Mythematics: solving the twelve labors of Hercules
2010; Association of College and Research Libraries; Volume: 47; Issue: 09 Linguagem: Inglês
10.5860/choice.47-5070
ISSN1943-5975
Tópico(s)Classical Antiquity Studies
ResumoM ichael Huber is not the first author to have been inspired by the enduring myth of the twelve labors of Hercules. In 1947, Agatha Christie published The Labors of Hercules, a novel in which her brilliant Belgian detective Hercule Poirot decides he will ease his way into retirement by solving precisely twelve final cases: cases selected only with reference to the ‘‘twelve labors of ancient Hercules.’’ In the hands of Dame Christie the foes of the mighty Hercules are wonderfully transformed. The fearsome Nemean lion becomes for Hercule Poirot a small Pekinese dog; the awe inspiring flock of Stymphalian birds becomes two ominous women with long curved noses dressed in cloaks walking by a lake at a European resort; the filth of the Augean stables becomes instead a political scandal at the very highest level of government, a mess which Poirot is called upon to clean up; and appropriately in his final ‘‘labor’’ Poirot is forced, as was Hercules, to deal with an all-too-real Cerberus guarding the gates of Hell. Each chapter in Mythematics: Solving the Twelve Labors of Hercules, by Michael Huber, is also based on one of twelve tasks imposed upon Hercules by Eurystheus. Hercules was born the son of the god Zeus and the mortal woman Alcmena. From infancy, the jealous wife of Zeus, Hera, had but one goal, the destruction of Hercules, and she almost succeeded. Hera was able to eventually drive Hercules mad and he murdered his own three sons. Hercules was thus forced into exile to serve Eurystheus and perform twelve labors. Upon the completion of these labors, he would become immortal. Each chapter of the book follows the same general format and begins with a quote from Apollodorus, the most reliable author of ancient times who wrote about Hercules and his labors, describing the particular task assigned to Hercules. Huber then uses this task as a springboard from which to pose three or four mathematical problems for the reader to attempt. Next, he provides detailed solutions for these problems and also—in passages that are by far the most entertaining sections of the book—elaborates further on the characters and stories from Greek mythology. There is much to be admired in this book. Michael Huber, who teaches mathematics at Muhlenberg College in Pennsylvania, has a real passion for Greek mythology and a creative flair for making connections with a wide range of mathematical topics. This book could be used in many ways. Its most obvious use will be as a source of lively versions of familiar problems that can be used in fresh new ways in courses. Or, more ambitiously, I can imagine using this book as the main text in an interdisciplinary course that is co-taught by a mathematician and a classicist where the goal is to introduce students simultaneously to the ancient Greek world and also many of the varied fields of mathematics. This is a course I would truly love to teach. Hercules’ first task is to bring back the skin of the Nemean lion, and he attempts to shoot the lion with an arrow. Huber uses this episode to pose a pair of routine questions: What is the speed at which an arrow strikes the lion at a distance of 200 meters given a launch angle of 20 degrees, and how long does it take the arrow to travel the distance from the bow of Hercules to the invulnerable lion? Huber does ‘‘solve’’ this problem in that he correctly finds the speed at which the arrow leaves Hercules’ bow (about 200 kilometers per hour) and also the time of travel, but he never gets around to saying how fast the arrow is going when it strikes the lion. Of course, the answer is ‘‘about 200 kilometers per hour’’ (here I would invoke conservation of energy, but one could also plug the time of travel into the velocity function to compute this speed). Unfortunately, all Huber says on the matter is ‘‘the speed of the arrow remains constant in flight’’, which of course is utter nonsense. So, while this book is both entertaining and at times inspired, it does need to be used with some care. Hercules’ third labor deals with capturing the Cerynitian deer. Huber turns the first part of this tale into a familiar problem in optimization. The deer, in trying to escape from Hercules, must swim across the Ladon River (which is 250 meters wide) and reach shelter in a forest 1600 meters along the shore on the other side. Of course, the deer runs faster than she swims (8 meters per second versus 5). Where should she land in order to reach the forest as quickly as possible? The artificiality of this particular problem reminded me of a similar problem I came across a few years ago in a new calculus book touting applications to biology and one ‘‘applied’’ problem involved a duck wishing to get from point A to point B as quickly as possible. This mathematically inclined duck could fly at a certain speed over land but could fly faster over water due to an often observed phenomenon whereby water birds fly extremely close to the surface of the water in order to increase efficiency. I was also somewhat bothered in Huber’s version of this problem by his unrealistic assumption that the deer maintained a constant swimming speed of 5 meters per second independent of the angle at which she was swimming relative to the river’s current. Once Hercules captures the deer (presumably by anticipating its landing point) he must carry the deer back to Eurystheus in Mycenae. Huber asks the reader to determine the work needed to carry the deer a distance of 80 kilometers given that the mass of the deer is 125 kilograms. He computes the animal’s weight (a vertical force) and multiplies this force by 80 kilometers (a horizontal distance) to get a completely meaningless answer of 98,000,000 newtonmeters (this is in fact the amount of work it would take to haul this deer to the top of a tower 80,000 meters high!). Huber makes a similar blunder about work later in the book when, having just computed the mass of the earth, he asks, ‘‘How much work does Hercules do in placing the earth on
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