The Calendar

by David Ewing Duncan

  In 1100 the prospects for this happening seemed next to nil, even if a few people were noticing that a great deal in nature and in commerce seemed to operate with its own coherent set of rules independent of church doctrine. Still, virtually all Europeans continued to believe that God controlled everything and that truth was revealed to humans only inasmuch as God allowed. So ingrained was this thinking that the earliest conservative reaction to the new knowledge was not only condemnation but dismay that anyone would waste time on such wrong-headed notions as attempting to more accurately measure time. One conservative writing in the mid-1100s assailed the ceaseless inquiries of certain scholars into ‘the composition of the globe, the nature of the elements, the location of the stars, the nature of animals, the violence of the wind, the life-processes of plants and roots’.

  A young Turk of the era, the French philosopher William of Conches (1100-1154), responded with an outburst of support for objectivity that sounds like Roger Bacon a century later:

  Ignorant themselves of the forces of nature and wanting to have company in their ignorance, they don’t want people to look into anything; they want us to believe like peasants and not to ask the reason behind things. ... If they learn that anyone is so inquiring, they shout out that he is a heretic, placing more reliance on their monkish garb than on their wisdom.

  Conches got away with such stridency in part because his argument remained obscure and his ideas outlandish to the mainstream. It would be another century before such new thinking became widespread enough that traditionalists would more actively try to thwart it. Besides, the sum total of the new knowledge remained modest in 1100, with scholars forced to search for answers in the few texts that had survived the dark years, many of them encyclopaedic summaries of certain ancient works and ideas, but incomplete and often poorly written.

  Yet even as scholars and would-be scholars despaired, a few pioneering thinkers from Europe were learning about and beginning to visit the great centres of Arab culture thriving just beyond their frontiers. What they saw and heard about stunned and shamed them as they realized the extent of their own ignorance; what one scholar called Latinorum penuria, the poverty of the Latins.

  Even the most enlightened scholars of the time could not imagine the extent of their loss. Trapped behind their veil of darkness, the Latins had entirely missed the Gupta’s flowering of mathematics and astronomy and knew nothing of Aryabhata, Brahmagupta and other Indian scholars. Some over the decades had heard rumours of Islam’s golden age, but few, if any, had ever heard the names of al-Khwarizmi, al-Battani or al-Biruni. Most Europeans were ignorant even of the Byzantines, beyond a few key ports and cities in Italy that had kept in furtive contact over the centuries.

  In part this was understandable. Most outsiders were enemies, including at times the Byzantines, who continued to challenge the Lombards and other Westerners for control of southern Italy, and were sometime rivals in the east during various crusades. As for the Arabs, they stood like a colossus astride the borders of Europe, a military superpower that fearful Christians thought of not as an enlightened culture of scholars but as the army of Satan himself. How else to explain their triumphs against God’s people?

  In a whirlwind they had snatched away Spain and stormed across the Pyrenees to seriously threaten France. Conquering large chunks of the old Roman Empire, including all of North Africa, they had launched raids throughout the 800s from the Mediterranean into France and Italy. In 827 they captured Sicily and in 838 their armies fought at Naples, summoned by Lombards as allies against the Byzantines. Four years later the Arabs garrisoned a base at Bari, on Italy’s heel. Four years after that, in 846, Arab squadrons landed at Ostia and threatened Rome. Unable to penetrate its walls, they sacked the Vatican cathedrals of St Peter and St Paul, which lay outside the main city walls, and desecrated tombs of the popes.

  During the 900s they launched raids from Italy and Spain deep into central Europe, capturing towns that still bear Arab names as far north as Switzerland. For three centuries, from the mid-700s to the mid-1000s, Arab armies and raiding parties menaced the western Mediterranean, dominating its sea lanes and leaving Europeans terrified they would launch a major invasion.

  But the Arabs brought far more to their new domains in Europe than curved sabres and copies of the Koran. Following the pattern of their earlier invasions in Asia and Africa, the era of conquest in Spain and Sicily soon gave way to periods of cultural assimilation and learning. Against the backdrop of raids and skirmishes on the frontier, art and scholarship flourished in the new Moslem cities, where scholars gathered under the patronage of caliphs and emirs who imported vast numbers of texts to fill new libraries built in Cordoba, Seville, Toledo and Palermo. This rush of knowledge finally brought to the frontiers of Latin Europe works by ancient Greeks, Romans and Indians, and the latest works by Arabs writing on everything from the anatomy of the human eye to Hindu numbers.

  In Spain, al-Khwarizmi’s Algoritimi De numero Indorum and other texts had reached Cordoba by the late ninth century, joining a vast treasure trove of manuscripts housed in a new library built by Caliph Abd ar-Rahman III (891-961)--a patron of art and learning who filled Cordoba with monumental buildings that fused Arab, Romanesque and Persian motifs in the style known as Moorish, with its graceful arches, fluted columns, onion domes and vast gardens. Under his successors, the collection of texts begun by Abd ar-Rahman was said to house 400,000 volumes, which if true meant it rivalled the number of volumes in Alexandria’s library.

  Likewise, the emirs governing Sicily imported texts and encouraged learning, though the island’s apex of Arab culture came not under their rule but after it was conquered by a Christian: Roger Guiscard (1031-1101), son of a baron in Normandy.

  Originally a mercenary seeking riches and adventure, Roger trekked to southern Italy from France in the 1060s to join four of his brothers in the long-simmering struggle over this disputed territory--which they ended by throwing out the Lombards and Byzantines and seizing the place for themselves.* With Roger in the lead, they also invaded Sicily, tossing out the Arabs by 1072.

  *Roger was one of twelve brothers.

  Once secure in his capital of Palermo, Roger renamed himself Roger I, Count of Sicily. He then established one of the odder amalgamations of cultures in the Middle Ages, blending Christian and Moslem with older currents of history on an island rich in Greek, Roman and Byzantine traditions. By Arab terms an uncultured Christian, Roger nonetheless won the loyalty and admiration of Moslems, whom he welcomed into his domain--including Arab soldiers and advisors, and a stable of Eastern scholars, philosophers and astrologers.

  Two of Roger’s successors expanded on this strange Arab-Norman cocktail. His son Roger II (1095-1154), known as the ‘half-heathen king’, ruled both Sicily and southern Italy like an Arab sultan, dressing in Persian silks and opening up his court to Moslem intellectuals. Roger II’s grandson and successor, Frederick II (1194-1250), inherited not only Sicily and southern Italy but also Germany and the crusader kingdom of Jerusalem. Elected Holy Roman Emperor in 1220 Frederick maintained an oriental-style harem and surrounded himself with philosophers and sages from Baghdad and Syria, dancing girls from the Orient and Jewish scholars. From Syria he imported experts on falconry; from Spain he brought a translator who created a Latin summary of Aristotle’s biological and zoological works. Frederick founded the University of Naples in 1224, endowing it with a large collection of Arabic manuscripts on Aristotle and other ancients. Copies of Latin translations were sent to the universities in Paris and Bologna. Frederick also led a successful Crusade to Palestine in 1228-1229--the fifth crusade--and recaptured Jerusalem, Bethlehem and Nazareth.

  Still, the infusion of Arabic knowledge was very slow, with only a few scattered documents making the journey from Cordoba, Palermo and Damascus before 1200. Some of the earliest translations were penned in northern Spain beginning in the mid-tenth century at the monastery of Santa Maria de Ripoll at the foot of the Pyrenees, mostly w
orks on geometry and astronomical instruments. Next came works by Plato, Euclid, Aristotle and others, coming out of Roger’s Sicily, northern Spain after the fall of Toledo to the Christians in 1085, and Byzantium and Palestine as the Crusaders stormed across the east starting in 1096.

  Leading translators and collectors of manuscripts in these early days included Gerbert of Aurillac (c. 946-1003), later Pope Sylvester II. He trekked to northern Spain to carry home Latin translations of Arab treatises on the abacus and the astrolabe. Another was Adelard of Bath (c. 1075-1160). He journeyed by ship along the new eastern trade routes to the Crusader-held coast of Syria, where he translated Euclid into Latin using Arabic translations of the original Greek. Most prolific of all these early translators was the Italian Gerard of Cremona (c. 1114-1187). Fluent in Greek and Arabic, he was a leading figure in the new college of translators set up by the Spanish archbishop Raymond after the capture of Toledo (and its library), rendering into Latin texts by Galen, Aristotle, Euclid, al-Khwarizmi and Ptolemy, among many others.

  Independent-minded thinkers in Europe welcomed each precious manuscript with fascination, though the transfer of knowledge was hardly swift or comprehensive. Most Europeans, even those with some education, remained locked in the timelessness of the Middle Ages and remained ignorant of the new knowledge. Others condemned the texts as products of pagans and devils. Still others resisted anything new because they either failed to understand it or preferred their own familiar ways and traditions--much as Americans today continue to use inches instead of centimetres. Even those who embraced Aristotle and al-Khwarizmi were often confused by poor translations and by the random selections that arrived: a fragment of a Platonic dialogue one year and a chapter or two of Euclid the next.

  An example is the reception of the new Hindu numbers as they completed their journey west from India to the Arabs and onward to the Latins. Indeed, the Europeans took centuries to fully integrate what the Arabs had largely absorbed just a generation or so after the 789 arrival of Kanaka in Baghdad.

  The first Hindu numbers known to have been scrawled on a European manuscript appeared in northern Spain in 976 and used the ‘western’ Arabic form of the numbers one through nine.

  Twenty years later, in the 990s, Gerbert of Aurillac taught the Hindu numbers to his students, undoubtedly picking them up after a stint in Spain. But Gerbert apparently failed to understand their computive power and limited his use of them to special counting boards. These boards failed to catch on, however, in part because people who tried to use the boards had no idea which way was up for the strange symbols. For instance, they seem to have confused a

  Mention of the numbers all but disappeared for another entire century until the Englishman Robert of Chester (c. 1100) visited Spain and translated al-Khwarizmi’s little book into Latin in 1120. This and other translations of al-Khwarizmi inspired several Latin textbooks on the ‘new arithmetic’, including descriptions of the decimal system and positional notation. Still, it took several more centuries before Europeans entirely abandoned Roman numerals, despite their clumsiness and inferiority to Hindu-Arabic numerals. Even bankers and merchants resisted them at first, worrying that they were easier to falsify than Roman numerals. Some less-educated merchants also suspected that the symbols were a secret code used by orientals and other Europeans to cheat them.

  As late as the fifteenth century, when Hindu-Arabic numbers took the form we now use, Europeans were still having trouble making the transition. In a preface to a calendar in 1430 the maker gives the length of the year as ‘ccc and sixty days and 5 and sex odde howres’. Later in the century, two years after Christopher Columbus sailed to America, another author described the year as MCCCC94--1494--Yet another used the new positional system along with the more recently arrived zero, but mixed up Hindu and Latin numbers to come up with the year, 1502, written as IVoII, with I (1) in the thousands place, V (5) in the hundreds, o (zero) in the tens, and II (2) in the digits. Dutch painter Dirck Bouts (c. 1400-1475) dated a painting he placed in the cathedral in Louvain with MCCCC4XVII. This may be 1447, but who knows?

  Progress was equally slow for other mathematic concepts crucial to fixing the calendar, including decimals and zero, neither of which was routinely taught in universities until at least the mid-fourteenth century. The first systematic treatment of decimal fractions in Europe had to wait until 1582, the year of the Gregorian calendar reform, when Dutch mathematician Simon Stevin (1548-1620) explained the system in a book called La Thiende (The tenth).

  But Stevin did not use our modern form for his decimals, having no decimal point. He would have written the fraction for the length of the solar year as:

  The invention of the decimal point is usually attributed to either mapmaker and Galileo rival G. A. Magini (1555-1617) in a 1592 work, or to the leading astronomer on Gregory XIII’s calendar commission, Christopher Clavius (1537-1612), who used them in a table of sines in 1593.

  As for zero, its first significant appearance in Europe comes during the eleventh and twelfth centuries, at roughly the same time as the other nine Hindu-Arabic numbers started to come into wide use--first as a place marker on counting boards devised by Gerbert and others, then as a digit in positional notation. It took longer for zero to be thought of as a real number in mathematical equations, though by the turn of the seventeenth century it and positional notation were familiar enough for William Shakespeare to use them as a metaphor for infinite gratitude in The Winter’s Tale, written in 1610:

  Like a cypher . . .

  I multiply with one, ‘We thank you,’

  Many thousands more, that go before it.

  This reticence over something as basic as numbers begins to explain why it took so long to reform the calendar, a process that was far more difficult and complicated than deciding whether to use 5 instead of V, or 365 instead of CCCLXV. For unlike numbers--or zero or a decimal fraction--the calendar belonged to God, and was assumed to be an immutable timetable of faith and worship that no one had dared challenge, not even the likes of Bede and Hermann the Lame. Which made the entire question of time and the calendar more and more perplexing as Europe reawakened and time ceased to be something that one could ignore or relegate exclusively to God.

  Whether traditionalists liked it or not, secular time was restarting in Europe, and with it a need to re-evaluate the nature of time--how to measure it, use it and understand it. This issue lay at the heart of a looming larger question: how to react to an influx of new ideas that in some cases directly challenged not only details of Church dogma but the fundamental beliefs of an entire society. This would become the central dilemma of scholars from 1100 to 1300: how to account for knowledge that seemed to come out of nowhere, and in essence offered a new kind of religion that put its faith in observation and logic. It was this debate that would ring across Europe during the High Middle Ages, primarily in the halls and courtyards of this era’s profound new invention: the university.

  11 The Battle Over Time

  Since the General Council forbade any alterations in the calendar, modern scholars have had to tolerate . . . errors ever since.

  John of Sacrobosco, 1235

  Imagine the 14-year-old son of a wealthy ship-owner in Pisa, or the second son of a prosperous squire in Kent, circa 1240. How would each have reacted to the news that his father, with the support of the local lord, was sending him to a university in Bologna, or in Oxford?

  They might have been dimly aware of the new knowledge arriving in Europe, particularly the boy in Pisa. In the harbour he would have seen dark-skinned Arab traders in turbans haggling with his father and scratching out strange, compact symbols for numbers that differed from the ones Latins used. He might also have heard from former university students about the halls at Bologna, where black-robed masters delivered lectures revealing untold secrets of the ancients: powerful knowledge that his father wanted him to learn so that he could help the family. But it was also dangerous knowledge, or so he might have been told by a l
ocal priest or elder looking out for the boy’s spiritual well-being, who warned him to beware ideas that would offend God and the Church.

  The boys in Kent and Pisa would have left home in the early autumn, sometime before lectures began on or just after St Michael’s day, 29 September, or some other date no one would have been precise about following. Beyond this, the boys probably gave no more thought to dates and exact times than our farmer on the Rhine or the weaver in France did in the year 800. By now a few people were using reasonably accurate water clocks, but mechanical clocks had not yet been invented--at least, there are no definitive records of any. And public bell towers clanging each hour from the town square remained decades in the future, with several rising up over cities near Pisa in the early and mid-1300s and the first large clock appearing in England at Windsor Castle in 1351.

  Otherwise, the boys would have reckoned time by looking up into the sky, eyeballing the arc of the sun as Geoffrey Chaucer does in The Canterbury Tales to move us through the timeline of his journey. As the day in his story ends, Chaucer writes (in updated English):

  From the south line the sun had now descended

  So low, it stood--so far as I had in sight--

  At less than twenty-nine degrees in height.

  Four o’ the clock it was to make a guess;

  Eleven foot long, or little more or less,

  My shadow was, as at that time and place,

  Measuring feet by taking in this case

  My height as six, divided in like pattern