interpolate

Imagine you're charting a course across a vast ocean, but your map shows only a few islands. To figure out what lies between them, such as the depth of the water or the shape of the coast, you have to work from the clues you already have. That is the basic idea of interpolate: to find or add what is missing by using what surrounds it.

This word appears in several common settings. In math or science, someone may interpolate a value between two known points on a graph. In writing or history, a person may interpolate a line into a text by adding material that was not there before. More broadly, it can also mean filling in a missing part from the evidence at hand. Think of it as filling in the blanks with care, not with guesswork alone.

To interpolate means to work out or insert something missing by using what comes before and after it. In the most common technical sense, it means estimating an unknown value within a range of known values, not beyond that range; going beyond is called extrapolation. The word also has an older text-based sense: adding words or passages into a piece of writing.

In mathematics, statistics, computing, and science, the idea is straightforward: you know some points, and you estimate what falls between them. A weather forecaster might interpolate temperature readings between stations to make a fuller map. A computer program might interpolate missing frames in a video or values in a digital image so that motion or color looks smoother. In these cases, the result is based on nearby known information.

In writing, history, or textual study, the meaning shifts slightly. Here it refers to putting extra words into a text. Sometimes that addition is helpful, like a brief explanation. Sometimes it is seen as a problem, as when a later writer adds material to an old manuscript and changes its meaning. You might also see the word used in a broader everyday way for piecing together a missing part from the evidence. The key idea in all these uses is the same: something missing is supplied from what surrounds it, rather than invented out of nowhere.