Once they had figured out how to cheat, the obvious progression was from the balance bar to implements of war. Schiefsky said the old manuscripts show that even in those days much of the technological progress came from weapons development, just as it does today. But some of the devices seem to be much more advanced than ancient math and physics could support.
The ancient Greeks had progressed well beyond the bow and arrow, "which has been around sort of forever," Schiefsky said, and they built catapults that could launch huge rocks at enemy fortresses, sort of precursors to cruise missiles.
"They built these boxlike frames that had long arms, which were stuck between twisted fibers of animal sinew, so they could launch very heavy rocks. This probably happened sometime in the fourth century B.C," he said.
By the next century, Archimedes was on the scene, and theories about proportions and leverage and so forth gave the old Greeks the tools they needed to refine their catapults, making them small enough to be moved, but big enough to get the job done. It's hard to do that kind of thing without math.
Schiefsky thinks those early craftsmen relied a little on trial and error, but it probably went beyond that. He got into studying mechanics because of his interest in the early history of medicine. Systematic testing of various herbs and remedies appear in some of the very early texts, suggesting that early practitioners had developed a crude form of clinical trials.
"You observe what works in one case and not in another, and gradually you build up a base of experience," and that's probably what helped the ancient Greeks develop some of their tools, Schiefsky said.
You don't have to understand the laws of thermodynamics to know that if you stick your hand in the fire you're going to get burned. But if you want to build a better stove, understanding such theories as heat conductivity would raise the ceiling considerable.
Archimedes provided a platform on which early workers could stand, and it was good enough to inspire technological innovation for many centuries. He remains one of the giants of early science, but even Archimedes stretched a point or two.
As the "inventor" of leverage, he claimed that if he had somewhere else to stand, he could move Earth.
It would take a very long pole, and a very strong pole, and my guess is he couldn't have done it. There is this stuff called inertia.
Archimedes' point, Schiefsky said, may have been a slight exaggeration, but "if you have a fixed resting point, and you have a fulcrum and you have a lever that's long enough and strong enough, in principle it's possible, even if it is a little bit of an exaggeration. It conveys the recognition of an exact proportionality. The lever is the main discovery of ancient theoretical mechanics."
After Archimedes, it took a couple of thousand years for Isaac Newton to come along and fill in a lot of gaps.
Lee Dye is a former science writer for the Los Angeles Times. He now lives in Juneau, Alaska.