
• During and for several years after World War I
  the U.S. Army issued the disks to units that
  needed a cipher that could be carried and used
  easily.
• Leave the setting on the same predetermined
  letter through the message or agree in advance to
  alter it after every letter of the message or
  daily or weekly.

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Caesar-cipher

• Invented by Julius Caesar.
• Shifts the alphabet forward three letters.
  (variations of this use a shift of 1 or 2 letters
  forward or backward).
• You can decipher the message by just writing the
  alphabet in columns down from the message. (add
  as many letters in each column as the maximum
  shift to be considered for the Caesar-cipher.)

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Caesar Box code writing

• This is a transposition cipher invented by Julius
  Caesar.
• Consider the encrypted message wiouannnsgcthtoy
• Notice there are 1642 letters so write them in
  the format of a 4 X 4 box.
• wiou
• annn
• sgct
• htoy

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Caesar Box (continued)

• Now read the box column by column.
• W I O U
• A N N N
• S G C T
• H T O Y
• So the deciphered message is
• Washington County.

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The Atbash cipher

• Dates to 500 BC
• A monoalphabetic substitution cipher (i.e. each
  plain letter is replaced by a single cipher
  letter from the same alphabet). 
• Rotational substitution scheme the first for the
  last second for next to last etc.
• Based on the 22 letter Hebrew alphabet.

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Clues from the verse

• Ancient word of wisdom frees the scroll
• Headstone praised by Templars
• Atbash will reveal the truth
• Langdon finally realizes the stone head is
  that of Baphomet so apply the Atbash cipher to
  Baphomet.

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Baphomet and Hebrew alphabet

• Vowel sounds not written in Hebrew spelling.
• With vowels in lower case and with Hebrew letters
  it becomes BaPVoMeTh which has five letters as
  desired.
• Using the cipher table we get Sh-V-P-Y-A.
• Sh can be pronounced as S and P as F.
• SVFYA becomes Sofya or Sophia when sounded
  out.
• Sophia means wisdom in Greek.
• But in ancient Greek is spelled sofia.

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Contents of the cryptex

• Inside the cryptex is a smaller cryptex which
  also has five dials that need to be set using a
  five letter code. This smaller cryptex is
  wrapped inside a protective lambskin vellum with
  another iambic pentameter verse written on it.
  The verse in English read
• In London lies a knight a Pope interred.
• His labors fruit a Holy wrath incurred.
• You seek the orb that ought be on his tomb.
• It speaks of Rosy flesh and seeded womb.

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Puzzles for the audience.

• What is the five letter word that is needed to
  open the second cryptex
• What character in the novel has a name that is a
  combination of the name of one of the plaintiffs
  in the recent lawsuit against novelist Dan Brown
  and an anagram of the other plaintiff
• What characters name is an anagram for the
  (possible) biblical reference Oh! Supine Eve

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Web sites related to Dan Brown and The Da Vinci
Code.

• www.danbrown.com is the authors own web site.
  A must read for those interested in pursuing some
  of the background on the novel and related
  information. Click on Common Questions to
  read Dan Browns own thoughts on some of the
  questions raised by and about the novel. You
  can even sign up for a Dan Brown newsletter if
  you explore the site deep enough.
• www.johnlangdon.net is the web site of John
  Langdon close friend of Dan Browns father
  creator of the ambigrams in Angels Demons and
  possibly the inspiration for the name Robert
  Langdon in The Da Vinci Code.

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Web sites (continued)

• www.symbols.com is an excellent site for
  studying symbols mentioned in The Da Vinci Code.
• www-groups.dcs.st-and.ac.uk/history/Mathematician
  s/Fibonacci.html and www.mcs.surrey.ac.uk/Persona
  l/R.Knott/Fibonacci/fib.html are good web sites
  for the Fibonacci sequence.

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Web sites (continued)

• http//math.cofc.edu/kasman/mathfict/search.phpgo
  yestopicsccorderbytitle gives annotated
  references of where cryptography appears in
  fiction. It is part of a much larger site
  dealing with Mathematical Fiction.
• http//math.cofc.edu/kasman/MATHFICT/mfview.phpca
  llnumbermf371 is part of the Mathematical
  Fiction site and deals specifically with The Da
  Vinci Code. (It is not very complementary of the
  mathematics in the book but includes a lot of
  interesting opinions submitted to the site.)

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Web sites (continued)

• www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fi
  bInArt.html provides good information and
  additional links about PHI the Golden Ratio.
• www.murky.org/cryptography/index.shtml contains
  a primer on cryptology and ciphers.
• www.wordsmith.org/anagram/advanced.html has an
  anagram builder.
• www.anagramgenius.com has software for purchase
  or a free trial basis that creates anagrams.
• www.wordles.com/getmycruypto.asp includes a
  cryptogram builder.

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Selected entries from Cracking the Da Vinci Code
Day Calendar 2006

• Saunieres mirror-image poem on the rosewood box
  provides the key to its own meaning Atbash will
  reveal the truth to thee. The Atbash Cipher
  which dates from around 500 BCE uses the letters
  of the Hebrew alphabet in a simple substitution
  system each letter is replaced by another an
  equal distance from the opposite end of the
  alphabet i.e. the first letter for the last the
  second for the second to last and so on.
  January 3
• The many meanings of the pentagram are at the
  heart of The Da Vinci Code. In Christian
  tradition the pentagram was once used to
  represent the five wounds or stigmata of
  Christ. To the Pythagoreans the five points
  represented the five classical elements fire
  earth air water and idea or divine thing. The
  Pythagoreans also saw within the pentagram the
  mathematical perfection of the Golden Ration of
  1.618. January 28

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• Leonardos drawing Vitruvian Man was
  originally an illustration for a book on the
  works of the architect Vitruvius. It was
  accompanied by a translation of Vitruviuss
  theory about the measurements of the human body
  that 4 fingers make 1 palm and 4 palms make 1
  foot 6 palms make 1 cubit 4 cubits make a mans
  height and so on. February 6
• The strange properties of the Golden Ratio -
  which occurs in the Fibonacci sequence meant
  historically that it was seen as divine in its
  composition and infinite in its meaning. The
  ancient Greeks believed that understanding the
  Golden Ratio would help them get closer to God
  God is in the number. Many things in the
  natural and man-made worlds conform to its
  proportions from the human face to widescreen
  televisions. February 25

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• Langdon finds a message of male and female
  harmony in Leonardo Da Vincis Vitruvian Man his
  drawing of a spreadeagled nude male contained
  within a circle. This is unlikely. The
  composition is based wholly on Vitruviuss
  dimensions of the human body the emphasis being
  on rationalization of the geometry by means of
  small whole numbers to build the composition.
  March 8
• On this date in 1727 Sir Isaac Newton died in
  what is now the London Borough of Kensington and
  Chelsea. He was buried in Westminster Abbey the
  first scientist to be accorded this honor. His
  study and understanding of light his invention
  of the reflecting telescope and his revelation
  in Principia of the mathematical ordering of the
  universe are all represented on his monument.
  March 20

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• The Golden Rectangle is one in which the sides
  are in proportion of the Golden Ratio in other
  words the longer side is 1.618 times longer than
  the shorter side. Aesthetically pleasing it is
  found throughout world art and culture. Leonardo
  da Vincis drawing of the Vitruvian Man has the
  outlines of a Golden Rectangle based on the head
  one on the torso and another over the legs.
  April 14
• The mortally wounded Louvre curator Jacques
  Sauniere scribbles the puzzling reference on the
  floor of the Grand Gallery to a Draconian
  devil. This briefly brings to Langdons mind
  the Athenian legislator Draco remembered for his
  harsh law code of 621 BCE which imposed the
  death penalty for relatively trivial crimes. In
  this contest the word draconian describes
  harsh or repressive legal measures. April 20

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• The flame-haired thirty-two-year-old Agent Sophie
  Neveu studied cryptography at the University of
  Londons royal Holloway College on the citys
  western outskirts. Cryptography the science and
  study of analyzing writing or deciphering codes
  and ciphers forms part of a relatively new
  Masters degree in Information Security of which
  Royal Holloways was the first course of its kind
  in the world and is reputed to be the finest.
  April 21
• Langdons experience of epigraphical ciphers by
  the English writer philosopher and scientist
  Francis Bacon (1561-1626) helps him crack
  Saunieres code. In Book VI of his Proficience
  and Advancement of Learning Divine and Humane
  Bacon expressed his preference for ciphers whose
  vertues include that they bee without
  suspition in other words for codes that do
  not appear to be enciphered messages. May 1

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• Leonardos mirror script featured in Saunieres
  cryptex riddle may have been a code or merely
  an idiosyncratic left-handers approach to
  writing. Either way he would not have wanted to
  broadcast his most mind-blowingly prescient
  observation that the driving creative force is
  not God but Nature for which necessity is the
  mistress and teacher. Some three hundred years
  later Darwins theory of evolution was still
  considered heresy. May 11
• Sophie and Robert Langdon puzzle over Sir Isaac
  Newtons tomb in Westminster Abbey for the
  solution to the final clue. The monument was
  completed in 1731 by Michael Rysbrack to the
  design of William Kent. Mathematical and optical
  instruments and some of his most influential
  books including the Principia surround the
  reclining figure of Newton. On top of the globe
  sits the figure of Astronomy. John Maynard
  Keynes said of Newton after his death He
  regarded the universe as a cryptogram set by the
  Almighty. June 2

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• The Da Vinci Code introduces to readers many
  complex words from the field of code-breaking
  pictogram codex symbology iconology cryptex
  and polyalphabetic substitution cipher to name
  but a few. Not all are inventions or adaptations
  by Dan Brown. June 25
• Jacques Saunieres use of mirror writing in the
  first riddle pays homage to Leonardo da Vinci
  whose virtually illegible scrawl travels from
  right to left across the pages of his numerous
  private notebooks. In these his observations
  accompanied by sketches and drawings touch on
  science philosophy art architecture
  engineering astronomy and anatomy. July 6

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• Langdon recalls his bewildered first impression
  of the Codex Leicester a compilation of
  loose-leaf notes written in Leonardos
  mirror-image version of Renaissance Italian
  between 1506 and 1510. It contains his
  observations on subjects ranging from astronomy
  to the properties of rocks water fossils and
  air. It is now owned by Bill Gates co-founder
  of Microsoft and worlds richest man and is on
  display at the Seattle Art Museum. July 10
• The downfall of the Knights Templar was partly
  brought about by charges of worshiping the
  mysterious idol Baphomet whose name is the key
  to opening the first cryptex in Dan Browns
  novel. By converting the name Baphomet into its
  Hebrew spelling (B PV M Th) and then applying
  the Atbash Cipher to these letters Sir Leigh
  Teabing reveals the word sophia the Greek word
  for wisdom. August 10

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• Sauniere arranged his dying body into the image
  of Leonardos iconic drawing Vitruvian Man.
  Vitruvius was a Roman engineer writer and
  architect of the late first-century BCE and early
  first century CE. His one extant book De
  Architectura contains ten huge encyclopedic
  chapters on human proportions. His rediscovery
  in the Renaissance fueled the growth of
  classicism. Vitruvian Man is Sophie Neveus
  favorite Leonardo work. September 7
• Knowledge of the Atbash Cipher enables Sir Leigh
  to open Saunieres first cryptex. The name
  Atbash comes from the first two letters of the
  Hebrew alphabet (aleph and beth a and b in
  English) and their equivalents in cipher (tac and
  shin for t and s). Hebrew scribes translating
  the books of the Old Testament applied the cipher
  to place names like Sheshach which biblical
  scholars later revealed as Babel. October 10

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• Jacques Saunieres scrambled Fibonacci sequence
  provides the ten-digit PIN for the Priory
  keystone at the Depository Bank of Zurich as
  well as an opportunity for some interesting
  musings on phi the Golden Ratio. Leonardo
  Fibonacci (c.1170-c.1250) was born in Pisa
  Italy and educated in North Africa. Returning
  to Pisa around 1200 his mathematical genius
  earned him a place at the court of the Holy Roman
  Emperor Frederick II. October 18
• Sir Leigh Teabing was not the first scholar to
  apply the Atbash Cipher to the word Baphomet to
  reveal sophia. This hidden meaning was in fact
  first brought to light by the Dead Sea Scrolls
  expert Dr. Hugh J. Schonfield author of The
  Passover Plot who felt that the Knights Templar
  must have known about the cipher through their
  dealings in the Holy Land. October 29

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• The device used to protect sensitive information
  in Dan Browns novel is called a cryptex said to
  have been constructed from Leonardos blueprint
  designs. Unfortunately this isnt true. The
  cryptex is Dan Browns invention and a flawed
  one at that the vinegar stored inside would not
  be acidic enough to destroy papyrus. November
  25
• Arguably the father of modern physics Isaac
  Newton was born on this date in 1642 (by the
  Julian calendar). His Principia described
  universal gravitation the laws of motion and
  formed the bedrock of classical mechanics. In
  The Da Vinci Code the line from the second
  cryptex In London lies a knight a Pope
  interred leads Robert Langdon and Sophie Neveu
  to Newtons tomb in Westminster Abbey London.
  December 25

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Bibliography

• Brown Dan The Da Vinci Code Doubleday 2003.
• Brown Dan The Da Vinci Code Special
  Illustrated Edition Doubleday 2004.
• Burnstein Dan Editor Secrets of the Code CDS
  Books 2004.
• Lewand Robert Edward Cryptological Mathematics
  The Mathematical Association of America 2000.
• National Security Agency Codes Ciphers and
  Puzzles Activity Book.
• Ross Debra Anne Master Math Geometry Thomson
  2005.
• Sharma-Jensen Geeta et.al. Milwaukee Journal
  Sentinel April 5 2006 pp. 1E 8E.

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End ofs for presentation