Secrets Of Practical Mathematics
In Biblical Times Hidden In Spherical Jugs

5 June, 2012

MessageToEagle.com - The ancient Egyptians used unique system of volume measurement based on sphere units - according to an interesting theory presented by Tel Aviv University researchers.

In the area of the eastern Mediterranean region, archaeologists find spherical jugs, used by the ancients for storing and trading oil, wine, and other valuable products.

"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," said Prof Itzhak Benenson of the Tel Aviv University's Department of Geography.

 Now the researchers have found that, far from relying on approximations, ancient merchants would have had precise measurements of their wares - and therefore known exactly what to charge their clients. "We examined 89 Iron Age I-IIA Phoenicia-made globular jugs. Three of them we measured manually: one jug from Megiddo in the Jezreel Valley, and two jugs from Tel Masos in the Beer-Sheba Valley. The other 86 jugs were measured according to their drawings; 55 come from Cyprus, seven from Tyre and 25 from various locations in Israel: Megiddo, Tel Dor, Tel Keisan, Hazor, Tell Qasile, etc…" , according to their paper.

The scientists discovered that the ancients devised convenient mathematical systems in order to determine the volume of each jug.

According to this original theory, 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 researchers believe that the system was developed by the ancient Egyptians and used in the Eastern Mediterranean from about 1,500 to 700 BCE.

A Phoenician globular jug from Tel Megiddo, with a maximal external circumference of 29.2 fingers and volume of 0.53 hekat. Photo Credits: E. Zapassky et al / Tel Aviv University

The system of measurement was revealed when mathematician and lead researcher 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," said co-author Dr Yuval Gadot.

Typical Egyptian beer jars

"A spherical jug that is 52 cm 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 said.

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.

"The Egyptian system of measurement gradually disappeared when the Assyrians took over the region, bringing their own methods of measurement with them," Dr Gadot said.

"The use of the Egyptian method is a strong indicator of Egyptian power in this region during a specific period of time," Prof. Israel Finkelstein of TAU's Department of Archaeology and Ancient Near Eastern Cultures added.

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

The theory is presented in paper in the journal PloS ONE.

@ MessageToEagle.com via Tel Aviv University

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