Return to the geometrical line. This is an abstraction, an idealization, not a physical thing. When we divide the geometrical line, we make a division in thought, not in physical matter, and so the problem that we had with the string disappears; no physical theory will ever intervene to tell us we have in fact cut a piece of line so small that we have changed to a new metaphysical category. There are no physical facts about mental abstractions, so nothing can tell us we have reached the atoms. Indeed, what could a spatial atom even be? The geometrical line seems absolutely continuous precisely because it seems infinitely divisible. And indeed infinite divisibility seems a hallmark of continuity.