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Wikimedia Commons
The man who brought
time to Europe
Sylvester II watches over his hometown of Aurillac.
Pierre Maillard
The life of Gerbert of Aurillac is an incredible story.
Elected to the papacy on April 2, 999 under the name
of Sylvester II as people awaited the new millennium
in superstitious terror, he fulfilled his destiny as a shepherd boy from the Auvergne region of France who not
only became the head of Christendom but also introduced the works of Aristotle, arabic numerals and the
figure zero to Western medieval civilisation. He
authored treatises on geometry and arithmetic,
invented the abacus and the measuring rod that bear
his name. He made astrolabes and wooden armillary
spheres to represent the universe. A musician and the
inventor of a notation system of tones, semitones, flats
and sharps, he also built a hydraulic organ in Reims
that used steam to produce sounds. He is even said to
have designed a mechanical bronze head that
answered questions with a “yes” or “no”, and to have
created a sundial in Magdeburg. His brilliance was so
revered that some have even gone so far as to credit
him with the invention of the horological balance. Had
he indeed solved the problem of regulating force,
Gerbert d’Aurillac would have presided over the birth
of mechanical horology.
major research on the origins of horology, the story
of Gerbert is nonetheless worth telling. Facts are
interwoven with legends – most of which arose
when he died in 1003 after four years as pope.
His precocious humanism and pronounced taste for
“pagan” sciences, his study of ancient manuscripts
and of the knowledge of the Saracens of Spain,
earned him a suspiciously heretical reputation. The
19th-century French author, Stendhal, echoed this
point of view in one of his biographical sketches,
Promenades dans Rome : “A brilliant Frenchman,
Gerbert, whom the famous Hugh Capet had instated
as Archbishop of Reims, became pope under the
name of Sylvester II. The contemporaries of this
superior individual, astonished by his successes,
regarded him as an extremely clever sorcerer.
Rumours were spread that he owed his position as
pope to the devil and serious prelates wrote that
Gerbert was killed by evil spirits.” In 1648, to find the
truth of this matter, Pope Innocent X opened his tomb
from which water had regularly seeped since his
death; his corpse dissolved into dust as soon as it
was touched.
Separating truth from legend. While all serious
authors refute such claims, including the medieval
scholar, Emmanuel Poulle, who has undertaken
Zero – the devil’s invention. Gerbert’s incredible
career first took off when the monks of the Saint
Géraud d’Aurillac abbey noted the precocious
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Gerbert’s abacus introduced into Europe the positional
numbers he learned from the Arabs in Spain. The columns
of his abacus were numbered 1 to 9 in arabic numerals.
intelligence of a child, who – according to another
legend – used to observe the sky through a hollowed elder branch, and duly enrolled him as an
oblate in their Benedictine monastery. In 963,
Count Borrell II of Barcelona, en route to his marriage with a certain Leutgarde, stopped over at the
monastery and took the brilliant child in charge,
successively entrusting him to the care of the
Ripoll and Vic monasteries.
During this period, the County of Barcelona, which
lay on the fringes of Christendom, was in direct
contact with the Umayyad caliphate of Cordoba,
then at its peak. Cordoba was a city teeming with
ideas and a major intellectual centre, boasting
libraries packed with more than 400,000 volumes.
At Vic, monks studiously translated and recopied
works on astronomy, mathematics and geometry,
compiled by the scholars of Cordoba. Gerbert
became acquainted with the writings of Aristotle,
Virgil, Cicero and Boethius, whose apices – symbols for the Gerbert abacus – are the forerunners
of our arabic numerals.
Around the turn of the first millennium, Christians
had not yet adopted the place-value numbering
system invented by the Indians and propagated by
the Arabs. Standard accounting procedures were
done using primitive abacuses and tokens, and the
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“devil’s
invention”
results of these operations were written in nonpositional roman numerals. The roman algebraic
system relies on adding the numbers represented
by letter symbols in descending order (M=1,000,
D=500, C=100, L=50, etc.) to arrive at the figure. A
letter followed by another representing a higher
number is subtracted from it. Thus IV=4, IX=9 and
CD=400. Needless to say, the Romans themselves
had problems with this system, even forgetting
about the subtraction rule when it came to thousands or more. Moreover, without a zero they
could only show whole numbers.
Gerbert thus became the first to provide an accurate description of the place-value numeration
used by the Arabs of Spain and applied it to the
ancient abacus-type calculator by numbering its
columns from 1 to 9. He thus established the way
we add, subtract, multiply and divide. And what
about the zero that the Arabs were already using ?
He showed it as an empty space, since the concept of zero only later developed from a symbol to
a number, allowing mathematics to emerge as a
science. But for several centuries zero would
remain terribly suspect as a “devil’s invention” in
the eyes of Christian prelates who resisted the
introduction of these “infidels’ numbers” for as long
as they could.
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Models of the universe. It was also Gerbert who
introduced the astrolabe to Christian Europe. The
“infidels” used this instrument to calculate the times
of their prayers or to find their bearings in the desert.
Invented in ancient times, the astrolabe provides a
flat representation of the universe for a certain latitude and at a given time. Based on a geocentric
vision of the universe, the mechanically incorrect
astrolabe nonetheless enabled the exact calculation
of a number of important data. By setting the position
of the sun in its ecliptic, the astrolabe served to determine the length of the solar day and thus the solar
time. The same procedure was employed at night by
targeting a star. Gerbert used the astrolabe in conjunction with an armillary sphere with copper rings
representing the celestial equator and the ecliptic.
Moreover, Gerbert authored what proved to be decisive studies in mathematics: two treatises on arithmetic, one introducing the Euclidian method of
division and the other dealing with multiplication. He
also wrote a treatise on geometry that laid down the
principles governing points, straight lines, angles and
triangles as well as easy ways of finding the area of
a triangle or the volume of a sphere.
Advanced political skills. In 970, after further
extending his studies of the quadrivium subjects
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Gerbert’s modern treatise on geometry established axioms
and theorems governing lines, angles, triangles and points.
(arithmetic, music, geometry and astronomy) under
the aegis of Hatto, bishop of Vic, the youthful prodigy
was taken to Rome by his protector, Borrell II, and
presented to the pope. The latter informed Holy
Roman Emperor Otto I of the existence of “a young
man well versed in mathematics and capable of
teaching them with zeal.” The emperor appointed
him as the tutor of his son and future emperor, Otto
II. This marked the start of Gerbert’s three-tier professorial, ecclesiastic and political career.
At the wedding of Otto II in Rome, he met a noted
academic named Garamnus who took him to
Reims, the most prestigious archbishopric of what
was then known as Francia. The archbishop,
Adalberon, soon appointed Gerbert as head of his
famous school. Alongside this influential clergyman, Gerbert exercised his talents as a teacher,
reintroducing the quadrivium subjects that had
been all but forgotten during the troubled times of
the preceding Viking, Saracen and Magyar invasions. He also found himself plunged for a lengthy
period in the geo-political intricacies of a Europe so
incredibly complex that it is hard to fathom today.
The continent was an immense tangled web of
often bloody vassalages involving a mix of territories, family ties, greed, struggles for influence and
wars for precedence. In one mission at the end of
980, Hugh Capet, who was then duke of the
Franks before becoming their king, took Gerbert
with him to Italy to meet the latter’s former pupil,
Otto II. The papal election was at stake. Gerbert
returned to Reims in 984, having acquired an even
greater reputation as an outstanding scholar. The
future Sylvester II had floored his opponents in
several disputations or philosophical debates,
including one in Ravenna on the classification of
knowledge, and another in Pavia where the issue
was the subordination of physics to mathematics.
This intellectual pre-eminence, as well as a set of
alliances, earned him an appointment as the Abbot
of Bobbio, where he found himself at the head of a
powerful monastery with a vast amount of land. He
imposed a rigorous Benedictine code of conduct
imported from Cluny on the dissolute monks there,
and presided over the richest library in the western
world. However, upon the death of his protector,
Otto II, from malaria at the age of 28, Gerbert was
expelled from Bobbio and returned to Reims.
As personal secretary, or chief minister, to
Adalberon, the multilingual Gerbert, by now well
acquainted with many powerful statesmen and
renowned for his eloquence, became caught up in
intense diplomatic activities. He was to play a key
role in the coronation of Otto II and the subsequent
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Sylvester II at the right hand of Holy Roman Emperor
Otto III – his former pupil who made him pope in 999.
election of Hugh Capet, whom he also served as
secretary. Capet founded a new dynasty that challenged Otto’s aspirations to reign over Europe at
the head of a universal empire. This move was to
lead to intense and obscure interplays of alliances
and betrayals, followed by a series of brief wars,
exchanges of territories and ecclesiastical appointments, all of which were punctuated by infinite
negotiations, secret councils, threats of excommunication and schisms. Throughout these twists and
turns of history, in which he often appeared as an
advocate of peace and compromise, Gerbert was
successively appointed archbishop and then cardinal. Finally, in 999, he was elected pope and took
the name of Sylvester II. During the four years of
his pontifical reign, his main focus lay in installing
powerful states in Europe. He notably conferred
royal titles on the Christian rulers of Poland and
Hungary, nations that he had helped create.
Establishing the foundations of time measurement. He never lost sight of his scientific interests
and while he vainly attempted to use his papal
authority to impose his “arabic” numerals, his
important discoveries nonetheless made a significant contribution to science. His abacus and the
computus helped calculate the date of Easter and
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other moveable feasts. But was he the father of
mechanical horology? The chronology of the birth
of the clock remains as obscure as ever. Even the
Latin word horologium is ambiguous, since the term
also described the clepsydra (water clock) and the
sundial, well before referring to the mechanical
clock. Gerbert and his pupils marked the temporal
hours, based on the changing proportions of day
and night throughout the year. These measurements and calculations led to the development of
tables showing the division of time into horae, with
five puncti in an hora and 12 ostenta in a punctus.
This gave an hour divided into 60 ostenta or minutes. But there is a huge blank between this theoretical work and the actual invention of a brake
enabling weight-driven wheels to turn at a constant
rate. There are no clocks or records that survive to
link the maths with the mechanics. The invention of
the verge escapement and foliot – a loaded horizontal bar that swung restlessly to control the
descent of a weight – appeared in the early 14th
century, 200 years after the death of the humble
shepherd turned great pope. But that is of small
matter. What we do know for certain is that Gerbert
d’Aurillac represented an essential milestone along
the long road leading towards the mastery of
mechanical time measurement.
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et imperatorum
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Sylvester II in league with the devil, circa 1460. The
Church was then suspicious of the Renaissance’s educated elite. Sylvester II was thus accused of having
acquired his knowledge and his election to the papacy by
a pact with the devil.
Gerbert’s rod
This device is in fact a small piece of wood, a rod
that is held vertically thanks to a plumbline, to
which a shorter rod is attached perpendicularly
near the top. The length of this short horizontal rod
equals the distance between its point of attachment (C) and the top of the vertical rod (A). This
rudimentary yet ingenious instrument makes it
easy to calculate the height of a tall object (G) such
as a tower or a tree. Its principle is simple : to
measure the height of the object, the user must
sight its summit along the end of the horizontal rod
(D) and the top of the vertical rod (A). The height of
the object will thus be equal to its horizontal distance from the rod (A-F or B-E), plus the height of
the rod itself (A-B or F-E). This simple calculation
can be easily grasped and performed by children.
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