The Abacus And The Cross Part 5

But the idea of a flat earth had not entirely disappeared. One writer who argued in favor of it was Lactantius, born in Africa in about A.D. 245. He was a professional rhetorician, a witty writer, and a convert to Christianity who possessed the convert's virulent opposition to anything that smacked of paganism. If the earth were a sphere, he scoffed, the people on the bottom side would have their feet above their heads, trees would grow upside down, and rain would fall up from the sky. For this and other theories-he claimed, for example, that Christ and Satan were twin angels, one good, one evil, created by G.o.d to balance each other out-Lactantius was condemned by the Church as a heretic. Saint Augustine may have been thinking of him and his followers.

Another known Flat Earther was a Greek merchant and later monk, Cosmas Indicopleustes (the name means "Sailor to India"). He described heaven in A.D. 547 as a rectangular arch above a rectangular earth, flat as a plate and surrounded by ocean. At the northern end of the earth, he wrote, rose a mountain, which hid the sun at night. In his lifetime, Cosmas was dismissed as an idiot-his critics quoted Saint Augustine's complaint, from more than a hundred years earlier, against Christians talking nonsense. Cosmas, however, was unknown to Gerbert. Cosmas wrote in Greek, and his cosmology was never translated into Latin during medieval times. It first came out in Latin in 1706.

In Gerbert's time there were no Flat Earthers to argue with. Gerbert and his peers followed the teachings of the Church, codified by Isidore of Seville and the Venerable Bede, who both described the earth as round like an egg. When Lady Geometry appeared in ninth- and tenth-century ma.n.u.scripts of the popular schoolbook by Martia.n.u.s Capella, the commentators writing the glosses between the lines made sure their students understood the shape of the earth. "I am called Geometry because I have often traversed and measured out the earth, and I could offer calculations and proofs for its shape, size, position, regions, and dimensions," says Lady Geometry, at which point one commentator interrupts: "It has a round shape." After explaining how Eratosthenes calculated the circ.u.mference of the earth, Lady Geometry continues to describe it: "Nor is it concave," she says. Adds this commentator, it is not "like a sponge, curved, but spherical, that is, like an egg." In the margin he drew a circle, labeled: "A disc. The earth is not like that."

The historian Ralph the Bald had never studied geometry. His education was limited, his Latin was poor. His point of view was overwhelmingly mystical: He attributed every act and event to the will of G.o.d. But even Ralph knew the earth was round. Describing the imperial insignia, he said it was "made in the form of a golden apple set around in a square with all the most precious jewels and surmounted by a golden cross. So it was like this bulky earth, which is reputed to be shaped like a globe."

Maps of the world before the year 1000 also depicted the earth as a sphere-if you know how to read them. Depicting a three-dimensional globe on a flat surface has always been problematic. Modern mapping conventions, for example, stretch the world into an oblong and cut off the far north and south. The tenth-century standard-in geometry texts as well as on maps-was to represent a sphere as a circle. With no concept of perspective drawing, the artist had little choice.

The earliest existing world map, from a chapter that Isidore of Seville added in 613 to On the Nature of Things On the Nature of Things, is a circle. It shows three continents-Asia, Europe, and Africa-encircled by ocean. In some copies of the map, Asia is at the top, Europe to the left, and Africa to the right. In others, with Asia still at the top, Europe is on the right, Africa on the left. Scholars have used this discrepancy to dismiss the entire map as nonsense. Yet what is usually pegged as an error proves instead that the mapmaker knew his astronomy: Just like putting the stars onto a celestial sphere, mapping the earth can be done from two perspectives.

One is the G.o.d's-eye view, made popular by a medieval textbook, the Commentary on the Dream of Scipio Commentary on the Dream of Scipio by the fifth-century writer Macrobius. Scipio is a character in Cicero's by the fifth-century writer Macrobius. Scipio is a character in Cicero's Republic Republic. Transported to the stars in a dream, he looks down on the little ball of the earth below, its great cities reduced to tiny spots surrounded by desert and wasteland, the known world itself but an island in the vast ocean. The moral? Man's struggle for fame is meaningless. This perspective is the one modern maps are made from-and why we recognize the continents as seen from outer s.p.a.ce. But there is another way. Feet firmly on the earth, looking up at the stars, the mapmaker can stand with his back to Asia and find Europe on his right hand and Africa on his left.

A world map that Gerbert might have seen was made in the monastery of Fleury while Abbo was abbot (see Plate 7). The ma.n.u.script that contains it collects several texts relating to computus, including some by Abbo himself. The map is drawn as a circle, from the G.o.d's-eye view, and accompanies selections from Macrobius's Commentary Commentary . A caption at the top says the circle depicts one hemisphere of the globe. Around the edge of the circle, another caption refers to the calculation of the earth's circ.u.mference by Eratosthenes. . A caption at the top says the circle depicts one hemisphere of the globe. Around the edge of the circle, another caption refers to the calculation of the earth's circ.u.mference by Eratosthenes.

Rather than being centered in the circle, as on Isidore's map, the known world here is scrunched into the top third, with Europe on the top left, Africa beneath it, and Asia on the right (very much like we would draw them). The Mediterranean and its islands divide the three. A band of ocean runs around the outer edge of the circle; little dots in the northern seas are labeled "Britannia," "Hibernia" (Ireland), and "Tile" (Thule, or Iceland). Two bands of ocean cross the hemisphere, leaving a large continent straddling the equator; this "torrid zone" is said to be uninhabitable. But below the southern band of ocean is another crescent of land, unnamed. This was the land of the Antipodes. The caption says it is inhabitable-though perhaps no people are yet there. For if people lived in this unreachable land, separated from civilization not only by the ocean but by the uncrossable deserts surrounding the equator, how could they be descended from Adam and Eve?

In spite of this biblical difficulty, many writers in Gerbert's time believed there were strangers on the opposite side of the globe-and thought the Church should send explorers out to find them. Those who disagreed quoted Saint Augustine's well-known dismissal of the Antipodes theory. As he wrote in The City of G.o.d: The City of G.o.d: It is not affirmed that this has been learned by historical knowledge, but by scientific conjecture, on the ground that the earth is suspended within the concavity of the sky, and that it has as much room on the one side of it as on the other: hence they say that the part which is beneath must also be inhabited. But they do not remark that, though it be supposed or scientifically demonstrated that the world is of a round and spherical form, yet it does not follow that the other side of the earth is bare of water; nor even, though it be bare, does it immediately follow that it is peopled.

And indeed, science could not say, in Gerbert's day, whether or not the unknown face of the globe was underwater or unpeopled. Those questions would not be answered, definitively, until Columbus discovered America five hundred years later.

Christopher Columbus is often given the credit for proving the earth was round, as well. Accepting that notion-as many modern textbooks do-means ignoring everything Gerbert knew and taught about the earth and the heavens. Such ignorance is not a product of chance: The Flat Earth Error, as it is called, was created.

The Error begins with the Italian poet Petrarch, who is known for two things: developing the sonnet, and coining the term "the Dark Ages." Sometimes called the first humanist, Petrarch divided history into ancient (before Rome became Christian in the fourth century) and modern (his own time, the fourteenth century). Everything in between was dark.

In Petrarch's version of history, the world suffered through a thousand years of ignorance and superst.i.tion. Then the humanists heroically resurrected the cla.s.sical truths of Greece and Rome-their art, literature, philosophy, science-or so they wanted people to believe. They also had a political motive. The Italian cities wanted to break free of the Holy Roman Empire. That meant denying all the contributions to civilization that Gerbert's emperors (Ottos I, II, and III) had sponsored, as well as those promoted by Charlemagne, not to mention by the Church itself. Petrarch and his fellow humanists saw no contradiction in the fact that all of the ancient art and learning they "discovered" had been copied, and so preserved, in the scriptoria of monasteries and cathedrals through the thousand years of the so-called darkness. Instead of promoting Gerbert and his celestial spheres, they revived Lactantius and his rain that falls "up" from the sky.

By the 1700s, the Dark Ages were more politely known as the Middle Ages (Latin Medii aevi Medii aevi, from which we get "medieval"). In Protestant circles they still represented a blank spot of barbarism and superst.i.tion (i.e., Catholicism) between antiquity and the Renaissance. Henry St. John Bolingbroke, whose political writings influenced Thomas Jefferson, among others, called studying the Middle Ages "a ridiculous affectation in any man who means to be useful to the present age." This intellectual att.i.tude made it easy for Washington Irving, in The Life and Voyages of Christopher Columbus The Life and Voyages of Christopher Columbus, to write a revisionist version of the discovery of the New World in 1492.

In the 1820s, having just published the stories "Rip Van Winkle" and "The Legend of Sleepy Hollow" to popular acclaim, Irving went to Spain, where he was given access to original doc.u.ments about Columbus. Finding the truth a little dry, he decided to embroider a bit on the historical Council of Salamanca, which had been convened to judge whether Columbus's proposed voyage to discover a western route to India was a good risk of the king's money. In the monastery of Saint-Stephen, "the most scientific college in the university," our hero "soon discovered that ignorance and illiberality may sometimes lurk under the very robes of science," Irving wrote. Facing a "learned junto" of professors, monks, and church dignitaries, this "plain and simple navigator, somewhat daunted, perhaps, by the greatness of his task" met their "ma.s.s of inert bigotry" with an "elevated demeanor" and a "kindling eye."

They threw the heretic Lactantius at him, Irving claims, as well as Saint Augustine's views on the Antipodes. "To his simplest proposition, the spherical form of the earth, were opposed figurative texts of Scripture," Irving writes: The Psalms and Saint Paul both describe the heavens as being like a tent, ipso facto the earth was flat like the floor of a tent. "Others," Irving concedes, "admitted the globular form of the earth, and the possibility of an opposite and inhabitable hemisphere, but maintained that it would be impossible to arrive there."

What in fact they maintained-and the original records of the council still exist-was that Columbus was fudging his numbers. Using the same methods Gerbert knew, the Council of Salamanca calculated the circ.u.mference of the earth to be about 20,000 miles (it is actually about 24,900 miles) and the distance between one degree of lat.i.tude or longitude at the equator to be 56 miles (it is actually 68 miles). Columbus thought the earth was much smaller. He said a degree at the equator was 45 miles and the span of ocean between the Canary Islands and j.a.pan only 2,765 miles-20 percent of the actual figure. If he had not providentially b.u.mped into America, Columbus would-as the experts in Salamanca believed-have run out of food and fresh water long before he reached j.a.pan. Columbus may have had courage and a "kindling eye" on his side; his opponents had science and reason on theirs.

Yet it was Washington Irving's version of history that became common knowledge, reprinted in 175 editions before 1900 and still appearing in textbooks and history books today. Why does the Flat Earth Error remain so popular? Americans like to think that before we were discovered, all the world was sunk in darkness.

There is also the War Between Religion and Science to take into account. The groundwork for the war was laid in the 1850s by William Whewell of Cambridge University, who coined the word "scientist" to replace "natural philosopher." His History of the Inductive Sciences History of the Inductive Sciences, which became a standard textbook, portrayed religion as inimical to science. He introduced two sources as proof that medieval Christians believed the earth was flat: the heretical Lactantius and the unread Cosmas Indicopleustes.

John W. Draper, a professor of medicine at New York University, expanded on Whewell's thesis. In 1860, in Britain, he presented a paper supporting Darwin's theory of evolution. He was attacked, viciously, by Bishop Samuel Wilberforce (son of William Wilberforce, the famous abolitionist). Remembering this painful experience as he wrote The History of the Conflict Between Religion and Science The History of the Conflict Between Religion and Science ten years later, Draper declared that science and religion were at war. Science stood for freedom and progress; religion meant superst.i.tion and repression. ten years later, Draper declared that science and religion were at war. Science stood for freedom and progress; religion meant superst.i.tion and repression.

Andrew d.i.c.kson White, the founder of Cornell University, put two and two together in 1896 in his History of the Warfare of Science with Theology in Christendom History of the Warfare of Science with Theology in Christendom. "A few of the larger-minded fathers of the Church," White conceded, thought the earth was round, "but the majority of them took fright at once." He ignores Augustine, Isidore, and Bede (not to mention Gerbert and Abbo) and gives the majority view to Lactantius and Cosmas.

Over a hundred years later, the idea that medieval Christians like Gerbert thought the world was flat has not disappeared. It remains a weapon in the war between science and religion that defines modern America.

CHAPTER VIII.

The Astrolabe Ptolemy the astronomer was riding along on a donkey carrying a celestial sphere in his hand, according to an Arabic folktale. He dropped the sphere, it rolled under the donkey's hooves, and squash squash-the astrolabe was invented.

The Latin version of this story is more restrained: It leaves out the donkey. Ptolemy excelled in the study of stars, says a book from Gerbert's time. Among the instruments he invented was one that was "both useful for learners and a mighty miracle for those looking at it.... For the Wazzalcora was obtained by a divine mind; in Latin it means 'flat sphere,' which also, by another name, is the astrolabe."

Astrolabe means "star-holder." Harder to make but handier to carry than a celestial sphere (as the donkey anecdote shows), the astrolabe had more than a thousand uses-an Arabic astronomer in around 960 claimed it had precisely 1,760 uses. You could tell time by sun or stars, in terms of twenty-four hours of equal length or using the medieval clock, in which day and dark are each divided into twelve parts. You could find the celestial coordinates of the sun, moon, stars, or planets, and the terrestrial lat.i.tude and longitude of any town. You could calculate sine functions, tangents, declinations, and right ascensions. You could predict the time of an eclipse. When al-Khwarizmi and the astronomers of the House of Wisdom calculated the circ.u.mference of the earth, traipsing through the Iraqi desert at the behest of the caliph of Baghdad in 827, they used astrolabes to track the alt.i.tude of the sun. means "star-holder." Harder to make but handier to carry than a celestial sphere (as the donkey anecdote shows), the astrolabe had more than a thousand uses-an Arabic astronomer in around 960 claimed it had precisely 1,760 uses. You could tell time by sun or stars, in terms of twenty-four hours of equal length or using the medieval clock, in which day and dark are each divided into twelve parts. You could find the celestial coordinates of the sun, moon, stars, or planets, and the terrestrial lat.i.tude and longitude of any town. You could calculate sine functions, tangents, declinations, and right ascensions. You could predict the time of an eclipse. When al-Khwarizmi and the astronomers of the House of Wisdom calculated the circ.u.mference of the earth, traipsing through the Iraqi desert at the behest of the caliph of Baghdad in 827, they used astrolabes to track the alt.i.tude of the sun.

Al-Khwarizmi's book on the astrolabe was known in Cordoba in Gerbert's time-no one can say how long it had been there. But in 978, Maslama of Madrid, the chief astronomer in al-Andalus, adapted al-Khwarizmi's star tables to the coordinates of Cordoba. To do so, he used al-Khwarizmi's book, as well as an Arabic copy of Ptolemy's Planisphere Planisphere, which explains the math behind the astrolabe.

Parts of both books were translated into Latin before the year 1000, possibly at the monastery of Ripoll. The author wrote a rough version, in sloppy Latin and peppered with Arabic words; he added a great deal of explanatory material, along with a preface pointing out the astrological significance of the star of Bethlehem. He seems to have had an actual astrolabe in front of him, along with someone who knew Arabic well; this person identified the Arabic names of the various components and explained them to him in Latin.

At about the same time, someone in Catalonia made the first European astrolabe-a rather crude beginner's model, but proof the concept was understood. With the addition of this tool, medieval Latin astronomy suddenly became a truly mathematical science.

What part did Gerbert, the leading mathematician and astronomer of the West, play in this transition? Did Gerbert know, read, or even write that first Latin book on the astrolabe? Was he the scribe sitting beside the Arabic speaker at Ripoll? (Was his Latin ever ever sloppy?) Did he write one of the more elaborate revisions of the text that soon circulated through Western Europe? Experts have argued these points for a hundred years. The sources, admittedly, are none too clear. Yet it seems likely, at least, that Gerbert learned about this magical instrument while he was in Catalonia, and that he introduced it to his students at Reims. sloppy?) Did he write one of the more elaborate revisions of the text that soon circulated through Western Europe? Experts have argued these points for a hundred years. The sources, admittedly, are none too clear. Yet it seems likely, at least, that Gerbert learned about this magical instrument while he was in Catalonia, and that he introduced it to his students at Reims.

William of Malmesbury-never too reliable-claimed that Gerbert "surpa.s.sed Ptolemy in knowledge of the astrolabe."

Michael Scot, who called Gerbert the finest necromancer in France, offered the astrolabe as evidence of his pact with the devil. Writing in the thirteenth century, he said Gerbert "borrowed" an astrolabe, conjured up his familiar demons, and forced them to explain how it was made, what it was good for, and how to work it. "He also made the demons teach him all astronomy. Afterwards the astrolabe came into the hands of many, and consequently there were many doctors of this art of various nations, regions, and times who compiled the books based on experiments." (If you subst.i.tute "Muslim" for "demon," this tale might be true.) One of those "books based on experiments" is quite specific about Gerbert's relation to the astrolabe. After introducing the instrument as useful for measuring heights, lengths, and depths, the author adds, "It should be noted that Gerbert wrote a book on the astrolabe, which one can find in this volume in the second part, but it is rather confused; it does not teach how to construct the instrument, but only how to use one. Having read it, Berenger ... asked his friend Hermann to provide him with a treatise on the construction of the astrolabe. It is in response to this demand that Hermann first composed this book, then he brought some order to that of Gerbert."

Berenger's complaint is that Gerbert told only how to use use the astrolabe, not how to the astrolabe, not how to make make it. It is the same criticism we could level at Gerbert's abacus book: He doesn't describe the instrument or provide any pictures. it. It is the same criticism we could level at Gerbert's abacus book: He doesn't describe the instrument or provide any pictures.

Richer of Saint-Remy, who described Gerbert's abacus in such detail (the shieldmaker, the thousand counters of horn, the nine signs), does not mention the astrolabe at all; to some, that's sure proof Gerbert had never heard of one. Richer, unlike William (writing in the early 1100s) and Michael (in the 1200s), at least knew Gerbert personally.

But Thietmar of Merseburg, writing ten years after Gerbert's death, also knew him. In his history of the three Emperors Otto, Thietmar pa.s.ses over the Scientist Pope in a few words. Yet what he points out is significant. In wording that strangely echoes the contemporary description of Ptolemy, Thietmar says Gerbert "was particularly skilled in discerning the movements of the stars and surpa.s.sed his contemporaries in his knowledge of various arts." By 1013, when Thietmar was writing, news of the astrolabe had spread throughout the West. Until the telescope came along in 1610, it would remain the most popular astronomical instrument. Gerbert could hardly have excelled in star-lore if he knew nothing about it.

Thietmar goes on. Gerbert made an horologium horologium for the emperor, he says. "Astrolabe" is one possible translation: The word contains the root for "hour," and telling time was a popular use for an astrolabe. Thietmar might instead have meant a water-driven clock or for the emperor, he says. "Astrolabe" is one possible translation: The word contains the root for "hour," and telling time was a popular use for an astrolabe. Thietmar might instead have meant a water-driven clock or clepsydra clepsydra, a mechanical clock (which William of Malmesbury also claimed Gerbert had made), or some type of sundial. But he adds that Gerbert could position his horologium horologium correctly only "after he had observed through a tube the star that sailors use for guidance," meaning the North Star. This detail fits one of Gerbert's celestial spheres or the instrument known as the correctly only "after he had observed through a tube the star that sailors use for guidance," meaning the North Star. This detail fits one of Gerbert's celestial spheres or the instrument known as the nocturlabe nocturlabe, which consisted of a sighting tube, like a primitive telescope, surrounded by a graduated circle marked off in degrees. But it does not rule out the astrolabe.

Finally there is Gerbert's own aside, in his letter to Constantine, about using the abacus to multiply "actual numbers" in order to compare "the theoretical and actual measurement of the sky and of the earth." These numbers, he said, were "measurements determined by the inclination and erection of the geometrical radius." By "geometrical radius" he might have meant the sighting device of an astrolabe.

Given al-Khwarizmi's book-or a sample instrument-making an astrolabe would not have taxed Gerbert's mechanical abilities. It called for a metal workshop and a good hand at engraving, as had the bra.s.s tubes, horizons, armillary rings, and stands for his celestial spheres. It called for knowledge of climate circles and constellations. It required, as well, a mathematical theorem to accomplish, more precisely, what Ptolemy's donkey had done to the sphere.

This theorem was ancient. According to Bishop Synesius of Cyrene, who made an astrolabe of silver and gold in about A.D. 400, the idea of mapping a sphere onto a flat surface was "vaguely shadowed" by Hipparchus of Rhodes, born in 180 B.C. Hipparchus's so-called stereographic projection was recorded three hundred years later by Ptolemy in his Planisphere Planisphere. Ptolemy did not invent the astrolabe, Synesius notes, but was content to have one as his "one useful possession, for the sixteen stars made it sufficient for the night clock." Synesius was a student of Hypatia, the first woman known to be a mathematician, and credits her help in making his deluxe astrolabe. The theory of the stereographic projection having been "neglected in the long intervening time" between Ptolemy and Hypatia, Synesius writes, "we worked it out and elaborated a treatise and studded it thickly with the necessary abundance and variety of theorems. Then we made haste to translate our conclusions into a material form, and finally executed a most fair image of the cosmic advance."

Where Synesius says "image of the cosmic advance," you could subst.i.tute "rotatable star map," "flat model of the starry sky," "a.n.a.log computer," or "two-dimensional model of the universe that one can hold in one's hands"-all these have been used to describe the astrolabe.

Bishop Synesius's astrolabe, and all succeeding ones, had three basic parts: the base, or mater mater ("mother"); the lat.i.tude plates (one or several); and the "spider," known in Latin as the ("mother"); the lat.i.tude plates (one or several); and the "spider," known in Latin as the rete rete, or "net." The rete rotates around a pin, which also holds the sighting device, the arm or pointer called an alidade alidade, to the back of the mater. The parts are locked in place by a "horse"-a wedge traditionally shaped like a horsehead-stuck through a hole in the pin. The astrolabe is carried by a ring at the top.

The spidery rete is the heavenly part of the instrument. The artistry of an astrolabe is in marking sixteen to fifty bright stars, in relation to each other and to the ecliptic, on a disc of bra.s.s, and then making that disc nearly transparent by cutting away every bit of metal that is not strictly necessary. What remains are thin bra.s.s circles and arcs. Delicate arrows and hooks, often labeled with the stars' names, jut from them to indicate the stars' locations: For the whole point is to be able to spin this map of stars above a lat.i.tude plate. One complete rotation of the star pointers over the lat.i.tude plate underneath it equals twenty-four hours of time.

A different plate is needed for the lat.i.tude of each location-Constantinople, Rome, Baghdad, Jerusalem, Cordoba-in which the owner hopes to use his astrolabe, so most medieval astrolabes were made with a stack of plates, each etched on both sides. Here's where Ptolemy's (or Hipparchus's) theory of stereographic projection comes into play. The great circles drawn on the surface of a three-dimensional celestial globe, or denoted by bra.s.s rings on an armillary sphere, are mapped onto a two-dimensional plate in a way that preserves the angles-two lines that cross at right angles on the globe will cross at right angles on the plate. Imagine you are standing at the south celestial pole and looking north, through the transparent earth, at the inner surface of the heavenly sphere, and that all the climate circles are visible: This is the point of view of the plate. The largest circle on the plate is the Tropic of Capricorn, the middle circle is the equator, and the smallest circle is the Tropic of Cancer. A series of arcs beginning at the horizon curve into full circles as they approach the zenith; these mark the degrees of alt.i.tude above the horizon (like lines of lat.i.tude on a terrestrial map). Large astrolabes can have an arc for each degree, whereas smaller ones make do with one arc for each 5 to 6 degrees. Another set of arcs, perpendicular to the horizon, emanates from the zenith point. These are the circles of azimuth, or direction measured around the horizon (like lines of longitude).

The lat.i.tude plates are held in place by the mater, a disc with a st.u.r.dy lip. On the back of the mater is engraved a calendar scale, showing days and months, and surrounded by a zodiac scale, telling what sign the sun is in each day. In the middle is a shadow square, for calculating the heights of towers and mountains using the geometrical princ.i.p.al of similar triangles. The rim of the mater is marked in 5-degree intervals to make a 360-degree alt.i.tude scale. To measure the alt.i.tude of the sun or a star, you dangle the instrument vertically from its ring and sight through the viewfinder of the alidade on the back; once the alidade is lined up with the star, you can read off the alt.i.tude from the scale on the astrolabe's rim.

To set the astrolabe to the correct time, take the alt.i.tude you just measured and find that star on the rete. Turn the rete until that star-pointer points to the correct alt.i.tude circle on the lat.i.tude plate. The result is a map of the sky at that very moment. Hours later, the star will be in a different place in the sky, at a different alt.i.tude above the horizon. To find out exactly how much time has pa.s.sed, first note the current setting of the rete. Take the new alt.i.tude of the star, and rotate the rete until the star-pointer correctly indicates the star's new position in the sky. The amount you turned the rete-read with a time-pointer that projects from the rete over the 360-degree scale on the mater's rim-gives the time: 15 degrees equals one hour, with noon at the top and midnight at the bottom. Telling time by unequal hours was possible if an hour scale was etched onto the lat.i.tude plate. This convenient, pocket-sized marvel could thus accomplish every measurement Gerbert could make with his much bulkier celestial spheres.

If Gerbert did make an astrolabe, we have no record of it. The first mention of astrolabe-making in the West comes from Liege in about 1025, in the series of letters already mentioned between Rodolf of Liege and Ragimbold of Koln. The two friends were in the midst of their investigation of angles and triangles-their letters demonstrating the spread of Gerbert's experimental approach to geometry. Now Rodolf wrote to his friend, "I would have sent the astrolabe for you to judge it; but it serves us as an exemplar to construct another. If you wish to know about it, please be so good as to come to Ma.s.s at Saint-Lambert's. I trust you will not regret it."

What did the astrolabe Rodolf brought to Ma.s.s look like? We cannot know: No astrolabes exist that were made near Liege or anywhere in the north before 1540. In fact, of the 150 medieval European astrolabes extant, only two can be dated to before 1200.

Because of the precession of the equinoxes, an astrolabe is only accurate for about a hundred years. (This concept, that the equinoxes appear to be slowly moving westward in relation to the fixed stars of the zodiac, was first pointed out by Hipparchus; al-Battani wrote a treatise on it in the tenth century. We now know it occurs because the earth's axis wobbles.) Unless it is a.s.sociated with someone famous, there's no reason to keep an out-of-date astrolabe. The bra.s.s is melted down and, especially in wartime, reused. As a result, most extant medieval astrolabes are "one-off" pieces-the only example known to have come from a single instrument maker or workshop. Yet most are not beginners' work. The Sloane astrolabe at the British Museum is the first English-made astrolabe, dating to about 1300. Its mind-boggling complexity suggests that English instrument makers had been producing astrolabes for hundreds of years. The oldest German astrolabe still extant is equally complicated.

Gerbert's name is linked to two astrolabes that do still exist. In Florence is a bra.s.s astrolabe long said to have been Pope Sylvester's. It was supposedly made for Gerbert in 990 or 1000 or 1002, in France or maybe in Cairo. Its later owners, the Medici family, however, kept it in a leather case along with an inscription on parchment saying it was made for King Alfonso X of Spain in 1252. A careful examination of the instrument shows it was made to be used in Baghdad. The distinctive form of Arabic kufi kufi script used in the star names and other inscriptions dates it to the tenth century-which means Gerbert (and later King Alfonso) could have owned it, but not used it (unless they traveled south to the lat.i.tude of Baghdad, or owned an additional lat.i.tude plate). Much later, probably in the nineteenth century, an antique dealer etched on Latin lettering for the months, presumably to make it look as if the astrolabe were made in Spain. His mistake was giving the length of February as 28 days-he forgot that tenth-century fractions were base twelve; to people of Gerbert's time, "" would have been unreadable. But the astrolabe itself is a well-made scientific instrument. script used in the star names and other inscriptions dates it to the tenth century-which means Gerbert (and later King Alfonso) could have owned it, but not used it (unless they traveled south to the lat.i.tude of Baghdad, or owned an additional lat.i.tude plate). Much later, probably in the nineteenth century, an antique dealer etched on Latin lettering for the months, presumably to make it look as if the astrolabe were made in Spain. His mistake was giving the length of February as 28 days-he forgot that tenth-century fractions were base twelve; to people of Gerbert's time, "" would have been unreadable. But the astrolabe itself is a well-made scientific instrument.

The other astrolabe that Gerbert could have seen or used or owned is not well made. Known as the Des...o...b..s astrolabe, it is bra.s.s, the size of an open hand. Now in Paris, it was made in Catalonia in the tenth century, at about the same time (or before) the earliest Latin astrolabe texts were being written there. The oldest European astrolabe still extant, this crude, seemingly unfinished instrument, clearly fashioned by a beginner, marks the pa.s.sage of Islamic science to the Christian West before the year 1000.

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The Des...o...b..s astrolabe is the first known astrolabe with inscriptions in Latin. A beginner's model, it was made in tenth-century Catalonia by someone who was, most likely, copying from another astrolabe, or, possibly, from an ill.u.s.tration of an astrolabe.

Curiously, the Des...o...b..s astrolabe is unlike any of the sixteen Arabic astrolabes remaining from tenth- or eleventh-century al-Andalus. The rete carries eighteen stars (none of them named) and is so clumsy it seems to have been copied from another astrolabe (Rodolf's plan) or even from a drawing of an astrolabe. But it bears no resemblance to any Arabic rete. Six of the star-pointers are too long: To accurately mark their stars, they should have been curled up at the tips; this was never done. The placement of the bright star Aldebaran is seriously off: It marks the path Aldebaran took through the sky in Ptolemy's time; for this one star only, the precession of the equinoxes was not taken into account. The other eleven stars are correctly placed, matching the data in the star tables made by Maslama of Madrid in 978.

The instrument can also be dated to before 986-no one can say how much before-based on an inscription on one of the lat.i.tude plates. (If one plate is more detailed than the others, you can a.s.sume the instrument maker favored that lat.i.tude-the astrolabe was meant to be used there, or the maker was working there.) The inscription reads, in good tenth-century Catalan script: Roma et Francia Roma et Francia. Working backward from the engraved circles, geometry proves the plate was designed for the lat.i.tude 4130', which is close to that of Rome (4153'). It is also within a few minutes of the lat.i.tude of Barcelona, the bordertown of "Francia."

Gerbert's letters to and about Spain reveal the significance of this inscription. As Gerbert shows, until 986 Catalonia was part of the kingdom of France; after that, the astrolabe maker would have written Roma et Burcinona Roma et Burcinona.

The story of Catalan independence, as Gerbert tells it, begins in 976 with the death of the scholarly caliph al-Hakam, to whom Gerbert's friend Miro Bonfill had been sent as amba.s.sador. Al-Hakam was succeeded by his ten-year-old son, who was overshadowed by the war-leader al-Mansur the Victorious. Al-Mansur propped up his power by warring on Christians. In July 985, he sacked Barcelona. Gerbert's friend Count Borrell called for aid to his overlord, the king of France. There was no reply.

The king of France died in early 986 and was succeeded by his young son, Louis V, known as "Louis Do-Nothing." On Borrell's behalf, Abbot Gerald of Aurillac wrote to Gerbert at Reims to ask "what sort of person" Louis was and whether he was "about to conduct the armies of the French as aid to Borrell." Replied Gerbert, "It is unnecessary to ask the first question of us, because, as Sall.u.s.t says: 'It is necessary that all men who take counsel about doubtful matters should be free from wrath, animosity, and compa.s.sion.'" As we will see, Louis had just accused Archbishop Adalbero of Reims of treason. "Considering the other question according to its nature," Gerbert continued, "... our opinion seems rather to incline to the negative."

Borrell pet.i.tioned France again in 987. This time he was answered by a letter Gerbert wrote as secretary to Hugh Capet, the third king to rule France within that span of two years. "If you wish to maintain the fidelity so often offered through intermediaries to our predecessors," said King Hugh, "hasten to us with a few soldiers in order to confirm the fidelity already promised, and to point out the necessary roads to our army." Borrell never left Catalonia, the king's army never left France, and historians date Catalan independence from 986.

We do not know if the Des...o...b..s astrolabe, or one like it, came north from Catalonia before 1025, when an astrolabe landed in Rodolf of Liege's hands. But news of this magical instrument had. Though Liege is a long way (nearly 900 miles) from Barcelona, Rodolf had no need to tell Ragimbold what an astrolabe was: The instrument had been integrated into the quadrivium long before, probably by Gerbert.

Fulbert of Chartres, for example, was master of the Chartres cathedral school by 1004. He wrote several mnemonic poems to help his students understand scientific concepts. One is on weights and measures, another on the calendar; a third, strangely, is mostly in Arabic: Abdebaran Tauro, Geminis Menkeque Rigelque, Frons et Calbalazet prestant insigne Leoni; Scorpie, Galbalagrab tua sit, Capricornie, Deneb, Tu, Bata.n.a.lhaut, Piscibus es satis una duobus.

In English it reads, "Aldebaran stands out in Taurus, Menke and Rigel in Gemini, / and Frons and bright Calbalazet in Leo; / Scorpio, you have Galbalagrab, and you, Capricorn, Deneb, / You, Bata.n.a.lhaut, are alone enough for Pisces." The Arabic words, of course, are the names of stars, some of the brightest in the sky. Though, like Gerbert, Fulbert never uses the term "astrolabe" (or Wazzalcora, for that matter), anyone familiar with the instrument would recognize these stars: They are the stars on the rete of the astrolabe that indicate the climate circles.

Fulbert also left a notebook in which he defined twenty-eight Arabic words used in connection with the astrolabe and supplied a chart showing the twelve signs of the zodiac in one column and the name of an astrolabe star (if there was one for that zodiac sign) in a second column. The Arabic terms, and most of the Latin translations, come from the first Latin book on the astrolabe, the rough and sloppy one compiled in Catalonia. But some of Fulbert's explanations expand on the Catalan book, showing that he had information from elsewhere, as well as a good grasp of how to use the actual instrument.

Fulbert, who became bishop of Chartres in 1006 and died in 1028, may have been Gerbert's student; the sources, again, are unclear. One theory of how he learned about the astrolabe, then, is that Gerbert wrote the first Latin book on the subject at Ripoll-or simply found it there and copied it-and brought news of the astrolabe north to Reims, where Fulbert was a student. Yet as an adolescent, arriving in Catalonia in 967, Gerbert was already known for his beautiful Latin style. The Ripoll book, besides being written in poor Latin, retains many Arabic terms; if Gerbert knew these Arabic words, why don't they show up in any of his other writings (as they do in Fulbert's)? Gerbert may have owned a copy of this first Latin book on the astrolabe, but he is unlikely to have written it.

Another theory concerning this book names Lobet of Barcelona as the author. Gerbert wrote to Lobet in 984 requesting "De astrologia, translated by you." He received it and subsequently revised it, the idea goes-just not very well, allowing later writers to say Gerbert's astrolabe book was "confused" and needed the help of Berenger's friend Hermann to bring some order to it.

Yet "De astrologia" is vague: On the Study of the Stars On the Study of the Stars might refer to this book on the might refer to this book on the astrolabe astrolabe. But it might better refer to a book on astrology astrology . The oldest Latin ma.n.u.script to contain Arabic words is, in fact, a book on astrology. Now in Paris, it is a rather thin little book, with a newish leather binding. The parchment is off-white with faded brown letters, undistinguished. Capital letters, meant to have been painted in red, are missing. Abruptly, midway, the writing becomes much smaller, to save s.p.a.ce. It was made in Limoges, 400 miles north of Ripoll, between 978 and 1000. Parts were copied from an earlier ma.n.u.script, now lost, that came from Catalonia; other parts came from the monastery of Fleury, including a work by Abbo on cosmology. Most of it, however, is about fortune-telling, not what we would call the science of the stars. The collection of astrology texts it contains, named the . The oldest Latin ma.n.u.script to contain Arabic words is, in fact, a book on astrology. Now in Paris, it is a rather thin little book, with a newish leather binding. The parchment is off-white with faded brown letters, undistinguished. Capital letters, meant to have been painted in red, are missing. Abruptly, midway, the writing becomes much smaller, to save s.p.a.ce. It was made in Limoges, 400 miles north of Ripoll, between 978 and 1000. Parts were copied from an earlier ma.n.u.script, now lost, that came from Catalonia; other parts came from the monastery of Fleury, including a work by Abbo on cosmology. Most of it, however, is about fortune-telling, not what we would call the science of the stars. The collection of astrology texts it contains, named the Alchandreana Alchandreana after one of its purported sources, Alchandreus, can be found in nearly a hundred ma.n.u.scripts, fifteen from before the year 1200. after one of its purported sources, Alchandreus, can be found in nearly a hundred ma.n.u.scripts, fifteen from before the year 1200.

The Arabic words appear on a page of diagrams. Two have not been deciphered. One clearly shows the twenty-eight lunar mansions, with a drawing of the stars in each. The star names are given in Arabic. Beneath the ill.u.s.tration starts a text identified in 2007 as having been written by Gerbert's friend Miro Bonfill. Based on the playful, pun-filled style, two of the other astrological treatises in the Alchandreana Alchandreana can also be attributed to Miro. The three others, which begin with can also be attributed to Miro. The three others, which begin with De astrologia De astrologia, have been ascribed to Lobet of Barcelona-with just as much (or as little) evidence as the book on the astrolabe from Ripoll is thought to be his work. We have a book about stars and Gerbert's letter asking Lobet for a book about stars.

The Alchandreana Alchandreana is three times as long as the Ripoll book on the astrolabe. Based on Arabic and Jewish sources, and using Hebrew, Latin, and Arabic letters, it is well-organized and clear, and it provides dozens of sample computations for predicting the outcome of an illness; the character of a child; the success of a journey, a marriage, or a battle; the site of buried treasure; or the ident.i.ty of a thief. Fifteen chapters tell how the is three times as long as the Ripoll book on the astrolabe. Based on Arabic and Jewish sources, and using Hebrew, Latin, and Arabic letters, it is well-organized and clear, and it provides dozens of sample computations for predicting the outcome of an illness; the character of a child; the success of a journey, a marriage, or a battle; the site of buried treasure; or the ident.i.ty of a thief. Fifteen chapters tell how the phisici phisici forecast the weather. forecast the weather.

Gerbert, a close friend of Miro Bonfill, most likely knew this book and practiced astrology himself-which was not considered pseudo-science in the tenth century. A knowledge of astrology would explain why Gerbert was so welcomed by the pope and the emperor, when he came to Rome from Spain in 970, as a master of mathesis mathesis-a word more commonly used for fortune-telling than for mathematics. According to Richer of Saint-Remy, mathesis mathesis was at the time unknown in Italy. was at the time unknown in Italy.

Astrology also explains Gerbert's later reputation as a necromancer. When William of Malmesbury says Gerbert "surpa.s.sed Ptolemy in knowledge of the astrolabe," he follows it immediately by saying he also surpa.s.sed "Alchandreus in that of the relative positions of the stars, and Julius Firmicus in judicial astrology." He then tells a fanciful tale of Gerbert using his knowledge to find buried treasure-something Miro describes how to do in the Alchandreana Alchandreana.

Nor was William the first to accuse Gerbert of being a wizard. A poem by Ascelin of Laon, the nephew of Adalbero of Reims, names King Robert's tutor "Nectanabo." Nectanabo is the name of the wizard in the legend of Alexander the Great, and Alexander is one of the authorities on astrology mentioned in the Alchandreana Alchandreana. Everyone hearing Ascelin's poem would have known Gerbert had in fact been the king's tutor and that his "wizardry" included telling horoscopes.

Finally, Gerbert uses astrological lore in his own writing. He dates the death of a duke to June 17, 983, by saying "the Sun found itself in the house of Mercury." To an astrologer, June 17 of that year was the day the Sun transited the last degree of Gemini, which is the "house" of Mercury. The theory of the houses of the planets is explained in the Alchandreana Alchandreana.

And then there is Gerbert's complaint about the floods on the way to Trier: "The hope for better weather has been shattered by the phisicis phisicis ," he writes. He may have meant himself. ," he writes. He may have meant himself.

Jotted on the last page of the ma.n.u.script is a horoscope that a monk worked out for himself in 1014. The monk was Ademar of Chabannes, who described Gerbert in his chronicle as seeking knowledge among the Arabs in Cordoba. The method Ademar used to compute his horoscope-the method taught throughout the Alchandreana Alchandreana-does not depend on a study of the stars, but on affixing numbers to a person's name. Ademar first translated his own name and that of his mother into Hebrew. Then, using a code in which the letters of the Hebrew alphabet stand for numbers, he found the numerical values of the names and began his calculations-for to be a fortune-teller meant being a very good mathematician. Depending on the question you were asking, you may have divided by the number of years since the creation of the world. If Saturn figured in your horoscope, you would have divided that number by 30 (the number of Earth years that makes one Saturn year); likewise, by 12 for Jupiter, or by 1 for Mars. For Venus, you used the number of days, not years, dividing by 300.

An abacus would come in handy, and many copies of this astrology book are bound with treatises on the abacus. They are also found alongside treatises on the astrolabe: To fully use the method, you needed to be able to tell the exact time.

Two ma.n.u.scripts, one from Lorraine and one from Bavaria, preserve short bits of the Alchandreana Alchandreana that are intelligent and well written-and appear alongside Gerbert's own works on mathematics. These bits could be all that is left of Gerbert's own textbook on astrology, based on Lobet's work. that are intelligent and well written-and appear alongside Gerbert's own works on mathematics. These bits could be all that is left of Gerbert's own textbook on astrology, based on Lobet's work.

If Lobet of Barcelona's De astrologia De astrologia was about astrology, how did Fulbert of Chartres and Rodolf of Liege learn about the astrolabe? Was Gerbert the link between Catalonia and the north? It's still possible. Gerbert was a teacher, not a writer. All of his known scientific treatises were written at the request of a student. Having learned about the astrolabe, his first impulse would not have been to write a book. Instead, he would have incorporated the astrolabe into his teaching of astronomy. His students would have spread the knowledge farther. was about astrology, how did Fulbert of Chartres and Rodolf of Liege learn about the astrolabe? Was Gerbert the link between Catalonia and the north? It's still possible. Gerbert was a teacher, not a writer. All of his known scientific treatises were written at the request of a student. Having learned about the astrolabe, his first impulse would not have been to write a book. Instead, he would have incorporated the astrolabe into his teaching of astronomy. His students would have spread the knowledge farther.

Fulbert, Rodolf, and Ragimbold were all members of the same scientific network. Rodolf and Ragimbold conferred with Fulbert on mathematical questions; as Ragimbold wrote, "I pa.s.sed by Chartres, and Lord Fulbert, bishop of the place, demonstrated to me your same figure, with an exposition of our first question concerning the triangle; and, after many conferences, he agreed with our opinion." And Fulbert knew Gerbert's scientific works: A tenth-century catalog shows that the Chartres library held copies of Gerbert's letters to Constantine on the abacus and the celestial sphere.

The key, in fact, is Gerbert's student Constantine, whom he called "sweet solace of my labors." Without Constantine, we would know very little about Gerbert. Under the pen name "Stabilis," as we have seen, Constantine preserved and copied Gerbert's letter collection. Constantine induced Gerbert to write about the abacus-an exercise he found "nearly impossible"-and shared Gerbert's treatise with other scholars, like Fulbert. Constantine quizzed his former teacher on those baffling problems in Boethian number theory. He requested instructions on making a celestial sphere. The sphere's star-viewing tubes "differ from organ pipes by being all equal in size," Gerbert notes, suggesting he and Constantine had also discussed his treatise on organ pipes, which would have greatly interested Constantine: He was known as "a remarkable musician." Gerbert recommended that the monks of Aurillac consult him about "the learning of music and the playing of organs," adding, "I will see to it that what I am unable to finish myself will be completed by Constantine."

Not surprisingly, Constantine also collected information on the astrolabe. He seems to have had the "confused" treatise later attributed to Gerbert-the one that "does not teach how to construct the instrument, but only how to use one." He may have received it from Gerbert. Or maybe not. We have no evidence. We know only that he sought to supply what was missing and was successful. "Ascelin the German, citizen of the city of Augsburg, to Stabilis of Orleans, monk of Micy, greetings!," begins one astrolabe ma.n.u.script. "Concerning how much effect firm friendship has in getting things done, ... I have decided that the effort of my whole talent should always reply kindly to the wishes of friends." After complimenting his "beloved" friend for "being of unsullied honesty" and "by your own name and at the same time truly by your character ... being 'Stable, Constant,'" and therefore "not unequal of the laws of friendship," Ascelin asks him to "accept, then, this work that you desire, worked out for constructing the instrument of the astrolabe, not completely, but diligently according to the small measure of my intelligence."

Ascelin's book is also confusing. It has no ill.u.s.trations. It is very difficult to follow his directions without a series of drawings, breaking them down step-by-step, as most later astrolabe treatises do; or without an actual astrolabe to look at. Perhaps Constantine had one. Astrolabes may have been more common in the late tenth century than we think. Certainly the knowledge of how to build them had reached Augsburg in Germany, 800 miles north of Barcelona, while Constantine was at Micy.

Knowing when that might have been requires some sleuthing among saints' lives and in church archives. We learn that Abbo of Fleury so disliked Gerbert's beloved Constantine that he refused even to hear his music played in the church at Fleury. Only after Abbo died, says the Life of Gauzlin Life of Gauzlin, the next abbot, was there "first performed at Fleury the story of the arrival of Saint Benedict which Constantine-a man raised in that place but later given the honor of the abbacy of Micy by Arnulf, the bishop of Orleans-had written." No surprise, then, if Constantine left Fleury as soon as he could after Abbo became abbot in December 988. He was clearly one of the monks who "perversely resisted" Abbo's election. In fact, Bishop Arnulf, Gerbert, and the archbishop of Reims had all lobbied for Constantine to be named abbot of Fleury himself.

Instead, Constantine went to Micy, a smaller monastery outside Orleans, about 30 miles from Fleury. A few years later, Bishop Arnulf named him abbot of that monastery. When? There are two possibilities. A Constantine became abbot of Micy in 1011, but this cannot be our Constantine-as most historians of science have thought-because Bishop Arnulf of Orleans died in 1003.

The first Abbot Constantine of Micy-our Constantine-was appointed before 994, for in that year the count of Aquitaine kicked him out. This news comes from a curious tale of miracle-working saints' relics owned by the monastery of Nouaille, over 100 miles away from Micy. The story was written by a monk named Letaudus of Micy. He was asked to write the story by Abbot Constantine of Nouaille, whom he had known for several years, he says, for Constantine had formerly been the abbot of Micy. The first church doc.u.ment to name an Abbot Constantine of Nouaille is dated August 994; he died there in 1014.

Constantine may have considered himself still the rightful abbot of Micy until his death, for by moving him to the less-valuable monastery of Nouaille, the count of Aquitaine had broken a solemn oath, sworn over holy relics, not to meddle in Nouaille's affairs. To Constantine, the new abbot of Micy was a usurper. To enshrine his dissatisfaction, he commissioned the story from Letaudus. Its moral: The saints will have their revenge on oathbreakers.

But Ascelin, the German, directed his book on the astrolabe to a "monk of Micy," not the abbot, thus dating it between December 988 and August 994. Gerbert was still at Reims, but while the cult of friendship, around which Gerbert organized his school, infuses Ascelin's letter, we can identify him only as Constantine's friend. The Ascelin we know to have been Gerbert's student, the nephew of Archbishop Adalbero (and the poet who called Gerbert "Nectanabo" the wizard), does not seem to have had any connection with Augsburg, Germany. Nor can we say what connection Augsburg had with Catalonia, where the astrolabe texts-and instruments-originated.

But one connection is clear: Gerbert and Constantine were the closest of friends. If Constantine was studying this magical instrument between 988 and 994, Gerbert knew of it. In December 988, upon Abbo's election as abbot of Fleury, Gerbert invited his friend to visit Reims. Perhaps they discussed the astrolabe then. Perhaps Gerbert gave him the "confused" treatise or simply explained what he had learned in Catalonia years ago. Why Constantine returned to the Orleans area and worked on his astrolabe book there, without Gerbert's further help, will become obvious as we explore the nonscientific side of Gerbert's life. For in January 989, his mentor Adalbero of Reims died, and Gerbert's world slipped "into primordial chaos." He could not answer Constantine's requests-a.s.suming he had asked-for more information on the astrolabe. He could not even finish the celestial sphere he had begun making for Remi of Trier. As he wrote to Remi, "Hence, endure the delays imposed by necessity, awaiting more opportune times in which we can revive the studies, now already ceasing for us."

The leading mathematician and astronomer of his day was about to become embroiled in some very messy politics: a coup and civil war in France, revolts and a.s.sa.s.sinations in Rome, the kidnapping of the heir to the imperial throne. Gerbert was at the center of the tumult, and his mastery of the abacus, Arabic numerals, geometry, acoustics, celestial spheres, the astrolabe, and astrology helped him not at all-except to bring him to the attention of counts, kings, and emperors.

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Plate 1 The Majesty of Saint Foy, from the Abbey Sainte Foy at the cathedral of Conques, France. This golden, jewel-encrusted reliquary, made in the tenth century from recycled Roman statuary and jewelry, holds the bones of a thirteen-year-old girl martyred six hundred years previously. It was so popular that the abbot of Gerbert's monastery in Aurillac had a similar majesty made of its founder, Saint Gerald. The Majesty of Saint Foy, from the Abbey Sainte Foy at the cathedral of Conques, France. This golden, jewel-encrusted reliquary, made in the tenth century from recycled Roman statuary and jewelry, holds the bones of a thirteen-year-old girl martyred six hundred years previously. It was so popular that the abbot of Gerbert's monastery in Aurillac had a similar majesty made of its founder, Saint Gerald.

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