What makes this work?

I was on an airplane recently and came across this signage in the rest room. Of course, most of us would recognize that it signals the existence of a fold-down table for changing babies.

But I had one of those moments where I looked at the components of the pictogram and wondered why it worked. There are two detached circles. There is a wide horizontal line. There is a squiggle that looks like a broad "u" with a serif on its top left. And then there is this odd assortment of combined shapes: A vertical post, a trapezoid attached at an angle to a rectangle, a short vertical post, and another post at an angle.

How do we know this odd assortment is a woman? Would this be understood in a culture where women only wear floor length dresses?

Likewise, how do we know the squiggle and the circle are a baby?

How do the detached circles persuade us that they are part of people? Why don't we think both people have been decapitated?

I am hoping there are people out there who can explain why this works, both visually and culturally. Please comment.