The Happiness Equation

By Rob Alvarez

We often confuse pleasure with happiness, so much so that we sabotage our own well-being. The temporary high from indulging ourselves with food, media, material things, or status, can fool us into thinking we’re happier because of them. In truth, we’re not. But we seek more, hoping the next hit will bring the permanent state of bliss we are looking for. The thing is, we’ve already established that happiness is not a permanent state to aspire to. I think we can all agree on that. So maybe a better way to think about happiness with the following integral math equation, which continually ebbs and flows.

…where the continuous function f(x) represents the resulting emotional effects of an action or decision. Therefore, your overall level of happiness over the period of time,x, is measured by H(x) or the total area under the curve f(x). Let’s look at a couple of examples.

Example 1: You have a rough day, so you stop by Costco to pick up your favorite double-dutch-chocolate cake and devour it before you even drive off the parking lot. You end up feeling literally sick to your stomach and hating yourself for the next two days for your lack of self-control.

Figure 1

Figure 1

Figure 1 shows your emotional curve over that time. Green is positive. Red is negative. Notice how you have a short high peak while enjoying that sweet, high-fat dessert, followed by a long downturn from the subsequent stomach ache, guilt, and self loathing. Looking at the time component of the equation, the pleasure derived from the binge is short lived, while the negative impact on your emotional state lasts so much longer. Ultimately, what you thought would make you happy at the time actually just lowered your overall level of happiness.


Example 2: You take your dog on a nice long walk, maybe even explore an unbeaten path, enjoying a nice warm summer afternoon. This gets you better connected with nature and your furry best friend, filling your body with vitamin D and some much needed exercise.

Figure 2
Figure 2

Although the peak emotional level derived from this activity pales in comparison to what you may experience from eating the entire cake in one seating, the positive feeling would likely last a long while. Therefore, as depicted in figure 2, integrated over the time this activity is additive to your overall level of happiness. This may not be your first choice for a stress-relieving activity, and your emotional level may start of in the negative (also shown on figure 2). However, once you actually get out there, you realize just how much enjoyment you draw from being outside and active.As an experiment, the next time you face a decision, big or small, take a minute and place it into the equation above. Play out how your emotional curve might run over time. Estimate its expected impact on your overall happiness. Then decide. These small thought exercises just might make you happier in the long run.


Part of the Fear and Happiness Series

Rob Alvarez

Rob Alvarez

Rob is editor-in-chief of WeRunWithYou. He is also an operations manager at the Chemours Company, and coaches the Newark Charter middle school track and field team. His current interests include exploring leadership, organizational development, and personal well-being.

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