Atomi, giochi geometrici e immaginario combinatorio in Lucrezio (2.772-787)

Lucr. 2, 772-787 tries to show that atoms have different shapes, but not qualities, which derive instead from their different combinations. For example, atoms do not have a color: in the sea, which albeit often changes its color, we do not see traces of atoms of different colors, while instead we still identify different geometric figures when they are combined to form a square. This passage by Lucretius alludes, without naming it, to the geometric game of the Stomachion, whose first and only Greek testimony is represented by a treatise by Archimedes. The game started from a phase in which 14 game pieces, of different geometric shapes, were arranged inside a wooden box to form a square; once removed from the box, the pieces could be combined in different ways, generating a potentially infinite amount of different figures. At this point, however, the second phase of the game intervened: after putting together the fantasy figures, and therefore after having completely disturbed and broken up the initial figuration, it was necessary to put the pieces back together in the box, reforming the initial square. Lucretius clearly alludes to this second phase of the game, namely the recomposition of the square through the different pieces of the Stomachion. This combinatorial image corresponds at least in part to the more famous image of the combination of the letters of the alphabet as a metaphor for the combination of atoms, and in ancient times it was part of a larger and more complex combinatorial imagery.