Archimedes’ bellyache

Having been subjected to X-ray fluorescence, and then some multispectral imaging, the 13th Century Archimedes Palimpsest may have finally revealed its last secret – “that Archimedes, working in the third century BC, considered the concept of actual infinity, something thought to have only been developed in the 19th century, and anticipated calculus.”

The Palimpsest, constructed in the 13th Century mostly from an erased 10th Century copy of  works by Archimedes, is currently the subject of an exhibition at Baltimore’s Walters Art Museum where it will be on display until 1 January 2012.  From the Walters Art Museum press release

Archimedes, in his treatise TheMethod of Mechanical Theorems, works with the concept of absolute infinity, and this Palimpsest contains the only surviving copy of this important treatise. He claims that two different sets of lines are equal in multitude, even though it is clearly understood that they are infinite. This approach is remarkably similar to 16th- and 17th-century works leading to the invention of the calculus.

Also found only in the Palimpsest is Archimedes’ Stomachion.  It is the earliest existing western treatise concerning combinatorics. It is thought that Archimedes was trying to discover how many ways you could recombine 14 fixed pieces and still make a perfect square. The answer is high and counterintuitive at 17,152 combinations. Combinatorics is critical in modern computing.

In addition to Archimedes’ works, six other erased books of history and philosophy were discovered. Twenty pages of the Palimpsest were created from the erased texts of ten pages from a manuscript containing speeches by Hyperides, an Athenian orator from the golden age of Greek democracy. Twenty-eight pages were from the erased text of 14 pages containing a Commentary on the Categories of the ancient Greek philosopher Aristotle. Aristotle’s Categories is a fundamental text to western philosophy. This commentary survives nowhere else.

When the Palimpsest was imaged at SSRL, the name of the scribe that erased Archimedes’ writings was discovered on the first page of the Palimpsest. His name was Johannes Myronas, and he finished transcribing the prayers on April 14, 1229, in Jerusalem.

Two handsome, and expensive, volumes about The Archimedes Palimpsest project are available.

[And the bellyache? – Ed]  From the Guardian report

The palimpsest also contains the only existing copy of Archimedes’ treatise Stomachion, in which he tries to discover how many ways 14 fixed pieces can be recombined to make a perfect square. The answer is 17,152 combinations. “Stomachion means bellyache – in antiquity you didn’t call them brainteasers, you called them bellyachers. It’s very interesting: not only is it completely different to his other works [but] it has been shown that it is actually the first work to develop the science of combinatorics – the maths of combinations which lies behind the mathematics of probability,” said Sharp. “Before we knew this it was thought that combinatorics arose in the 17th or 18th century.”