10-year-old just got to function stuff and I'm having trouble explaining in general why you should care which variable is dependent vs independent? Other than that, in stats, you should know the direction of causality, does this sort of thing matter?
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I find this way of thinking about functions very confusing. The way I imagined functions is that they're a "computational" primitive that takes some inputs and gives some outputs back. This model admits natural composition, reasonably natural argmax&al and inverses. In it the notion of dependence of variables is, depending on your pov, either trivial or not really a thing.
@ZachWeinersmith
Ah, and in an area where this becomes somewhat more confusing -- probability -- I found that describing everything in terms of stochastic "experiments" and then talking about random variables corresponding to some values observed during the experiment is the least confusing approach.
The area where IMO we don't have good terminology for this is partial differential equations. There, we very often talk about curves through some space and functions applies to e.g. the point the curve provides and its tangent. We sadly create a ton of confusion by not naming the arguments to that function (rather using `curve(t)` and `curve'(t)` in their place). I think this is an area where talking about (in)dependent variables is a reasonable crutch for the ambiguity that's typically introduced.