The Sticks of Thales
How tall, exactly, is a telephone pole? the Star-Splitters asked ourselves in class in October 2021, after Henry told us that when we were reading Beowulf, he had imagined Grendel to be just that height.
After some great conversation about how we could come to know that fact (what human experts would we trust to tell us? why? what web sources would we trust to tell us? why? do telephone poles' heights differ? why? what experiments could we run with our own resources?), we recalled that Thales of Miletus, an originator of mathematics and natural philosophy, answered a similar question in the 6th century BCE, when visiting the Great Pyramid of Cheops.
Using only a stick, two shadows, and his keen mind, he determined the pyramid's height. First, he envisioned the vertical leg of the implied right triangle embedded in the pyramid (a triangle composed of that leg, the sun's rays, and the leg cast by the pyramid's shadow), then he created a measurable model of the same with a hand-held stick that he planted perpendicular to the sand. Measuring the stick's shadow at the same time a compatriot measured the pyramid's shade, he applied what he'd learned from experience about the mathematical relationships between like-angled triangles: he cross-multiplied the ratios of the legs' lengths, solved for X, and, voila, he discovered, with exactness, the Great Wonder's height.
All of which is to say we tried our hands and minds at being Thales that October morning, measuring--with great accuracy, given the limitations of our conditions!--the height of a wooden board we placed in the midst of our courtyard.
Ian's timeline of the thinkers we studied today: Thales of Miletus; Euclid of Alexandra, who codified the geometry Thales helped discover; Eratosthenes of Cyrene, who like Thales solved problems of measurement using only sticks and shadows and a penetrating mind, determining, for instance, the shape and circumference of the Earth; American poet Edna St. Vincent Millay of Maine, who, inspired by her study of science at Vassar College, wrote a timeless sonnet about the genius of Euclid, his ability to see the eternal forms of things within the daily shapes we know; Carl Sagan of Brooklyn, New York, whose video we watched in order to understand Eratosthenes’ achievement; and then, in our own time, Laura Fargas of Washington D.C., who in her poem "October-struck," reminds us that in fall our vision can expand to see more, see, for instance, the structural shapes of trees more clearly--see more of what we love, and thus can come to love it more.