After searching for blogs about gardening and writing today, I came across one at http://fairegarden.blogspot.com/ with a posting regarding gnomons. The posting got me to thinking about a student presentation I gave for a math class (for liberal arts majors) in 2007:
What is a Gnomon?
Though gnomon is a Greek term meaning "that which allows one to know," and refers most often to the vertical pin on a sundial, invented by the Greek Anaximander sometime around 575 B.C., it originates from a more ancient and primitive Egyptian instrument, the merkhet, a sun clock first used about 2000 B. C. to measure the passage of time. The ancient Greeks translated merkhet, meaning "instrument of knowledge" to the word gnomon, which also stood for the L-shaped piece of metal that casts a shadow on a sundial. Greek intellectuals were familiar with Egyptian arts and sciences because they traveled frequently to Egypt and studied with Egyptian priests, who had preserved centuries of information on scrolls and stone tablets. The Greeks (according to Midhat Gazale, author of Gnomon: from Pharaohs to Fractals), "stood on the shoulders of Egyptian and Mesopotamian giants" to build on or expand the Egyptians' knowledge of many things, including geometry.
By studying geometric similarities, the ancient Greeks observed some interesting properties about certain numbers. They were obsessed with looking for a theory which could unify different branches of knowledge and thought they had discovered something truly magical about the way geometric shapes can be expanded in a particular way without losing their original structure.
For instance, when observing that 1+3=4, 4+5=9, 9+7=16. . ., they were fascinated by the fact that sequentially adding an odd number to a square number resulted in another square number and so on, and they could depict this phenomenon geometrically by adding an L-shape, or gnomon, to the original square. Mathematicians today like Gazale, following in the footsteps of his Egyptian ancestors in wanting to know the seemingly unknowable, study these and other figurate numbers and apply their properties to such things as the calculation of surds, logarithmic spirals, and silver pentagons.
The gnomon's ambiguity, or alternate meanings, seems to have appealed to other intellectuals, including literary figures such as James Joyce, the author of Dubliners, which is a collection of short stories based on people in his hometown. He introduces the term gnomon in the first story "The Sisters," as something a boy remembers from having studied the Euclid. The boy seems unsure of its meaning, but the very sound of it intrigues him. In the rest of the stories, the gnomon may be seen to represent dead people, who are shades or shadows of the people once alive. They add subtle meaning, texture, and clarity to the text, with its odd and often confusing characters, somehow squaring it up and expanding our understanding of Joyce's perspective.
My interest in the gnomon, I must confess, comes not from its mathematical application but rather a literary one. I learned from reading the Dubliners to look for the oddity in a story, the unexpected, perhaps even just a simple gesture which seems peculiar but speaks volumes about the character displaying it. For example, in recently re-reading Wuthering Heights, a novel I have read many times over the years, I noticed for the first time that, from the outset, the character Heathcliff sticks his hand in his coat, a gesture familiar to us as Napoleon's characteristic pose. I expanded upon that one enigmatic, L-shaped gesture to write a 10-page research paper for a Victorian Lit class. I believe that Emily Bronte's reading audience in the mid-1800s would have instantly recognized that pose and made the connection to Napoleon because, even though dead by that time, his name was constantly in the news and on the minds of many people. His nephew, Louis Napoleon Bonaparte, was vying for control of France, and the British were still reeling from the effects of their battles with his uncle's army. The year 1848, when Bronte's book was first published, saw Louis reentering French politics, and four years later he declared himself Emperor Napoleon III. Emily's little book, though originally published under a male pseudonym and after her death, eventually established her credibility among her mostly male peers and critics, perhaps because of her shrewd grasp of how to make the unknowable known.