A picture is worth a thousand words ... and vice versa??

While discussing art with my mom and Ben today, she asked about the notion that a picture is worth a thousand words. However, she argued, there were words that could not be well expressed in pictures, or would certainly take a detailed picture.

After an initial reaction that this is right, I came upon the example of "addition". How do you draw addition? You kinda can't. You can draw a specific case of addition (ex: 2 + 3 = 5), but can you really express this concept with only images? You may be smarter than me and come up with something, but I suspect it'll at least meet the requirement that it's more complex than explaining the concept of addition using words. So what's the deal here?

Addition is an abstraction. I posit that abstractions are hard to draw. Why? Because drawings are concrete. They, by their nature, have details: a particular color, or arc, or shading, or specific item(s), etc. Instantly, there are many attributes to describe if we want to convey the picture accurately. Hence, a thousand words (you know, plus or minus) are needed. But, their concreteness also means they express only an instance of an abstraction, thereby reducing the generalization of the abstraction. Thus, an abstraction is worth a thousand pictures (you know, plus or minus, to give people a pattern from which to construct the abstraction, perhaps).

So a picture is worth a thousand concrete words.
And non-concrete words are worth a thousand pictures.

Since it's a disjoint set of words in the two statements, the pair of equations doesn't explode or spiral into some black hole.