## Monday, June 29, 2009

### Fibonacci

Leonardo of Pisa, also known as Fibonacci (son of Bonacci) was born around 1170 in Pisa, Italy. he was given the name Fibonacci after his death. It meant "son of Bonacci", which was the nickname of his father.
Fibonacci was a mathematician that many consider "the most talented mathematician of the Middle Ages." His most notable contributions are introducing the Hindu-Arabic numeral system to Europe and a number sequence known as the Fibonacci numbers.
Fibonacci's father directed a trading post in Bugia, a port east of Algiers in North Africa. Young Leonardo often traveled there to help his father and began to pick up the Hindu-Arabic number system. He recognized that doing mathematical functions would be a lot easier with these numbers rather than with Roman numerals. He began traveling around the Mediterrean, learning as much as he could about the Hindu-Arabic system. He returned to Pisa around 1200 and in 1202 he published Liber Abaci (Book of Abacus or Book of Calculation.) Thus the system was introduced to the Western world.
Liber Abaci advocated using the numerals 0-9 and place value. He referred to this as modus Indorum (method of the Indians). He showed the practicality of it by applying it commercial bookkeeping, conversions of weight, calculation of interest, money-changing and other applications. The book was well-received and had huge impact on European thinking.
Liber Abaci also introduced to the West a mathematical sequence now known as the Fibonacci sequence. The sequence was known to Indian mathematicians as early as the sixth century.
Fibonacci died around 1250.
In the 19th century a statue of Fibonacci was erected in Pisa. It is located in the western gallery of the Camposanto, a historical cemetery on the Piazza dei Miracoli.
Fibonacci Sequence
The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8,13,21,34,55,89,.... By definition the first two numbers are 0 and 1 ( although some some omit the 0 and begin with 1,1) and each remaining number is the sum of the previous two. In Liber Abaci Fibonacci posed the following problem:
The following paragraphs are from
How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on?
It is easy to see that 1 pair will be produced the first month, and 1 pair also in the second month (since the new pair produced in the first month is not yet mature), and in the third month 2 pairs will be produced, one by the original pair and one by the pair which was produced in the first month. In the fourth month 3 pairs will be produced, and in the fifth month 5 pairs. After this things expand rapidly, and we get the following sequence of numbers:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ...
This is an example of a recursive sequence, obeying the simple rule that to calculate the next term one simply sums the preceding two:
F(1) = 1
F(2) = 1
F(n) = F(n – 1) + F(n – 2)
Thus 1 and 1 are 2, 1 and 2 are 3, 2 and 3 are 5, and so on.
This simple, seemingly unremarkable recursive sequence has fascinated mathematicians for centuries. Its properties illuminate an array of surprising topics, from the aesthetic doctrines of the ancient Greeks to the growth patterns of plants (not to mention populations of rabbits!).
(I do not want to get bogged down in mathematics. To read the whole article use the above link)
The Greeks believe that the equation they refer to as f(phi)
was the most most pleasing, indeed the aesthetically perfect proportion, and all of their artwork, sculpture, and especially architecture made use of this proportion. A rectangle whose sides had this proportion was called the Golden Rectangle.
Whether or not you agree with the Greeks’ aesthetic judgment, it's a safe bet that Nature herself does:
The growth of this nautilus shell, like the growth of populations and many other kinds of natural “growing,” are somehow governed by mathematical properties exhibited in the Fibonacci sequence. And not just the rate of growth, but the pattern of growth. Examine the crisscrossing spiral seed pattern in the head of a sunflower, for instance, and you will discover that the number of spirals in each direction are invariably two consecutive Fibonacci numbers.
The Fibonacci sequence also occurs in music.

## Thursday, June 25, 2009

### Matteo Ricci

Well, the first post was of a famous king. Now the not so famous. Matteo Ricci S.J. For non-Catholics S. J. means Society of Jesus. In other words, a Jesuit.
Matteo Ricci was born October 6, 1652 in Italy. He died May 11, 1610. He studied theology and law at a Jesuit school. In 1577 he applied to be a missionary to India and in 1578 he was dispatched to Goa, a Portuguese colony in India. In 1582 he left India and went to China. And it is here that his story gets interesting.
Right before arriving in China he spent some time on the Portuguese island of Macao. There he began to learn the Chinese language and customs.He became one of the very few western scholars to master the classical Chinese script. He moved inland and settle in Zhaoqing, where he stayed for 6 years. It was here that he composed the first European style map of the world in Chinese. He, along with Michele Ruggieri, also complied the first ever European-Chinese dictionary. They developed a consistent system for transcribing Chinese words into the Latin alphabet. Unfortuneately the manuscript was lost in the Jesuit archives in Rome and not re-discovered until 1931. It was published in 2001.
Ricci traveled around China for a few years. He spent a couple of months in Beijing but had to leave because of a war with Japan. He did not return to Beijing until 1601. After presenting the Emperor with a chiming clock he became the first westerner to be allowed in the Forbidden City. He did not meet the Emperor himself for several years but was given free access to the city and met other important
officials and leading members of the cultural scene.
The Emperor did grant him patronage and allotted him a generous stipend that helped the Jesuits in China.
What got me interested in Matteo Ricci was a book I read several years ago called The Memory Palace of Matteo Ricci by Jonathan D. Spence. It was a common memorization tool in the Middle Ages and Renaissance to place what you wanted to remember in a mental room, house, etc. depending on how much you wanted to remember. People had to rely on their memories back then. There were no notepads to jot things down, computers, blackberries. The majority of people didn't read or write, especially in the Middle Ages. They kept everything in their memory. Father Ricci showed the Chinese how to do this. He told them that the size of the building depended on them. It could be an intricate palace with hundreds of buildings or a simple pavillion. They could even just use a corner of a room or a closet. The structures were solely in their head and could be based on real places, made-up places, or a combination of both. To everything that we wish to remember, wrote Ricci, we should give an image; and to every one of these images we should assign a position where it can repose peacefully until we are ready to reclaim it by an act of memory. Since this entire memory system can work only if the images stay in the assigned positions and if we can instantly remember where we stored them, obviously it would seem easiest to rely on real locations which we know so well that we cannot ever forget them.But that would be a mistake, thought Ricci. For it is by expanding the number of locations and the corresponding number of images that can be stored in them that we increase and strengthen our memory. Therefore the Chinese should struggle with the difficult task of creating fictive places, or mixing the fictive with the real, fixing them permanently in their minds by constant practice and review so that at last the fictive spaces become "as if real, and can never be erased."*(from J. Spence's book).
Matteo Ricci taught the Chinese about Christianity and Catholicism by using concepts they already knew. He also allowed them to keep certain customs that were part of their heritage, such as veneration of the dead. Later missionaries such as the Dominicans and Franciscans complained to the Vatican about Fr. Ricci's methods.
When Father Ricci was still in Beijing when he died. Foreigners were not allowed to be buried in China, they were buried in Macao. The Chinese made an acception for Father Ricci. His tomb is located in the campus of the Beijing Communist Administrative College. His statue stands in front of Beijing's South Cathedral.
In China today, Father Ricci is still hailed as the world's greatest "foreign guest".His contributions to Chinese science, math, and various other subjects continued to be appreciated by the Chinese.
Next year is the 400 anniversary of Father Ricci's death. Pope Benedict XVI has asked the bishop of Macerata, Italy (Fr. Ricci's birthplace) to prepare for a Jubilee Year in honor of this anniversary.
for more on Matteo Ricci:
http://www.ignatiusinsight.com/features2009/tclark_mricci_may2009.asp
http://www.nndb.com/people/483/000096195/
The picture above is Matteo Ricci (left) and Xu Guangqi (徐光啟) (right) in the Chinese edition of Euclid's Elements (幾何原本) published in 1607.

## Sunday, June 21, 2009

### Charlemagne

This blog will center on people of the Middle Ages and the Renaissance. I am starting off with a king but I hope to concentrate on lesser known people

“He was six feet four inches tall, and built to scale. He had beautiful white hair, animated eyes, a powerful nose...a presence ‘always stately and dignified.’ He was temperate in eating and drinking, abominated drunkenness, and kept in good health despite every exposure and hardship.”
- EINHARD (the King's secretary) describing Charlemagne

Charlemagne - Charles the Great, King of the Franks, Holy Roman Emperor - was born on April 2, 742. There are two Charlemagnes - the historic and the legend. Only King Arthur vies for the title of the ideal Christian king in the Medieval world. (with Richard the Lionheart a distant third.) But whereas Arthur is mostly myth (although there was a real King Arthur; that will be another day), Charlemagne is mostly fact.
He was the eldest son of Pepin II, also known as Pepin the Short. When Pepin died the Frankish kingdom was divided between his two sons - Charles and Carloman. In 771 Carloman suddenly died and Charles, age 29, became sole king of the Frankish kingdom.
The Franks originated in were a western Germanic tribe. Between the third and fifth centuries many of the Frankish tribes had raided Roman territory, while others joined the Romans. As the Roman Empire collapsed, the Franks were taking over. By the fifth century they had taken over the Western Roman Empire, but the it was not one kingdom, but several different ones.
By 490, King Clovis had conquered all the Frankish kingdoms except one and formed one Empire.Clovis I was the first King of the Franks in 509. (guess where we get the name France). But Clovis continued the tradition of dividing the kingdoms between sons. So he left each of his 4 sons part of his kingdom. Then they had sons so it was divided even more. By 534 it was a mess, with constant feuding and rivalry.
Eventually three subkingdoms emerged - Austrasia, Neustria, and Burgundy. These ups and downs continued until 751 when Pepin I had himself crowned and began a new dynasty - the Carolingians.
When Charles became sole king Europe was splintered and returning in turmoil. The Franks had reverted to their barbarian ways, neglecting education and religion. In the North, the Saxons were pagans, In the south, the Catholic Church was trying to recover lands taken by the Lombards. Charles was determined to strengthen his kingdom and bring order to Europe. He launched a 30 year military campaign. By 800 he was the ruler of Europe. With the establishment of a central government, Charles restored a great deal of the unity of the old Roman Empire and
paved the way for the development of modern Europe.*
In 773 pope Hadrian II sent Charlemagne an plea for aid against the Lombards who were invading the Papal States. Charlemagne complied, took the crown of Lombardy, and accepted the role of protector of the Church. Over the next several years he commanded 53 campaigns, leading almost every one of them himself. He conquered and Christianized Bavaria and Saxony which helped to shield Italy and put off the Moors of Spain from invading Francia. There were several other campaigns, all which were successful.
In 799 Pope Leo III was arrested by the Romans and beaten. The Pope escaped and fled to Charlemagne, asking Charlemagne to intervene. Charlemagne agreed and went to Rome in Nov. 800. By Dec. 23, Leo was restored. On Christmas Day, Charlemagne was

at Mass. As he knelt at the altar to pray, the pope crowned him
"Emperor of the Romans. Supposedly Charlemagne did not know
the Pope's intention and really did not want it. They were not happy
in the East Roman Empire - in Byzantium. (modern day Turkey,
Syria, etc). Byzantium had controlled the Roman Empire for the past
3 or 4 centuries. it wasn't until 812 that the East recognized
Charlemagne as emperor. Thus power was re-established in the west.
Also by this act, pope Leo III established papal supremacy over a unified Christiandom. (at right Charlemagne being crowned Holy Roman emperor)
Europe was re-united, power was, for the most part, back in the west. But this was not Charlemagne's only accomplishment. Charlemagne is known as much for his reforms as for his military accomplishments. After his crowning, Charlemagne returned to France. He put in place a more efficient government. He divided the kingdom into several administrative districts, appointed military governors along the borders, sent out messengers to check on how things were in the kingdom and then report back to him. He also traveled through the kingdom himself in order to keep in contact with the people. He standardized coin minting and encouraged trade with other nations. And, probably most significantly, brought literacy back.

Charlemagne was a great admirer of learning and education. He saw to it that all his children and grandchildren were well educated and set about educating himself as well.(But he never could learn to write.) His actions in this area brought about what is called the Carolingian Renaissance. He did it with the help of a monk named Alcuin, an Anglo-Saxon from York. Alcuin set up a classical curriculum for the palace school that was set up to educate the monks and clergy, most of whom were illiterate.Schools were organized in the parishes, not only for the nobility but for everyone.
A scriptorium was set up, not only manuscript copying but for correcting the hundreds of manuscripts that had been copied by illiterate monks. By doing this, Charlemagne instituted a standard form of writing style. Letters were now written in upper and lower case, with punctuation and separation of words. It is the script that we still use today.
He standardized medieval Latin, encouraged uniform religious practices, roads and bridges were repaired,laws were put into place to protect peasants from serfdom, and many other reforms..
Unfortunately, much of what he put in place disintegrated a generation or two after his death in 814. Not only was Charlemagne no longer around but the barbaric tribes once again began their invasions. These invasions came to an end by the latter part of the 11th century with the rise of feudalism. But the roots of modern Europe were now planted.

Charlemagne's throne

Charlemagne's Tomb Charlemagne entered the world of legends and songs during the feudal era. In France, chansons de geste (heroic poems) were written about his exploits, the most famous one being the Chanson de Roland (The Song of Roland).

*www.lucidcafe.com/library/96apr/charlemagne.html