Interpolation Error — When Logic Wears a Disguise
Interpolation error occurs when values between observed data points are estimated by assuming a particular functional relationship, such as a straight line or smooth curve, without sufficient evidence for that assumption. While generally safer than extrapolation, interpolation can still produce misleading results when the true relationship has features — such as peaks, thresholds, or discontinuities — that fall between measurement points and are therefore invisible.
Also known as: Inter-point estimation error, Smoothing assumption error
How It Works
The assumption that data varies smoothly between observations seems reasonable and is computationally convenient. However, real-world processes can be erratic, and sparse measurements may miss important events or nonlinear behavior between observation points.
A Classic Example
A river's water level is measured at 6 AM and 6 PM, showing similar readings both times. Linear interpolation suggests a stable water level all day. In reality, a flash flood peaked at noon, causing severe but unrecorded flooding between measurements.
More Examples
Air quality sensors in a city record pollution levels at 8 AM and 8 PM each day. Linear interpolation between these readings suggests moderate, stable pollution throughout the day. In reality, a sharp midday traffic peak causes pollution to spike to hazardous levels for several hours — a pattern entirely invisible to the interpolation.
A climate researcher has temperature proxy data from ice cores at roughly 500-year intervals. Connecting these points with straight lines implies gradual, continuous temperature change between measurements. However, abrupt century-scale warming events occurred between sample points and are completely smoothed away by the linear interpolation.
Where You See This in the Wild
Occurs in environmental monitoring with infrequent sampling, in medical records between clinic visits, in economic data released quarterly when monthly fluctuations matter, and in geophysical surveys with sparse measurement points.
How to Spot and Counter It
Increase the density of observations in critical regions. Use domain knowledge to select appropriate interpolation methods. Validate interpolated values against independently collected data. Report the assumptions underlying interpolation and assess their plausibility.
The Takeaway
The Interpolation Error is one of those reasoning errors that sounds perfectly logical at first glance. That's what makes it dangerous — it wears the costume of valid reasoning while smuggling in a broken conclusion. The best defense? Slow down and ask: does this conclusion actually follow from these premises, or am I just connecting dots that happen to be near each other?
Next time someone presents you with an argument that "just makes sense," check the structure. The feeling of logic is not the same as logic itself.