Ancient jugs hold the secret to practical mathematics in Biblical times

Jun 04, 2012

Archaeologists in the eastern Mediterranean region have been unearthing spherical jugs, used by the ancients for storing and trading oil, wine, and other valuable commodities. Because we're used to the metric system, which defines units of volume based on the cube, modern archaeologists believed that the merchants of antiquity could only approximately assess the capacity of these round jugs, says Prof. Itzhak Benenson of Tel Aviv University's Department of Geography.

Now an between Prof. Benenson and Prof. Israel Finkelstein of TAU's Department of and Ancient Near Eastern Cultures has revealed that, far from relying on approximations, would have had of their wares — and therefore known exactly what to charge their clients.

The researchers discovered that the ancients devised convenient mathematical systems in order to determine the volume of each jug. They theorize that the original owners and users of the jugs measured their contents through a system that linked units of length to units of volume, possibly by using a string to measure the circumference of the spherical container to determine the precise quantity of liquid within.

The system, which the researchers believe was developed by the ancient Egyptians and used in the Eastern Mediterranean from about 1,500 to 700 BCE, was recently reported in the journal PLoS ONE. Its discovery was part of the Reconstruction of Ancient Israel project supported by the European Union.

3D models unveil volume measurement system

The system of measurement was revealed when mathematician Elena Zapassky constructed 3D models of jugs from Tel Megiddo — an important Canaanite city-state and Israelite administration center — for a computer database. The jugs are associated with the Phoenicians, ancient seafaring merchants who had trading hubs along the coast of Lebanon. Using a statistical methodology, the team measured hundreds of vessels from the excavation, and discovered something surprising — large groups of these spherical or elliptic jugs had a similar circumference. This prompted the researchers to look more deeply into how the ancients measured volume.

The Egyptian unit of volume is called the hekat, and it equals 4.8 liters in today's measurements, explains Dr. Yuval Gadot, a researcher on the project. A spherical jug that is 52 centimeters in circumference, which equals one Egyptian royal cubit, contains exactly half a hekat. "In a large percentage of the vessels we measured, the circumference is close to one cubit, and the merchant could know that the vessel's volume is half a cubit by just measuring its circumference," he says.

When the researchers adopted the Egyptian system of measurement themselves instead of thinking in metrical units, many things became clear. For example, the tall round "torpedo" jugs packed into Phoenician ships in the 8th century BCE were found to contain whole units of hekats. Dr. Gadot believes that the Egyptian system of measurement gradually disappeared when the Assyrians took over the region, bringing their own methods of measurement with them.

A measure of political power

According to Prof. Finkelstein, elements of standardization in the ancient world hold interest because they are indicative of bureaucratic systems and reflect political and cultural influences. "The use of the Egyptian method is a strong indicator of Egyptian power in this region during a specific period of time," he explains.

"Working together with experts in mathematics and statistics, we have been able to provide new solutions for longstanding archaeological problems and debates."

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User comments : 12

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Rosser
5 / 5 (3) Jun 04, 2012
Someone got their hekats and their cubits confused in the last sentence of paragraph five. I believe this should read "...merchant could know that the vessel's volume is half a HEKAT (not cubit) by just measuring its circumference..."
ryggesogn2
1 / 5 (4) Jun 04, 2012
The profit motive moves science.
_ilbud
1 / 5 (2) Jun 04, 2012
"metrical units" no, that's gibberish.
nkalanaga
5 / 5 (3) Jun 04, 2012
ilbud: No, it isn't gibberish, because it isn't from "Metric". From Google's definition service:
met·ri·cal/metrikl/
Adjective:
1: Of, relating to, or composed in poetic meter: "metrical translations of the Psalms".
2: Of or involving measurement.

"Metric", as in the system, came from "metrical", not the other way around. Any measuring system is a "metrical" system.
flashgordon
3 / 5 (2) Jun 04, 2012
Israel Finkelstein is one of the authors of "The Bible UnEarthed"; one of the first archaeology and scientific accounts of anything biblical I read. Actually, it's the first book about the Bible I ever read.

The article doesn't really say what this can be usefull for; but, knowing what Israel Finkelstein, I would think his use of this finding would be used by him in a most scientific way, and not maybe what some think.
Terriva
1 / 5 (1) Jun 04, 2012
we're used to the metric system, which defines units of volume based on the cube, modern archaeologists believed that the merchants of antiquity could only approximately assess the capacity of these round jugs..
This misinterpretation has some wider consequences. For example the legendary Pandora box was probably just an amphora, as the ancient Greeks didn't use boxes for storage of their stuffs at all.
TheGhostofOtto1923
1 / 5 (3) Jun 04, 2012
Israel Finkelstein is one of the authors of "The Bible UnEarthed"; one of the first archaeology and scientific accounts of anything biblical I read. Actually, it's the first book about the Bible I ever read.

The article doesn't really say what this can be usefull for; but, knowing what Israel Finkelstein, I would think his use of this finding would be used by him in a most scientific way, and not maybe what some think.
The documentary is kind of tedious but is on youtube. Lots of nice scenery.
http://www.youtub...0bxhn1qA

Marcus_Harvey
not rated yet Jun 05, 2012
"According to Prof. Finkelstein, elements of standardization in the ancient world hold interest because they are indicative of bureaucratic systems and reflect political and cultural influences. 'The use of the Egyptian method is a strong indicator of Egyptian power in this region during a specific period of time,' he explains."

By this logic, the use of English measurements such as gallons and pounds in the United States would be a "strong indicator" of England's power in America during the present period in time, but we know this is not the case. In fact, England has adopted the metric system, like the rest of Europe, while the Americans largely hold on to the English system of weights and measures, for cultural reasons. Yet the English have not had power over America for more than two centuries...
TheGhostofOtto1923
1 / 5 (3) Jun 05, 2012
By this logic, the use of English measurements such as gallons and pounds in the United States would be a "strong indicator" of England's power in America during the present period in time, but we know this is not the case.
No that is a different logic. You are comparing apples and oranges.
Vendicar Dickarian
1.8 / 5 (5) Jun 05, 2012
"Ancient jugs hold the secret to practical mathematics in Biblical times"

My guess is that ancient "jugs" were every bit as nice as modern-day jugs. And likely distracted ancient mathematicians in much the same way as the modern variety.
Bigbobswinden
not rated yet Jun 06, 2012
Read "Before The Pyramids" by Christopher Knight & Alan Butler and have your eyes opened about ancient methods of measurement. It is a fantastic book. (No, I have no motive other than to recommend a great book).
Marcus_Harvey
not rated yet Jun 06, 2012
No that is a different logic. You are comparing apples and oranges.

How so, Ghost? We reason from the known to the unknown, from present day examples involving measurements and political power to ancient examples of measurements and political power.