A train is at the platform. For a while, it is still. Then the stationmaster waves his flag, and, very slowly, the train begins to move. A familiar enough scene. But below the surface lurks a subtle mystery. It is natural to suppose, before we start thinking about it, that there is a last moment of rest before the train starts to move, and a first moment of motion. But, if time is infinitely divisible, then there cannot both be a last moment of rest and a first moment of motion. The interval between any two moments can always be further divided. -- Robin Poidevin Is this puzzle about transition, from the last moment of rest to the first moment of motion, a puzzle also for other transitions? For example, from non-existence to existence? (Or existence to non-existence?) From the last moment the water was boiling at 212 Fahrenheit (boiling point of water at sea level) to the first moment of its being cooler? Elaborate