Things are either equal or they aren’t – mathematically speaking, at least, right? Not so fast, says Eugenia Cheng in her new book, Unequal: The maths of when things do and don’t add up. In mathematics, as in life, some things are more equal than others.
Take equations: the really interesting ones assert a sameness where there is also a difference. The equation 180 = 180 tells us nothing, but x + y + z = 180°, where x, y and z are the angles of a triangle, is a claim of another kind. And it is only true in certain circumstances – in a two-dimensional plane, yes, but not on the surface of a sphere.
Cheng’s aim is to explore how we decide when things are “the same” in mathematics. Her approach is both playful and deeply serious, leavening abstract concepts with entertaining tangents on everything from knitting Möbius strips to making an iterated Battenberg cake. Neither is she afraid to discuss important political and rights-based questions around equality.
Having opened with equations, Cheng moves on to numbers, joking that the good thing about them is that they are boring. By this, she means that they reduce potentially confusing complexity to a single quantity. Numbers can be powerful tools because they let us focus on one aspect of a situation in detail.
They can also be misleading if we forget they are a simplification of reality. It would be dangerous to assume, for example, that two people who get the same score on an IQ test are equally intelligent. As Cheng says, “it’s fine to forget details, but we must remember that we forgot them”.
