wisdom

I used to say on a semi-regular basis, “In all areas of life, the answer seems to lie in the middle of two extremes.” I thought it to be a pearl nugget of ultimate wisdom. I now understand a deeper (and potentially superior) concept: in some areas of life, the answer can lie in a process whose average value is the center of two extremes, but the process itself comprises regular oscillation between the two extremes. For a mathematical demonstration of the concept, picture the graph of cosine(x). The average value taken to infinity is zero.