Showing posts with label Ptolemy. Show all posts
Showing posts with label Ptolemy. Show all posts

Wednesday, February 23, 2022

Gerard of Cremona x 2

Gerard of Cremona (1114-1187CE) was an important translator of Arabic texts into Latin. Born in Cremona in northern Italy, he went to Toledo in the Kingdom of Castile because he desired to learn more about Ptolemy. Why did an Italian travel to Spain to learn about a Greek? Because Ptolemy's writings, although the man and his importance were known to Europe, were not available except in Arabic translations from the Greek.

Why Toledo? We'll delve into that more deeply tomorrow. For now, know that Gerard learned Arabic sufficiently that he not only translated Ptolemy's Almagest, the definitive work on astronomy until it was replace by Copernicus, but also he is credited with translating a total of 87 Arabic works.

Many of them were Arabic translations of Greek originals. Gerard's work made available to Latin readers works by Archimedes, Aristotle, Euclid's Elements of Geometry, and Arabic works on algebra and astronomy. He also edited the Tables of Toledo, a compilation of astronomical data.

There was a second Gerard of Cremona, however, and some of the 87 works attributed to Gerard might have been translated by Gerard, if you follow. This second Gerard was working in the 13th century, and seems to be the translator of medical works, whereas the first concentrated on astronomy and science. Roger Bacon's access to Al-Kindi's work, which would have been after 1240, is likely to be due to the second Gerard. Modern scholarship on the work of Gerard points out that many of the words he uses in his Latin translations are still used today; diaphragm, orbit and sagittal are examples. (To be fair, some of the modern scholarship also suggests that his translations look like the work of a hurried graduate student.)

But back to Toledo. In the 12th and 13th centuries, there was a robust Toledo School of Translators. I'll tell you about it tomorrow.

Monday, April 7, 2014

The Huns

Today is the anniversary of Attila the Hun's attack on the town of Metz in Gaul.

In the 1st century CE, the Roman historian Tacitus mentioned a group of people living near the Caspian Sea. They were nomadic, and supposedly had come from the east. Tacitus called them Hunnoi. Ptolemy in 139 CE called them Chunnoi and said they were on the southern shores of the Black Sea. It is not certain if these two were the same peoples, or if they were the same as the Xiongnu people who lived north of China in the 3rd century BCE and later moved westward, as one 18th century scholar proposed.

We know, however, that there was an "empire" of Huns established in eastern Europe by the 4th century CE. They were so feared, conquering and absorbing peoples and dominating their lands, that it has been suggested that the Huns caused the great westward migration of other groups into western Europe.

Its peak of power was under a pair of brothers, Bleda and Attila. They were nephews of the leader Rugila, and took over when Rugila died in 434. The Huns at that time had been causing trouble for the Eastern Roman Empire, and they were in negotiations with Emperor Theodosius II. Several tribes that had been conquered by the Huns had taken refuge within the borders of the Roman Empire, and the Huns wanted them "back home."* Theodosius' legate agreed to push those tribes out of the Empire; the Empires of the Romans and Huns also agreed to trade with each other, and 350 pounds of gold as tribute was paid to the Huns to seal the deal (as well as gold ransoms for the Roman soldiers Huns had captured in recent fighting).

The Huns then turned their attention to invading the Persian Empire, leaving Rome alone for the next five years. They eventually turned back to attacking Europe when conquering Armenia proved difficult, falling into conflict with Rome again.

Bleda, the elder brother, ruled for 11 years. Upon his death, Attila took over. There has been speculation for centuries that Attila killed Bleda, but there is no evidence for it. The Hun Empire lost its focus after Attila's death in 453.

*Sounds a little like Putin annexing the Crimea.

Thursday, October 24, 2013

Cross-referencing an Eclipse

Diagram of an eclipse from a modern translation of Hipparchus
It is not always easy to figure out dates from classical or medieval writings. Chroniclers did not necessarily strive for the kind of historical accuracy which 21st-century audiences expect. When they wanted to be precise, they often expressed themselves in ways that do not provide a proper context for the modern scholar.

Consider, for instance, Pappus of Alexandria, whom the Encyclopedia Britannica calls "the most important mathematical author writing in Greek during the later Roman Empire." [source] He wrote many important texts, but we knew little of his life.

I mentioned the other day how Suidas' Lexicon gives us data on works and events otherwise lost to history. The entry for Pappus reads:
Alexandrian, philosopher, born in the time of the elder emperor Theodosius, when the philosopher Theon also flourished, the one who wrote about Ptolemy’s Canon. His books [are] Description of the Inhabited World; Commentary on the 4 Books of the Great Syntaxis of Ptolemy; The Rivers in Libya; Dream-Interpretations. [source]
We know that Theodosius reigned from 372-395 CE, so it gives us a time frame for Pappus. This creates a small head-scratcher, however. Pappus claims to have calculated and observed an eclipse in the month of Tybi (the fifth month of the Coptic calendar). There is a problem with this dating: no eclipse occurred during the month of Tybi during the reign of Theodosius that Pappus could have observed! Could the Suidas be wrong? Certainly. But then... what is right?

There is, as it turns out, a 10th century copy of a work by Theon of Alexandria (the one mentioned in the Suidas entry) that has a marginal note next to an entry on the Emperor Diocletian (who reigned from 284-305 CE), stating "at that time wrote Pappus." Is it possible that the composer of Suidas had access to that work and assumed that it meant Pappus flourished when Theon did? If we look closer to the reign of Diocletian, we discover that there was an eclipse in the month of Tybi which would place it (using the modern method of dating) on 18 October 320 CE. If Pappus observed it himself in 320, it isn't likely that he was flourishing over 50 years later. This places him firmly in the earlier part of the 4th century.

Pappus is far more important than as an example of the care with which modern historians must date historical events. Some of his eight-volume work on mathematics is extant; and deals with many facets of geometry and carefully lays out the mathematical findings of his predecessors and how their work builds on each other over time. He also worked on several problems such as inscribing regular polyhedrons inside a sphere, conic sections, trisecting an angle, and many more. He has a theorem named after him, as well as the Pappus chain, the Pappus configuration, and the Pappus graph.

His commentary on Ptolemy provides us with insight into some lost works of classical astronomy, such as an astronomical work by Hipparchus on eclipses (illustrated in the above figure).

Friday, December 14, 2012

The Rotating Earth

Nicholas Oresme
While re-examining Aristotle, Jean Buridan used observation and brainpower to anticipate some of the ideas we attribute to Galileo and Newton. He carried his ideas further when he put his mind to the question of the Earth's movement.

For most scholars of the Classical and early Medieval eras, the Earth was fixed, and the Heavens rotated around the Earth once each day. Buridan didn't like this: the Heavens are so much larger than the Earth; why would God design such an inelegant system? Moving the Earth would be easier.

Ptolemy knew this could not be, because if the Earth were rotating, there would be a constant rushing of wind as the air of the atmosphere passed over the land underneath it. Buridan scoffed at this: the atmosphere would be rotating just as the land does. There was no reason to dismiss the idea that Earth rotated daily.

For Buridan, however, empirical evidence was crucial. Of course, his predecessors argued, the Earth clearly does not move; we can see that. Buridan, however, likened the situation to being in a boat on a river. An observer on a second boat that was tied to the bank would see the first boat moving, but if the observer on the second boat could not see the surrounding landscape, then he would not know which of the boats were moving. The problem, Buridan knew, was that without an outside frame of reference, one cannot tell if it is the Earth or the Heavens that is moving. He needed an experiment, and he thought of one.

...and that's when he made his mistake.

Here was his idea: shoot an arrow straight up above your head. If it comes back down where you are standing, then the Earth is stationary. If the Earth rotated under it, then the arrow would come down somewhere off to the side.

He didn't realize that the same property that moves the atmosphere along with the ground would carry the arrow along as well. It would be Buridan's most brilliant student, Nicholas Oresme (c.1325-1382), who would realize and state that the arrow moves along with the Earth and atmosphere. Lacking a way to definitively prove his ideas, however, Oresme would ultimately fall back on the Bible for guidance on this issue.

Saturday, December 8, 2012

The Ring of Fire vs. The Flood

15th century portrayal of Ptolemy's map
Prior to the Age of Exploration, human beings in the western hemisphere did not attempt to travel long distances by sea and discover distant lands.* This was partially because ships that could handle a very long voyage were not able to be built or provisioned easily for such a journey.** Another reason is that the world was "known" to be shaped so that long voyages were fruitless.

Eratosthenes (c.276-c.195 BCE) had established in the Classical Era the spherical nature of the Earth through simple and clear experimentation; no one disputed that. (His math on Earth's diameter was probably a little off: the unit of measurement he used probably gave him an Earth 4000 miles larger around than it is.) What was up for debate was the question of what existed "over the horizon."

Aristotle (384-322 BCE), upon whose scholarly shoulders the Middle Ages tried to stand, loved symmetry. It made sense to him that there were five zones (from the Greek word meaning "girdle") around the Earth. The extreme top and bottom were icy cold and uninhabitable. Just inside of them were the temperate zones where humans and animals lived—note: he believed both temperate zones were inhabited. In the middle it was so hot—and clearly, the further south you go from Greece and the Mediterranean the hotter it got—that it was uninhabitable. Pliny (23-79) said that this central zone was so hot that it was actually a ring of fire and was unlivable and impassable, so we would never be able to visit the people living in the southern hemisphere.

Wait, said Christianity. That can't be. The Flood covered the whole world, and when the waters receded, the Ark of Noah came to rest on Mt. Ararat in Turkey, from which all the animals strolled away and repopulated the world. If the ring of fire at the equator is impassable, how can there be animals living beyond it? Worse, if there are people living in the southern temperate region, how are we going to reach them with the Word of God?

Proving that classical scholars did not always agree, Ptolemy presented different problems in geography. His Geography was translated and made available to Western Europe in 1406. His map (depicted above in a 15th century version printed in Ulm) showed that all you had to do was sail far enough south to reach the southern lands in the world, but he also extended the bottom of Africa eastward, enclosing the Indian Ocean. This meant you could not sail to the Indian Ocean and therefore to India, but would forever have to use the Silk Road (and incidentally pay tolls at every border crossing, something sailors get to avoid).

The Age of Exploration changed all this. In 1473, Aristotle was proved wrong with a Portuguese ship exploring the west coast of Africa passed south of the Equator. In 1488, another Portuguese ship sailed around the Cape of Good Hope and reached the Indian Ocean. India and the east were accessible by ship after all, and the Portuguese quickly established those shipping routes.

Ptolemy's Geography was erroneous in another way. He estimated the Earth's circumference at thousands of miles smaller than Eratosthenes. Since no one cared to duplicate Eratosthenes' experiments and determine the distances involved, Ptolemy might have been taken as truth by some. His estimates of the size of a spherical Earth would put Asia thousands of miles closer to Europe by sailing west. With Portugal dominating southern routes to the East, was it Ptolemy's miscalculation that prompted Spain's Columbus to try a bold plan to establish a different and (he thought) shorter route?

*Perhaps some day we'll get to some of the rare cases of accidental discovery of previously unanticipated lands.
**I have been aboard replicas of Columbus' ships; they are frighteningly small considering the journey they made.

Friday, August 3, 2012

How far are the stars?

Rabbi Levi ben Gerson, also known as Gersonides, lived from 1288-c.1344. He was from a family of scholars: his father, Gerson ben Solomon of Arles, was the author of the Sha'ar ha-Shamayim, an encyclopedia of natural science, astronomy, and metaphysics.* Levi is credited with first mentioning, and possibility inventing, Jacob's Staff. (He references Genesis 32:10 when he describes the device; this is likely the origin of the name.)

At a time when religion, philosophy, astronomy, astrology and science were overlapping (and in some cases, interchangeable), Gersonides' greatest work, which was philosophical, contained his greatest contribution to astronomy. He put twelve years (1317-28) of effort into the Milhamot Adonai ("Wars of the Lord"), whose six books dealt with 1) the soul, 2) prophecy, 3) & 4) god's knowledge of facts and providence, 5) astronomy/astrology, and 6) creation and miracles. Gersonides firmly accepted astrology and the celestial hierarchy of powers inherited from neo-Platonists and pseudo-Dionysius (far too complex to go into here), but he also brought mathematics and observation to his work with extraordinary results for the time.

Postage stamp honoring Gersonides.
Gersonides rejected the Ptolemaic system of epicycles to explain the erratic motion of planets affixed to their crystal spheres surrounding the Earth. According to Ptolemy, epicycles explained the changing size of planets; he said, however, that Mars varies by a factor of six; Gersonides' observations told him that Mars's apparent size varies only two-fold. Gersonides used the Jacob Staff and a camera obscura (pinhole camera) to make careful observations over several years. For Gersonides, 48 crystalline spheres were needed to explain the apparent motion of various heavenly bodies. This expansion of the "physics" of the Ptolemaic model was nothing, however, compared to the actual physical expansion he proposed.

Careful observation with the Jacob Staff, the camera obscura, and math made Gersonides declare heavenly objects to be much farther away than previously calculated. Ptolemy claimed the distance to Venus was 1079 Earth radii; Gersonides estimated it to be 8,971,112 Earth radii away. Ptolemy said the fixed stars were 20,000 Earth radii away; Gersonides estimated them to be at a distance 10 billion times greater.

Pope Clement VI had the "Wars of the Lord" translated into Latin in 1344, making it available to the west. Its impact was minimal, however; we know of a few scholars who were influenced by it, and Kepler asked a friend to send him a copy in the 17th century. But it took Copernicus two centuries later to "confirm" to Western civilization's satisfaction that Gersonides was on the right track.

*As I have mentioned about medieval encyclopediæ before, they were often compilations of previous works; this one drew from Claudius Ptolemy's Almagest and the Morah Nebukim, or "Guide for the Perplexed" of Maimonides. A 1547 edition of ben Solomon's work can be had from Kestenbaum & Company.