Every autumn the fire service came to the school. They parked the engine in the yard, let the children hold the helmet, and finished with the part everyone waited for: they sent a jet of water straight up into the air.
This year the officer turned it into a question. "That jet leaves the hose at twenty metres a second," he said, pointing at the school wall. "The top-floor windows are twenty metres up. The mast on the roof is twenty-five metres up. Which of them can we reach?"
The children guessed. Some said both. Most said the windows only. Nobody could say why.
The officer had done the arithmetic the night before, and he did not need to calculate how high the water went to answer him. He had asked a smaller question instead: is there any moment at all when the water is twenty-five metres up? The arithmetic of that question ended in a negative number, and a negative number there means there is no such moment. Not later, not sooner, not ever. The mast was safe.
He asked the same small question about the windows, and this time the arithmetic ended in zero. Not a negative, not a comfortable positive — exactly zero. The water reaches the top-floor windows at one single instant and then falls away.
"So we can reach them," he told the class, "but only just, and only for a moment. If your window is on the top floor, do not rely on us hosing it from the yard. We will come up the stairs."