These are notes rather than an essay: a handful of observations about compounding, set down in the order they came rather than built into an argument.
Growth on growth
Compounding is growth applied to the results of earlier growth. The mechanism is simple enough to state in a sentence. What makes it interesting is that its effects are small for a long time and then, apparently suddenly, large. Nothing changes in the mechanism at the turning point. What changes is the size of the base it is acting on.1
Nothing changes in the mechanism at the turning point. What changes is the size of the base it is acting on.
Hard to feel
Intuition tends to project in straight lines. Asked to imagine where something will be after many periods, most estimates extend the recent past at a constant rate. Compounding breaks that habit. Early on it looks slower than a straight line would predict; later it looks impossibly fast. Both impressions come from the same curve.
Interruptions are expensive
Because later periods contribute far more than earlier ones, an interruption late in a compounding process costs much more than the same interruption early on. The loss is not just the period that was skipped. It is everything that period would have grown into. This is one reason patience is so often described as the scarce ingredient rather than the rate itself.
It runs both ways
Compounding is usually discussed as a benefit, but the mechanism is neutral. Costs compound, small frictions compound, neglected maintenance compounds. The same patience that makes growth remarkable makes slow deterioration hard to notice until it is well advanced.2
An open question
What would it look like to measure things on a compounding scale rather than a linear one: to judge a habit, a relationship or a body of work by its rate of growth on itself rather than by its current size? These notes do not answer that. It seems like a question worth returning to.