The word "order" is unfortunately overloaded. The first kind, like what you're talking about, is whether you use the left port or the right port of the first o

The word "order" is unfortunately overloaded. The first kind, like what you're talking about, is whether you use the left port or the right port of the first object when joining it to the second object. That certainly can matter, like with the stack of paper example. The second kind is joining things through time, where it is not supposed to matter when you join things. If you have three stacks of paper, you can stack the first onto the second and put that on the third, or you can stack the second on the third and put the first on top of that, and you get essentially the same pile in either case. Piles are supposed to be an analogue of arrays, where the first kind of order matters. Lots of times, the second kind of order (associativity) actually does matter, too, where you get literally different objects, but it's ok since there are "equal" in a useful sense. For example, when you make a text editor, you might use the rope data structure to represent strings. If so, when you concatenate a list of strings, the literal tree structures you get in the representation of the rope might vary depending how you did it, but they'll all be equal in the sense that the strings they represent are equal --- the same characters in the same order.