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Zero

The Biography of a Dangerous Idea

Charles Seife

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Zero by Charles Seife
Early Origins+
Greek Rejection+
Eastern Embrace+
Western Integration+
Zero & Infinity's Bond+
Modern Physics+

Quiz — Test Your Understanding

Question 1 of 7
Why did the ancient Babylonians initially invent the concept of zero?
  • A. To represent the philosophical concept of a void or nothingness in their religion.
  • B. To act as a placeholder to distinguish between ambiguous numbers in their base-60 system.
  • C. To calculate the area under a curve in early geometry.
  • D. To solve quadratic equations that resulted in negative numbers.
Question 2 of 7
Why did the ancient Greeks, heavily influenced by Aristotle, reject the concept of zero?
  • A. They believed numbers should only be used for practical counting, not theoretical math.
  • B. Their base-10 counting system already had a different symbol for nothingness.
  • C. It conflicted with their philosophical belief in a strictly finite universe with an outer sphere and a definitive beginning to time.
  • D. They lacked the mathematical formulas to divide or multiply by zero.
Question 3 of 7
What was a major reason ancient Indian mathematicians were able to embrace zero and negative numbers while the Greeks could not?
  • A. They viewed numbers in abstract terms rather than strictly as representations of physical shapes and proportions.
  • B. They were trying to solve Zeno's paradox, which required the invention of calculus.
  • C. They used a base-60 system that required a placeholder to prevent commercial errors.
  • D. They rejected the concept of infinity, making zero easier to mathematically define.
Question 4 of 7
What ultimately drove the Christian Western world to adopt zero during the Middle Ages despite theological suspicions?
  • A. The translation of Aristotle's lost works supporting the concept of a void.
  • B. Commercial pressure from Italian merchants who found the Arabic numeral system much simpler to use.
  • C. The discovery of calculus, which required zero to calculate planetary orbits.
  • D. The need for a unified calendar system across the Holy Roman Empire.
Question 5 of 7
How did the concept of zero contribute to the development of calculus by Newton and Leibniz?
  • A. It provided a way to avoid using imaginary numbers in complex equations.
  • B. It allowed them to calculate areas under curves by using an infinite number of rectangles with areas infinitely small, or essentially zero.
  • C. It proved that the universe was infinite, allowing for infinite spatial coordinates.
  • D. It replaced the Cartesian coordinate system with a more accurate three-dimensional grid.
Question 6 of 7
How does the Riemann sphere conceptualize the relationship between zero and infinity?
  • A. They are shown as parallel lines that never intersect on a two-dimensional grid.
  • B. They are placed at the center of the sphere, proving they have the exact same value.
  • C. They represent the exact same mathematical limit when dealing with real numbers.
  • D. They are positioned as equal and opposite poles at the top and bottom of the sphere.
Question 7 of 7
How does the concept of zero manifest in Albert Einstein's theories regarding black holes?
  • A. A black hole reaches a temperature of absolute zero, stopping all movement of particles.
  • B. A dying star collapses until it takes up zero space, yet still retains mass, curving space-time.
  • C. The gravitational pull of a black hole reduces the surrounding dimensions to zero.
  • D. A black hole emits zero energy, making it completely undetectable in the universe.

Zero — Full Chapter Overview

Zero Summary & Overview

Zero (2000) is the fascinating story of a number banned by the ancient Greeks and worshipped by ancient Indians. Zero – as well as its twin, infinity – is a number that’s been at the heart of both mathematics and philosophy over the centuries.

Who Should Listen to Zero?

  • Popular science enthusiasts
  • History buffs curious about how concepts have evolved over time
  • Philosophers interested in everything . . . and nothing

About the Author: Charles Seife

Charles Seife is a journalist and author who teaches at New York University. He studied mathematics at Princeton and Yale, and his other books include Proofiness, Alpha & Omega, and Decoding the Universe.

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