Some things vary in a stepwise fashion — the number of people in a family, the number of sheep in a flock, the number of pebbles in a pouch. These are groups of discrete things about which we can ask, "How many?" Other things vary smoothly — distance, age, weight. Here the basic question is, "How much?"

The first kind of magnitude might be called spotty and the second kind called smooth. The study of spotty magnitudes leads to numbers and arithmetic, while the study of smooth magnitudes leads to notions of length and geometry.

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The word "complementarity" was first introduced into philosophy by the quantum physicist Niels Bohr. He used this expression to sum up his belief that basic physical reality is both spotty and smooth. An electron, according to Bohr, is in some respects like a particle (like a number) and in some respects like a wave (like space). At the deepest level of physical reality, things are not definitely spotty or definitely smooth. The ambiguity is a result of neither vagueness nor contradiction. The ambiguity is rather a result of our preconceived notions of "particle" and "wave" not being wholly appropriate at very small scales.

One might also ask whether a person is best thought of as a distinct individual or as a nexus in the web of social interaction. No person exists wholly distinct from human society, so it might seem best to say that the space of society is fundamental. On the other hand, each person can feel like an isolated individual, so maybe the number-like individuals are fundamental. Complementarity says that a person is both individual and social component, and that there is no need to try to separate the two. Reality is one, and language introduces impossible distinctions that need not be made.