There have been a pile of news reports about the Archimedes Palimpsest this week … near as I can tell, what is new in these reports is the revelation that Archimedes’ thoughts on infinity in the palimpsest are different than previously thought. The salient excerpt (via the Live Science version):
“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, as Netz describes on the Web site ArchimedesPalimpsest.org. The calculations involved adding infinite numbers of sums, such as the number of triangles inside a prism, as well as the number of lines inside a rectangle. Archimedes tried to argue that these values are equal to each other, making a statement about actual infinity, not just potential infinity, Nets writes.
The project website mentioned above (which I wasn’t aware of) has a pile of interesting stuff, including a digital version of the palimpsest and interviews etc. with those involved. You could easily kill an hour or so there.
- Idea of Infinity Stretched Back to Third Century B.C. (Live Science)
- Uncovering ancient secrets beneath the surface (AP via Google)
- Scholars uncover writings of ancient mathematician (Detroit News)