 But an infinite number of solid and therefore indivisible atoms of finitely many kinds, such as Epicurus’ theory provides, are enough to avoid the possibility of the universe crumbling into nothing. Why did Epicurus complicate matters still further with the doctrine that atoms themselves consist of still smaller parts in the form of mathematically minimal expanses, as we saw above that he does? Finite bodies, according to Epicurus, had to be composed of smaller expanses, and if there were no lower limit in size to such expanses, one would have to imagine traversing such a body in an infinite number of moves — but then, however small these infinitesimals might be, the object that contained them, Epicurus reasoned, would have to be infinitely large (LH 56–57). What are such minima like? Epicurus asks us to think of the smallest perceptible thing. It differs from larger visible entities in that it has no sub-parts to be traversed with the eye: if you do attempt to visualize such sub-parts, they simply coincide with the original perceptible minimum. Since such minimal visible entities have no parts, they do not touch edge to edge (edges are parts), and yet they measure out the body that contains them, larger bodies having more such minima. By analogy with the visible, then, we conceive of the smallest part of an atom (LH 58–59). This conception resembles the way points exist in a line, according to Aristotle, since they too do not touch, nor can they exist independently. But Epicurean minima differ from points in that they are physical expanses and so have extension. This looks like a contradictory state of affairs: can we imagine, for example, an atom consisting of just two minima? Or ten? It would be like counting up the least visible bits of a perceptible object. Geometrical problems arise as well, since it was known that the side and diagonal of a cube, for example, were incommensurable, yet both must, it would appear, be composed of finite and hence commensurable numbers of minima. On the assumption that Epicurus was aware of and cared about such puzzles, it has been suggested that he thought any atom consists of a not strictly infinite, but inconceivably large — and so “not strictly finite” — number of minima (see Konstan 1989a): thus, the minimum may be imagined as the inverse of the number of kinds of atoms postulated by Epicurus, a quantity that takes on a quasi-technical status as a special order of magnitude. But sufficient evidence for this hypothesis is lacking.