By Vandebril R., Van Barel M., Golub G.
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The learned dust that Cicero speaks of, pulvis eruditus, was the sand in which mathematicians drew their diagrams — but that doesn't make their surface a counting board; so that when he dismissively says: 'You have never learnt mathematics,' numquam eruditum ilium pulverem attigistis (literally, never touched learned dust), the reference is probably to geometrical figures or those figurate numbers of page 21. The counting board sprinkled with green sand and blue sand that Remigius of Auxerre described in 900 AD sounds like something one would dearly love to own - but since he says that figures were drawn on it with a pointer (radius), it belongs to the same tradition, which also produced the wax tablets that Horace's schoolboy hung over his arm, and the slates that long after screeched in village schoolrooms.
The counting board sprinkled with green sand and blue sand that Remigius of Auxerre described in 900 AD sounds like something one would dearly love to own - but since he says that figures were drawn on it with a pointer (radius), it belongs to the same tradition, which also produced the wax tablets that Horace's schoolboy hung over his arm, and the slates that long after screeched in village schoolrooms. But the Roman board on which pebbles (calculi) were placed in columns was sanded too, and the Greek word for counting board,'abacus' (abax), may well have come not from 'legless table' but the Semitic abq, 'dust'.
Some exceed the number of the grains of sand ... ' This monstrous vision, which puts in the shade such fairy-tale excesses as the mill grinding out salt forever on the floor of the sea, Archimedes makes precise by an ingenious sequence of multiplications. Take it, he says, that there are at most 10,000 grains of sand 29 THE NOTHING THAT IS in a heap the size of a poppy-seed; and that a row of 40 poppy-seeds will be as wide as a finger. To keep things simple, picture each seed as a sphere. Since the volumes of spheres are to each other as the cubes of their diameters, this line of 40 seeds becomes the diameter of a sphere with a volume (40) 3 = 64,000 times the volume of one seed; and since that one holds 10,000 grains of sand, we're already talking about 64,000 x 10,000, that is, 640,000,000 grains.
A bibliography on semiseparable matrices by Vandebril R., Van Barel M., Golub G.