Idea of infinity stretched back to third century B.C.

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Washington, Feb 18 (ANI): A new analysis of a medieval manuscript has pushed back the first mathematical use of the concept of actual infinity by some 2,000 years, all the way back to the third century B.C.

The manuscript in question is a tattered page of parchment on which a medieval monk in Constantinople copied the third century B.C. work of the Greek mathematician Archimedes.

Infinity is one of the most fundamental questions in mathematics and still remains an unsolved riddle.

Mathematicians today refer to actual infinity as an uncountable set of numbers such as the number of points existing on a line at the same time, while a potential infinity is an endless sequence that unfolds consecutively over time.

The parchment page, which pushes back the first use of the concept of infinity, comes from the 348-page Archimedes Palimpsest, the oldest copy of some of the Greek genius' writings.

They were hidden for centuries because a monk partly scraped them off the animal-skin parchment in the 13th century A.D. to clear the pages to print a prayer book.

Also, a forger painted pictures over the prayer book hundreds of years after that.

A scholar named Johan Ludvig Heiberg in 1906 studied the written remnants behind the religious words to discover the Palimpsest, finding evidence of Archimedes' systematic use of the concept of infinity in a portion of the document called the Method of Mechanical Theorems.

In the past few years, the Palimpsest was re-examined at a far higher level of detail using a hair-thin X-ray scanning technique at Stanford University's Synchrotron Radiation Lightsource in California.

Stanford classicist Reviel Netz asked Uwe Bergmann of the Stanford scanning facility to focus on the edge of a torn page, where Heiberg had figured just one line of text was missing.

The X-rays produced images of phosphorus and calcium from the ink used on the document.

Netz examined the scan and was able to deduce the presence of previously unseen Greek letters, kappa and alpha, which were likely followed by an iota to spell the Greek word for "and."

This led Netz to conclude that two lines were missing, rather than one and to arrive at a new reading of the passage, according to Bergmann.

"Scholars are now talking about some new words which are emerging in the reconstruction of the evidence in introduction to the Method, that Archimedes' concept of infinity was rather different from what was previously thought," Bergmann said.

In fact, the new reading reveals that Archimedes was engaged in math that made conceptual use of actual infinity. (ANI)

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