Almost never in nature

Walking, lifting, stacking wood, walking home: those are equal steps. A day’s hunt does not double overnight. That is why a quiet Monday still looks safe. Exponential progress is rare in the world a body grew up in. The fridge fools Dev for the same reason.

Fog is one of the few times the math shows up in the eyes. Each equal stretch of haze keeps about the same fraction of the remaining light. If one stretch leaves half, two stretches leave a quarter, three leave an eighth. The village does not fade in even slices. It drops away. Physicists call that the Beer–Lambert law, a rule about how light fades through haze. It is exponential decay, not progress. You feel it as “I thought I could still see the camp.”

A cooling pot and a dying fire are cousins of the same fade. They are not a training ground for harvests that double.

So the chessboard later in this lesson is not “what nature already taught.” It is what nature almost never taught, which is why the second half of a climb is so easy to miss.

The tempting mistake is to collect pond-and-yeast stories and call them how people learned doubling. Those are puzzles we fail, not childhood drills.

That is what lets you distrust a small strip on a fridge.