We are taught to think of life as a launchpad. You line up the trajectory, light the fuse, and then gravity and momentum carry you along a smooth, unyielding arc until you hit the ground at the end. It’s a comforting fiction. It tells us that if we just find the right track, the rest of life will follow a beautiful, continuous line.
In physics, we describe smooth, unbroken paths like this using integrals.
A deterministic life is the one where a single, overarching identity is locked in at the start and dragged across time.
If you were to write down the formula for such a life, it would look something like this:
\(P = \int_{t_0}^{t_f} C_0 \, dt\)
On the left-hand side, you have P, the person. On the right, you are integrating a single, constant choice (C0) over time, from birth (t0) to death (tf).
Mathematically, it implies your identity is just that one initial choice multiplied by the number of years you managed to stay alive. It implies that who you are is a monolith. If you make a catastrophic mistake at thirty, the whole area under the curve is tinted by it. The past rigidly dictates the future because the function is continuous. You are trapped in the momentum of your own timeline.
But the longer I live, and the more pivots I observe in myself and the people around me, the more I realize that this equation is a lie.
People are not integrals. We are discrete summations:
\(P = \sum_{n=1}^{N} c_n \)
Look closely at what changes here. The integration sign—that smooth, elegant S-curve—is replaced by the jagged, step-by-step architecture of the Greek letter Sigma (Σ). The continuous variable of time (t) disappears, replaced by an index (n), which counts every single independent choice you make from your first conscious breath (n = 1) to your final gasp (n = N).
This shift changes everything. It means:
Identity isn’t a single, unbroken line; it is a sequence of discrete events.
When we look at someone who has made a catastrophic mistake, our instinct is to treat them like an integral. We take that single, terrible point in time, draw a continuous line through it, and declare that the entire area under their curve is now permanently corrupted. We freeze them in their worst moment, transforming a single event into their lifelong identity.
The mathematics of the summation is incredibly forgiving. True forgiveness is simply acknowledging the discrete nature of human behavior. It means recognizing that a person’s mistake at index n = 750 is a real, fixed term in their life’s equation—it happened, and it counts—but it is only one term. It does not possess the mathematical power to rewrite the values of n = 1 through 749, nor does it have an existential monopoly over what they choose to write for n = 751 and beyond.
When we forgive, we aren’t pretending the bad term doesn’t exist. We are simply refusing to let it dictate the rest of the summation. We are allowing the index to move forward, giving someone the space to contribute positive numbers to the sequence again.
So…
Stop treating your life like a train track you can derail. You are not a locked trajectory. You are a living vector sum, built piece by piece, choice by individual choice. You are not forced to integrate the momentum of your worst days into your best tomorrow. And until your index hits N, you still have the power to change the value of the very next term.
Don’t forget to subscribe!
You can also read:
Comments
Nothing yet. Say the first thing.
Sign in to join the conversation.