There are days when I can read large stretches of technical material and feel like it is going straight in. Definitions collapse into structure. Arguments compress. I move quickly without feeling sloppy. And then there are days when I cannot reliably add two numbers without checking myself several times. The gap between these states is large enough that it feels discontinuous.
For a long time, I treated that discontinuity as a failure of understanding. I assumed comprehension should be stable, and that variance meant I was doing something wrong. I kept waiting for things to even out. They never did. What eventually became clear is that the variance itself is the constant. Any sustainable way of learning has to be built around it.
The problems do not respond to who shows up. A theorem does not simplify on a bad day. A dense paper does not adapt to limited working memory. The material is indifferent. It offers no encouragement, only resistance.
On days when execution is unreliable, I avoid precision. I read, trace ideas, and try to understand why definitions are shaped the way they are. I focus on structure rather than correctness. On days when things hold together, I return to calculations and proofs. Nothing is lowered. Nothing is excused. The order is conditional.
This only works if you are willing to stay with problems that reward persistence. Many days end without any sense of progress. Often the only change is familiarity. A symbol stops looking foreign. A paragraph acquires edges. That does not feel like improvement at the time, but it accumulates.
I keep old notebook pages for this reason. Some are wrong in basic ways. Definitions misused. Arguments that collapse halfway through. I used to see these pages as evidence that I was not capable of this kind of work. Now I see them as records of contact. They show that I was close enough to be wrong in specific, structured ways.
The problems themselves never change. They do not reward effort with encouragement. They do not soften when you struggle. But they are consistent. If you return often enough, even in an unreliable state, they begin to reveal what they demand.
I no longer expect understanding to feel continuous. It arrives in bursts, and it leaves just as easily. My job is not to force it to stay, or to judge myself when it goes. My job is to build a way of working that can tolerate absence without collapsing.
Staying, it turns out, is not about confidence or discipline. It is about accepting that learning happens under constraint, and choosing a process that survives it.
No comments:
Post a Comment