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The Ancient Mechanics and How They Thought


April 1, 2008



CAMBRIDGE, Mass. — Consider the galley slave, clad in rags, chained to a hardwood bench and clinging to an oar as long as a three-story flagpole. A burly man with a whip walks back and forth shouting encouragement. You’ve seen the movie.

That galley slave would have known that the rowing stations in the middle of the ship were best, although he might not have known why. That took scholars to figure out. “Think of the oar as a lever,” Prof. Mark Schiefsky of the Harvard classics department said. “Think of the oarlock as a fulcrum, and think of the sea as the weight.”

The longer the lever arm on the rower’s side of the fulcrum, the easier to move the weight. In the middle of the ship, as the rowers knew, the distance from hands to oarlock was longest.

This explanation is given in Problem 4 of the classical Greek treatise “Mechanical Problems,” from the third century B.C., the first known text on the science of mechanics and the first to explain how a lever works. It preceded, by at least a generation, Archimedes’ “On the Equilibrium of Plane Figures,” which presented the first formal proof of the law of the lever.

Dr. Schiefsky teaches Greek and Latin as his day job and reads Thucydides and Sophocles in ancient Greek for fun. He also majored in astronomy as an undergraduate, and about nine years ago, feeling science-deprived, he joined a multinational research endeavor called the Archimedes Project, based at the Max Planck Institute for the History of Science in Berlin.

The Archimedes team studies the history of mechanics, how people thought about simple machines like the lever, the wheel and axle, the balance, the pulley, the wedge and the screw and how they turned their thoughts into theories and principles.

The textual record begins with “Mechanical Problems,” moves to Rome and then through the medieval Islamic world to the Renaissance. It ends, finally, with Newton, who described many of the basic laws of mechanics in the 18th century.

There are a surprising number of old, and extremely old, scientific texts that have survived the ravages of time in one form or another. The Archimedes Web site lists far more than 100, including Euclid’s geometry, Hero of Alexandria’s Roman-era technical manual on crossbows and catapults, medieval treatises on algebra and mechanics by Jordanus de Nemore and Galileo’s 17th-century defense of a heliocentric solar system.

The nice thing for Dr. Schiefsky is that hardly anyone reads the stuff. Scientists generally are not into ancient Greek or Latin, let alone Arabic, and most of Dr. Schiefsky’s colleagues work on literature, philosophy, philology or archaeology. In fact, Dr. Schiefsky suggests “about 100 people” worldwide work on both science and the classics.

By following the historical record, the Archimedes researchers have discovered that the evolution of physics — or, at least, mechanics — is based on an interplay between practice and theory. The practical use comes first, theory second. Artisans build machines and use them but do not think about why they work. Theorists explain the machines and then derive principles that can be used to construct more complex machines.

The Archimedes researchers say that by studying this dialectic they can better understand what people knew about the natural world at a given time and how that knowledge may have affected their lives.

“What do you do when you want to weigh a 100-pound piece of meat and you don’t have a 100-pound counterweight?” Dr. Schiefsky asked. “You use an unequal-armed balance, with a small weight on the long arm and the meat on the short arm.”

The uneven balance, known as a steelyard, is a kind of lever, and Dr. Schiefsky notes that it has a cameo in Aristophanes’ “Peace,” a comic fantasy about ending the Peloponnesian War. When a furious arms dealer cannot figure out what to do with a surplus war trumpet, Trygaeus, the central character, suggests pouring lead in the bell to make a steelyard.

Referring to the mouthpiece, Trygaeus says, “Attach at this end a scale-pan hung on cords, and you’ll have the very thing to weigh out figs to your servants out in the country.”

One reason why Archimedes scholars find mechanics so attractive is that devices like the steelyard and lever have such long histories. “Practitioners knew about the lever long before the development of scientific theory, pretty much since the origin of civilization,” Dr. Schiefsky said. At some point, theorists decided that the phenomena had to be explained. “It was an accident,” Jurgen Renn, a lead investigator for the Archimedes Project, said in a telephone interview from Berlin. “In China and Greece, you get many urban centers with vigorous debate. In China, the tradition dies out with Confucianism and the formation of empires. It is legitimized in the West by Aristotle.”

“Mechanical Problems” arrived in the modern world along with Aristotle’s works. In fact, it was thought for centuries that Aristotle wrote it. “Most scholars discount that now,” Dr. Schiefsky said. Aristotle cast wide theoretical nets, he added, while “Mechanical Problems” “is much more focused.”

The author of “Mechanical Problems,” Dr. Schiefsky said, clearly knew about Aristotle and adopted his matter-of-factness to describe a seemingly intractable dilemma in neat, practical terms. Problem 3 describes the lever’s property.

“For it seems strange that a great weight is moved by a small force,” the author wrote. “For the very same weight, which a man cannot move without a lever, he quickly moves by taking in addition the weight of the lever.”

Problem 4 is the oarsmen, demonstrating the principle in a different context. The oarsmen sit in a row from stern to bow. The oars are the same length, but the distance between hands and oarlock, the lever arm, is longer amidships, because the ship is wider there. The midships oarsmen exert less force than their bow or stern co-rowers to move the same weight of water. Conversely, if the midships oarsmen row as hard as the others, they will move a greater weight of water and contribute more to the ship’s movement.

Although the author of “Mechanical Problems” certainly understood how a lever worked, it was Archimedes who described the precise relationship between the weights and their distances from the fulcrum.

“He made this into a fundamental principle of theoretical mechanical knowledge that could be used by practitioners,” Dr. Schiefsky said. Classical tradition credits Archimedes as having said, “Give me a place to stand, and I will move the Earth.”

“And the principle,” Dr. Schiefsky added, “is that there is a proportionality between the force and the load, no matter how big the load. This is an intellectual transformation.”

In the Middle Ages, the Arab world was a source for new scientific knowledge, as well as the custodian for much classical tradition, translated from Greek into Arabic beginning in the ninth century. By the 13th century, Western scholastics translated Aristotle from Arabic into Latin.

“Mechanical Problems” arrived later in the Renaissance, along with Greek copies of Aristotle’s works, rediscovered in libraries, monasteries and other Middle East repositories. It inspired many commentaries by Renaissance scholars and was read by Galileo and other theorists. Indeed, “Mechanical Problems” is in many respects as useful today as it was 2,500 years ago, as anyone who has twiddled the weights on a health club scale can attest.

Or consider the New York Athletic Club rowing coach, Vincent Ventura, a close student of Problem 4, even though he has never read it: “It’s different for our people, because the length of the oar to the oarlock is the same no matter where you sit in the boat. Everybody pulls the same weight,” he said in a telephone interview. Still, “once in a while we might shorten oar for a guy who’s not as big as the others.”

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