by Will Durant
Certain names stand out in this period as pundits of the occult. Peter of Abano almost reduced philosophy to astrology; and Arnold of Villanova, a famous physician, had a predilection for magic. Ceceo d’Ascoli (1257?-1327), who taught astrology at the University of Bologna, boasted that he could read a man’s thoughts, or tell what he concealed in his hand, by knowing the date of his birth. To illustrate his views he cast the horoscope of Christ, and showed how the constellations at the Nativity had made the crucifixion inevitable. He was condemned by the Inquisition (1324), abjured, was spared on condition of silence, went to Florence, practiced astrology for numerous clients, and was burned at the stake for denying the freedom of the will (1327). Many sincere students—Constantine the African, Gerbert, Albertus Magnus, Roger Bacon, Vincent of Beauvais—were accused of magic, and of relations with devils, because the people could not believe that their knowledge had been obtained by natural means. Michael Scot earned the suspicion by writing famous treatises on the occult: a Liber introductorias on astrology; a Physiognomia on the correlation of qualities of character with peculiarities of body; and two texts of alchemy. Michael condemned magic, but enjoyed writing about it. He listed twenty-eight methods of divination, and seems to have believed in all of them.21 Unlike most of his contemporaries he made careful observations, and some experiments; on the other hand he suggested that carrying a jasper or topaz would help a man to preserve continence.22 He was clever enough to keep on good terms with both Frederick II and the popes; but the inexorable Dante consigned him to hell.
The Church and the Inquisition were part of the environment of European science in the thirteenth century. The universities for the most part operated under ecclesiastical authority and supervision. The Church, however, allowed considerable latitude of doctrine to professors, and in many cases encouraged scientific pursuits. William of Auvergne, Bishop of Paris (d. 1249), promoted scientific investigation, and ridiculed those who were ready to see the direct action of God in any unusual event. Bishop Grosseteste of Lincoln was so advanced in the study of mathematics, optics, and experimental science that Roger Bacon ranked him with Aristotle. The Dominican and Franciscan Orders made no known objection to the scientific studies of Albertus Magnus or Roger Bacon. St. Bernard and some other zealots discouraged the pursuit of science, but this view was not adopted by the Church.23 She found it hard to reconcile herself to the dissection of human cadavers, for it was among her basic doctrines that man was made in the image of God and that the body, as well as the soul, would rise from the grave; and this reluctance was fully shared by the Moslems and the Jews,24 and by the people at large.25 Guido of Vigevano in 1345 spoke of dissection as “forbidden by the Church”;26 but we find no ecclesiastical prohibition before the bull De sepulturis of Boniface VIII in 1300; and this merely forbade the cutting up of corpses and the boiling away of their flesh in order to send the sterilized bones of dead Crusaders back to their relatives for burial at home.27 This may have been misinterpreted as forbidding post-mortem dissection, but we find the Italian surgeon Mondino boiling and dissecting corpses about 1320, without any known ecclesiastical protest.28
If the achievements of medieval science in the West should seem meager in the following summary, let us remember that it grew in a hostile environment of superstition and magic, in an age that drew the best minds into law and theology, and at a time when nearly all men believed that the major problems of cosmic and human origin, nature, and destiny had been solved. Nevertheless, after 1150, as wealth and leisure grew, and translations began to pour in from Islam, the mind of Western Europe was aroused from its torpor, curiosity flared into eagerness, men began to discuss the brave old world of the unfettered Greeks, and within a century all Latin Europe was astir with science and philosophy.
II. THE MATHEMATICAL REVOLUTION
The first great name in the science of this period is Leonardo Fibonacci of Pisa.
Sumerian mathematics, born of forgotten parentage, had descended through Babylonia to Greece; Egyptian geometry, still visible in the pyramids, had passed, perhaps through Crete and Rhodes, to Ionia and Greece; Greek mathematics had gone to India in the wake of Alexander, and had played a part in the Hindu development that culminated in Brahmagupta (588?-660); about 775, translations were made of Hindu mathematicians, and soon afterward of Greek mathematicians, into Arabic; about 830 the Hindu numerals entered Eastern Islam; about 1000 Gerbert brought them to France; in the eleventh and twelfth centuries Greek, Arabic, and Hebrew mathematics streamed into Western Europe through Spain and Sicily, and came with Italian merchants to Venice and Genoa, Amalfi and Pisa. Transmission is to civilization what reproduction is to life.
Another line of transmission appeared in the sixth century B.C. in the form of the Chinese abacus (Greek abax, a board), an instrument for counting by transferring little bamboo rods from one group to another; its descendant, the suanpan, is still used by the Chinese. In the fifth century B.C., says Herodotus, the Egyptians reckoned with pebbles, “bringing the hand from right to left”; the Greeks proceeded contrariwise. The Romans used several forms of the abacus; in one form the counters slid in grooves; they were made of stone, metal, or colored glass, and were called calculi, little stones.29 Boethius, about 525, mentioned the abacus as enabling one to count by tens; but this invitation to a decimal system was ignored. The merchants of Italy used the abacus, but wrote the results in clumsy Roman numerals.
Leonardo Fibonacci was born at Pisa in 1180. His father was manager of a Pisan trade agency in Algeria; Leonardo in adolescence joined him there, and was taught by a Moslem master. He traveled in Egypt, Syria, Greece, and Sicily, studied the methods of the merchants, and learned to reckon, he tells us, “by a marvelous method through the nine figures of the Indians”;30 here at the outset of their European career the new numerals were properly called Hindu, and what is now a bore and chore of our childhood was then a wonder and delight. Perhaps Leonardo learned Greek as well as Arabic; in any case we find him well acquainted with the mathematics of Archimedes, Euclid, Hero, and Diophantus. In 1202 he published his Liber abaci; it was the first thorough European exposition of the Hindu numerals, the zero, and the decimal system by a Christian author, and it marked the rebirth of mathematics in Latin Christendom. The same work introduced Arabic algebra to Western Europe, and made a minor revolution in that science by occasionally using letters, instead of numbers, to generalize and abbreviate equations.31 In his Practica geometriae (1220) Leonardo, for the first time in Christendom so far as we know, applied algebra to the treatment of geometrical theorems. In two smaller works of the year 1225 he made original contributions to the solution of equations of the first and second degree. In that year Frederick II presided at Pisa over a mathematical tournament in which different problems were set by John of Palermo and solved by Fibonacci.
Despite his epoch-making work, the new method of calculation was long resisted by the merchants of Europe; many of them preferred to finger the abacus and write the results with Roman numerals; as late as 1299 the abacists of Florence had a law passed against the use of the “new-fangled figures.”32 Only a few mathematicians realized that the new symbols, the zero, and the decimal alignment of units, tens, hundreds… opened the way to such developments of mathematics as were almost impossible with the old letter numerals of Greeks, Romans, and Jews. Not till the sixteenth century did the Hindu numerals finally replace the Roman; in England and America the duodecimal system of reckoning survives in many fields; 10 has not finally won its thousand-year-long war against 12.
Mathematics in the Middle Ages had three purposes: the service of mechanics, the keeping of business accounts, and the charting of the skies. Mathematics, physics, and astronomy were closely allied, and those who wrote on one of them usually contributed to the others as well. So John of Holy wood (in Yorkshire), known to the Latin world as Joannes de Sacrobosco, studied at Oxford, taught at Paris, wrote a Tractatus de sphaera—Treatise on the (Earthly) Sphere—and an exposition of the new m
athematics, Algorismus vulgaris—Mathematics for the Millions (c. 1230). Algorismus, a corruption of the name al-Khwarizmi, was the Latin term for an arithmetical system using the Hindu numerals. John credited the “Arabs” with the invention of this system, and was partly responsible for the misnomer “Arabic numerals.”33 Robert of Chester, about 1149, in adapting the astronomical tables of al-Battani and al-Zarqali, brought Arabic trigonometry to England, and introduced the word sinus (bay, sine) into the new science.
Interest in astronomy was maintained by the needs of navigation and the passion for astrology. The immense authority of the oft-translated Almagest petrified the astronomy of Christian Europe into the Ptolemaic theory of eccentrics and epicycles, with the earth at the hub of the world; alert minds like Albertus Magnus, Thomas Aquinas, and Roger Bacon felt the force of the criticisms that the Moorish astronomer al-Bitruji had aimed at this system in the twelfth century; but no satisfactory alternative to Ptolemy’s celestial mechanics was found before Copernicus. Christian astronomers in the thirteenth century pictured the planets as revolving about the earth; the fixed stars, snared in a crystal firmament, and steered by divine intelligences, revolved as a regimented host around the earth; the center and summit of the universe was that same man whom the theologians described as a miserable worm tainted with sin and mostly doomed to hell. The suggestion offered by Heracleides Ponticus, four centuries before Christ, that the apparent daily motion of the heavens was due to the axial rotation of the earth, was discussed by Semitic astronomers in the thirteenth century, but was quite forgotten in Christendom. Another notion of Heracleides, that Mercury and Venus revolve about the sun, had been handed down by Macrobius and Martianus Capella; John Scotus Erigena had seized upon it in the eighth century, and had extended it to Mars and Jupiter; the heliocentric system was on the verge of victory;34 but these brilliant hypotheses were among the casualties of the Dark Ages, and the earth held the center of the stage till 1521. All astronomers, however, agreed that the earth is a sphere.35
The astronomical instruments and tables of the West were imported from Islam, or were modeled on Islamic originals. In 1091 Walcher of Lorraine, later Prior of Malvern Abbey, observed lunar eclipses in Italy with an astrolabe; this is the earliest known case of observational astronomy in the Christian West; but even two centuries later (c. 1296) William of St. Cloud had to remind astronomers, by precept and example, that the science grew best on observation rather than on reading or philosophy. The best contribution to Christian astronomy in this period was the Alfonsine Tables of celestial movements, prepared for Alfonso the Wise by two Spanish Jews.
The accumulation of astronomic data revealed the imperfections of the calendar established by Julius Caesar (46 B.C.) from the work of Sosigenes, which made the year too long by eleven minutes and fourteen seconds; and the increasing intercourse of astronomers, merchants, and historians across frontiers exposed the inconvenience of conflicting calendars. Al-Biruni had made a useful study of the rival systems of dividing time and dating events (c. 1000); Aaron ben Meshullam and Abraham bar Hiyya furthered the study in 1106 and 1122; and Robert Grosseteste and Roger Bacon followed with constructive proposals in the thirteenth century. The Computus (c. 1232) of Grosseteste—a set of tables for calculating astronomic events and movable dates (e.g., Easter)—was the first step toward the Gregorian calendar (1582) that guides and confuses us today.
III. THE EARTH AND ITS LIFE
The least progressive medieval science was geology. The earth was the chosen home of Christ, and the shell of hell, and weather was the whim of God. Moslem, Jew, and Christian alike covered mineralogy with superstition, and composed “lapidaries” on the magical powers of stones. Marbod, Bishop of Rennes (1035–1123), wrote in Latin verse a popular Liber lapidum, describing the occult qualities of sixty precious stones; a sapphire held in the hand during prayer, said this erudite bishop, would secure a more favorable answer from God.36 An opal folded in a bay leaf rendered its holder invisible; an amethyst made him immune to intoxication; a diamond made him invincible.37
The same eager curiosity that spawned superstitions upon the minerals of the earth sent medieval men wandering over Europe and the East, and slowly enriched geography. Giraldus Cambrensis—Gerald of Wales (1147–1223)—roamed over many lands and topics, mastered many tongues but not his own, accompanied Prince John to Ireland, lived there two years, toured Wales to preach the Third Crusade, and wrote four vivacious books on the two countries. He weighed down his pages with bias and miracles, but lightened them with vivid accounts of persons and places, and lively gossip of the trivial things that make the color of a character or an age. He was sure that his works would immortalize him,38 but he underestimated the forgetfulness of time.
He was one of thousands who in the twelfth and thirteenth centuries made a pilgrimage to the East. Maps and routes were drawn to guide them, and geography benefited. In 1107–11 Sigurd Jorsalafare, King of Norway, sailed as a crusader with sixty ships via England, Spain, and Sicily to Palestine; after fighting Moslems at every opportunity he led his lessened band to Constantinople, and thence overland through the Balkans, Germany, and Denmark to Norway; the story of this adventurous journey forms one of the great Scandinavian sagas. In 1270 Lanzarotte Malocello rediscovered the Canary Islands, which had been known to antiquity. About 1290 Ugolino and Vadino Vivaldo, acording to an unverified tradition, set out from Genoa in two galleys to sail around Africa to India; all hands, it appears, were lost. A famous hoax took the form of a letter from a mythical “Prester John” (c. 1150), who told of his dominions in Central Asia, and gave a fantastic geography of the Orient. Despite the Crusades, few Christians believed in the antipodes; St. Augustine considered it “incredible that a people inhabits the antipodes, where the sun rises when it sets with us, and where men walk with their feet toward ours.”39 An Irish monk, St. Fergil, had suggested, about 748, the possibility of “another world and other men under the earth”;40 Albertus Magnus and Roger Bacon accepted the idea, but it remained the daring concept of a few until Magellan circumnavigated the globe.
The chief contributions to European knowledge of the Far East were made by two Franciscan monks. In April 1245 Giovanni de Piano Carpini, sixty-five and fat, was sent by Innocent IV to the Mongol court at Karakorum. Giovanni and his companion suffered in the enterprise every hardship this side of death. They traveled for fifteen months, changing horses four times a day. Pledged by the Franciscan rule to eat no meat, they almost starved among nomads who had hardly any other food to give them. Giovanni’s mission failed, but after his return to Europe he compiled an account of his journey which is a classic in the literature of geography—clear, impersonal, matter-of-fact, without a word of self or complaint. In 1253 Louis IX sent William of Rubruquis (Wilhelm van Ruysbroeck) to the Creat Khan to renew the Pope’s suggestion of an alliance; William brought back a stern invitation to submit France to the Mongol power;41 and all that came of the expedition was William’s excellent account of Mongol manners and history. Here, for the first time, European geography learned the sources of the Don and the Volga, the position of Lake Balkhash, the cult of the Dalai Lama, the settlements of Nestorian Christians in China, and the distinction of Mongols from Tatars.
The most famous and successful of medieval European travelers in the Far East were the Polo family of Venetian merchants. Andrea Polo had three sons—Marco the elder, Niccolò, and Maffeo—all engaged in Byzantine trade, and living in Constantinople. About 1260 Niccolò and Maffeo moved to Bokhara, where they remained three years. Thence they traveled in the train of a Tatar embassy to the court of Kublai Khan at Shangtu. Kublai sent them back as emissaries to Pope Clement IV; they took three years to reach Venice, and by that time Clement was dead. In 1271 they started back to China, and Niccolò took with him his boy Marco the younger, then seventeen. For three and a half years they traveled across Asia via Balkh, the Pamir plateau, Kashgar, Khotan, Lop Nor, the Gobi Desert, and Tangut; when they reached Shangtu Marco was almos
t twenty-one. Kublai took a fancy to him, gave him important posts and missions, and kept the three Poli in China for seventeen years. Then they sailed back, through three years, via Java, Sumatra, Singapore, Ceylon, and the Persian Gulf, overland to Trebizond, and by boat to Constantinople and Venice, where, as all the world knows, no one would believe the tales “Marco Millions” told of the “gorgeous East.” Fighting for Venice in 1298, Marco was captured, and was kept for a year in a Genoese jail; there he dictated his narrative to a fellow prisoner. Nearly every element in the once incredible story has been verified by later exploration. Marco gave the first description of a trip across all Asia; the first European glimpse of Japan; the first good account of Pekin, Java, Sumatra, Siam, Burma, Ceylon, the Zanzibar coast, Madagascar, and Abyssinia. The book was a revelation of the East to the West. It helped to open new routes to commerce, ideas, and arts, and shared in molding the geography that inspired Columbus to sail westward to the East.
As the orbit of commerce and travel widened, the science of cartography crept laboriously back toward the level it had reached in Augustus’ days. Navigators prepared portolani—guides to the ports of trade, with maps, charts, itineraries, and descriptions of the various harbors; in the hands of the Pisans and Genoese these portolani reached a high degree of accuracy. The mappae mundi drawn by the monks of this period are by comparison schematic and incomprehensible.
Stimulated by the zoological treatises of Aristotle and the botanical classic of Theophrastus, the awakening mind of the West struggled to graduate from legend and Pliny to a science of animals and plants. Nearly everyone believed that minute organisms, including worms and flies, were spontaneously generated from dust, slime, and putrefaction. “Bestiaries” had almost replaced zoology; since monks did almost all the writing, the animal world was considered largely in theological terms, as a storehouse of edifying symbolism; and additional creatures were invented in playful fancy or pious need. Said Bishop Honorius of Autun in the twelfth century:
