Derivative: An expression representing the rate of change of a function with respect to an independent variable.

Some phenomena are not about themselves. They take you one level, one dimension down into the substance of things, they are measurements of change, gauges of the inner workings of the world, consequences of movement.

Every atom in existence is a player in a giant set of games of variability. Imagine the collection of all of these games as threads, clusters, and fabrics. These threads of things happening, let’s say, are not even, they display changes in speed; they have lumps and thinnings; they stop and change direction, they soar, plummet or disappear. Their changes imprint a secondary metric into our world, a measure of variability, a smoothing over of its irregular nature. These measures show trends and directions, they clean the world of detail to reveal only the impulses of motion. They are diagrams of change.

Take, for instance, the line of highest slope. The water always follows it when it flows down the hill. Or the line of lowest slope. A donkey will always find it when it carries burdens up the hill. These lines are not obvious, they are abstract measurements of the change in incline and they only become visible when the water, or the donkey, reveals their existence.

You will say to yourself that it is not reasonable to guide yourself by the wisdom of lesser things, and that is a vanity of human thought, which deems itself the arbiter of things only because it gathered a few droplets from an infinite sea of knowledge constantly refreshing itself.