Armillary Spheres

The "wooden terrestrial spheres" mentioned here are what we now call "armillary spheres." An armillary is a spherical arrangement of rings designed to mimic the orbits of the sun and planets around the Earth—or around the Sun, depending on the prevailing theory at the time. If the Earth is the center, it is a Ptolemaic sphere; if the Sun is at the center, it is a Copernican sphere. China and Greece each invented them BCE. Hipparchus credited Eratosthenes (276 - 194BCE) as the inventor.

An early Christian philosopher, John Philoponus, wrote the earliest extant treatise on the armillary sphere and the astrolabe. The oldest example of one we have today dates to the 11th century.

Gerbert d'Aurillac (946 - 1003), who became Pope Sylvester II in 999, had brought the armillary sphere to Western Europe. He was also responsible for introducing Western Europe to the abacus, the Hindu-Arabic numeral system we use today, and (possibly) the mechanical clock.

Sylvester used the armillary sphere and sighting tubes to determine the definitive position of the pole star and to record measurements for the tropics and the equator. His work was improved upon in the Renaissance by Tycho Brahe (1546 - 1601). Public figures would have an armillary sphere incorporated into their portraits to indicate their wisdom and knowledge.

I've written about clocks before, but I don't recall learning that Gerbert d'Aurillac invented it. I want to check that out; I'll let you know what I find.

The Ottonian Renaissance

Although we use the term "renaissance" to refer primarily to a rebirth of art and culture that started in 14th century Italy and spread throughout Europe, the truth is that there were several rebirths of culture between the Fall of Rome and the 14th century. I discussed this a decade ago here. One such rebirth took place during the Ottonians in Germany in the 10th century.

Part of this was not so much a rebirth as an influx of culture from the east: the Byzantine Empire maintained some of what Western Europe "lost" during those centuries. When Otto I married his son, Otto II, to Theophanu, the daughter of the Byzantine Emperor John I Tzimiskes, he opened the door to Byzantine art and increased commerce. Another important figure involved was Gerbert of Aurillac, who became Pope Sylvester II during the reign of Otto III.

Sylvester II introduced the abacus for computation, and wooden terrestrial spheres for the study of the movement of planets and constellations. He composed De rationalis et ratione uti (Of the rational and the use of reason) and dedicated it to Otto III. Promoting reason over faith was an important step in the study of the sciences. Sylvester also promoted the expansion of abbey libraries, particularly at Bobbio Abbey (where St. Columbanus wound up earlier), which had almost 600 works.

Arts and architecture also stand out in an examination of the Ottonian Renaissance. The revival of the Holy Roman Empire brought inspiration to think on a grander scale and create art and buildings that reflected the grandeur to which the Ottonians believed they were heir. Large bronze doors on churches and gilded crosses became more common. Ottonian patronage of monasteries produced grand illuminated manuscripts. One of the most famous scriptoria was Reichenau, which produced Hermann of Reichenau. This is also the period of the literary output of Hrotsvitha of Gandersheim.

A campaign of renovating churches and cathedrals also took place. (The illustration is an ivory plaque showing Otto I on the left, shown smaller than the saints, presenting Magdeburg Cathedral to Christ.) Longer naves and apses were inspired by Roman/Byzantine basilica. Many of these church designs and re-designs came form the hand of Otto I's brother, Bruno the Great. Bruno extended the cathedral in Cologne to rival the size of St. Peter's in Rome (Cologne Cathedral burned down in 1248, alas). He also built a church dedicated to St. Martin of Tours.

Ivory carving and cloisonné enamels were also widely produced in this era. A major workshop for cloisonné enamels was established by Archbishop Egbert of Trier, using a Byzantine technique of "sunken" enamel, where thin gold wire was soldered to a base, and colored glass melted into the spaces, as opposed to the original style of affixing gemstones as an inlay.

I find Ottonian art, though lovely, does not tickle my interest as much as those "wooden terrestrial spheres" of Pope Sylvester, so I'm going to look into those for next time.

Asking Questions

Image from Adelard's translation
of Euclid's Elements of Geometry

Being inquisitive is the first step to learning.* In the early Middle Ages, the presence of many classical authorities circulating in Latin, such as Aristotle and Plato, eliminated the need for inquiry in the opinions of many.

The 12th century saw an influx of more works, many of them Greek writings (preserved by Arabs) or Arab writings. The widening of philosophical and scientific horizons by this wave of knowledge caused many scholars to re-think what had been established.

Adelard of Bath (c.1080-c.1152) was an English philosopher who was in a position to translate into Latin for the first time many of the Greek and Arabic works becoming available to the West. After studying at Tours and teaching at Laon in France, he traveled for seven years through Italy, Sicily, Syria and Palestine. He translated Al-Kwarizmi's astronomical tables and Euclid's Elements of Geometry from Arabic, wrote works on the abacus and on his love of philosophy, and a book called Questiones Naturales (Natural Questions) in which he tackled, in dialogue form, 76 questions about the world. One of his themes is the choice of using reason rather than merely accepting authority.

For what should we call authority but a halter? Indeed, just as brute animals are led about by a halter wherever you please, and are not told where or why, but see the rope by which they are held and follow it alone, thus the authority of writers leads many of you, caught and bound by animal-like credulity, into danger. Whence some men, usurping the name of authority for themselves, have employed great license in writing, to such an extent that they do not hesitate to present the false as true to such animal-like men. [...] For they do not understand that reason has been given to each person so that he might discern the true from the false. [Questiones Naturales, VI]

To be clear: Adelard's science is not ideal: his periodic table of elements contains only four substances, which are mixed in various proportions to create all materials. Some animals see better by day or night because of either white or dark humor in their eyes. We see because an extremely light substance (Plato's "fiery force") is created in the brain, gets out of the brain through the two eyes, swiftly reaches an object and learns and retains its shape, then returns to the brain through our eyes so that we "see" what is in front of us. A mirror, whose surface is smooth, bounces back the fiery force, which on returning to us picks up our image on its way and allows us to see our reflection.

Still, his works were copied and distributed, and influenced much of what was to come. His assertion of reason over blind acceptance of classical authorities was an important milestone in scientific thought. Many of his ideas are seen again in the writings of Robert Grosseteste, Roger Bacon, and Hugh of St. Victor. Once the printing press was perfected, Adelard's translation of Euclid became a standard text for a hundred years.


*One of the followers of this blog is part of a group trying to promote inquiry-based learning in young people. Visit Prove Your World to learn more.

The Abacus

After mentioning Fibonacci's work, the Liber Abacus, it occurred to me that the place of the abacus in history deserved a little attention.

The Salamis Tablet, 300 BCE

Like the etymology for book, the word "abacus" does not start out to "mean" a frame with wires and beads. The word "abacus" first enters print in the English language in 1387. The Latin word from which it is lifted refers to a sandboard, a counting board covered in sand that allows you to draw with your finger. Latin took the word from the Greek abax, abakos, a board covered with sand for the purpose of drawing figures and calculating. At some point, the sand was replaced with counters of wood or stone that were moved from column to column for calculations, and the board itself was designed to facilitate calculations

In 1846, on the island of Salamis, a white marble counting board was discovered. The Salamis Tablet has been studied extensively, and one scholar has made a video of its proper use.

But when did abacus come to refer to the wooden frame with beads on wires? A reconstruction of a 1st century Roman abacus shows a board with grooves to keep the round beads in line. Visually, it resembles the abacus with which we are familiar. Gerbert of Aurillac (c.946-1003), one of the most influential scientific minds of his era, pushed the use of the abacus as a method of calculating much more swiftly than when using Roman numerals. He was able to promote its use even more when he became Pope Sylvester II.

The abacus in the form we think of it seems to come from China in the 2nd century BCE. Called a suanpán ("counting tray"), it was built with rods that held beads, 2 on an upper deck and 5 on a lower. Now called the "2/5 abacus," the two decks allowed the user to use larger numbers without adding 1+1+1+1, etc. Other versions had different numbers of rods, and different numbers of beads on them.

Abacus showing 87,654,321

Visually, it is very much like the Roman abacus mentioned above. Commerce between Rome and China was not unknown, but a direct influence cannot be proven. Still, the wooden-framed Chinese suanpán was so much like the Roman abacus that it was natural that the West would use the same name for the new device. In fact, no one type of the many objects used for calculating universally replaced the others. Counting boards of clay or wax were used well past the Middle Ages. In fact, until just after 2000, some accounting schools in China required proficiency in using the bead abacus.