In one of the more important breakthroughs of my life, it occurred to me the other day that calculus is not really a deeper understanding of reality. It's a method for approximating values so close that you can figure out what they actually are. It's a way of tricking the math into telling us exact figures no one was able to figure out until the 1600's.
So differential calculus tricks math into telling us the slope of a tangent line to some other function, its instantaneous rate of change. Integral calculus tricks math into telling us the area under a curve, the sum of all the infinitesimal rectangles under it.
But it's all a trick to tell us a reality we already knew about, we just didn't know what its value was exactly.
I thought you'd want to know.