system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Why is it that a covariance of 0 does not imply that two variables are independent?

I'm kind of having trouble with coming up with an example/thought experiment that could explain this. I tried to look around for a simpler explanation but wasn't really able to find any. I do know that two independent variables have a covariance of 0 but why is it that the other way around does not work?
gpt
Covariance is a measure of how linearly related two variables are. Independent variables are not related and therefore have a covariance of 0; however, the covariance can also be 0 if the variables are dependent but do not have a linear relationship, for example the points that make a circle. For that reason, you can not assume two variables are independent given that their covariance is 0.