Order of Approximation

Order of approximation is the practice of solving problems at the right level of precision for the decision at hand. A zeroth-order approximation ignores all nuance and gives a rough ballpark. A first-order approximation captures the dominant variable. Higher orders add correction terms for smaller effects. The key insight isn't mathematical — it's strategic: most decisions don't require third-order precision, and pursuing it wastes time while the window for action closes. A founder estimating market size doesn't need four decimal places; they need to know whether the opportunity is a $10M market or a $1B market. Getting the order right — knowing how precise to be — is often more valuable than getting the exact number right. The model warns against two failure modes: acting on estimates too rough for the stakes, and paralysis from pursuing precision the decision doesn't require.

Before any analysis, ask: what order of approximation does this decision require? If you're choosing between two fundamentally different strategies, a rough estimate is sufficient. If you're optimizing pricing by 2%, you need precision. Match the resolution of your analysis to the resolution of your decision. Start at zeroth order and add precision only when the rough answer is insufficient to act.

Order of approximation means matching the precision of your analysis to the precision your decision requires. Start rough, refine only if the rough answer doesn't resolve the question, and resist the trap of pursuing third-order precision on first-order problems.