Zero: The Biography of a Dangerous Idea

Astronomical anomalies, black holes are infinitely dense masses spawned by stars that collapse under their own gravitational pull. Their mass remains finite but compacted into a singularity—a zero-dimensional point that breaks through the space-time fabric of the universe. Seife considers black holes exemplars of the power and mystery of zero and infinity.

Calculus is the mathematical study of continuous change. It involves differentiation (calculating rates of change in functions) and integration (calculating areas under curves). Seife elevates calculus as a perfect example of The Revelation of Zero; it enlightened those mathematicians who embraced its illogical division by zero about the laws governing nature.

General relativity, a theory developed by Albert Einstein, is the current scientific understanding of how gravity affects the fabric of space-time. Seife discusses two significant astrological and cosmological implications of general relativity: black holes and the unending expansion of the universe.

Geometry is the mathematical study of the properties and relations of shapes, lines, points, angles, distances, curves, and more. As Seife traces the history of zero, he examines how early geometry hindered its acceptance. The Pythagoreans, for example, equated numbers with shapes, but as zero has no shape, they could not accommodate it. However, later advances in geometry, including the progressive abstractions of the cartesian plane, the complex plane, projective geometry, and the Riemann sphere, eventually gave zero and infinity their places in geometric calculations; these two rogue ideas could exist in harmony with shapes after all.

Infinity is not strictly a number but a concept of endless or limitless quantity or size. In Chapter 0, Seife reveals that his book is as much about infinity as it is about zero—he treats them as complementary concepts, different but inseparable, like the positive and negative charges of a magnet. Exploring The Dualism of Zero and Infinity is among the main objectives of Seife’s book: In his telling, infinity and zero intersect each other repeatedly in surprising situations, revealing their underlying similarities.

Quantum mechanics is a field of physics concerned with the behavior of matter and its interactions with energy on the scale of atomic and subatomic particles. Quantum mechanics is famously paradoxical and counterintuitive, and Seife describes some of the strange principles of quantum mechanics with the goal of enabling readers to understand zero-point energy.