The Archimedes Codex

  • Reviel Netz &
  • William Noel
Weidenfeld & Nicolson/Phoenix/Da Capo Press: 2007. 336/336/320 pp. £18.99 (hbk)/£8.99/$27.50 (pbk) 9780306815805 9780297645474 | ISBN: 978-0-3068-1580-5

In April 2004, biologist Lewis Wolpert won a debate at the Royal Institution in London entitled 'Who was the first scientist?' He championed Archimedes. Although I reckon Roger Bacon comes closer to deserving that label, the result reflects the respect still felt for Archimedes' work. Yet our knowledge of his output has never been complete. The Archimedes Codex describes the recent uncovering of text from the Archimedes canon not read since the parchment forming the codex was reused to make a prayer book in 1229.

Only three of Archimedes' books in the original Greek are known, two of which have been lost since first being transcribed. The third, this codex, had never been fully deciphered. Access to the earliest known version (from the tenth century) was important because of a recent shift in interpretation of Greek texts. The Greeks approached mathematics visually. The diagrams and the exact wording used are crucial in understanding the thinking of a Greek mathematician — yet when the lost Archimedes manuscripts were transcribed, no thought was given to capturing the visual nature of the information.

Analysing the Archimedes palimpsest with different wavelengths of light. Credit: G. STEINMETZ/CORBIS

In The Archimedes Codex, Reviel Netz and William Noel contribute alternate chapters, with Noel describing the history of the codex and the work undertaken to decipher it, and Netz exploring Archimedes' mathematics. This discontinuous style is initially unnerving — both authors write in the first person, and it isn't clear that the 'I' of chapter 1 is not the same person as the 'I' in chapter 2. But it soon settles into an engaging account.

Noel, director of the deciphering project, explains the intricacies of dealing with a manuscript of this age and of uncovering the hidden text beneath the overwriting. His contribution has a personal tone ideal for the palimpsest story but rather too lightweight for scientific technicalities such as the mechanism of the multispectral imaging used to bring out the obscured text. Netz, a classicist at Stanford University, makes less allowance for his audience. His valuable examples may warrant several re-readings for non-mathematicians.

The most exciting of the discoveries in the newly deciphered text was Archimedes' use of infinity. The Greeks were wary of infinity, a concept they endowed with implications of chaos and disorder. When infinity was considered in Greek mathematics, it was treated as potential infinity, rather than the real thing. A potentially infinite pile of logs will never run out — there are always more — but it contains a finite, if indefinite, number.

Before the codex was deciphered, it was thought that, apart from some playful consideration of true infinity by Galileo Galilei, the concept was hardly touched on until the nineteenth century. Netz painstakingly retrieves text from the codex proposing that two infinite sets have the same size because the elements in them can be put in a one-to-one correspondence. Such sets are now said to have the same 'cardinality', the modern concept that establishes that two sets are equivalent in magnitude. Yet here was Archimedes using this argument more than 2,000 years before Georg Cantor added it into the mathematical armoury.

Netz also shows how Archimedes used a remarkable physical extension of geometry to calculate the area under a parabola, and undertakes some work based on a game called the stomachion (bellyache). However, it is Archimedes' use of the infinite that has the biggest impact on our understanding of the history of mathematics and that best demonstrates the value of Netz and Noel's work.