The Abacus and the Cross: The Story of the Pope Who Brought the Light of Science to the Dark Ages
As a young lad, Gerbert Aurillac entered the monastery, receiving a Church education. He served as a schoolmaster teaching future bishops, became a tutor and counselor to kings and emperors, advanced to abbot, then to archbishop, and eventually was elected Pope Sylvester II in 999 A.D. With a resume like that in the tenth century, it may come as quite a shock to hear that Gerbert was the first Christian known to teach mathematics using the Arabic numeral system. He also created the modern abacus based on Arabic numerals and the base ten place system used universally today (Gerbert’s abacus could add, subtract, multiply and divide numbers as large as 1027), explored questions of geometry, systematically observed the stars, and studied mathematical astronomy. The cultural myths of the Middle Ages as “dark” coupled with the ahistorical banter of contemporary militant atheism would lead us to believe that no person could be a serious Christian and a serious natural philosopher–roughly the scientist of the times–let alone be the leader of the Western Church while being enthusiastic about the cutting edge of astronomy, mathematics, and natural philosophy of the day. After all, according to the popular myths, science and religion have been at war with each other throughout the ages.
Nancy Marie Brown’s The Abacus and the Cross: The Story of the Pope Who Brought the Light of Science to the Dark Ages is an engaging biography of Gerbert of Aurillac that pounds one more nail in the coffin of this tired, worn-out science-religion conflict view. Along the way of narrating Gerbert’s life, we get glimpses of monastic learning (including the trivumand quadrivium), monastic rivalries (vying for pilgrim visits through collecting relics and building libraries), some of the treasures of the early Islamic kingdom’s learning (such as the development of algebra), the religious tolerance of tenth-century Islamic Spain, personal and political intrigue in the court and Church, the intertwining of astronomy and astrology in the ancient and Medieval worlds, and the role friendship played in establishing and maintaining circles of natural philosophic and mathematical inquiry.
Born into a poor family in 949, Gerbert was a shepherd boy who was fascinated by the night skies. From various legendary sources, the young Gerbert entered Saint-Gerald’s monastery in Aurillac, France, after an encounter with its abbot in a field one day. Impressed with the lad’s intelligence, the abbot offered Gerbert a place in the monastery. What we know for sure is that Gerbert became a monk in Saint-Gerald’s as a boy. He excelled at learning Latin and his intelligence was recognized early on. From Saint-Gerald’s, Gerbert was sent to Spain to continue his studies (roughly at the age of twenty-one) where the most advanced learning was available. Evidently Gerbert continued to excel in his studies with a particular aptitude for mathematics and astronomy. He eventually became the schoolmaster at the important monastery at Reims where he taught a generation of bishops and tutored the sons of kings. Gerbert became a counselor to emperors Otto II and Otto III (there was hardly anywhere in Europe where Gerbert’s name was not known). Despite being excommunicated and exiled due to political and personal intrigue, Gerbert was appointed Pope Sylvester II by Otto III and served in that capacity for the remaining four years of his life.
Gerbert likely had one of the best grasps of geometry and arithmetic of his time and is credited with being the first to introduce Arabic mathematics to Medieval Europe (52). Indeed, his book on geometry (which included significant discussion of arithmetic) became a staple text in the monasteries only to be replaced by Euclid’s own work when it was retranslated back into Latin in thetwelfth century. Given that the sources on Gerbert’s relationship to the astrolabe are murky, Brown makes a very plausible case that he was quite skilled at the use of the pre-seventeenth-century astronomer’s workhorse instrument and probably made several (ch. VIII).
In her enthusiasm for telling Gerbert’s story, however, Brown sometimes over-interprets his work. For example, in discussing one of Gerbert’s letters where she describes him as anticipating “the scientific method,” she exclaims: “Those who believe there was no experimental science in the Dark Ages, only memorization and appeals to authority, have never read the letters of Gerbert” (84). Brown is right that natural philosophy in the Middle Ages of Europe was much more than memorization and citing authority. Gerbert was engaged in the practice of comparing calculations in mathematical astronomy with systematic astronomical observation, and he also systematically observed the effects of different organ pipe lengths on sound quality and pitch. Unfortunately, Brown confuses these activities with the practice of controlled experiment that developed later in the sixteenth and seventeenth centuries (“the scientific method”). The kinds of systematic observations in which Gerbert was engaged had been in use for centuries in the Aristotelian natural science tradition. In his work and writings on organ pipes, Brown describes Gerbert as “searching for a mathematical truth: a law for computing the dimensions of an organ pipe” (106) when she must mean that Gerbert was searching for a mathematical proportion—a Pythagorean emphasis—as no one had the concept of laws of nature until the beginning of theseventeenth century. As a final example, Brown refers to Gerbert as engaging in “experimental geometry” (109-111) because he was comparing Boethius’ arithmetic rule for calculating the area of a triangle with Euclid’s geometric rule by cutting out small squares and laying them over model tri-angles. Here, again, Gerbert was following a longstanding tradition of mathematical proof that is mischaracterized when described as “experiment.” In her eagerness to demonstrate how advanced Gerbert’s natural philosophy was, Brown tends to mislead her readers into thinking that Gerbert was developing and practicing modern scientific methods in the10th century when he was actually doing something significantly different.
This occasional interpretive overreaching does not detract from her account of intellectual activity in the eighth through the tenth centuries. Brown does a good job of giving readers a picture of how vibrant intellectual life was in the monasteries and the church hierarchy in those times. Not only were books by Aristotle and Boethius, among other authors, being copied and distributed, new books were being written summarizing the most advanced learning of the day for the monastery schools and church leaders. Up to the tenth century, Christian Europe was keeping rough pace with intellectual developments in the Islamic empire to the south (mostly through friendly, cooperative relationships in Spain). Gerbert’s correspondence is a window on how vigorously knowledge was pursued in the ninth century including challenges to venerable lights such as Boethius. The “dark ages” were far from dark.
The Abacus and the Cross is an entertaining and engaging read, but what of its history? Though Brown’s historical narrative is basically solid when it comes to Gerbert—thanks to the many letters from and to Gerbert that have been preserved—much of the history more incidental to Gerbert’s story is mixed. For example, she rightly traces the myths that the foruth to about the twelfth centuries were “dark” and that people in this period in Europe generally believed in a flat Earth to the Italian Renaissance poet Petrarch (this period was far from intellectually dark and flat earthers were practically nonexistent). Brown also describes how Mediaevals were not obsessed with the year 1000 as marking the end of the world (this apocalyptic myth was started by later historians).
On the other hand, she mischaracterizes Archimedes’ method as involving calculus (112) when it only involved a precursor to the idea of infinitesimal elements. She tells us that “In Gerbert’s day, the sun, moon, and planets were thought to circle the earth in eccentric, not perfectly round, orbits” (121). However, everyone in Gerbert’s day believed all heavenly bodies moved in perfect circular orbits executing uniform circular motion. Brown mistakes the eccentric point–a point some distance away from the center of the orbit at which Ptolemy located the Earth–with the shape of planetary orbits (although it is possible she confuses particular two-dimensional projections in illustrations, which sometimes look slightly noncircular, with beliefs about the actual three-dimensional motions). Brown reports that Pythagoras thought that all heavenly bodies orbited “around a central fire” (125), but this was Philolaus’s theory—he was a Pythagorean natural philosopher who lived a century after Pythagoras—and everyone rejected it including Plato (who Brown reports adopted the theory after considering a geocentric theory).
After Gerbert’s death, the largely cooperative and peaceful relationship between Christian Europe and the Islamic empire was replaced by increasing tensions, incriminations, and war. Within the church, tensions increased between learning and inquiry, on the one hand, and relic worship, intercession for the dead, and other rituals, on the other hand. Gerbert’s death did not usher in these developments. They were the result of a number of complicated intellectual, spiritual, and moral trends already underway (in some ways, many of the misfortunes Gerbert suffered were due to these trends). He lived in the last age when a churchman dedicated to learning and inquiry could rise to become Pope. Men skilled in other arts were becoming preferred in most sectors of the church, and natural philosophy, among other forms of learning, was slowly being eclipsed until an intellectual reversal starts in the twelfth century.
There is a sense in which Gerbert and his times are a mirror reflecting an image of the recent history of Christianity’s struggle with learning and the intellectual life (told so well in Mark Noll’s The Scandal of the Evangelical Mind). Then, as in contemporary times, many in the church preferred that Christians be skilled in anything sacred in comparison with “secular learning.” Then, as now, the need for intellectually informed, prayerful Christian engagement was great, but many opportunities for such engagement were missed. Gerbert and his times offer us a chance to reflect once again on what it means to be prayerfully engaged Christ followers in a broken world.