A strip of wood unearthed during 2001 excavations at the site of the ancient Japanese capital city of Fujiwara-kyo is a far more sophisticated artifact than it appears at first glance. After more than two decades of careful analysis, experts from Japan’s Nara National Research Institute for Cultural Properties have proven that this object is approximately 1,300 years old, and that it contains figures that reveal it to have been part of a larger tablet inscribed with a detailed multiplication table.
Oldest Multiplication Table in Japan
As of now, this inscribed piece of wood is the oldest remnant from a multiplication table ever recovered on Japanese soil. Having been found in the ruins of the ancient Fujiwara Palace, a structure built by the rulers of Fujiwara-kyo, it is believed the multiplication tablet would have had some type of official use. The Nara Institute researchers think it belonged to an administrative entity known as the Emon-fu guard, a bureau responsible for managing the day-to-day affairs of the capital city’s government.
This identification actually narrows the manufacture and use of the inscribed wooden artifact to a specific point in time. The capital city of Fujiwara-kyo, which was modeled after the great cities of China, was established in 694 and remained the political and administrative hub of Japanese life only until the year 710. The assumption is that the multiplication tablet would have been used by Emon-fu personnel during this period of time, for duties such as calculating taxes or organizing the work schedules of government employees.
The wood strip recently identified as the corner of a multiplication table. It was excavated in 2001 from a site where the ancient capital of Fujiwara-kyo once stood. (Provided by Nara National Research Institute for Cultural Properties)
Exploring the Role of Mathematics in Ancient Administrative Affairs
The ruins of the ancient capital of Fujiwara-kyo can be found in modern-day Kashihara in Japan’s Nara Prefecture, along the nation’s southeastern Pacific coastline. Excavations have been going on there for quite some time, and when the wooden strip inscribed with ancient Japanese characters was found in 2001 researchers weren’t sure exactly what it was at first.
The brown wooden strip is approximately 6.4 inches (16.2 centimeters) long and a half-inch (1.2 centimeters) wide. It was apparently chipped or pealed off one corner of the larger multiplication tablet. While the characters on its surface are visible, they proved hard for experts to decipher at first because of their irregular nature.
Eventually, the Nara National Research Institute researchers examined the wooden strip using infrared scanning, and this proved to be the key to unlocking the artifact’s secrets. With these images it became clear that a series of familiar multiplication equations had been inscribed on the tablet, in five rows running left to right that made it possible to perform advanced mathematical calculations. Only a few of these equations were visible on the surface of the strip, but there were enough of them to identify the larger pattern.
“If the multiplication table was whole, the wooden tablet would measure 33 centimeters [13 inches] in length with all the equations written out,” Kuniya Kuwata, a senior researcher at the Nara Institute, said in an interview published the Asahi Shimbun, a Japanese newspaper.
The tablet containing the multiplication table would have been essentially a desktop device, something that was easy for Emon-fu personnel to hold and use.
Interestingly, the design of the multiplication table discovered at Fujiwara-kyo has a more ancient lineage. It matches the five-row layout of multiplication tables used in China during the period when that country was ruled by the Qin and Han dynasties (from the third century BC through the third century AD).
Since it is well-known that Chinese culture had an influence on developments in Japan, it is likely the design of the Japanese multiplication table was borrowed from that source. The five-row design in a Chinese context was an improvement on earlier versions of multiplication tables, which only featured two or three rows of characters.
Tracing the Historical Roots of Japan’s Ancient Multiplication Tables
While the wooden strip came from a multiplication tablet made about 1,300 years ago, the Nara Institute researchers are certain it was not the first of its type. They are intrigued by the possibility that the first multiplication tablets with the complex five-row design may have been created much earlier, possibly during Japan’s Kofun Period (300 to 538 AD).
During the Kofun Period and extending into the early seventh century AD, Japan experienced a construction boom of large megalithic tombs and burial mounds, which had a unique keyhole shape. These structures were known as kofun tombs, hence the name given to that historical era. The researchers believe that complex multiplication tables could have been immensely helpful in the design and building of such tombs, although as of now there is no evidence to prove any connection.
Perhaps future excavations in and around these ancient structures will lead to the recovery of more pieces of multiplication tablets, or maybe even fully intact tablets. This could verify they were used during the construction of some of Japan’s most famous ancient monuments.
Top image: Fujiwara-kyō ruins in Kashihara, Nara prefecture, Japan. Insert; Wood strip from multiplication table. Source: 663highland/CC BY-SA 3.0, Insert; Nara National Research Institute for Cultural Properties
By Nathan Falde
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