Posted on 10/02/2007 5:58:55 PM PDT by blam
Source: Harvard University
Date: October 2, 2007
Even Without Math, Ancients Engineered Sophisticated Machines
Science Daily — 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."
Schiefsky's research is funded by the National Science Foundation and the Max Planck Institute for the History of Science in Berlin.
Note: This story has been adapted from material provided by Harvard University.
math just systematizes what becomes common sense to any practitioner.
While this is not a homeschooling article, parents who homeschol may want to bring this to the attention of their children. Who knows? It could ignite their imagination the way a basic chemistry from his mother book ignited Thomas Edison’s.
I find this statement to be an assumption on the part of Harvard's finest. JMHO...
There is absolutely nothing common sense about non-euclidean geometry.
Should read as:
A researcher at Harvard University is finding that ancient Greek craftsmen were able to understand the mathematical theory behind their construction and engineer sophisticated machines without necessarily having to learn how to quantify the knowledge in a scientific manner.
Better.
Only an academic would be surprised by this.
Imagine that. They knew by application that 2+2=4 without knowing what 2+2=4 means.
It makes a little more sense to say that they were able to use and calibrate these devices because they knew the law of the lever just fine. In a sense, knowing how to use and calibrate a device based on the law of the lever is knowing the law of the lever.
Actually, only an academic would assume this.
Duh, you just move the support points around until the 10# and 100# weights balance. School kids on a seesaw understand that without knowing math.
That being said, it would be interesting to see the craftsman "rules" that they are referring to.
Academia, today, couldn't do that without a $10 million government grant.
Made sense to me although I could not have described the math behind the fact that it worked 100% of the time.
The flow of energy, and resulting stresses, are just visible, if you have the eyes to see them. Much of education is only valuable,to those with little common sense. A good Blacksmith can hold a chunk of alloy in his hand, drag his nails across the surface, and tell you what he has.
Am I to take it that you doubt I Euclid V?
Heathen.
;)
Like the proof of Fermat's Last Theorem?
And Galen did sophisticated eye surgery. So, can you tell me why these ancient wizards and their technology didn’t continue to evolve? It is said that ancient minos had advanced sewerage systems that weren’t equaled until france/paris in the 18th century. Are there smart/dumb cycles in history, like bio-rhythms?
It wasn't until I was introduced to optics in high school physics that I learned the mathematical explanation for what I had done. (Unfortunately, several years before that, I read Paul de Kruif's "Microbe Hunters" -- and learned that Aton Von Leuwenhoek had beat me to the punch [high-powered simple microscopes] by several hundred years...) :-{
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