My favorite computer game was the old Moon Lander game. It simulated a moon lander firing retro-rockets to safely land on the moon. The player controlled how much fuel was used, and the object of the game was to land safely and quickly, before fuel ran out. In this game the amount of fuel and the starting altitude of the moon lander were independent variables. The game player did not control them, at least not within the game.
Another game might have the player control the direction of a vehicle with the speed and obstacles fixed at the start by the computer, so they were independent variables. Any variable might be the independent variable. The possibilities are endless.
Independent variables have a life of their own not controlled by “us” – the players, the users, the drivers, the scientists, the people who live within a world of particular independent variables. One could say that independent variables “flow” as a river flows beyond our control.
For a game, a problem, a situation, the independent variables of motion are chosen by us or for us out of their flow, their continual change. These are unbound variables until they’re bound for a certain context. For time that means a game lasts a specified time, a travel distance during a specified time, a change that happens during a certain time.
Since time is the main independent variable, we associate time with independent variables. That is, an independent variable may feel like time because it changes independently of us, as we ordinarily think of time. Independent variables are time-like in this sense.
But sometimes we do have some control of time, as when we’re driving a vehicle in a non-congested setting. Then time has more the character of a dependent variable. Time is less time-like the more it depends on us or something in our control. Time doesn’t always flow beyond our control.
A stopwatch measures time as a dependent variable, as in a race. In that case, time starts and stops with the stopwatch. Time doesn’t flow on because it’s not an independent variable.