In going over the section of the Cuil derivative, I quite like the idea of this a lot. If we're going to claim such things work, is there a reality continuum this is related too, so I have to assume limits and various approaches to abstraction exist. Now, in the spirit of actual Calculus, shouldn't derivatives be a measure of the rate of change between realities? How fast we are moving from one to another per se.
I also propose the concept of integration, the sum of realities. In this we can measure the area and volume of realities. I think these kinds of things would make more sense in the context of using the Calculus terminology.