## Sunday, May 03, 2015

### Mathematical Connections with Nature, Art, and Religion

Mathematical Connections with Nature, Art, and Religion

Jay Dolan
Professor Beyer
December 8, 2004

In the novel, The Da Vinci Code, Dan Brown discusses numbers such as Phi, 666, and the Fibonacci sequence. Brown briefly mentions each number in short passages of his novel; however, he still conveys each number’s connection with our every day lives. Recently, Brown’s novel has been subject to criticism regarding its blend of fact and fiction. He makes several bold statements about groups such as the Roman Catholic Church, Opus Dei, and the Priory of Sion which have caused some devout Christians to question their faith. Many people believe Brown has misled his readership in an effort to make more money. This paper looks into the accuracy of Brown’s statements regarding the numbers he mentions in his novel and how art, nature, and religion are associated with the numbers Phi, 666, and the Fibonacci sequence.
The number Phi, which is also known as the Magic Ratio, the Divine Ratio, and the Golden Mean, appears in chapter twenty of Brown’s novel. The numerical value of this number comes to approximately 1.618. The date this number was discovered is unknown. Many people believe it has been, “discovered and rediscovered throughout history, which explains why it goes under several names.”[i] In his novel, Brown states that the number is, “generally considered the most beautiful number in the universe.”[ii] Fortunately for Brown, this is a difficult statement to prove or disprove. Despite this fact, it is still worthwhile to look at its presence in nature, art, and architecture.
Phi has an undeniable presence in nature that is seen, “from the spirals of galaxies to the spiral of a Nautilus seashell.”[iii] Phi is essentially everywhere. Brown points out other examples of Phi’s presence in nature when he talks about the spirals of a sunflower’s seeds, which increase by the ratio 1.618. He also discusses how the ratio of male honey bees to female honey bees in a beehive is approximately 1.618. Finally he points out the presence of the Magic Ratio in our own bodies. He does this by describing how one will discover the number Phi if one divides the distance from shoulder to fingertips by the distance from the elbow to the fingertips. This not only works for that part of the body, but for other parts of the body as well. Another example is to measure the distance from head to toe and divide by the distance from the naval to the toe. The number Phi is even present in the most fundamental structures of our world. For example, each helix of a DNA molecule can be divided into a number that is approximately the value of the magic ratio. Brown fails to mention this example in his book. “(DNA) measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral.”[iv] Even though Brown only scratches the surface of Phi’s actual presence in nature, all of his examples are true statements regarding the proportion.
Brown also references Phi’s presence in art. He mentions works by Leonardo da Vinci such as the Vitruvian Man which is, “considered the most anatomically correct drawing of its day”(95) which holds true to the proportion of Phi. Leonardo’s painting The Last Supper also strictly adheres to the divine proportion, “from the dimensions of the table at which Christ and the disciples sat to the proportions of the walls and windows in the background.”[v] Another example of Phi’s presence in art is seen in the works of Phidias (500 B.C.-432 B.C.), a Greek sculptor who used the divine proportion in his sculptures for the Parthenon. Phidias served as part of the inspiration for the name Phi which was coined in the 1900’s by an American mathematician named Mark Barr.[vi]
Phi is also seen in the architecture of ancient and modern civilizations. For example, the Egyptians built pyramids that had sides which closely followed the number Phi. Also, the Greeks used the Divine proportion to construct their famous Parthenon, and Paris’s Notre Dame Cathedral can be divided into proportions of Phi as well.[vii] Even modern day architecture has elements of the Magic Ratio, including the United Nations Building in New York. Brown mentions almost all of these examples in his novel, which are found to be true when further researched. He omits the reference to Notre Dame.
Brown makes one more reference to the number Phi: “The ancients assumed the number PHI must have been preordained by the Creator of the universe.”(94) This seems like a bold statement to make regarding a simple number; however, facts show that the name “the divine proportion” directly stemmed from the idea that God had used Phi as the building block of the universe. The idea of Phi being considered this way is seen through its symbol. The symbol commonly used to represent the divine proportion is Φ, which is the Greek capital letter for PHI. This symbol is a combination of 0 (which is nothing) and I (which is unity/God). When nothing is split by unity, they create Phi, “the constant of creation.”[viii]
Brown’s second number, the Fibonacci sequence, plays an important role in the development of his story. During the last moments of his life, Sauniére scribbles the famous sequence on the floor of the Louvre in order to leave Sophie, his granddaughter, with enough clues to recover the Priory keystone. When Sophie makes Captain Fache aware of the code, Brown briefly describes the Fibonacci sequence as, “one of the most famous mathematical expressions in history.”(60) In the novel, the sequence is carefully laid out as:

1-1-2-3-5-8-13-21

Brown states that the Fibonacci sequence is, “a progression in which each term is equal to the sum of the two previous terms.”(61) He also says that, “Mathematician Leonardo Fibonacci created this succession of numbers in the thirteenth-century.”(61) All three of these statements are true. Leonardo Pisano Fibonacci was a real person who lived from 1170-1250 and he published the sequence in a book called Liber abaci in 1202.[ix]  Throughout the course of history, Fibonacci’s sequence has proven to be, “extremely fruitful, and [it] appears in many different areas of mathematics and science.”[x]
The Fibonacci sequence is closely related to the number Phi. The proportion Phi can actually be derived from the Fibonacci sequence by finding, “the ratio of successive pairs.”[xi] Consequently, this important sequence is just as evident in nature as the divine ratio. In fact, the series appears in flower patterns, shells, and other plants. The Fibonacci sequence is used every day to solve mathematical problems that deal with growth rates, as well as, “botany, biology, physics, music, and art.”[xii] Fibonacci had originally created the sequence in an effort to predict the growth rate of a rabbit population. Plants also exhibit the sequence through the number of petals they have. Finally, the branches of a plant grow in a succession identical to the Fibonacci sequence.[xiii]
The last number that Dan Brown references is the number 666. The number originated in the Babylonian civilization and pagan religion. The Babylonians based their religion on many Gods. There were 37 Gods in all, but one God that was above the rest, the sun God. Each of the 36 lesser Gods was given a number and the sum of all of those numbers was the number of the sun God. That number was 666, which came to be known as the number of the Supreme God. The Babylonians feared each of the Gods and feared that any one of them would strike them down at any time. In order to protect themselves, they made “amulets with a 6 x 6 matrix of the numbers 1 through 36.”[xiv] They wore these amulets around their necks throughout the day. Each number in a row added up to 111 and in turn each row added up to the supreme 666. Today, the number has become known as the sign of the devil. The Book of Revelation even mentions 666 as “the mark of the beast.”[xv] This originated when Christianity began to consume the Roman Empire. During this time, Babylonian traditions were carried over into the Church. This was so the, “followers of the Babylonian religion (would) convert to Christianity.”[xvi] Basically, Christianity took the three supreme Gods of the Babylonian religion and created God the Father, God the Son, and God the Holy Spirit. The movement of Babylonian practices into the Christian Church sparked the condemnation of Babylon in Revelation 17: 1-18 of the Bible.
Many people believe the number 666 only carries a negative connotation; however, Brown is able to show how this number is misunderstood. He also references the fact that the pyramid outside of the Louvre, “had been constructed of exactly 666 panes of glass.”(21) Even though Brown’s general reference to the number 666 is correct, this statement is completely false. The pyramid is actually constructed of “675 diamond-shape and 118 triangular panes”[xvii] of glass.
Even though Brown does not necessarily say anything false about the Fibonacci sequence, he makes a few mistakes with his facts about these numbers which are revealed in Dan Burstein’s The Secrets of the Code. In fact, Brown might be overstating the power of the Fibonacci sequence. During Langdon’s lecture to his students, he talks about how Phi (which also implies the Fibonacci sequence) serves as the “fundamental building block in nature.”(94) This is not a false statement, but Brown fails to mention the other important sequence in nature. “Lucas numbers, for instance, are generated using the same addition as the Fibonacci sequence, except the first two numbers are 1 and 3; so the sequence is 1, 3, 4, 7, 11, 18, 29, 47, 76, 123.”[xviii] The presence of Lucas numbers in nature refutes the argument that the Fibonacci sequence is the only building block of nature. This point is further supported by H. S. M. Coxeter in his book Introduction to Geometry: “We must face the fact that [the Fibonacci sequence] is really not a universal law but only a fascinating prevalent tendency.”[xix]
Brown also makes small mistakes in referencing the number Phi. First of all, he writes the word entirely in capital letters. In actuality, “mathematicians use ‘Phi’ to mean the divine proportion and ‘phi’ to mean it’s reciprocal.”[xx] Another mistake Brown makes occurs on page 94 when he says, “the number PHI was derived from the Fibonacci sequence.”(94) This is not true, because the number Phi existed long before Fibonacci discovered his famous sequence. Records of the number reach as far back as 300 B.C.[xxi]
In spite of Brown’s mistakes in referencing these numbers, the majority of his facts are valid. The numbers are all used correctly and he does not seem to falsify their qualities. His only big mistake he makes occurs when he says the pyramid is made up of 666 panes of glass. Brown obviously uses these numbers for a reason. The question is, why does he incorporate these numbers into his novel?
First, Brown may be using these numbers to make his theological ideas credible to the reader. This would not be unheard of, especially since he does the same thing in his novel Angels and Demons. In the novel, a young scientist asks Langdon whether or not he believes in God. After dodging the question, Langdon asks the woman what she thinks of religion. “Faith is universal… Some of us pray to Jesus, some of us go to Mecca; some of us study subatomic particles. In the end we are all just searching for truth, that which is greater than ourselves.”[xxii] Here, Brown is speaking through this character about the universal search for truth. The woman then goes on to say, “Science tell me God must exist. My mind tells me I will never understand God. And my heart tells me I am not meant to.”[xxiii]
Brown uses this same technique when he inserts the Divine ratio. He slightly overstates its universality in order to convince the readers that it is truly a fundamental part of our universe. In doing so, he suggests that the universe exists on a set of basic principals. By pointing out fundamental building blocks, one can support the idea of a God because it suggests a greater order to the universe. Kellmeyer supports this idea in his book Fact and Fiction in The Da Vinci Code. He says, “Despite the last sentence of the discussion, the number might be used to demonstrate divine order.”[xxiv]
Brown may also be incorporating the mathematical properties of Phi and the Fibonacci sequence in his novel for more than theological reasons. His entertaining and fast-paced thriller is considered very controversial because of his bold statements on The Roman Catholic Church, Opus Dei, and the Priory of Sion. Brown may be using these facts to set his reader up for more controversial ideas. By integrating factual information with controversial opinions of the same nature, Brown is able to convince his readership that everything he says is true, when in fact many of his ideas are a matter of opinion and speculation. This could serve as an effective strategy because his readers do not know what is true and what isn’t.
Through Brown’s use of fact, he is able to make his readership believe that the rest of his novel is true. Even though Brown declares that his book is a work of fiction, he still wants his readers to believe his ideas. The use of facts such as 666, Phi, and the Fibonacci sequence allows Brown to, “Help readers suspend belief and give Robert Langdon credibility.”[xxv] Essentially, Brown wants his readers to trust that what Langdon is saying is true and therefore accept everything else as truth.
It is clear that Brown intertwines fact with fiction in his novel. Say what you want about him, he incorporates his ideas into a successful novel. Many people think he is a liar and a manipulative human being, but the truth is that Brown wanted to create an entertaining story, communicate his theological ideas to others, and make money.
Brown is neither a liar, nor a fool. He is a man who discovered a way to write what appeared to be a credible, factual novel, but with his own creative license. Brown essentially was able to take areas of uncertainty and make them into his own facts. By placing the small phrase, “a novel,” on the cover of his book, he can basically say whatever he wants. Brown should not be held accountable for the scientific truth of his writing. Readers should filter out what is fact and what is fiction. It is not Brown’s fault if someone reads his novel and believes certain ideas are true. He may even be happy if they do. While this may seem like a deceptive form of literature, Dan Brown has not done anything illegal, or immoral.
Intertwining fact and fiction can be an efficient way of persuading people to believe in certain ideas. In his novel, Brown is able to embrace this idea and use it to his benefit. Dan Brown is not a criminal, at worst he is a successful con-artist. He is a man who can take an idea and sell it to the public. His book has sold millions of copies and sparked discussions throughout the world. Even if we do not agree with his practices, it is safe to say that even by analyzing and writing about his novel, we have fallen into the pitfall that he laid down from the beginning. We have all become trapped in his mosaic of fact and fiction. There are already dozen of books written on his novel, and many of them dissect the book into every possible detail. Dan Brown has trapped us. He has made us become obsessed with his ideas and study them for hours at a time. That is what it takes to determine what is fact and fiction, true and untrue, in Dan Brown’s novel.

Works Cited

"A History of the Golden Number". The Evolution of Truth. 10/18/2004 .

"A Quick Overview of the History of the Number 666". Pacific Press Publishing. 10/18/2004 .

Brown, Dan. Angels and Demons. Pockets Books, 2000.

Brown, Dan. The Da Vinci Code. Doubleday, 2003.

Burstein, Dan. Secrets of the Code. Squibnocket Partners LLC, 2004.

Eble, Betsy Friedman. Depth and Details: A Reader's guide to Dan Brown's The Da Vinci Code . Self-published, 2004.

"Fibonacci Facts". 10/27/2004 .

Fibonacci Numbers in Nature". World-Mysteries. 10/27/04 .

Kellmeyer, Steve. Fact and Fiction in the Da Vinci Code. Bridegroom Press, 2004.

"Leonardo Pisano Fibonacci". University of St. Andrew's, Scotland. 10/27/2004 .

"Revelation".10/18/2004 .

"The Divine Proportion". Summum. 10/18/2004 .

[i] “A History of the Golden Number”, http://goldennumber.net/classic/history.htm , October 18, 2004
[ii] Brown, Dan. The Da Vinci Code, Doubleday, 2003. (93)
[iii] “The Divine Proportion”, http://www.summum.us/philosophy/phi.shtml , October 18, 2004.
[iv] “A History of the Golden Number”, http://goldennumber.net/classic/history.htm , October 18, 2004
[v] “A History of the Golden Number”, http://goldennumber.net/classic/history.htm , October 18, 2004
[vi] “A History of the Golden Number”, http://goldennumber.net/classic/history.htm , October 18, 2004
[vii] Ibid
[viii]  “A History of the Golden Number”, http://goldennumber.net/classic/theology.htm , October 18, 2004
[ix] “Leonardo Pisano Fibonacci”, http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Fibonacci.html, October 27, 2004.
[x] Ibid
[xi] “Fibonacci Numbers in Nature” , http://www.world-mysteries.com/sci_17.htm , October 27, 2004.
[xii] “Fibonacci Facts” , http://www.cs.rit.edu/~pga/Fibo/fact_sheet.html , October 27, 2004.
[xiii] Ibid.
[xiv]“A Quick Overview of the History of the Number 666”, http://www.666man.net/666ReligionHistoryOverview.html , October 18, 2004
[xvi] Ibid
[xvii] Eble, Betsy Friedman, Depth and Details: A reader’s guide to Dan Brown’s The Da Vinci Code, Self Published by Betsy Eble, 2004.
[xviii] Burstein, Dan. Secrets of the Code, Squibnocket Partners LLC., 2004. (340)
[xix] Ibid (340)
[xx] Ibid (353)
[xxi] Burstein, Dan. Secrets of the Code, Squibnocket Partners LLC., 2004. (353)
[xxii] Brown, Dan. Angels and Demons, Pocket Books, 2000 (110)
[xxiii] Ibid
[xxiv] Kellmeyer, Steve. Fact and Fiction in the Da Vinci Code, Bridegroom Press 2004. (39)
[xxv] Ibid