Inflection Points

  

HS #92 2023.3.9

 

Inflection Points

 

You are about to experience an inflection point. In eleven days, to be exact. You won’t feel it, this inflection point is too subtle, but it will influence your life, as most inflection points do. 

 

If you drive through downtown Grand Rapids, you will encounter one there. You often create one when coming to stop lights. Two years ago during the thick of COVID the press told us of inflection points even though most of them likely didn’t know exactly what they were talking about. 

 

It’s time to learn. 

 

Imagine walking up a smooth hillside or dune from the bottom of a valley to the top.  As you begin the trek from the bottom, the slope becomes increasingly steep. Your legs get sore because each step is a bit steeper than the last. But as you approach the top, even though you’re still climbing, the RATE of climbing decreases. You can feel the gratitude in your muscles. You have passed the inflection point. 

 

The mathematical definition of an inflection point is where the concavity changes. Think of an “S” lying on its side. The bottom of the “S” which bends up is said to be concave up. The top of the “S” which bends down is “concave down” The middle of the “S” is the inflection point. Driving north along the S-curve in Grand Rapids, the inflection point is the place where you transition from turning left to turning right. 

 

You can feel an inflection point if you’re slowing down as you approach a stop light, but then the light turns green, so you start accelerating. The transition from slowing down to speeding up is the inflection point. 

 

What’s the inflection point we will all experience shortly? Since this past December 21, the amount of daylight has been increasing. But not only increasing, it’s been increasing at an increasing rate. In early January we got an extra minute daily. As we approach the first day of spring (March 20), we are gaining 3 minutes daily. Once we enter spring, the length of days will continue increasing, but increasing at a decreasing rate. 

 

Not to worry, both equinoxes are inflection points. In September, the days will continue getting shorter until Dec 21, but they will be getting shorter more slowly. 

 

Why are inflection points important? Suppose a graph (a curve) represents the overall welfare of a person’s life. One would think that a higher graph (better welfare) would lead to more happiness. But not the case! Studies have shown, for example, that a lottery winner and an amputee are equally happy several months after their life-changing events. Surprising? 

 

Instead, happiness seems more tied to the CHANGE in a person’s welfare. A sick person on the road to recovery is generally in good spirits. For those who watch stocks, if the market goes up on a particular day (even if down for the year), it makes one happy. Similarly, a person enjoying a luxury vacation can get bummed by burnt toast. 

 

How do inflection points and concavity affect us? I submit that they are related to our hopefulness. Again, consider your stocks. If after bad economic news, the stock market goes down daily 300, then 200, then 100, you may feel badly for the decrease, but the trend makes you hopeful that it’s reaching the bottom of the “S” and in coming days it will start increasing again. 

 

Understanding that hopefulness is related to inflection points, you can perhaps appreciate why during COVID epidemiologists were concerned about them. They accepted that lots of folks had COVID, they even accepted that the number was increasing weekly. But they were carefully watching the rate of increase. Even though the number of COVID cases was increasing, the rate of increase was decreasing. So there was hope that eventually the total number would reach the top of the “S” and start declining. Which it did!

 

Our present inflation provides another example. Prices were increasing at an increasing rate. Now prices are still increasing but at a decreasing rate.  Prices had an inflection point. We’re breathing a bit easier as a result. We’re more hopeful that the future will bring economic normality. 

 

This is all good news of sorts. No matter a person’s lot in life, some days are still better than others. And a person’s happiness is tied to those changes. Moreover, even if things are getting worse, if you can see an inflection point coming, there is reason for hope.