Zero: The Biography of a Dangerous Idea

In subsection “Life without Zero,” Seife notes that most ancient people had no concept of zero. He explains that zero had no practical purpose: “You never need to keep track of zero sheep or tally your zero children. […] This is why people got along without zero for so long” (8). Even the Egyptians, whose mathematical talents enabled them to invent a solar calendar and use geometry to measure plots of land, had no zero.

“The Birth of Zero” compares the ancient Greek and Babylonian counting systems, explains how the abacus introduced place value to calculations, and shows how the Babylonian placeholder zero eliminated ambiguities in number notation. Seife then contrasts this placeholder zero—“a digit, not a number” (15)—with the true zero of the Mayan counting system. Then he reports the Greeks’ decision to prefer the zero-less Egyptian counting system over that of the Babylonians’, which permitted zero.

“The Fearsome Properties of Nothing” connects zero to “a primal fear of void and chaos” (19), referencing several creation myths from different cultures in which the void preceded creation. Seife states that the ancients also feared zero because of its mathematical unruliness. He explains how zero messes with multiplication and makes division not merely impossible but absurd, incoherent, and illogical.

The subsection “The Origin of Greek Number Philosophy” considers the cult of Pythagoras and his eccentric philosophy: “[T]o Pythagoras the connection between shapes and numbers was deep and mystical” (27). Seife explains why Pythagoras viewed the pentagram as sacred, how his invention of musical scale reflected his belief in the universal influence of ideal ratios and proportions, and how he developed a neat planetary model upon this belief. Seife also explains the golden ratio. Pythagoras’s vision of the universe profoundly influenced the course of Western thought, and zero was not in that vision—both because it could not be conceptualized as a shape and because it broke ratios. Seife concludes this subsection by showing how irrational numbers challenged Pythagoras’s philosophy and reminding readers that the Greeks willfully ignored zero despite having access to the zero-tolerant Babylonian counting system.

“The Infinite, the Void, and the West” discusses Zeno and his famous paradox, the zero- and infinity-intolerant worldview of Aristotle, and the speculations of Archimedes. Seife explains Zeno’s paradox of Achilles and the tortoise and reveals that its solution lies in zero, which the Greeks persisted in ignoring. While the Greek atomists resolved the paradox by imagining the universe as an infinite void occupied by indivisible atoms, Aristotle’s cozy, finite cosmology of spinning celestial spheres and his rejection of both zero and infinity as merely imaginative proved more influential. Aristotle’s system seemed to prove the existence of God, but it also made the universe eternal. This worldview set the trajectory of Western thought for centuries to come. Seife concludes by revealing how Archimedes came close to adopting infinity in his studies of parabolas but was ultimately hindered by his Aristotelian thinking.

“Blind Dates” jumps ahead to the Middle Ages to attend to one consequence of the West’s rejection of zero through Aristotle—calendar confusion. From Dionysius Exiguus’s calculations of Easter dates to Bede’s recalculations, the absence of a year zero resulted in celebrating the advent of the third millennium a year early. Seife briefly explains how astronomers track time independently of confusing calendars.

“The Zeroth Number” explains the difference between cardinality and ordinality, and “The Gaping Void” reports that the mistakes of the Middle Ages were the result of adopting the ancient Greek biases against zero and the void.

Seife argues that in India, the idea of zero was sheltered within Hinduism and its reverence for a mystical Absolute of destruction and creation, embodied by the deity Shiva. “Zero’s Reincarnation” explains how the Indians gave zero a place on the number line, fully admitting its power. He summarizes the history of their counting system, which developed largely independently of the Greek system. Because the Indian system did not tie numbers to shapes and measurements, it entertained negative numbers, zero, and infinity.

“The Arab Numeral” considers how Islamic civilization made contact with the idea of zero while conquering India. Seife mentions the work of Al-Khowarizmi, elaborates on the Hindu and Arabic etymology of the word “zero,” and reports that Muslim thinkers rejected Aristotle’s ideas in favor of atomism so they could retain the ideas of zero and the void.

“I Am That I Am: Nothing” explores how Jewish thought likewise abandoned Aristotelian thinking to obtain zero and infinity. The 12th-century rabbi Maimonides retained Aristotle’s proof for God but rejected his eternal universe, clinging to the Old Testament doctrine of the universe created ex nihilo, or from nothing. Seife then shows readers how the Jewish mystical tradition of Kabbalah developed calculations to relate scriptural passages to numbers to discern hidden meanings, one of which was that God’s name revealed that God was everything and nothing simultaneously. By this point, even Christendom was beginning to question Aristotelianism, as evidenced by Étienne Tempier’s 1277 Condemnation and the gradual adoption of Arabic numerals.

“Zero’s Triumph” explains how Fibonacci demonstrated the value of Arabic numerals—including zero—in his Liber Abaci and describes how Italian merchants subsequently adopted his system, letting zero infiltrate Western thought just as Aristotelianism was fading.