Part 2 (1/2)

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.

[image]

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.