- Sylvia Berryman
The ancient Greek mechanical art addressed itself to the manufacture of assorted working artifacts, which were loosely organized into categories that reflected different understandings of the techniques by which they worked. Theories positing mathematical relationships were one reason for regarding groups of devices as part of a technical field; common physical principles governing their operation were another reason. The view that ancient Greek mechanics was regarded as working by magic has been discredited: although mechanics as a field produced “wonders” or show-pieces, this does not seem to have informed the understanding of the technê—a term often translated as art, but bearing implications of systematicity and method—by its practitioners. Aristotle classified mechanics, along with harmonics, astronomy, and optics, as one of the fields intermediate between mathematics and physics (Posterior Analytics 1.13, 78b37; 1.9, 76a24), based on mathematical principles.
Balance and weight-lifting technologies, like levers and pulleys, were understood to exhibit mathematical proportions. A weight twice as far from the fulcrum could counterbalance another object twice its weight, or a lever twice as long could be used to raise twice the weight with the same power. Similar principles were thought to connect the operation of the balance to that of the lever: the power used to raise a weight would be slightly more than that required to hold it suspended. Of the so-called “five simple powers” listed by Hero of Alexandria (mid-1st century ce)—windlass, lever, pulley, wedge, and screw—only the last is not included in the pseudo-Aristotelian text, found in Aristotle’s corpus but also ascribed to his second successor Strato of Lampsacus ([Aristotle] Mechanica; Hero Mechanica 2.5). Ballistic devices were another kind of technology considered to work by mathematical principles, since the mathematical formula for duplicating a cube—finding cube roots—was used in formulae for scaling up catapults from smaller prototypes. Plato's associate Archytas was said to have first systematized mechanics, presumably because of his development of a method for finding cube roots; Philo reports that these formulae were in use in catapult building in Alexandria (Ph. Bel. 55.12). The pseudo-Aristotelian Mechanica tries to understand the mathematical principles governing a number of weight-lifting devices by examining the properties of moving circles. The treatise analyses the movement of the radius of a turning circle as composed of two components, one along the tangent and another pulling toward the centre, and attempts to explain why a point further from the centre is moved more quickly by the same force. The treatise connects the principles governing the balance to that of the lever, and regards a number of other simple devices (sail, rudder, pulley, windlass, forceps, etc.) as operating in a similar manner.
The ancient Greek notion of mechanics was not limited to weight-lifting devices or those based on torque. An important branch of the mechanical art concerns devices that can raise water or hold it suspended against its natural tendencies to fall (see pneumatics). Various pressure-driven techniques were used to power display pieces, some of them decorated to resemble living creatures. These were animated by various techniques exploiting flowing water and air pressure, such as self-starting siphons, whistles, or a steam turbine. Elaborate theatrical displays were built by Hellenistic engineers including Ctesibius of Alexander (early 3rd century bce ), Philo of Byzantium (late 3rd century bce), Vitruvius (late 1st century bce), and Hero. Ctesibius apparently built a water-organ, and tried to use the spring of air trapped in pistons to power catapults. Spheres showing the relative movements of heavenly bodies came in various versions: reconstructing these requires making assumptions about the technology and planetary theory they were modelling, as literary reports are often underspecified. Modelling the relative positions of sun, moon, and earth could help explain the cause of eclipses, even before the mathematics to predict them became available. Time-pieces and calendrical devices were considered part of mechanics: ongoing reconstruction of an archeological find, the Antikythera mechanism, has shed new light on the sophistication of ancient Greek technology.1
Theories of the workings of mechanical devices were investigated further by Philo, Archimedes, Hero, and Pappus of Alexandria (early 4th century ce). Ctesibius’ experiments with pistons and compressed air seem to have drawn attention to the existence of elasticity as a property of matter: not only that some materials can be deformed, but that they have a tendency to return to their original shape. Philo seems to have tried to articulate some general principles of projectile force. Archimedes may have tried to connect the account of weight-lifting devices to the explanation of fluid-driven pneumatic devices, using the notion of equilibrium or centre of weight. Hero tried to conceptualize the forces operating on bodies in freefall by analogy to the weight-lifting devices that would have held them in equilibrium. He consciously abstracts features of a real case to an idealized conception, and uses the idea that a force sufficient to move a body is slightly more than one required to hold it at rest. Pappus writes of three central mathematical problems of the mechanical art: how to lift a given body with a given weight; how to duplicate the cube; and how to mesh cogged teeth of intersecting wheels of different sizes. The presentation of mechanics in late antiquity shows evidence of a more systematic attempt to portray the field as based on mathematical principles.
There is scattered evidence that some thinkers in the Hellenistic period and late antiquity toyed with the possibility that the natural world could be understood systematically as working like a mechanical device. Archimedes’ boast that he could move the earth if he had a place to stand was interpreted as a hyperbolic statement of the notion that it would be possible—in theory, and with a sufficiently large gear train—to produce a device that could enable any given power to move any given weight, just as Archimedes had hauled a ship single-handedly. This assertion of the indefinite extensibility of the principles of mechanics may have been implicitly questioned by some writers on mechanics, such as Philo and Vitruvius, who doubted the notion of the additivity of forces, and by some Neoplatonists and Aristotelians, who posited lower limits or thresholds to the applicability of mechanical principles to the natural world.
The author is grateful to Paul Keyser and the editor for helpful comments on an earlier version.
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