The Fibonacci Series, Phi, Shapes, and Numbers: Sacred Geometry in Nature and Culture

For eons, human beings have felt that certain numbers, ratios, and shapes have sacred significance. For instance, the number ‘7’ has had great significance in various aspects of many cultures, geometric shapes have been associated with numbers, and the Fibonacci series and Golden Ratio are still instrumental in everything from Art to Music.

Sacred Meanings in Geometric Numbers and Shapes

Symbolic and sacred meanings are also ascribed to certain geometric
numbers, shapes, and geometric ratios or proportions. Through the ages, especially in the ancient world, some numbers had symbolic meaning attached, aside from their ordinary use for counting or calculating. In geometry, figures such as triangles, squares, polygons, hexagons, and so forth are all related to numbers. Triangles, for example, relate to three angles, squares to four, and so on.
As an example of attaching sacred meanings to geometric numbers, the number ‘seven’ occurs consistently in diverse cultures around the world. And more, the religious and mythologies of the world are filled with sevens. Consider some of these:

Pyramids of Giza: Image by Darren Krape

• The shape of the pyramids of Egypt produces the number seven by combining the three-sided triangle and four-sided square.
• In music, the seven musical notes in a scale repeat at the octave.
• There are seven terraces of purgatory in the Roman Catholic beliefs.
• The Christian Church recognizes the seven virtues and seven deadly sins.
• There were seven steps taken by Buddha at his birth.
• There are seven heavens and seven earths in Islamic tradition.
• There are seven worlds in the Hindu universe.
• The seven-branched Jewish menorah is the oldest symbol in Judaism.

The ancient Greek philosopher Pythagoras believed that integers represented fundamental meanings. He regarded seven as the “vehicle” of life. To him, the number seven signified the union of spirit and matter – the union of three (the triple nature of the spirit) combined with the four elements of matter (earth, air, fire, and water).
Seven was also associated with growth, whereby a phenomenon tends to be completed in seven stages, such as the “seven stages of man” expressed by Shakespeare in  As You Like It, or the biblical Creation by God in seven days. According to some beliefs, the human body needs seven energy vortices known as chakras to be open for spiritual growth; that is, one has to move focus from the three lower (physical) chakras to the four higher (spiritual) centers.

The Fibonacci Sequence is present in the nautilus shell. Image by jitze

How then is the Fibonacci sequence related to Sacred Geometry? The Fibonacci sequence is a series of numbers in which each number is the sum of the previous two. It starts with 0 and 1,which equals 1. Then 1 plus 2 equals 3, 2 plus 3 equals 5, and so on. Why are these numbers significant? Simply, they are nature’s numbering system and they give rise to the mystical Phi, what is referred to as the “golden section” or “golden ratio.” It should be noted that the ratio of successive pairs from the Fibonacci series tends toward Phi or 1.618 and out of this ratio comes the golden rectangle and the spiral shape, which is the most widespread shape in the universe.
The Fibonacci numbers are represented practically everywhere. In the petals on a flower, or the arrangement of leaves along a stem, you will find this sequence of numbers. The petals on most flowers display one of the Fibonacci numbers. The numbers also appear in certain parts of sea shell formations. Parts of the human body also reveal these ratios, including the five fingers, and a thumb on each hand. Fibonacci also can be seen in a piano that produces harmony through a beautiful music. A piano has one keyboard with five black keys (sharps and flats) arranged in groups of two and three, and eight white keys (whole tones) for the 13 chromatic musical octaves.
The Phi or 1.618 was described in the past as a divine number because it signifies beauty and harmony. Egyptian architects made use of Phi relationships in the construction of temples and the Great Pyramid, and so did the Greeks in their Parthenon in Athens, and the Europeans, for their Gothic cathedrals.

The Sacred Geometry

Simply described, the Sacred Geometry arises out of the set of numbers from the Fibonacci series or the “golden ratio.”  Through the years since ancient times, it has been significantly used in the planning and construction of religious structures (churches, temples, mosques, tabernacles, altars and monuments), as well as sacred spaces (like holy wells and sacred groves), and the creation of religious art.
Consciously or not, humans seem to be genetically programmed to respond to these sacred numbers, ratios, and shapes. Thanks to Italian mathematician Leonardo Fibonacci for introducing his famous Fibonacci sequence, its associated mystical ratio, the Phi, and paving the way for the shapes that greatly defined the world’s magnificent structures and amazing wonders.

The Fibonacci Sequence appears in both art and nature. Image by labcstm

Fibonacci numbers, ratios and shapes have been used to explain creation, growth and harmony – from a number of petals on a flower and grandiose architecture, to a spiraling galaxy. And to music lovers, it’s one beautiful harmony of musical scale that pleases the ear and ultimately the spirit.  A sacred geometry!

Sources:

Bradley, P.  Great Mysteries. New Holland (2010).

Calter, P. Polygons, Tilings, & Sacred Geometry. Dartmouth. Accessed September 22, 2011.

Sacred Geometry. Spiraloflight. Accessed  September 22, 2011.

George Cadbury Chocolates

Cadbury chocolates, anyone?

Any chocaholic will easily recognise the name "Cadbury." It doesn't matter whether your favourite chokkie is Lindt or Belgian or any other confectionary. Perhaps Vienna's Mozartkugeln? A chocolate is a chocolate is a chocolate (with apology to Gertrude Stein's "a rose is a rose is a rose... by any other name.)

George Cadbury, the founder of famous chocolate manufacturing company, George Cadbury, was born on September 19, 1839. He was the third son of a Quaker, John Cadbury, who pioneered Cadbury's cocoa and chocolates.

Anton Rubinstein Romance in E-flat Major, Op. 44, No. 1

Classical Music / Anton Rubinstein Music

Anton Rubinstein "Romance in E-Flat Major, Op. 44, No. 1" 


Enjoy this lovely piece of music "Romance in E-flat major" by Anton Rubinstein.  Isaac Stern: violinist, with Columbia Symphony Orchestra, conducted by Frank Brieff, 1972. Arranged by Arthur Harris.



This heart-warming music is popularised by Frank Sinatra, with a song of the same name, "If You Are But a Dream," written in 1942 by Moe Jaffe, Jack Fulton and Nat Bonx, based on Anton Rubinstein's "Romance in E flat, Op. 44, No. 1." It was recorded by Frank Sinatra, for Columbia Records on November 14, 1944 in New York, arranged and conducted by Axel Stordahl. In 1945 it was included in the Academy Award-winning short film, The House I Live In, which featured Frank Sinatra. The song can be found on the Columbia CD box set, The Best of the Columbia Years, 1943-1952 and The Columbia Years 1943 -- 1952: The Complete Recordings: 12 CD Box Set.  Enjoy this all-time favourite piece, both the music and the song. 

Andreas Vesalius and De Humani Corporis Fabrica

Andreas Vesalius was a Belgian physician, anatomist and teacher. He is the founder of modern human anatomy, and is famous for his textbook Fabrica, considered the greatest medical book in his time. The actual name of the book is De humani corporis fabrica (On the Fabric of the Human Body), written in 1543.


In the early 16^th century, before Vesalius came into the medical scene, knowledge of human anatomy was based essentially on guesswork, and surgery was something unheard of. Medical students learned human anatomy not by studying bodies and dissecting them, but by reading the works of the Roman physician Galen (AD129-c. 216), considered a great authority at that time. The Greek philosopher Aristotle also studied anatomy closely, and, along with Leonardo da Vinci, was another forerunner of Vesalius.

Vesalius Challenges the Human Anatomy Dissection Process

One of the problems before Vesalius was the taboo on dissecting human bodies. A 14th century Bolognese doctor called Mondino DeLuzzi was one of the first to carry out a dissection. With his work, Vesalius broke two taboos.

• First, Vesalius challenged the more than one thousand year old authority of Galen.
• Second, Vesalius actually dissected human bodies, looking at anatomy closely, and encouraged his students to do the same.

The anatomical knowledge Vesalius gained was put into his great  book Fabrica, which laid the foundations of modern medicine.

Early Life of Andreas Vesalius

Andreas Vesalius (December 31, 1514 – October 15, 1564) was born into a Flemish family in Brussels, Belgium. His father was a court official in the service of the Holy Roman Emperor, and so was his grandfather. His ambition was to emulate them by serving his country.

As a teenager, he began medical studies at Louvain University in Brussels, and his desire to study anatomy was already evident. At the age of 16, he was stealing corpses for dissection in the middle of the night. In 1533, when he went to study in Paris, his pursuit was even gruesome. He scoured graveyards to find fresh bodies, and sometimes secretly dissected them in his room to avoid attention.

Despite what may appear to be an appalling pursuit, the anatomical knowledge he gained by dissecting cadavers paid off. In Paris, his skill came to the attention of university professors Jacob Sylvius and John Guinter, the two greatest anatomists in Europe at the time. Aged 23, Vesalius was made Head of the Department of Surgery and Anatomy of the University of Padua in Italy, which was then the most prestigious medical school in the world.

Vesalius Performs Dissection in Padua, Italy

Unlike Galen, Vesalius opted to perform the dissection himself while describing to his students exactly what he was uncovering and discovering.

In 1538, Vesalius got an artist, John Stephanus of Calcar, to draw versions of six of the charts he had sketched for his students. Published as Tabulae anatomicae sex (Six anatomical charts), three of these charts showed views of the human skeleton, while the other three showed:

1. The portal vein near the heart
2. The heart and all the body’s veins
3. The heart and all the arteries.

The Tabulae was an instant hit, and Vesalius’s reputation as an anatomist grew. For four years, he embarked on a huge project to create a comprehensive and accurate guide to human anatomy based on dissections, and worked with a brilliant team of artists to that end. After everything was prepared, he sent the manuscript in Basel to John Oporinus, a distinguished professor and printer, with Vesalius’s orders to use the finest paper and best typography.
At age 29, Andreas Vesalius finished De humani corporis fabrica, libri septem (in seven volumes). Vesalius sent a magnificent purple silk-bound presentation copy to Emperor Charles V, complete with over 200 fabulous hand-coloured illustrations. The Emperor was so impressed that within a few months, he invited Vesalius to become the Emperor’s Personal Physician.

The Royal Physician Gives up Academic Career

Bronze Statue of Andreas Vesalius in Brussels, Belgium: Image by infomatique
In less than a year, Vesalius abandoned his academic career entirely. Having achieved his ambition to become a court official, he settled down to a distinguished but conservative career, marrying a Brussels girl, Anne van Hamme. The couple had a child, also named Anne.

Over the years, Andreas Vesalius became a highly distinguished physician respected across Europe. He was summoned by royalties to help court physicians, including Henry II of France, and Don Carlos, the Crown Prince of Spain.

Final Years of Andreas Vesalius

In 1564, Vesalius set out on a pilgrimage to the Holy Land for unknown reasons. The man who revolutionized the study of anatomy never returned, dying on the ship on his way home from Jerusalem.

His famous textbook, De humani corporis fabrica, or Fabrica in short, is still acclaimed for its highly detailed illustrations of human dissections, often represented in allegorical poses.


Resources: 

1. McGovern, Una. (ed). Chambers Biographical 
2. Chambers Dictionary. Chambers. (2002).
3. Farndon, J., et al. The Great Scientists. Capella / Arcturus. (2005).

Note: This article was originally published at Suite101.com, September 7, 2008.


(c)  September 2011. Tel. Inspired Pen Web. Inspired Pen Web.

Violinist Joshua Bell at D.C. Metro Station and the Chain Email

Famous Violinist Joshua Bell performs at the Washington D.C. Metro subway incognito.

A chain email on Joshua Bell's performance at L'Enfant's Plaza Metro station lives on after four years.

Since early 2007 to this day, 3rd of September 2011, a chain email has proliferated about American virtuoso violinist Joshua Bell performing incognito at Washington D.C. Metro station. The message is a lesson on our perception, taste, and attitude.

After four years, the latest from this chain email I got was just the other day, Sept 2.  A friend meant well in sending it, to share I'm sure.

The email forward claims that violinist Joshua Bell performed incognito at a metro station in Washington D.C. playing on a violin worth millions of dollars but his performance received very little interest from passersby.


 

Tim Berners-Lee and the World Wide Web (WWW)

Inventor Tim Berners-Lee and the WWW

The internet has become an enormous network linking billions of computers worldwide. It came a long way when it began as a small operation the U.S. Department of Defense.

The Internet's Early Years

The Internet came about in the early 1960s. The Defense Advanced Research Projects Agency (DARPA) was the birthplace of the Internet. That time, dial-up phone lines were used to form the basis of Internet connections. In the mid-60s, the first real wide-area connection came through when a computer at the famous Massachusetts Institute of Technology (MIT) eventually connected with a California computer. With the inadequacy of the telephone's lines, the concept of packet switching was began, giving birth to the ARPANET in 1966.