I don't have any grand point to make here (though if you do, please make it), just thought you might find this interesting. It's on the relationship between mathematics and technology:
Even without math, ancients engineered sophisticated machines, EurekAlert: Move over, Archimedes. A researcher at Harvard University is finding that ancient Greek craftsmen were able to engineer sophisticated machines without necessarily understanding the mathematical theory behind their construction.
Recent analysis of technical treatises and literary sources dating back to the fifth century B.C. reveals that technology flourished among practitioners with limited theoretical knowledge.
“Craftsmen had their own kind of knowledge that didn’t have to be based on theory,” explains Mark Schiefsky, professor of the classics in Harvard’s Faculty of Arts and Sciences. “They didn’t all go to Plato’s Academy to learn geometry, and yet they were able to construct precisely calibrated devices.”
The balance, used to measure weight throughout the ancient world, best illustrates Schiefsky’s findings on the distinction between theoretical and practitioner’s knowledge. Working with a group led by Jürgen Renn, Director of the Max Planck Institute for the History of Science in Berlin, Schiefsky has found that the steelyard—a balance with unequal arms—was in use as early as the fourth and fifth centuries B.C., before Archimedes and other thinkers of the Hellenistic era gave a mathematical demonstration of its theoretical foundations.
“People assume that Archimedes was the first to use the steelyard because they suppose you can’t create one without knowing the law of the lever. In fact, you can—and people did. Craftsmen had their own set of rules for making the scale and calibrating the device,” says Schiefsky.
Practical needs, as well as trial-and-error, led to the development of technologies such as the steelyard.
“If someone brings a 100-pound slab of meat to the agora, how do you weigh it"” Schiefsky asks. “It would be nice to have a 10-pound counterweight instead of a 100-pound counterweight, but to do so you need to change the balance point and ostensibly understand the principle of proportionality between weight and distance from the fulcrum. Yet, these craftsmen were able to use and calibrate these devices without understanding the law of the lever.”
Craftsmen learned to improve these machines through productive use, over the course of their careers, Schiefsky says.
With the rise of mathematical knowledge in the Hellenistic era, theory came to exert a greater influence on the development of ancient technologies. The catapult, developed in the third century B.C., provides evidence of the ways in which engineering became systematized.
With the help of literary sources and data from archaeological excavations, “We can actually trace when the ancients started to use mathematical methods to construct the catapult,” notes Schiefsky. “The machines were built and calibrated precisely.”
Alexandrian kings developed and patronized an active research program to further refine the catapult. Through experimentation and the application of mathematical methods, such as those developed by Archimedes, craftsmen were able to construct highly powerful machines. Twisted animal sinews helped to increase the power of the launching arm, which could hurl stones weighing 50 pounds or more.
The catapult had a large impact on the politics of the ancient world.
“You could suddenly attack a city that had previously been impenetrable,” Schiefsky explains. “These machines changed the course of history.”
According to Schiefsky, the interplay between theoretical knowledge and practical know-how is crucial to the history of Western science.
“It’s important to explore what the craftsmen did and didn’t know,” Schiefsky says, “so that we can better understand how their work fits into the arc of scientific development.”