The view from my window, with the Lakeshore Limited passing by.
Above: Archimedes, as painted by Domenico Fetti, ca. 1620. Staatliche Kunstsammlungen Dresden.
Celebrating Pi Day
On March 14, fans of mathematics celebrated Pi Day. The numeric equivalent of the date is 3.14, representing the mathematical constant pi, usually written with the Greek letter
It is the closest approximation of the ratio between the circumference of a circle and its diameter. The value of pi is often given as 3.14159, but even this is an approximation, as the true value, if there is one, has never been ascertained, although many ingenious mathematical methods have been tried. In 2020 there was a claim that the value had been computed to 50 trillion digits. The use of the letter pi comes from its being the first letter of the Greek periphereia, the circumference of a circle — the Latin circumferentia being an exact translation of the Greek, "a carrying around."
To commemmorate Pi Day, some restaurants offer free or discounted helpings of pie!
For our Quotation of the Month, we celebrate the life of one of the ancient scientists who developed an ingenious method of approximating the value of pi, Archimedes of Syrcuse.
Archimedes of Syracuse, scientist and inventor
The Greek Archimedes (ca. 287 B.C. - 212 B.C.), famous for his inventions, developed a method of approximating pi by computing the dimensions of a series of polygons within the figure until he approached the desired value. His computations were achieved without the aid of modern calculus. Archimedes was not the first to compute a value for pi. The Chinese, Babylonians, and Egyptians also developed methods for approximating its value. But this was only one of many mathematical calculations made by Archimedes.
Archimedes, born in Syracuse on the island of Sicily, is most famous for his practical inventions, especially the Archimedes Screw, used even today for lifting water as well as other materials. A corkscrew-shaped blade inside of a cylinder is made to revolve by turning a crank by hand or machine, so that as it turns, anything placed or scooped onto it is lifted. (See the diagram at the bottom of this item.) He also invented innovative types of pulleys and defined the principle of the lever, of which he is supposed to have said "Give me a place to stand, and I can move the world." He also designed war engines with which the army of Syracuse was able to fend off the invading Romans for two years.
Archimedes the mathematician
Less well known in popular lore is his work in pure mathematics, which he considered his most important work. This included his aforementioned computation of pi. He also made other geometrical computations, including the volumes and areas of various geometrical figures. In a famous anecdote told by Vitruvius, he discovered that the volume of an object could be determined by seeing how much water it displaced. He made this discovery while taking a bath, seeing how the water level rose as he got in, uttering the famous phrase "Eureka!" (heureka!) "I have found it!" In one of his favorite discoveries, he computed the ratio of the surface area and volume of a sphere to a cylinder of equal height and radius, which he determined to be 2:3. He considered this latter discovery to be of such importance that he requested that a representation of it be inscribed on his tombstone. This was done, and the tombstone was seen and described by Cicero in 75 B.C. when Cicero was serving as quaestor in Sicily. Cicero found the tomb in neglected condition, and had it cleaned up. (See the figure above.)
Archimedes left several treatises on his mathematical work, but none on his practical inventions, considering them to be, by comparison, "ignoble and vulgar" (agennê kai banauson), according to Plutarch (Life of Marcellus 17.4).
The Siege of Syracuse by the Romans under Marcellus
During the Second Punic War, fought by Rome against the Carthaginians under Hannibal, Sicily, including the city of Syracuse, had defected to the Carthaginian side. Syracuse proved to be particularly difficult to crack, thanks in large part, to the inventions of Archimedes. In 214 B.C., the Romans, under the proconsul Marcus Claudius Marcellus laid siege to Syracuse. He brought the full might of the Roman navy against the city's defenses. Archimedes, however, designed engines that could lob huge stones and other weights down upon the ships, as well as other machines. Perhaps his most amazing device was an enormous crane or claw that could seize a ship and dash it against the cliffs beneath the city walls or lift it up and shake it about until all the crew fell out.
Marcellus was finally able to take the city by entering it by an unguarded tower while the inhabitants were celebrating a festival of Artemis. When Marcellus looked down upon the beautiful and prosperous city, he is said by Plutarch to have wept to think that it would soon be plundered and destroyed, for there were many who wanted it burned to the ground. This he would not permit, although he was unable to stop his men from plundering it.
Marcellus mourns the death of Archimedes
Archimedes is said to have died at the hands of a Roman soldier while he was intent on solving a mathematical problem. According to Plutarch, a soldier summoned Archimedes to go with him to Marcellus, but he refused to leave until he had solved the problem and completed its demonstration. The soldier, angered, drew his sword and killed him. Plutarch also offers two other versions, one in which the soldier threatened him as soon as he came in, and another in which Archimedes was carrying some astronomical instruments to Marcellus, and some soldiers thought he was carrying gold, for which they killed him. Marcellus, in obvious admiration for the genius of Archimedes, was outraged, and shunned the killer as a polluted person, going to the relatives of Archimedes and paying them honor.
Marcellus took as his only loot from the city two of Archimedes' devices, which showed the motions of the Sun, Moon, and planets. According to the narrative told by Cicero in his dialogue de Re Publica, Marcellus kept one for himself and donated the other to the Temple of Virtue in Rome.
The world's first oceangoing steamship using a screw propeller was the British ship SS Archimedes, launched in 1839.
Quotation of the Month, from Plutarch's Life of Marcellus
For our Classical Quotation of the Month, we bring you, in Latin and English, part of Plutarch's Life of Marcellus that describes the death of Archimedes. Both the text and the translation are from the Loeb edition of 1917.
Diagram of Archimedes' screw. By turning the device, an object can be lifted, or a ship propelled.
The Chicago River, from the Michigan Avenue Bridge, January, 2008. (Photo by C.A. Sowa.)
CHICAGO COLLOQUIA ON DIGITAL HUMANITIES AND COMPUTER SCIENCE
Since their inception in the fall of 2006, I have been attending the Chicago Colloquia on Digital Humanities and Computer Science (DHCS), held at a rotating group of universities around Chicago. These Colloquia now draw participants from all over the world, who present projects covering many fields, including such interests as visual arts, archaeological reconstruction, musical composition, literary criticism, social trends, popular culture, history, and many fields yet to be discovered. Of the projects I have submitted under the name of Minerva Systems, a couple have been presented as poster exhibits. Others I have informally circulated among the participants. But whether one is presenting a paper or simply taking part in discussions, the Colloquia offer an opportunity to exchange a wealth of ideas. Workshops and smaller discussion groups, too, are well worth while.
For information about the Colloquia, visit the DHCS Web site at "http://chicagocolloquium.org". Information about all previous Colloquia (2006, 2007, 2008, 2009, 2010, 2011) can also be accessed from there.
The Reliance Building, at State and Washington Streets in Chicago, January, 2008. (Photo by C.A. Sowa.) The Reliance Building, like the MINERVA System, was built on principles of modularity and extensibility.
Read about it!
My thanks to all those who have reviewed and used my self-study CD course on using computers and quantitative methods in the study of literature, The Loom of Minerva: An Introduction to Computer Projects for the Literary Scholar, and my thanks to those who continue to give me comments.
You can read Chapter 1, "A Guide to the Labyrinth: The Problem and Its Solution" on this Web site. (Note: this chapter now describes a greater variety of ways to structure a project, e.g., top-down, bottom-up, etc. It will continue to be revised.) You can also see images from two demonstrations of the MINERVA System, from 2006 (emphasizing individual applications programs), given at the First Chicago Colloquium on Digital Humanities at the University of Chicago and 2007 (emphasizing new project planning programs) given at the Second Chicago Colloquium on Digital Humanities at the Northwestern University.
The MINERVA System
The MINERVA System for Study of Literary Texts is a set of tools, some automated, some not automated, for planning and carrying out a project in literary study. Methods of Systems Analysis, borrowed from the scientific and commercial world, are adapted to the study of literature. This methodology emphasizes the use of diagramming techniques and modular design, offering a way to construct a project as a set of units or modules that can be worked on separately and moved around without disturbing the whole. A project is defined as an enterprise that has a goal and an organized way of achieving that goal.
The Loom of Minerva combines the methods of Systems Analysis with the insights of traditional belles-lettres literary criticism. All analysis takes as its point of departure the value of the piece of literature itself to the critic and the reader, as well as the historic, social, or aesthetic qualities attached to it. These alone confer significance on any work of scholarship. Examples grow directly from study of various works of literature, from Vergil to Coleridge to Baudelaire to Victor Hugo to Edna St. Vincent Millay and Gertrude Stein, and works of criticism from Sainte-Beuve to Swinburne to Gertrude Stein (criticizing her own work).
Emphasis is placed on analyzing the language of criticism itself, analyzing exactly what we mean by such terms as "beautiful," "ugly," "pompous," "like a spring garden," etc. By defining our terms with an exactness that can be quantified, we learn to give precision to our thoughts, whether using a computer or not.
What is in The Loom of Minerva
The CD contains both a set of narrative chapters and a set of programs, called the MINERVA System for Study of Literary Texts. The narrative chapters explain and amplify the programs, and the programs illustrate the chapters. The programs are provided in both executable form and source code, to satisfy both non-programmer scholars and programmers who want to play with the code.
MINERVA stands for Model INteractive Engine for Recognizing Verbal Artifice.
Advantages of the MINERVA System
The MINERVA programs do not require the use of data that is in a proprietary format. They use plain ASCII text, such as that downloaded from the Internet. The OwlData programs can be used to put downloaded or scanned text in the correct format for the MINERVA programs. The mathematics and statistics used are fairly elementary, such as can be understood as an introduction to basic concepts of what the computer and quantified methods can do. The programs are open-source, as they are intended to be extensible.
For more information:
If you are interested in finding out more about the Loom of Minerva or the MINERVA System, contact me at firstname.lastname@example.org.
Reconstruction of one of Babbage's engines at the Computer History Museum, Mountain View, California. Click on the picture to watch it in action. (Photo by J.F. Sowa).
Charles Babbage's Difference Engine and Analytical Engine
Charles Babbage, prolific Victorian inventor, is most famous for two of his inventions, the Difference Engine (1812) and the Analytical Engine (1833), which are perhaps the truest forerunners of the modern computer. The Difference Engine, a mechanical device of rotating gears, was designed to automatically generate mathemetical tables. It was called the Difference Engine because it was based on the principle of computing the differences between successive values of an expression, then the difference between the differences. Versions of the Difference Engine were eventually built and used, but Babbage himself dropped work on it to pursue his real dream, the Analytical Engine. The Analytical Engine was, or would have been, the first "real" computer, capable of performing any kind of mathematical operation, and able to be "programmed," that is, to perform a sequence of operations without human intervention, and to choose, when necessary, between alternative paths of action. It was to be powered by steam, and programs were to be entered into the machine by means of punched cards, an idea borrowed from the then-new Jacquard power looms. Babbage, sad to say, was never able to complete the Analytical Engine.
Ada, Lady Lovelace, "the world's first programmer"
Babbage's collaborator on his Engines was one of history's most remarkable women, Ada, Lady Lovelace, daughter of the poet Lord Byron. These lines from Childe Harold's Pilgrimage are thought to be addressed to her:
A gifted mathematician in her own right, Ada worked with Babbage until her untimely death in 1852 at the age of 36. In 1842, the Italian engineer Luigi F. Menabrea published a description, in French, of Babbage's Analytical Engine. Lady Lovelace translated Menabrea's article into English, expanding it with commentary so extensive that her "Notes upon the Memoir" are virtually an original work. She provides detailed directions for using the machine to calculate answers to mathematical problems, leading modern writers to call her "the world's first programmer." Her words relate computing to other artistic endeavors:
We may say most aptly that [Babbage's] Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.
A Babbage Engine in London and California
In 1985, the Science Museum in London set out to build a working Difference Engine No. 2, based on Babbage's original designs. It was completed in 2002, and is on public display at the Science Museum. An identical Engine, completed in 2008, is presently on loan to the Computer History Museum, Mountain View, California, where it is on display until May, 2009. Read more about this recreated machine at the Computer History Museum Web site.
Click here or on the picture below to watch the Babbage engine in action, in a video taken by John F. Sowa.
Reconstruction of one of Babbage's engines, detail view. Click on the picture to watch it in action. (Photo by J.F. Sowa).
Read about the 1845 Eureka Machine for Composing Hexameter Latin Verse
Another Victorian machine which could be called an early special-purpose
computer was the Eureka machine designed by John Clark in 1845 for automatically
composing Latin hexameter poetry. It still survives, in a museum in Somerset,
England. Click here to read about it.
Book: Traditional Themes and the Homeric Hymns
The book, out of print for a while, is again available by "on-demand" production. Contact the publisher for information.
New selections are available on this Web site for free reading. You can read Chapters 1 ("Introduction") and 10 ("Conclusion: the Place of the Hymns in the Ancient Greek Oral Tradition"), Appendix I ("Outlines of Themes Identified in the Hymns"). You can also see diagrams of the themes as they appear in the Hymns.
Article: "Thought Clusters in Early Greek Oral Poetry"
An article, by Cora Angier Sowa and John Sowa, describes in detail
the quantitative and mathematical methods used on the computer to
identify thematic elements in Hesiod and the Homeric Hymns.
Material from this study was later integrated into into the more
comprehensive Traditional Themes and the Homeric Hymns. Click on
"Thought Clusters in Early Greek Oral Poetry".
A version of the CLUMP cluster analysis program used to identify thematic
repetitions is now also being integrated into the MINERVA suite of programs
in the self-study CD The Loom of Minerva.
In orally composed poetry like Homer's Iliad and Odyssey, and Hesiod's Theogony and Works and Days, there was no written text (the alphabet being barely known at the time, around 750 B.C.). The bard, like a jazz musician, recomposed his story each time (to a melody now lost to us), using stock phrases or "formulas" and repeated scenes. Since the story was enjoyed not by reading but by hearing it, there were no punctuation marks or chapter headings to tell listeners where they were in the narrative or its episodes. The skilled singer used, instead, repeated words and phrases to serve as "oral punctuation" to articulate the story and provide emphasis for important themes and concepts.
Reissued here is my article Verbal Patterns in Hesiod's Theogony, which explores the use of verbal repetition in Hesiod's tale of the origins of the gods.
We think of computers as being very modern, although calculating machines and computer-like devices have been around for a long time. In particular, we think of using such a machine to do such non-scientific tasks as composing poetry as a modern concept. But in 1845, John Clark built the Eureka Machine for Composing Hexameter Latin Verse. It still exists in a museum in England. Read about the Eureka Machine and read the original description of it from the Illustrated London News of July, 1845.
There is more about early computers and their mechanical ancestors in the self-study CD The Loom of Minerva: An Introduction to Computer Projects for the Literary Scholar, described above.
"Minerva" has long been a popular name for ships. There are cruise ships named "Minerva," including Greek vessels whose owners chose that name as a synonym for their own city patroness Athena. Warships named "Minerva" have graced the navies of Europe from the time of Nelson and Napoleon to the present, whether British "Minerva" or French "Minerve."
It is an interesting choice, considering that Athena, with her gift of the olive, defeated Poseidon, lord of the sea, with his gift of the horse, in the contest to be patron deity of Athens. (See the depiction of Athena and Poseidon below.)
The name "Minerva" for a British warship belongs in the splendid tradition of naming vessels after names from Classical history and mythology. Along with names like "Invincible," "Audacious," "Irresistible," "Insolent," "Victory," and "Dreadnought," we find "Gorgon," "Phoenix," "Achilles," "Apollo," "Dryad," "Endymion," "Hector," "Helicon," "Medusa," "Meleager," and, famously, "Arethusa." The most famous ship named for the Sicilian nymph Arethusa was known for her victory over the French "Belle Poulle" in 1778. Training ships for over a century inherited the name, one after the other.
A frigate "Minerva" participated in the Battle of Cape St. Vincent against the navy of Napoleon on February 14, 1797. The marine painter Thomas Buttersworth (the elder) painted a portrait of "Minerva" in 1810, and the "Minerva" Pub in Hull, England (built in 1831) uses the frigate's symbol, the owl, on its sign. Of course, some ships have been named "Athena" and "Poseidon," too; there was a movie about such a ship called The Poseidon Adventure.
There is a further connection between ships and this Minerva Systems site. In the self-study CD The Loom of Minerva (described above), an analysis of Coleridge's The Rime of the Ancient Mariner is used as a case study to demonstrate methods of Systems Analysis and computer techniques.
A feminist note on the gender of ships: Because of the living qualities of ships, I like to refer to a ship as "she" rather than "it." While some may compare a vessel to a woman because of the supposedly capricious nature of both (although there seems nothing wrong with an occasional playful moment), I think that this view overlooks other qualities. Ships, like women, are beautiful, swift, intelligent, and powerful. I am glad to acclaim them as my sisters!
Signed vase painting by the Athenian potter/painter Amasis (6th cent.
B.C.), depicting Athena and Poseidon. The two figures are labeled
ATHENAIA and POSEIDON. The inscription down the middle reads
AMASIS MEPOIESEN ("Amasis made me"). Amasis may well have been
African. (Illustration from a lithograph by Kaeppelin et Cie., ca. 1840.
The actual vase is in the Cabinet des Médailles, Bibliothèque
Nationale de France, Paris.)
Essays and reviews on building and architecture
Among the selections on this site is the previously published "Holy Places", a study of myths of landmarks. In addition, there is an epilogue to that essay, on "The World Trade Center as a Mythic Place". This piece continues the author's interest in relating ancient ideas to things that we care about in the modern world.
Cora Angier Sowa has combined humanities and technology for many years. She has a BA in Latin and an MA in Classics from the University of California, Los Angeles, and a PhD in Classical Philology from Harvard University. She spent a year studying archaeology at the American School of Classical Studies at Athens. She taught Greek and Roman literature and history at Mt. Holyoke, Vassar, and Brooklyn Colleges. For a number of years, she was a programmer/analyst at Chemical (now Chase) Bank in New York. She has taught classes in computers and humanities at the College of Staten Island and at St. John's University in Queens, New York. She served twice on the Committee on Computer Activities of the American Philological Association, once as chairperson of the committee. She was the recipient of a Fulbright Scholarship (for study in Greece) and of a grant from the American Council of Learned Societies (for work on computers and ancient Greek literature).
In addition to the book Traditional Themes and the Homeric Hymns (described above), Dr. Sowa has published articles and reviews on Classics and on the mythology of architecture and motion pictures. A harp player, she is also on the board of trustees of the International Percy Grainger Society , an organization dedicated to preserving the home and archives in White Plains, New York of Percy Grainger -- composer, piano virtuoso, collector of folk songs, and inventor of an early mechanical music synthesizer. Dr. Sowa is Webmaster for the Grainger web site.
A lifelong railfan, Dr. Sowa is a member of the New York Chapter of the National Railway Historical Society and is on its Board of Directors. She is National Representative for the New York Chapter and is on the Advisory Council of the national organization. She is also a member of the New York Railroad Enthusiasts.
Dr. Sowa lives in Croton-on-Hudson NY, and in New York City, with her husband, Dr. John F. Sowa, an expert in Artificial Intelligence and computer design, and several cats.
All selections on this site, unless otherwise identified, are copyright by Cora Angier Sowa.
Send e-mail to Cora Angier Sowa.
On this Web site, you are visitor number: