The first derivative of a function at an inflection point is zero. Visually, an inflection point is a flat line tangent, a point where the value of the function is going neither up nor down. The forces of increase and decrease are balanced and for a moment, the function is unchanging. The Yijing calls it the balance of yin and yang. Some functions are always at an inflection point. These functions are constant, like the gravitational constant throughout the universe, or step-wise, like the amount of postage on an old-fashioned letter that is 49 cents or 70 cents, never in between.
Functions that are always at an inflection point are oddballs. In nature, in life, things change gradually, always going up or down. In most lives, inflection points are rare: the instant when a potential addict decides to take or not to take that hit of heroine, the moment when a college student decides to study classics instead of chemistry, when an employee decides to tell the bosses they are wrong. The Yijing calls it the balance of yin and yang. But we have all experienced inflection points, sometimes realizing what they are at the time, sometimes not. They are easy to spot in the rearview mirror, but hard to see through the windshield.
If your life is not at an inflection point, it will continue to go sour, or get better and better, but, most often, you eventually run into an inflection point and fortunes change. If you don’t like the direction and don’t accept free will, all you can do is wait for the next inflection point and hope it goes your way.
Some of us accept free will and look for ways to induce inflection points. How can you induce an inflection point in your life? Or recognize one when it arrives?
If I could tell you, I would control your destiny. But life is far too complex for me, or anyone else, to control anyone else’s future. But I do believe we all have the power to look at ourselves. In fact, try as we might, we can’t avoid knowing what we feel, what is happening around us. There may be forces we don’t comprehend or detect, but we still know something about what we feel in our surroundings and we can use that knowledge to change our direction.
Inducing an inflection point in our life is possible but hard. You must use every faculty as intensely as you can, and when you do, you do not know what will happen. You don’t know what the new direction will be, only that it will be different. But there have been times in my life when I have known that I had to make my life change, and I changed it. Sometimes I liked the results, sometimes not. That’s life in the vine maples.