Which one is better to use:
Interaction of x with y
Interaction between x and y?
Or are they equally correct? In that case, is there a difference between them, or are they basically interchangeable?
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My instinctive response is: "interaction of x with y" is to describe what x is doing to y, but not what y is doing to x.
"Interaction between x and y" describes what both are doing with each other.
See, one is one way, and the other is both ways.
However, the word "interaction" itself assumes that there is already a 2-way action going on.
So the combination of the symmetric concept interaction along with the one-way structure "of x with y" makes the phrase ambiguous. Which is meant, "x on y", or "both x on y and y on x"?
Hence I would always go with the second, especially if I were writing a technical document meant to explain something. Otherwise I would write "the action of x on y" if I meant just the one-way action.
They are different and not necessarily interchangeable. You would need to provide greater context for us to determine which would be correct.
To illustrate; interaction of x with y does not necessarily imply any agency on the part of y (although it could), simply that x is acting.
Conversely, interaction between x and y necessarily implies agency with both parties, x and y.
To get almost exactly the same meaning between both, you would have the following:
Interaction of x and y
Interaction between x and y