The ball's state can be described by its y coordinate, and it converges to zero. The lightbulb's state can be described by Boolean variable (on/off), but it doe

The ball's state can be described by its y coordinate, and it converges to zero. The lightbulb's state can be described by Boolean variable (on/off), but it doesn't converge, just oscillates between on and off with an exponentially increasing frequency. If we have instead used a variable intensity light switch, and turned it like 0%, 100%, 0%, 50%, 0%, 25%, 0%, 12.5% ..., with an exponentially increasing frequency, it would have also converged to the 0% state like the ball did. So the variables that describe the system's state has to converge.