The Abacus And The Cross Part 2

In 948 the Arab traveler Muhammad ibn Hauqal was working on his Description of the World Description of the World. Al-Andalus was a magnificent land, he wrote, "of forests and fruit trees and rivers of sweet water." Most of it was cultivated and well-settled. "Abundance and ease" were the dominant aspects of life there, and a great deal of gold was in circulation. Spanish fabrics-linen, wool, silk, brocade, and "the most beautiful velvet you can imagine"-were sought after in Egypt, Mecca, and Yemen. Spain raised the best mules in the world and sold the best slaves. In particular, it was the source of "all the eunuch Slavs found on the face of the earth," these having been brought south by German and French merchants and castrated in Cordoba by Jewish doctors who specialized in the practice.

The Jewish vizier Hasdai ibn Shaprut described his country in a letter at about the same time. Al-Andalus "is rich, abounding in rivers, springs, and aqueducts; a land of grain, oil, and wine," he wrote. Among its resources were "the leaves of the tree upon which the silkworm feeds, of which we have great abundance," as well as cochineal and crocus, for dying the cloth. Silver, gold, copper, iron, tin, lead, sulphur, porphyry, marble, and crystal, he added, were mined in the mountains.

Other resources of Spain are described in the Calendar of Cordoba Calendar of Cordoba, written in about 960. It tells when to plant and harvest such crops as sugar cane, rice, eggplant, watermelon, and banana-all of which were brought to Spain by Arab settlers. They also introduced cotton, oranges and grapefruits, lemons and limes, apricots, olives, spinach, artichokes, and hard wheat, as well as the techniques of crop rotation, fertilization, and irrigation using ca.n.a.ls and water wheels.

Another technology Arab settlers brought west was paper-making. The surname al-Warraq, "the papermaker," was first seen in Spain in the tenth century, and a water-powered papermill was built near Valencia before the century's end. Paper, made from linen rags, was both cause and effect of the Muslim love of books. Any young man who could afford it went east for his education and brought back the latest scientific and philosophical tomes. They made quick copies on cheap paper and, once home, transferred the text to more durable parchment. It would be several hundred years before Christian scholars learned to do the same.

Some of the travelers to the east were professional bookbuyers. Abd al-Rahman III, who reigned from 912 to 961, was known as a learned man-it added to his prestige. But his son, al-Hakam II, who would have to wait until he was forty-five to succeed his long-lived father, was the true scholar. With the wealth of Spain at his disposal, he employed bookbuyers in every Muslim land, as well as a team of copyists. His Royal Library in Cordoba, just west of the Great Mosque, was said to contain 400,000 books in 976. By contrast, the greatest Christian library of the time, at the monastery of Bobbio in Italy, held only 690 books.

Four hundred thousand may be an exaggeration. The catalog of the library, now lost, was said to fill forty-four books, each with a hundred pages. For the full set to contain 400,000 t.i.tles, each page would need to hold ninety t.i.tles-difficult, if not impossible. One-tenth of that number, nine t.i.tles per page, would easily fit. Even at only 40,000 books, the library of Cordoba was far and away the largest library in Europe.

Compared to the other superlatives used to describe Cordoba in the tenth century, a library of 40,000 books is not absurd. The city was nearly half as big as Baghdad, the largest city of its day. It held hundreds-maybe thousands-of mosques. Running water from aqueducts supplied nine hundred public baths. The goldfish in the palace ponds ate 12,000 loaves of bread a day. The paved streets were lit all night. The postal service used carrier pigeons. The munitions factory made 20,000 arrows a month. The market held tens of thousands of shops, including bookshops, and seventy scribes worked exclusively on producing Korans.

Cordoba impressed everyone who heard of it. In 955, the nun Hrosvit of Gandersheim met an amba.s.sador from Cordoba at the German court of Otto the Great. She recorded in a poem what she had learned of his city. "The brilliant ornament of the world shone in the west," she wrote. "Cordoba was its name and it was wealthy and famous and known for its pleasures and resplendent in all things, and especially for its seven streams of wisdom"-these streams being the seven liberal arts: grammar, rhetoric, and dialectic; and the ones Gerbert was pursuing, arithmetic, geometry, astronomy, and music.

Significantly, only about half of Cordoba's residents were Muslim. The Koran teaches that, since Moses and Jesus had both been given books by G.o.d, Jews and Christians, like Muslims, were "People of the Book," and thus to be tolerated. In al-Andalus, this general creed of tolerance was codified in the form of a dhimma dhimma, a pact or covenant between the rulers and their subjects. Christians and Jews were not forced to convert to Islam, but could practice their religions-as long as they did so quietly and didn't proselytize. Other than having to pay a head tax (which Muslims did not) they were not excluded from the city's social or economic life. They could, and did, fight in the army. Depending on the ruler's interpretation of the law, and their own talents, they could advance to the highest political posts. The amba.s.sador whom Hrosvit met in Germany, the Christian Bishop Racemundo, was one of the caliph's closest confidants (he may also have written the Calendar of Cordoba Calendar of Cordoba). Another was the vizier, Hasdai ibn Shaprut. Prince of the Jews in al-Andalus, Hasdai is one of the most famous figures of tenth-century Spain, equally well known as a politician and an intellectual.

Gerbert arrived in Spain during the time that later poets would name its Golden Age. Arabic was the lingua franca, not just the language of religion. Christians wrote erotic poetry in Arabic; they also sang Ma.s.s in that language. They studied the latest translations sent out from Baghdad, sitting side by side with their Muslim and Jewish peers, without any suggestion they were betraying their faith. This vision of a kingdom based on religious tolerance and scholarly inquiry was the second lesson Gerbert would learn living on the border of al-Andalus.

An anecdote recorded by the Cordoban doctor Ibn Juljul in 987 gives just such a picture of the city's intellectual life. In 949 the caliph had sent Bishop Racemundo to the emperor of Constantinople. The gifts Racemundo brought home included a green onyx fountain and two books: "the book of Orosius the narrator, which is a wonderful Roman book of history, containing records of past ages and narratives concerning the early monarchs," and Dioscorides' On Medicine On Medicine, "ill.u.s.trated with wonderful pictures of the herbs in Byzantine style." A Christian scholar was given the task of translating the Latin Orosius into Arabic. But the Dioscorides was in Greek and none of the Christians of al-Andalus, Ibn Juljul noted, read Greek. The library of Cordoba had another copy of Dioscorides from Baghdad. But the translators at the House of Wisdom could not identify all of the medicinal herbs and left many plant names in the original Greek.

"There was in Cordoba a group of doctors who were keen to find out by research and inquiry the Arabic names of the simple remedies of Dioscorides that were still unknown," Ibn Juljul wrote (he would join that group in the 960s). He continued, "They were encouraged in that research by the Jew Hasdai ibn Shaprut."

The caliph sent word of their difficulty back to the emperor of Constantinople, and in 951 there arrived in Cordoba a monk named Nicholas who was fluent in both Greek and Latin. Hasdai "favored and honored" Nicholas, says Ibn Juljul, above all the rest of the group-Christians, Jews, and Muslims-who sat down together to translate On Medicine On Medicine. Hasdai himself wrote the final Arabic version.

Though there's little record of it, we can imagine a similar collaboration of Christians, Jews, and Muslims, Arabic-speakers and Latin- or even Greek-speakers, sitting down together to translate and learn from the many books of mathematics and astronomy that came from Baghdad before the year 1000.

Writers in the eleventh and twelfth centuries credit Gerbert himself for bringing the new mathematics and astronomy north from Cordoba. Gerbertus Latio numeros abacique figuras Gerbertus Latio numeros abacique figuras runs a verse on two mathematical ma.n.u.scripts: "Gerbert gave the Latin world the numbers and the figures of the abacus," meaning-as the ill.u.s.trations show-the Arabic numerals 1 to 9, as explained by al-Khwarizmi. Seven ma.n.u.scripts (out of eighty) give him credit for the first Latin book on the astrolabe, again based on al-Khwarizmi's work. runs a verse on two mathematical ma.n.u.scripts: "Gerbert gave the Latin world the numbers and the figures of the abacus," meaning-as the ill.u.s.trations show-the Arabic numerals 1 to 9, as explained by al-Khwarizmi. Seven ma.n.u.scripts (out of eighty) give him credit for the first Latin book on the astrolabe, again based on al-Khwarizmi's work.

Even William of Malmesbury, whose twelfth-century history of Gerbert's stay in al-Andalus otherwise reads like The Arabian Nights The Arabian Nights, mentions these two scientific instruments. Gerbert, he says, "surpa.s.sed Ptolemy in knowledge of the astrolabe" and "was the first to seize the abacus from the Saracens." (Gerbert also learned "to interpret the song and flight of birds" and "to summon ghostly forms from the nether regions," William adds, before launching into a tale of Gerbert finding buried treasure in Rome by interpreting a statue.) Richer of Saint-Remy, writing in the 990s, does not mention the astrolabe, though he goes into detail about Gerbert's abacus. He does not mention Saracens, only Spain and Bishop Ato. But Ademar of Chabannes, in about 1030, clearly states that Gerbert, "thirsty for knowledge," went to Cordoba.

It's possible that he did. In the cathedral treasury of Girona is an Arabic arqueta arqueta, an elaborate casket of gilded silver embossed with medallions of lilies (see Plate 4). It is big enough to fit two substantial books; it could also have been used as a reliquary. These boxes of ivory, wood, or precious metals were common diplomatic gifts. This one was given to Gerbert's patron Count Borrell by Caliph al-Hakam II sometime between 961 and 976, dates that overlap with Gerbert's stay from 967 to 970.

In fact, travel between Cordoba and Barcelona had been frequent since 940, when a detente between the two kingdoms was brokered (while twelve Cordoban wars.h.i.+ps blocked the harbor of Barcelona) by Hasdai ibn Shaprut. The great Jewish intellectual spent at least four months in Catalonia in 940; then he returned to Cordoba, shepherding Barcelona's amba.s.sador, a monk named Gotmar. An Arabic source says Gotmar brought Prince al-Hakam a history he had written of the French kings-al-Hakam's scholarly leanings were well known.

How long Gotmar remained with Hasdai in Cordoba is unknown, as are the gifts he returned with. But if any translated books were among them, they could have reached Gerbert. News of Cordoba's intelligentsia certainly would have, for Gotmar was named bishop of Girona in 944. Ato was his archdeacon there until 957, when he became bishop of Vic and, in 967, Gerbert's mentor.

Heading south from Aurillac with Count Borrell in 967, young Gerbert may have seen Conques and the golden majesty of Saint Foy for the first time. Doubtless their route led from monastery to monastery. Traveling 20 to 30 miles a day (not difficult on a soft-ambling Spanish mule), it would have taken about two weeks to reach Vic. They rode through Rodez in its wide valley, picking up Borrell's bride if she was not already in the party, and past Albi, its red sandstone towers rising bright above the river Tarn. Beyond the Black Mountain with its deep forests, the landscape changed to a dry, windy scrubland; a bank of hills approached, snowy mountains rearing up behind. On an old Roman bridge, well built of pink and tan stone, they crossed the river Aude.

Entering the foothills of the Pyrenees, they squeezed through river gorges and clung to rocky cliffs. Wine grapes grew on every possible acre, some still watered by Roman aqueducts. Across a high pa.s.s, where cattle grazed beside a dolman more ancient even than the aqueducts, they saw ahead the great white face of Mount Canigou. At its foot was the monastery of Cuxa, nestled in a bowl of wooded hills. Cuxa's tile-roofed cathedral was one of the tallest churches of the tenth century. When Gerbert visited, it was still under construction; it would not be consecrated until 974. Its 130-foot belltowers were not built until the eleventh century, but the lofty grandeur of its nave would have impressed the young monk. He may even have noticed the strange keyhole shape of its archways, derived from Arabic architecture.

High in the hills above Cuxa were hot springs, popular since Roman times. Even higher was a white stone chapel dedicated to Saint Martin, with a square nave and rounded apse just like the original church at Aurillac. It clung to the side of a cliff with an ethereal view: It was called the "balcony of Canigou" until another church and monastery were built, still higher, in the eleventh century, and took over the t.i.tle. Trails radiated out from each church, some marked with scallop sh.e.l.ls as the road to Compostela: The Pyrenees were routinely crossed here. For some years, the abbot of the monastery at Cuxa was simultaneously abbot of Ripoll, on the south side of the mountains.

Coming down through thick chestnut forests, past another round-ended white church and fields full of horses, Gerbert could glimpse the Mediterranean sparkling in the distance. The way led them through a deep river gorge to the monastery of Ripoll, at the confluence of two rivers. South again, the landscape opened up, a wide fertile plain spreading 20 miles to Vic, where Gerbert would meet his new mentor.

The Romans had settled Vic and named it Ausona. But when Guifre the Hairy reclaimed the area from the Arabs in 880, he had a castle built on the site of the Roman temple and a church on the outskirts, or vicus vicus, of the town. When the bishop became more powerful than the castellan, the name of the town was changed to Vic. It was a prosperous bishopric, surrounded by good agricultural land. Compared to the steep hills and deep gorges of the Pyrenees, Vic was flatter, its soil lighter, its rivers more easily tamed for gristmills and irrigation. To the southeast, the hills of Montseny blocked the Mediterranean breezes, making Vic colder and foggier than sunny Barcelona, 30 miles away. East was an-other jagged range of hills clothed in beech woods, the rugged land beyond pockmarked with volcanic craters. Churches and monasteries crowned many a sheer bluff, providing a fortress refuge-and a look-out point, for from Vic the flat plain continued to the border and beyond. No mountains blocked the armies of al-Andalus-or the merchants and craftsmen bringing silk, gold, and science, along with the technique of building archways in the shape of keyholes, to the north.

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An arch in the Arabic keyhole style at the restored cathedral of Cuxa. The cathedral was built by Gerbert's friend Abbot Garin and consecrated in 974.

Vic was Bishop Ato's main residence, but Gerbert probably studied at Cuxa and Ripoll as well during the three years he lived in Spain. There were no scientific ma.n.u.scripts at the cathedral of Vic, according to an inventory made in 971. Its tiny library of fifty-nine books held nothing that couldn't be found in Aurillac. Gerbert left us none of the letters he might have written while he was in Spain-he did not begin saving copies of his letters until 982-and no Catalan doc.u.ment mentions the young monk from Aurillac. But other evidence links both Cuxa and Ripoll to the study of mathematics-particularly, to Arabic mathematics.

At Cuxa, Abbot Garin's interest in Arabic science can be seen in the design of the church he built-particularly in the keyhole arches. Originally from the monastery of Cluny, Garin was abbot of four monasteries in southern France, in addition to Cuxa, when Gerbert met him; he ran them all in the reformist style of Odo of Cluny, with an emphasis on strictness and learning. He was a wily politician as well, an idealist who hoped to see the restoration of Charlemagne's empire in his lifetime. This was a dream he shared with Gerbert-and he offered Gerbert valuable insights on how to achieve it. Garin traveled to Venice at the request of the pope, to keep that vital city from allying with Constantinople instead of Rome, and brought home with him the penitent doge. Garin had convinced the Venetian ruler that betraying Rome was betraying G.o.d; the doge lived his last years at Cuxa as a hermit. A few years later, Garin took a pilgrimage to Jerusalem, taking up a collection along the way for the Church of the Holy Sepulchre. At the consecration of his Arab-influenced cathedral at Cuxa in 974, Miro Bonfill, the bishop of Girona and count of Besalu, called Garin "a dazzling star" who "shook up the world."

But Gerbert remembered Garin best as a mathematician. Many years later, in 984, he would write to Abbot Gerald of Aurillac asking for a copy of "a little book on the multiplication and division of numbers by Joseph the Wise of Spain" that Garin had left there. This "Joseph the Wise" may have been Hasdai, the caliph's vizier: Hasdai's full name was Abu Yusuf Yusuf (Joseph) Hasdai ben Ishaq ibn Shaprut. A casual mention of him in a book by a tenth-century Jewish intellectual in Tunisia underscores Hasdai's interest in the mathematical sciences. Describing the lunar phases, the Tunisian points out: "We have explained this phenomenon and represented it in figures in our astronomical work sent to Abu Yusuf Hasdai ben Ishaq." Unfortunately no ma.n.u.scripts of that astronomical work (or the "little book on the multiplication and division of numbers") have been found. (Joseph) Hasdai ben Ishaq ibn Shaprut. A casual mention of him in a book by a tenth-century Jewish intellectual in Tunisia underscores Hasdai's interest in the mathematical sciences. Describing the lunar phases, the Tunisian points out: "We have explained this phenomenon and represented it in figures in our astronomical work sent to Abu Yusuf Hasdai ben Ishaq." Unfortunately no ma.n.u.scripts of that astronomical work (or the "little book on the multiplication and division of numbers") have been found.

Gerbert wrote Miro Bonfill asking for this same book on numbers, and he may also have asked Garin directly for a copy. In 985, Gerbert did Garin a favor by composing his appeal for alms for the Holy Sepulchre. The same year he told his teacher Raymond at Aurillac that he was looking for a new patron and, "influenced by the encouragement of our friend Abbot Garin," was "considering approaching the princes of Spain."

The school at Ripoll was also famous in the Middle Ages as a center of learning. But the abbot Gerbert met there was best known for his military prowess: He would die leading an attack on Cordoba in 1010. Ripoll's reputation seems mostly due to the famous scholar and statesman Oliba.

Oliba was a count before he joined the Church and would become a bishop. Entering the monastery at Ripoll as an adult in 1002, he jumped quickly from novice to abbot and embarked on a building program that transformed the churches Gerbert had wors.h.i.+pped in thirty-some years before. He introduced the Romanesque style, marked by tall square bell towers with many rows of arched windows, from Italy into Spain. The stone portal he commissioned for Ripoll is sixty-six feet wide, its arches and rows filled with hundreds of low-relief carvings telling stories from the Book of Kings and the Apocalypse. Ten larger figures, five on a side, portray the concept "harmony": On the left is an orchestra of viol, bells, recorder, and horn, the bishop conducting; on the right Christ gives the church to Peter, beside whom stand a bishop, a soldier, and a judge-a good emblem for the Catalonia Gerbert knew.

Oliba is also given credit for the huge jump in the number of books in the Ripoll library between 979 (when an inventory listed 65 ma.n.u.scripts) and 1047 (when, just after his death, another inventory listed 246). Nor was it only the number of books that made the scriptorium famous: Many of the new books were about science.

One of the most controversial books still exists. Known as Ripoll 225, it is a collection of ill.u.s.trated treatises on geometry and astronomy, including a description of how to use an astrolabe. Brief sections are literal translations from al-Khwarizmi's Arabic book on the astrolabe. Scholars have argued bitterly over whether Ripoll 225 is old enough for Gerbert to have seen it-or even to have written it himself. Today, based on the evidence of paleography-which examines how the parchment was prepared, the ink made, the letters shaped-the ma.n.u.script is thought to have been made in the eleventh century, during Oliba's time, at least thirty years after Gerbert left Catalonia. And yet it is not the translator's rough draft, with the cross-outs and additions and corrections a draft would have. It is a clean copy of something older, some translation of Arabic science that Gerbert might indeed have seen.

Another incident links Ripoll to Arabic science and both to Gerbert's circle of friends. Ripoll, too, had a new cathedral under construction while Gerbert was there. In 977, seven years after Gerbert left Spain, it was consecrated. Bishop Ato was dead. Garin of Cuxa was in Venice. But several of Gerbert's friends attended the ceremony. Miro Bonfill again wrote the consecration speech. In the audience were Count Borrell and a deacon of Barcelona, Seniofred, known by his nickname, Lobet; in 984, Gerbert would write to Lobet requesting "the book De astrologia De astrologia, translated by you," which could be a treatise on the astrolabe or one on astrology, translated from Arabic.

Also attending the consecration ceremony was a monk named Vigila from the monastery of Albeda in the kingdom of Navarre. Vigila is famous for copying Isidore of Seville's encyclopedia, a project he is thought to have completed in 976. This copy, now known as the Codex Vigila.n.u.s, is the earliest Latin ma.n.u.script to contain what we call Arabic numerals-but which al-Khwarizmi, in the first book on this numerical system, called "Indian numerals." To Isidore's description of arithmetic, Vigila added a comment: "It should be noted that the Indians have an extremely subtle intelligence, and when it comes to arithmetic, geometry, and other such advanced disciplines, other ideas must make way for theirs. The best proof of this is the nine figures with which they represent each number no matter how high. This is how the figures look." Then he lists them, from 9 to 1, shaped a little differently than we would write them today.

Vigila does not sound as if he were announcing a great discovery, only fitting into Isidore's seventh-century text a bit of knowledge that had become common in the intervening three-hundred-some years. We don't know how or when he learned of Arabic numerals-nor whether he spoke of them with Miro or Lobet during his visit to Ripoll. But the Codex Vigila.n.u.s and Ripoll 225 prove that Arabic science and mathematics were making their way north from Islamic Spain around the year 1000, with the eager a.s.sistance of Catalan churchmen.

Miro Bonfill, the cousin of Count Borrell (and the count of Besalu in his own right), may have been Gerbert's closest friend in Spain. Miro became bishop of Girona in 971; in the same year-the year after Gerbert left Spain, if our dates are correct-he was sent on his own emba.s.sy to Cordoba. Miro left no account of his mission. But we can learn something about him and his knowledge of Arabic science from his other writings: the speeches celebrating the new churches built at Cuxa in 974 and Ripoll in 977, a charter dated 976, and a book on astrology, in which he wrote: "What follows now has been translated by the wisest scholar among the Arabs, as he was instructing me."

"The wisest scholar" could have been Maslama of Madrid, the chief mathematician and astronomer during al-Hakam's reign. His school was supported by the caliph, who provided books and other resources, such as astrolabes. Maslama produced a renowned star table, drawn up in 978, that adapted the work of al-Khwarizmi to the coordinates of Cordoba. He wrote a commentary on Ptolemy's Planisphere Planisphere and a treatise on the astrolabe. He was also an astrologer: It was common for Arabic mathematicians and astronomers to tell fortunes. It was lucrative and (depending on the fortune) kept their patrons happy. Maslama lived until 1007. and a treatise on the astrolabe. He was also an astrologer: It was common for Arabic mathematicians and astronomers to tell fortunes. It was lucrative and (depending on the fortune) kept their patrons happy. Maslama lived until 1007.

Gerbert, likely, was also an astrologer. When Richer of Saint-Remy wrote that Gerbert "studied mathematics extensively and successfully" under Bishop Ato, he did not use the common Latin word mathematica mathematica . He used . He used mathesis mathesis. We don't really know what Richer's idea of mathesis mathesis was. Boethius is the only other author known to use was. Boethius is the only other author known to use mathesis mathesis to mean mathematics. It more often meant astrology. to mean mathematics. It more often meant astrology.

Miro may have been Gerbert's mentor in this science. His astrology book, now in the national library in Paris, is the oldest left from the Middle Ages. It shows an uncommon deftness with numbers: Its hundreds of multiplications and divisions contain absolutely no errors. The playful, provocative writing style, and the Catalan provenance of the ma.n.u.script, further link it to the bishop of Girona, though Miro did not sign this work. He did sign his speeches consecrating the churches at Cuxa and Ripoll, as well as the charter of 976. Like the astrology book, these writings are rife with puns.

Miro was obsessed by complexity. He regularly used synonyms and words so rare that his readers (or listeners) needed a glossary to understand them-and in fact, all of his odd word choices can be found in a set of glossaries in the library of Ripoll. These glossaries were, luckily for the history of science, in Barcelona being rebound when the library at Ripoll burned down in 1835. There are five in one volume, thirteen in another. Some offer synonyms for unusual Latin words found in Isidore of Seville's encyclopedia or in the cla.s.sics of Roman poetry. Others are bilingual-Greek to Latin-or even trilingual-Hebrew to Greek to Latin. Miro played with them all.

Nor did his love of complications end with words: Miro played with numbers as well. Instead of "twenty-eight," he said "four times seven." Not "six months," but "twice three months." To say "976" in his charter of that year takes him three lines.

This puckish wit seems unlike the man Gerbert addresses in his letter, dated 984. Gerbert begins, "The great reputation of your name, indeed, moves me not only to see and speak with you, but also to comply with your orders." He would have done so sooner, he explains, but he had been engaged by Emperor Otto II; freed of his obligations by the emperor's death, "it is right for me both to talk with friends and to obey their commands." He closes with his request for the book On the Multiplication and Division of Numbers On the Multiplication and Division of Numbers by Joseph the Wise. This extremely formal letter is the only one in Gerbert's collection addressed to Miro, and, sadly, Miro died before it could reach him. And yet it makes three things clear: Gerbert has corresponded with Miro before (or at least received orders), considers him a friend, and expects him to have a copy of the math book by Joseph the Wise. by Joseph the Wise. This extremely formal letter is the only one in Gerbert's collection addressed to Miro, and, sadly, Miro died before it could reach him. And yet it makes three things clear: Gerbert has corresponded with Miro before (or at least received orders), considers him a friend, and expects him to have a copy of the math book by Joseph the Wise.

And yet, a souvenir of their friends.h.i.+p-and Miro's playfulness-does remain. In the cathedral at Elne, on the Mediterranean coast close to the modern border of Spain and France, is a large gray stone. Carved on the far left of one edge is the name "Miro." On the right, "Gerbertus."

The Elne stone was discovered in the 1960s when the altar of the cathedral was moved. The altar itself was a slab of white marble, just like the altar at Cuxa on which are inscribed more than a hundred names dating back to the tenth century, including that of Oliba of Ripoll. There was a tradition of such sacred graffiti: It marked the making of a vow. At Elne, the marble altar was bare-the incised stone was found under under the altar, and the names were not visible. The stone had apparently been moved from its original site and reused. Based on cuts in the corners of the stone, it might once have served as the lintel of a doorway, perhaps the lintel into the crypt where the sacred relics were kept when not on display-a plausible place to make public note of a vow. the altar, and the names were not visible. The stone had apparently been moved from its original site and reused. Based on cuts in the corners of the stone, it might once have served as the lintel of a doorway, perhaps the lintel into the crypt where the sacred relics were kept when not on display-a plausible place to make public note of a vow.

Stranger is the fact that both names are puns.

Gerbert's signature is very fine, deeply carved, its edges still sharp after all these years. It is about three inches in height and breadth and shaped like a cross: GER (s.p.a.ce) BER, with the T above the s.p.a.ce and the US (written in Latin as VS), twined around each other, below.

MIRO is as long but not as high as GERBERTVS, and not as well carved, and it is backwards: Miro backwards: Miro in Latin means to look in a mirror. in Latin means to look in a mirror.

Gerbert couldn't find an equivalent Latin pun for his name: It is Germanic. So this twenty-year-old monk matched his friend's playfulness with a set of intensely intellectual puzzles. Pieced together, they reveal how he thought of himself as a young man-and how his sojourn in Spain had affected him.

To make his name into a cross, Gerbert pulled out T-V-S, recognizable to any medieval churchman as the Trinity, Thevs Verb.u.m Spiritvs Thevs Verb.u.m Spiritvs, or Father, Son, and Holy Ghost. The letters could also stand for Tav Votvm Solvi Tav Votvm Solvi, "I have accomplished my vow to the Cross." He constructed the cross itself with one letter, two letters, and three plus three letters. According to the accepted mathematical theory, one, two, and three were the basis of G.o.d's creation of the universe, making number the key to wisdom. Finally, the letters were to be read left to right, then up to down, making the symbol known as the chrismon, still used in baptisms. The chrismon is the sign of the emperor Constantine, the first Christian emperor, and the one who moved the capital of his empire from Rome to Constantinople.

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Graffiti carved by Gerbert at the cathedral of Elne. Like his friend Miro's signature, which is backwards, Gerbert's autograph is a pun, signifying church, wisdom, and empire.

To read GERBERTVS was thus to summarize the three great forces acting on Gerbert's life: church, wisdom, and empire. The Church would be his home, the search for wisdom-through numbers-would be his pa.s.sion, and the restoration of the empire, and its return to Rome, would be his lifelong goal.

CHAPTER IV.

The Schoolmaster of Reims In December 970, Gerbert left Spain, accompanying Count Borrell and Bishop Ato on a mission to Rome. Winter seems an odd time to attempt crossing the Alps, but there are many stories of similar expeditions. Odo of Cluny crossed in January. As the custom was, he hired local guides-Muslims, who from their fortress at Saint-Tropez on the coast had ruled the Alpine pa.s.ses for almost a hundred years. Even then, the road was perilous. A blizzard struck at sunset. "We were so covered with snow and our limbs so frozen that we could not speak," one of Odo's companions wrote. "Suddenly, the horse on which our father was sitting slipped sideways and they both fell together down the steep slope. Letting go of the reins Odo raised both his hands to heaven as he fell, and immediately his arms found the branch of a tree from which he hung suspended until those in front turned back at his cries and rescued him. ... The horse was never seen again."

River crossings could be chancy at any time of year. Odo was in midstream once when "one of the horses kicked at another and struck the side of the boat in a place where there was a knot in the planking. As soon as the side of the boat was pierced, so great a torrent of water came in through the hole that the boat was quickly filled." Odo reached sh.o.r.e only "by the manifest help of G.o.d."

Richer of Saint-Remy wrote of reaching a bridge on a rainy night at dark. It was "pierced with holes so large and so numerous that [we] ... would have had difficulty pa.s.sing it even in the daytime." His escort, an experienced traveler, had a plan. "Over the gaping holes, he placed his s.h.i.+eld for the horses to step on, or one of the loose boards that were lying around, and sometimes bending, sometimes straightening, sometimes on tiptoe, sometimes running, he succeeded in getting the horses and me across."

Then there were the tolls-or bribes. Count Gerald the Good of Aurillac, on his way to Rome, was stopped at Piacenza by the cleric in charge of the ford, who "for some reason ... was in a very bad temper, flinging angry words about." Count Gerald "subdued" him with some "small gifts," and the man not only took them across the Po River but also refilled their flasks with wine. ("Small" should be read in the context of the count's well-known generosity: The Muslim guides who controlled the Alps "thought nothing more profitable than to carry Gerald's baggage through the pa.s.s of Mont Joux.") Finally, the travelers had to beware of brigands. Count Gerald had just arrived at the city of Asti when a thief stole two of his packhorses. "Coming to a river, he was not able to get them across before he was taken by Count Gerald's men." Having retrieved his horses, the magnanimous count pardoned the man.

Count Borrell and Bishop Ato were attacked on their way home from Rome-but not by such simple thieves. They had gone to Rome to convince the pope to separate the churches of Catalonia from the archbishopric of Narbonne. The pope agreed. In a series of five papal bulls, he established a new archbishopric of Vic with Ato at its head. In revenge, the archbishop of Narbonne saw to it that his new rival never reached home: Ato was murdered in August 971.

Gerbert was not with him. He had impressed important people in Rome. According to Richer of Saint-Remy: "The pope did not fail to notice the youth's diligence and will to learn. And because musica musica and and astronomia astronomia were completely ignored in Italy at that time, the pope through a legate promptly informed Otto, king of Germany and Italy, that a young man of such quality had arrived, one who had perfectly mastered were completely ignored in Italy at that time, the pope through a legate promptly informed Otto, king of Germany and Italy, that a young man of such quality had arrived, one who had perfectly mastered mathesis mathesis and who was capable of teaching it effectively." and who was capable of teaching it effectively."

Otto the Great, who had been crowned Holy Roman Emperor in 962, took Gerbert into his court to tutor his heir, Otto II, then sixteen to Gerbert's twenty. Otto II was not a scholar by nature. Gerbert may have improved his Latin-he mentions Otto's "Socratic disputations" in a letter, and Otto later proved himself a book-lover-but Gerbert's mastery of the quadrivium was not appreciated until a year later, when Archbishop Adalbero of Reims came to visit the pope.

Adalbero, brother to the count of Verdun, wanted to improve the teaching of the seven liberal arts at his cathedral's school. Reims, now in the shadow of Paris, was then the leading city in France. Kings were anointed in the Reims cathedral, and the point of the cathedral school was not to turn out country priests but to train young n.o.blemen for the king's service as bishops. It's a misconception that a bishop or archbishop had to be pious. They were as much counts and courtiers as churchmen, valued for their tact and managerial skills. And for this they needed the best education.

"While he was thinking along these lines," Richer of Saint-Remy wrote about Adalbero's plans for the school at Reims, "Gerbert was directed toward him by G.o.d himself." Or, as he enthused elsewhere, "when Divinity wished to illuminate Gaul, then shrouded in darkness, with a great light," it inspired Count Borrell to bring Gerbert to Rome, where he would meet the archbishop of Reims.

Gerbert needed a new post. After Otto II wed a Byzantine princess, Theophanu, on Easter Sunday 972, he no longer required a tutor. At the wedding, Gerbert struck up a friends.h.i.+p with Gerann, who taught the trivium of grammar, rhetoric, and logic at Reims. Gerann had sought out the young scholar, at Adalbero's request, to recruit him. Gerbert agreed to teach the quadrivium, the mathematical arts, at Reims in return for lessons from Gerann in dialectic. Taking his leave of the emperor, he rode with Gerann to Reims and became a canon of the cathedral. When Gerann died a few years later, Gerbert was named schoolmaster, a position he held, with only a short interruption, until Adalbero's death in 989, when Gerbert replaced him as archbishop.

n.o.ble and wealthy and well aware that his diocese was the most powerful in France, Archbishop Adalbero of Reims was better called a prince-bishop, being the holder of many castles and overlord of several counts himself. His church lands stretched from the suburbs of Paris well across the border of France into the Holy Roman Empire, giving the archbishop ready access to the emperor, who likewise made sure the archbishop was his man.

To King Lothar of France-already under the eye of his mother Gerberga, sister to Emperor Otto the Great, and his uncle Bruno, the emperor's brother-Adalbero, when he was elected to the post in 969, seemed yet one more imperial spy. Eventually Lothar and his son, Louis V, would use a harsher term, traitor traitor-an accusation they would extend to Gerbert, too, for Gerbert became Adalbero's secretary and confidant. To Gerbert, Adalbero was the pilot of the s.h.i.+p, the equipoise of the balance. "We were of one heart and soul," Gerbert wrote upon his friend's death in 989. Without him, "one might think the world is slipping into primordial chaos."

They were joined not only by their love of books and learning: Both were captivated by the idea of empire. The rightful order of the universe, they agreed, included an emperor, sovereign over all the Christian world, to whom the king of France would naturally pay homage. This respect for hierarchy in no way lessened King Lothar's honor, they argued. He was the representative of Christ within his realm. His dignity was reflected by the wealth and splendor of its churches.

The first thing Adalbero did upon becoming archbishop of Reims was to raze the vaulted foyer of the cathedral and make it "more worthy" of his king, according to Richer of Saint-Remy-even though that meant destroying the ramparts built to protect the church from Viking raids. He raised a bell tower. He commissioned a cross of gold for the main altar and surrounded it with bal.u.s.trades sparkling with precious stones. He gave the church elegant new reliquaries, a seven-branched candelabrum, a portable altar with gold and silver statues of the four evangelists, marble floors, brilliant frescos on the walls, and some of the earliest stained-gla.s.s windows, or, as Richer described them, "windows containing various stories." Finally, he hung golden crowns over the altars, symbolically linking earthly kings.h.i.+p to the eternal throne of Christ the Lord. He hoped Lothar would rise to the occasion.

Adalbero brought order to the many monasteries under his care and cracked down on the independent canons of Reims, building a dormitory where they were required to sleep. They had to eat together in silence, take part in the night offices, and wear identical, sober clothing. We don't know what the canons had been wearing before, but the monks like Richer had to make do without their "bonnets with long ear flaps," their "excessive breeches whose leggings stretch the length of six feet and yet do not protect ... the shameful parts from onlookers," their costly tunics that were "so tight across the b.u.t.tocks" that the monks' "a.s.ses resembled those of prost.i.tutes," and their tall, tight boots with up-curved toes.

Yet the rules at a cathedral were looser than those of a monastery-it was more like a gentlemen's club than a cloister. The canons of a cathedral sang Ma.s.s and celebrated holy festivals. They maintained the church buildings, the altars and ornaments, relics and vestments, and oversaw the church lands and other revenues, such as the taxes on markets, the tolls on bridges and roads, the fines from lawsuits, the collecting of the t.i.the, and the coining of money. They cared for the poor and sick, gave hospitality to travelers, and acted as go-betweens in feuds, often being the ones to ransom captives.

Being a canon, not just a monk, was a mark of status. Canons could eat meat, wear linen, and-most important to Gerbert-acquire possessions of their own. While monks were only allowed to use the word "my" to refer to their parents or their sins, canons owned books, rings, coins, goblets, rugs, barrels of wine, Saracen slaves (according to the wills of some Spanish canons), houses, and land. Many canons came from wealthy families who had dedicated a son to the church, not only to ensure the family's salvation, but also to have influence with the archbishop. With the boy, or oblate, had come an estate: Its income was meant to support the child, in style, throughout his life, and it was the oblate, once grown, who had control of it.

Gerbert's position as master of the cathedral school likewise brought him wealth. In his letters he mentions the houses that "at great expense we built, together with their furnis.h.i.+ng. Also the churches that we obtained by solemn and legitimate gifts," and the vast sums he was spending on books. When he left Reims in 981 to become (briefly) the abbot of Bobbio, he scandalized the Italian monks with the number of servants and quant.i.ty of goods he brought from the north. His enemies whispered to the emperor that he must secretly be keeping a wife to require such a lavish household. After he escaped Bobbio in 983 and fled empty-handed back to Reims, he bemoaned for years the fact that "the best part of my household paraphernalia" had been left behind in Italy. He had been fond of his treasures.

As long as a canon made it to church for prime at sunrise and vespers at sunset, he could be "in the world," not cloistered like a monk, for most of the day. At some cathedrals, canons spent much of their time managing their property: their vineyards, estates, and townhouses. They were repeatedly censured for disgraceful behavior, including gambling, hunting, and the keeping of concubines. Other cathedrals were more like universities, with most of the day given over to cla.s.ses. The first universities, founded in the 1200s, were cathedral schools that had cut their ties to the Church.

Reims, through the combined efforts of Adalbero and Gerbert, developed into a proto-university. Gerbert taught all seven of the liberal arts after Gerann's death, being expert in the trivium as well as the more advanced quadrivium. Students flocked to his school from throughout France and Germany; they even crossed the Alps from Italy. Among them were sons of n.o.blemen, being readied for court life or positions high in the Church. Between 972, when he first came to Reims, and 996, when he left in disgrace, Gerbert taught, for example, thirteen future bishops or archbishops, six abbots of important monasteries, Emperor Otto III's chancellor, the secretary to Emperor Henry II, the future Pope Gregory VI, and King Hugh Capet's son Robert the Pious, who would rule France from 996 to 1031. Says The Life of King Robert The Life of King Robert, "His mother sent him to the school of Reims and confided him to master Gerbert to be taught by him and instructed in the liberal arts in a manner in every way pleasing, by his virtues, to G.o.d."

Not all of his students were of n.o.ble blood. Many were simply inquisitive monks and canons, wandering scholars who in the course of their education "pillaged many schools," in one medieval description, or visited "masters of schools far away, like a prudent bee which goes from flower to flower collecting sweeter honey." To attend, they needed permission from their abbots or bishops, and Gerbert and Adalbero did their best to arrange it. Adalbero writes to the abbot of Ghent, "We have adopted one of your brothers, but you are detaining one of ours who ought to return." To the archbishop of Trier, Gerbert says, "If you are wondering whether you should direct students to us ... on this matter we have an open mind."

Gerbert's letters hint at his teaching philosophy. He speaks of the importance of "a mind conscious of itself," of studying mathematics "for the utmost exercise of the mind" and astronomy "in order not to grow inwardly lazy." To the abbot of Tours, he explains the importance of rhetoric to those who are "busied in affairs of state": "For speaking effectively to persuade and restraining the minds of angry persons from violence by smooth speech are both of the greatest usefulness. For this activity, which must be prepared beforehand, I am diligently forming a library."

And though learning required books-ever more books-teaching did not. Gerbert was an orator, not a writer. He shared what he knew through speech and demonstrations, not texts. Only very reluctantly, under pressure of a student's request, did he write things down. For instance, when Gerbert wrote his Book on the Abacus Book on the Abacus, he sent it off with a letter that began: "Only the compulsion of friends.h.i.+p reduces the nearly impossible to the possible. Otherwise, how could we strive to explain the rules of the abacus unless urged by you, O Constantine, sweet solace of my labors?"

Constantine, who seems to have been Gerbert's favorite student, was raised in the monastery at Fleury, near the French city of Orleans. Like Gerbert, he was singled out for his intelligence and sent off to learn the quadrivium. Of aristocratic birth and said to be devastatingly beautiful, he attracted a following at Reims. When the time came for him to leave, an unknown monk (probably not Gerbert) wrote a parting ode dripping with learned allusions, Greek words, and strained grammar. Wisdom herself was Constantine's teacher. The G.o.ddess had built a temple in this "man magnificent above others and always loveable." That temple s.h.i.+nes with "the excellent light of virtues," with "n.o.bility of merits" and "probity of manners." The poet's beloved Constantine is chaste as a dove, cunning as a serpent, a mirror of justice, the light of the learned. "These pages will bring happiness when your presence cannot," says the poet of his "sweetest" friend.

Constantine and Gerbert kept up a correspondence-dense and technical and including many of Gerbert's known scientific writings-on such subjects as how to make a hemisphere for studying the heavens, the solution to a seemingly insolvable problem on sesquiquartal numbers in Boethius's On Arithmetic On Arithmetic, the equally abstruse theory of super-particular numbers from Boethius's On Music On Music, and the rules of the abacus. Constantine copied and shared these scientific notes from his teacher with other like-minded monks.

Constantine also preserved Gerbert's formal letter collection. When Gerbert was forced to leave Reims, he sorted through his letters and confided a selection to Constantine. Shortly after Gerbert was named pope in 999, Constantine made a copy of these papers. Though the originals are lost, Constantine's copy still exists in the library of the University of Leiden. One page gives the pen name of the scribe, Stabilis Stabilis, meaning "stability" or "constancy."

Gerbert's letter collection was carefully edited. Like Cicero, Gerbert chose letters that showed his rhetorical skill and historical importance. In some ways, he was creating a textbook on rhetoric; notably, he chose not to include any of his scientific papers. He was also writing his autobiography. His letters reveal what was important to him: Second only to lifelong learning was friends.h.i.+p, and the two were inextricably intertwined.

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Constantine made this copy of Gerbert's letter collection sometime between 999, when Gerbert became pope, and 1014, when Constantine died. Just above the large capital letter, which falls in the middle of a page, you can read: Incipit exemplar epistolarum Girbirti Papa . .. Incipit exemplar epistolarum Girbirti Papa . .., "Here begins the copy of the letters of Pope Gerbert ..."

"I do not know that divinity has given to mortals anything better than friends," Gerbert wrote.

Friends.h.i.+p is honorable and sacred, he told the abbot of Tours. "Since you hold the constant memory of me among things worthy of honor, as I have heard from a great many messengers, and since you bear me great friends.h.i.+p because of our relations.h.i.+p, I think I shall be blest by virtue of your good opinion of me, if only I am the sort of man who, in the judgment of so great a man, is found worthy to be loved."

This conflation of love and friends.h.i.+p is found throughout Gerbert's letters. Writing to a monk from Aurillac, Gerbert describes a teaching tool he had devised "out of love" for his students: It was a "table of the rhetorical art, arranged on twenty-six sheets of parchment fastened together in the shape of an oblong ... a work truly wonderful for the ignorant and useful for the studious in comprehending the fleeting and very obscure materials of the rhetoricians and keeping them in mind." He closes, saying, "Farewell, sweetest brother; always enjoy my love which is equal to thine, and consider my goods to be for both of us."

Many of his friends received such fond treatment. To one, he writes, "I am unable, sweetest brother, to display my genuine affection for you." To others, "We congratulate you, sweetest brother, ..." "your good will, beloved brother, ..." "your request is indeed a large order, dearest brother, ..." "I am well aware that you understand the emotions of my mind, and on this account I love and embrace you, ..." "your request, sweetest brother, so often repeated. ..."

All of this "sweetest brother" stuff, like his epithet for Constantine, "sweet solace of my labors," sounds a little precious, even pathetic. But we should not be fooled into thinking the love Gerbert pined for was h.o.m.o-erotic. Though his sweet words were uttered monk to monk, they were also uttered king to king. The language of love was the speech of courtiers. Here is the French king, writing to the Byzantine emperors-through Gerbert's pen-asking for a royal bride for his son: "Not only the n.o.bility of your race but also the glory of your great deeds urges and compels us to love you. You seem, indeed, to be such preeminent persons that nothing in human affairs can be valued more highly than your friends.h.i.+p."

Love was a sign of the highest respect. One loves, as the king's letter outlines, what is n.o.ble and glorious in another person. Fondness was possible only between two virtuous souls, for true friends.h.i.+p, as Cicero said, was the love of goodness in another. Gerbert's school at Reims was founded on this Ciceronean code of friends.h.i.+p, on the mutual desire of friends to better each other. It was for love of his students in this cla.s.sical way that Gerbert "expended quant.i.ties of sweat," as Richer of Saint-Remy put it, on his teaching.