Numbers allow us to focus on one aspect of a situation in detail, but can also oversimplify things
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Unequal
Eugenia Cheng (Profile Books (UK, on sale) Basic Books (US, 2 September))
Mathematically speaking, things are either equal or they aren’t, right? Well, not according to Eugenia Cheng in her latest book, Unequal: The maths of when things do and don’t add up. In mathematics, just like in life, some things are more equal than others.
Cheng delves into the concept of equality in mathematics, exploring how we determine when things are “the same”. She uses playful examples and entertaining tangents, from knitting Möbius strips to creating iterated Battenberg cakes, to make abstract concepts more accessible. Additionally, she addresses important political and rights-based issues related to equality.
Starting with equations, Cheng highlights that the most intriguing ones assert a sameness in the presence of difference. For instance, the equation 180 = 180 is trivial, but x + y + z = 180°, where x, y, and z represent the angles of a triangle, carries significant meaning. However, this equation holds true only in specific circumstances, such as in a two-dimensional plane but not on a spherical surface.
Numbers, Cheng notes, have the power to simplify complex situations by focusing on a single quantity. While numbers can be valuable tools, they can also be misleading if their limitations as simplifications of reality are overlooked. Cheng warns against assuming that individuals with the same score on an IQ test possess equal intelligence, emphasizing the importance of remembering the nuances that numbers may overlook.
Moving beyond numbers, Cheng explores the concepts of “local” versus “global” sameness through discussions on manifolds, which are surfaces composed of stitched-together flat areas that can exhibit global curvature, like a sphere. She argues that adopting “manifold-like thinking” can offer valuable insights for navigating real-world scenarios, akin to understanding when to apply local or global perspectives in politics.
In her exploration of category theory, Cheng delves into the abstract nature of sameness, drawing parallels to appreciating complex works of art without fully understanding their technical intricacies. By challenging the perception of mathematics as rigid and black-and-white, Cheng’s book invites readers to appreciate the richness and nuances of equality, both in mathematics and in broader societal contexts.
Sarah Hart, professor emerita of geometry and provost at Gresham College, UK, is the author of Once Upon a Prime
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