Update wiki/math/estimation-and-sanity-checks.md
ef5afb92b387 harrisonqian 2026-04-12 1 file
index e4f4f8e..85934ec 100644
@@ -8,15 +8,9 @@ Fermi estimation, order-of-magnitude thinking, and the discipline of checking wh
## Fermi estimation
-named after Enrico Fermi, who was famous for estimating quantities with almost no data. the classic: "how many piano tuners are in Chicago?" you don't know the answer, but you can break it down:
+named after Enrico Fermi, who was famous for estimating quantities with almost no data. the method: break a hard question into sub-questions you can roughly answer, multiply the estimates together, and get within an order of magnitude (factor of 10) of the real answer.
-- population of Chicago (~3 million)
-- fraction of households with pianos (~5%? → 150k pianos)
-- how often a piano needs tuning (~once a year → 150k tunings/year)
-- how many tunings a tuner can do per day (~4) × working days (~250) → ~1000 tunings/year per tuner
-- answer: ~150 tuners
-
-the point isn't precision. it's getting within an order of magnitude — within a factor of 10. if your estimate says 150 and the real answer is 100 or 300, you're doing fine. if it says 15 or 1500, something is wrong with your decomposition.
+the point isn't precision — it's getting close enough to be useful with minimal data.
## why this matters for modeling