In physics and calculus, there’s a classic graph that plots time on the x-axis, and velocity on the y-axis. If you draw a line on this graph, it represents velocity over time. If you shade in the area under that line (under the curve), you can find the distance– the distance is just the area under the curve (AUC), or the sum of velocity x time. How fast we travel matters, but the length of time we are traveling at that speed also matters.
Using the idea of area under the curve is a highly useful lens through which to view many of the challenges we face. We love stories of dramatic transformation. Someone quits smoking overnight, or loses 50 pounds after declaring, “From this day forward, everything changes.” These stories are inspiring, but they can also mislead us. They suggest that change comes from single moments of willpower or inspiration– that there is a clear before and after. While sometimes this is true, most of the time it is not.
The problem with chasing perfection is that it sets us up to fail. When we approach change with an all-or-nothing mindset, any slip feels catastrophic. One missed workout, one relapse, or one off day convinces us that we’ve blown it, so we might as well give up entirely. “I guess I’m just not serious about change,” we might tell ourselves. Perfection is fragile. Persistence is resilient.
Area under the curve helps us move away from this way of black-and-white thinking. It’s also helpful because it is how long-term processes work, and how actual change happens. Smoking is not destructive because of one cigarette, but because of thousands of cigarettes over many years. Exercise doesn’t change us in a single workout, but month after month, it reshapes our bodies and minds. When we think about exposure to harmful substances, we’re really trying to focus on minimizing the area under the curve– both the amount of exposure and the duration of exposure. When we are trying to think about eating well, it's a similar perspective: both the content of the meals and the number of meals eaten matter. One healthy meal does not move things too far forward, just like one lousy meal doesn’t set us too far back.
I think about the area under the curve all the time when I’m talking with patients. When talking about managing blood sugar in diabetes, it's not any hour, day or week that I’m too concerned with; instead, it's lifetime exposure. We often worry a lot because of short-term variations, but that doesn’t end up mattering much. An hour, day or a week of hyperglycemia does not matter too much when viewed across a lifetime. To extend the distance analogy– if we are walking for a month, a 5 minute sprint does not have much impact on the total distance traveled.
Area under the curve thinking is especially useful in addiction. We often say relapse is part of recovery, and this framework helps us see why. Picture a calendar where every sober day gets an X. At first, the calendar may have only a few X’s. But as recovery progresses, more and more days fill in until the month is almost entirely marked. The area under the curve—total sober time—keeps growing. In this context, one missed day isn’t catastrophic; what matters is the steady accumulation of sober days over time.
This framework also helps understand a challenge of the “Then I’ll be happy” framework. We often tell ourselves stories that we will be happy at some future date, when a certain event happens– we get a promotion, reach a certain level of wealth, achieve a certain milestone. This happiness is often fleeting, and it allows us to rationalize unhappiness in the present. Yes, sometimes we have to do unpleasant things, but constantly living in a miserable present with the hopes for a happy future works poorly. Viewing this as an area under the curve problem, we are not really adding to the area under the happiness curve. If we are trying to live happy lives, we need to consider the total happiness in life as a summation of all the moments of our life– not short sprints of happiness in an otherwise miserable existence.
When we apply area under the curve thinking to goal setting, the emphasis shifts away from goals. Reaching a certain weight or never relapsing again are tempting because they feel clear and measurable—but they are also brittle. AUC thinking reframes progress as the accumulation of choices and habits over time. Every walk we take, every sober day, every balanced meal adds to the shaded area under the curve. Instead of seeing lapses as catastrophic, we can view them as small dips in a much larger picture. What matters is not a single day’s result but the accumulated pattern. This mindset reminds us that growth is about expanding the curve steadily over time. It also can keep us accountable; when we are not accumulating more area under the curve, we notice that too, and need to make adjustments.
Ultimately, this is just a framework, and like any tool, it can be used wisely or unwisely. We can link it to goals that leave us stagnant—like maximizing comfort while avoiding any real growth—or we can connect it to pursuits that give life meaning. If the aim is peace and presence, we can think of meditation as area under the curve. If the aim is connection, we can see time with people we love in the same way. And if the aim is to contribute, then every positive impact we make in the world adds to the curve. In physics, the area under the curve is distance traveled. In life, it becomes the record of how we spent our time. The question we each face is whether the curve we’re filling in is one that reflects what matters.
Cheers,
Doc
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