What is time invariance?
In: Mathematics
A time-variant system is any system were the inputs vary by time. But the “inputs” really depend on how you define the problem.
* So in the example of getting to work, the drive time depends on rush hour which depends on the time of day. Leaving 1 hour earlier might save 30 minutes off your commute.
* Crossing a river might depend on the water level, which might depend on the season.
* Transferring a file on the internet might depend on congestion, which might depend on the time of day (everyone watches NetFlix after work, but fewer people are watching early in the morning).
* Solving a Rubik’s Cube can be considered time-variant if you assume people will be slower if you wake them up in the middle of the night to do the task.
* Walking around a track can be considered time-variant if the track is crowded at certain times, forcing you to change your pace.
A time-invariant system has inputs that don’t depend on the time:
* Making a baby takes 9 months ([no matter how many women are assigned to the task](https://en.wikipedia.org/wiki/The_Mythical_Man-Month)). Sure, not every baby takes 9 months, but it’s not like you can change the gestation period by deciding to star earlier or later.
* Solving a Rubik’s Cube can be considered time-invariant if you only consider small delays (starting now vs 1 hour from now)
* Walking around a empty track can be considered time-invariant. (You could turn that into a time-variant task by saying “the lights are turned off at night, so it’s harder to navigate”)
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