Displacement Equals Zero

Published on 2024-05-23

When I was in high school and my friends and I were learning kinematics for the first time, I remember we had this joke that if you died in the same hospital you were born, then the displacement of your entire life would equal zero. This isn't a joke so much as an observation, because it is true within a rounding error: displacement is characteristically a relative way of thinking about movement from a point. If you were to hike a 2km circuit trail, the distance you would have travelled would be 2km, but your displacement over the course of the journey is ultimately zero, as you end exactly where you started.

I thought about this the other day, while lying in bed, waiting to fall asleep. Similarly, if you sleep in the same bed every night, your daily displacement is always zero. It was weird, and at first, very uncomfortable. It's a strange way of thinking about your journey through life. It communicates something really valuable—that is, your change in position relative to where you started your day, but it erases so much all the same. No matter what I do in a day, I always end it in the same place.

I guess what made the displacement-equals-zero joke funny was that it feels absurd. It feels absurd for this very reason. It's absurd in a way that almost casts doubt on the usefulness of displacement as an idea. But displacement is useful, and while your "displacement from birth to death (assuming you were born in a hospital, you died in a hospital, and the hospital you were born in was the same as the one you died in)" may communicate nothing about what you did during your life, it does communicate at least one really interesting detail: your life ended in the same way it began.

Similarly, for all my escapades during the day, I still find myself in the same comfortable environment as the one in which I woke up. While I can't help but get the sense that this conveys some sort of stagnation, I do take a lot of comfort in it. It means I have a home, and somewhere safe to be.

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