"The Abacus and the Cross: The Story of the Pope Who Brought the Light of Science to the Dark Ages" is available December 7.
A thousand years ago, the pope studied the stars and found God in numbers. Mathematics ranked among the highest forms of worship, for God had created the world, as the Book of Wisdom said (chapter 11, verse 21), according to number, measure, and weight. Our modern tension between faith and science did not exist.
Pope Sylvester II (999-1003) was known as "the Scientist Pope." Born Gerbert of Aurillac, he rose from peasant beginnings to the pinnacle of the Christian church "on account of his incomparable scientific knowledge" -- not in spite of it. Such is the testimony of men who knew him and wrote during, or right after, his lifetime. They call him "acutely intelligent" and "deeply learned in the study of the liberal arts." He was the leading mathematician and astronomer of his day.
Gerbert of Aurillac left us over 200 letters and a handful of scientific treatises. His biography has been known to historians for hundreds of years. Some overlooked it. Some twisted it. Others suppressed it. For the picture Gerbert paints of the Dark Ages -- the thousand years between the fall of Rome and the Renaissance -- is lovely and surprising.
Born a peasant in the mountainous Cantal region of France in about 950, Gerbert entered a Benedictine monastery -- the only elementary school of his day. To teach reading and writing, the monks used the Psalms. To teach rhetoric, they used Cicero, Virgil, and other Latin classics.
When Gerbert showed an aptitude for mathematics, his abbot sent him south to Spain. He spent three years near Barcelona, whose Christian count had signed a treaty with the Muslim caliph of Cordoba in 940. For more than 35 years, the Muslim and Christian kingdoms of Spain were at peace. Trade and scientific exchanges flourished.
Islamic Spain was an extraordinarily tolerant culture in which learning was prized. The Royal Library in Cordoba, just west of the Great Mosque, contained 40,000 books. (By comparison, the greatest Christian library in Europe held only 690.) Many of the caliph's books came from Baghdad, known for its House of Wisdom, where for 200 years works of mathematics, astronomy, physics and medicine had been translated from Greek, Persian and Hindu and further developed by Islamic scholars.
During Gerbert's lifetime, the first of these science books were translated from Arabic into Latin through the combined efforts of Muslim, Jewish and Christian scholars. Many of the translators were churchmen, and some became Gerbert's lifelong friends.
Gerbert was a professor at the cathedral school in Reims, France, for most of his career. He is the first Christian known to teach math using the nine Arabic numerals and zero -- although he called them Hindu numerals, as did his Arabic sources. Using these new numerals, Gerbert devised an abacus, or counting board, that mimics the algorithms we use today for adding, subtracting, multiplying, and dividing. It has been called the first computer. In a chronology of computer history, Gerbert's abacus is one of only four innovations mentioned between 3000 B.C. and the invention of the slide rule in 1622.
Like a modern scientist, Gerbert questioned authority and performed experiments. He noticed that the math books of his time gave two different methods for finding the area of an equilateral triangle -- and that their answers did not agree. As he wrote to a friend, "Thus, in a triangle of one size only, there are different areas, a thing which is impossible." He found the correct solution by drawing a triangle with equal sides, each seven units long. Then he cut out little squares of parchment, each one unit square, and laid them on top of the triangle.
To learn why organ pipes do not behave acoustically like strings, he built models. He came up with an equation, using what physicists call "opportune constants" (or "fudge factors"), that allowed him to switch, mathematically, from strings to pipes and back. A modern physicist who evaluated his work called his solution ingenious, though labor intensive.
Gerbert made sighting tubes to observe the stars and constructed globes on which their positions were recorded relative to lines of celestial longitude and latitude. He made an armillary sphere -- a primitive planetarium -- to explore the movements of the planets. He believed Mars, Jupiter and Saturn, along with the sun, circled the earth (everyone did until Copernicus placed the sun at the center of the universe in 1543). But Gerbert knew Mercury and Venus orbited the sun.
He (or more likely his best student) wrote a book on the astrolabe, an astronomical instrument introduced by the Muslims to Spain during his lifetime. An astrolabe was handy for telling time and making measurements by the sun or stars. You could even use it to calculate the circumference of the earth, which Gerbert and his peers knew very well was not flat like a disc. It was a globe, they wrote, round as an apple.
Gerbert's love of science was not unusual for a 10th-century monk -- though he was an exceptional science teacher. Churchmen from throughout France, Italy and Germany came to study with him, returning to their cathedrals to set up science schools of their own.
Even the rulers in the Dark Ages sought to be technologically literate. Gerbert was asked to tutor the future king of France and two future Holy Roman Emperors. He caught the attention of one of them by sending him a math book. Asked to explain it, he complimented the young emperor on realizing that "the power of numbers contained both the origins of all things in itself and explained all from itself."
The emperor and the Scientist Pope shared a dream. But their plans for a Christian empire based on peace, tolerance, law and the love of learning died with them. The emperor succumbed to malarial fever in 1002, age 22; the pope a year later, some say of a broken heart.
Just before the First Crusade in 1096 redefined the relationship between the Christian and Muslim worlds, Gerbert was posthumously branded a sorceror and devil-worshipper. Instead of the Scientist Pope, he became known as the Magician Pope. The interests of the Church had changed. Science had lost its central place. Much of what Pope Sylvester II had known and taught would be forgotten for hundreds of years.
The Vatican tried to rehabilitate the Magician Pope in 1602. "Gerbert was nothing but a learned man who was ahead of his time," wrote Cardinal Baronius, the Vatican librarian. "Those who want to efface his name from the catalogue of popes are ignorant fools."
But the story of a Magician Pope sold books. As late as 1988, a historian could write, "Did he not practice black arts such as astronomy? ... It was thought that he had sold his soul to the devil in order to obtain knowledge." Another, in 1998, titled a chapter "Gerbert the Wizard" and declared, falsely, that Gerbert's studies "got him in real trouble" with the church.
The Vatican fought back. In 1999 Pope John Paul II summed up the official church position. Gerbert, he wrote, was "a learned humanist and wise philosopher, a true promoter of culture ... He reminds us that intelligence is a marvellous gift from the Creator."
Pope Benedict XVI celebrated the World Year of Astronomy, 2009, by noting that, "Among my predecessors of venerable memory there were some who studied this science, such as Sylvester II." He added, "The laws of nature which, over the course of centuries, many men and women of science have enabled us to understand better are a great incentive to contemplate the works of the Lord with gratitude."
Yet the Scientist Pope remains little known. In the popular mind today, the Dark Ages are wrongly considered a time of superstition and hysteria, when the Christian church suppressed all scientific investigation.
Just the opposite is true. A thousand years ago, Christian monks were busily collecting, translating and investigating the scientific wisdom compiled by their Islamic neighbors. Science transcended faith and faith encompassed science.
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