Thompson paradox

A lamp is turned on for 1/2 minute, off for 1/4 minute, on for 1/8 minute, off for 1/16 minute, on for 1/32 minute, and so on. At the end of one minute, will the lamp be on or off? At least in Zeno cases we know what will happen: the arrow will move, the wall will be reached, the turtle will be passed, etc. But here... will the lamp be on or off?