Interpolation and extrapolation are two kinds of generalisation: ways of applying an idea in a broader domain than we've seen so far. Interpolation asks what lies between the examples we've already seen, while extrapolation asks what lies beyond. They are widely used concepts that find technical application within science and engineering (especially in data science, numerical analysis, machine learning, economics, and computer graphics), where many different mathematical methods for interpolation and extrapolation are used. These concepts are also used in a less formal manner in many other areas, such as philosophy, art, and futurism, where we might make more qualitative interpolations and extrapolations. For instance, we might ask whether an emerging kind of music is mainly an interpolation between two existing genres; or whether affordable land travel, sea travel, and air travel are likely to be followed by affordable space travel. In all these contexts, interpolation and extrapolation are seen as twin concepts; an inseparable pair. I want to suggest that what appear to be twins are in fact two triplets -- that they have a hitherto unknown sibling.