I first encountered recursion as a formal definition. It took me much longer to understand what kind of structure it actually describes. Because the rest of my work depends on that structure rather than the formalism, I will briefly outline the version of recursion that matters here.
Recursion is a process that defines its next step using its previous state.
Imagine you are inside a wagon traveling at constant speed along a closed circuit. At any moment, you can confidently predict where you will be in one minute. You can look back and know precisely where you were a minute ago. The terrain is clearly visible. Nothing interferes.
That is recursion in a stable, fully observable system. The rules are fixed, the system does not alter the rules, the environment does not respond in any significant way.
"Now the wagon stops."
You step out and begin running along the same circuit, trying to follow the wagon’s trajectory.
Your speed is no longer constant. Fatigue accumulates; you gradually slow down. The wind pushes you sideways, forcing small deviations from the optimal path. The ground is sand. Every step you take alters its surface. On the next round, you never place your foot exactly where you did before. You reshape the path as you move — and the reshaped path changes your movement in return.
Now predicting where you will be in one minute is harder. Remembering exactly where you were a minute ago is also harder. You are constantly readjusting your trajectory while moving. That self-adjustment is closer to what recursion looks like in real environments.
In the first case, the path stays the same. In the second, the path slowly changes because of you.
Recursion is not just repetition of a rule.
It is the repetition of a rule under conditions that the repetition itself modifies.
That difference is the kind of recursion that matters for what follows.
Most systems we care about are not wagons on rails. They are runners on sand.