Sand is not the measure of all things, but it can serve as a metaphor to introduce two versions of infinity. The tiny grains that slip through our hands give an account, if possible, of the infinitely small, while their number (usually termed incommensurable) offer a way to suggest the infinitely large. It is not the measure of all things but rather, above all things, it measures time, thus transforming a spatial pass into a temporal pass. Time confined there is rapidly merged into an instant, invoking the Greek idea of Eternity: time that lasts forever. However, discussing what does not elapse brings us to the idea of nothing. This idea is also slippery: to figure it, the philosophers envisioned a knife -perhaps a dagger- without a blade, which is missing the handle.
Writing on sand can be dangerous. It led Archimedes to his death; he was murdered, precisely, by a brutal dagger - that of a Roman soldier. The dagger pierced the sage’s body while he was gazing at the geometric figures he had drawn in the soil in Syracuse. It can also be very dangerous to lean on the edge of the irrational. Legend tells that Hipassus of Metaponto discovered that the diagonal of the square is not commensurable with the side and was killed by other brothers of the Pythagorean fraternity driven by their fear of his disclosure. Drawn on sand, the argument (that can be called Sand Hipass) is simple: an isosceles right triangle folds on one of its legs to make a new right triangle, which is again isosceles. Meticulous repetition of this step results in an infinite sequence: successive triangles that shrink in size but do not vanish, thus revealing the incommensurable nature of the hypotenuse.
Prologue to Sand Pass