New Math: Getting to the Root of Things

A Hot Debate:
It was pointed out to me that there is a difference between a square inch of ginger and a cubic inch of ginger. I don't think I could actually produce a square inch of ginger unless I moved to Flatland. No matter how you slice it, it isn't possible to not have a third dimension to your slice of ginger. I could take intellectual refuge in the claim that I meant an inch of ginger squared, but that would be dishonest. No, I will take full responsibility for my impossible portion of ginger.

The book [I'm not sure it qualifies as a novel] Flatland is a wonderful story on perspective: set in a world of two dimensions, with status conferred based on the number of sides a character presents to the world, the premise is, "what happens when someone shows up who magically changes sizes?"

A round character appears who can change from a point to a progressively larger circle, which boggles the minds of the two-dimensional characters. It turns out that this circular character actually is part of a third dimension. Difficult as he finds it to explain himself to the denizens of Flatland, he is actually a sphere. Thus as he travels up and down across the plane of the world of Flatland, his two-dimensional size changes.

Things are not always as they appear.