Vol. 2 No. 8

January 2004
General File
  Eureka! Archimedes found 17,152 solutions to puzzle

Twenty-two hundred years ago, the great Greek mathematician Archimedes wrote a treatise called the Stomachion. Archimedes asked - 14 pieces, 17, 152 solutions - how many ways these pieces can be put together to make a square. Now a historian of mathematics at Stanford appears to have solved the mystery of what the treatise was about, by discovering a clever way to determine whether a king's crown was pure gold. The Stomachion, concludes the historian, Reviel Netz, was far ahead of its time: a treatise on combinatorics, a field that did not come into its own until the rise of computer science. The goal of combinatorics is to determine how many ways a given problem can be solved. And finding the number of ways that the problem posed in the Stomachion (pronounced sto-MOCK-yon) can be solved is so difficult that when Netz asked a team of four combinatorics experts to do it, it took them six weeks. Recently, at Princeton University, three dozen academics heard Netz and congratulated him . Among all of Archimedes' works, the Stomachion has attracted the least attention, ignored or dismissed as unimportant or unintelligible. Only a tiny fragment of the introduction survived and as far as anyone could tell, it seemed to be about an ancient children's puzzle - also known as the Stomachion. The answer - 17,152 - required a careful and systematic counting of all possibilities. Perhaps as remarkable as the discovery that Archimedes knew. Combinatorics is the story of a manuscript that dates to 975, written in Greek on parchment. In the 13th century, Netz explained, Christian months, needing veluum for a prayer book, ripped the manuscript apart, washed it, folded its pages in half and covered it with religious text, which was found in 1906 by Johan Ludvig Heiberg, a Danish scholar. It appeared in the 1970s, in the hands of a French family that had bought it in Istanbul in the early '20s and held it for five decades before trying to sell it. In 1998, an anonymous billionaire bought it for $2 million and lent it to the Walters Art Museum in Baltimore, where it still resides. "You see nothing with naked eye," Netz said. "The major problem is the combination of the fact that many characters are hidden with the fact that many are so faint that they are invisible," Netz said. Computer imaging helped Roger Easton of the Rochester Institute of Technology etc. "The product of the software is incredible," Netz said.
                                 (Gina Katata, New York Times Service)
Note: It is worth reading the write-up in its entirety.

The Asian Age - December 15, 2003.

Suicide bombings declared 'illegal' under Muslim Law

Jakarta - December 17, 2003 - The Indonesian highest Islamic authority has issued an edict declaring terrorism and suicide bombings illegal under Muslim law - but adding that jihad, or holy war, is a religious obligation if the faith is under attack. Indonesia has more Muslims than any other country in the world, but its Government and laws are secular. Indonesian has been threatened in recent yeas by rising extremism and a series of terror attacks by Al-Qaeda-linked militants. Some of more than 30 people convicted over the Bali bombing (October 12, 2002 - 202 people, mostly foreigners, were killed) have claimed the attack was permitted under Islam. Mainstream Muslim groups have already denounced the blasts, but have been under pressure to formally condemn them. Mr. Syamsudin said the council edict, issued late on Tuesday, outlawed terrorism - 'both that committed by people and states' - and suicide bombings.

The Hindu - December18, 2003.

Food for Thought

It is unwise to be too sure of one's own wisdom. It is healthy to be reminded that the strongest might weaken and the wisest might err.

Mahatma Gandhi

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Wisdom out weights any wealth.

Sophocles

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To handle yourself, use your head; to handle others, use your heart.

Donald Laird