Zero

Zero Plot Summary

Introduction

On September 21, 1997, the USS Yorktown, a billion-dollar missile cruiser, suddenly shuddered to a halt off the coast of Virginia. The cause wasn't enemy fire or mechanical failure, but something far more insidious: zero. A single zero in the ship's computer system created a division-by-zero error that rendered 80,000 horsepower instantly worthless. It took nearly three hours to establish emergency controls, and two days to fully repair the damage caused by this seemingly innocent number. This naval incident is just a faint shadow of zero's true power throughout history. Zero has been feared, outlawed, and battled over for millennia. It has toppled philosophical systems, transformed mathematics, and revolutionized our understanding of the universe. From ancient Babylon to modern quantum physics, zero's journey spans continents and civilizations, leaving profound changes in its wake. The concept that began as a mere placeholder in calculation systems eventually became the gateway to understanding both the ineffable and the infinite, challenging our most fundamental assumptions about reality itself.

Chapter 1: The Ancient Fear of Nothing: Zero's Contested Birth

Imagine life without zero. For most of human history, this was reality. Early counting systems simply had no need for it. Stone Age mathematicians used wolf bones with notches to count possessions or track time, but they never marked "nothing." As civilizations developed more sophisticated counting systems based on groups of five, ten, or twenty (reflecting our fingers and toes), they still managed without zero. The ancient Egyptians, master astronomers and architects who built the pyramids, developed elaborate hieroglyphic numerals but never conceived of a symbol for nothing. The first glimmer of zero appeared around 300 BCE in Babylon, where astronomers created a placeholder symbol—two slanted wedges—to distinguish between numbers like 21 and 201 in their sexagesimal (base-60) system. This innovation was purely practical; it prevented confusion in calculation but wasn't considered a number in its own right. Meanwhile, across the world, Mayan mathematicians independently developed their own zero symbol, represented by a shell-like glyph, which they used in their elaborate calendar system counting days from 0 to 19. Why was zero so late to emerge and so reluctantly accepted? The answer lies in its deeply troubling properties. Zero wasn't just a practical counting tool—it represented the void, nothingness itself. When mathematicians began experimenting with it, they discovered its strange behaviors: multiply any number by zero and it vanishes; divide by zero and the foundations of mathematics seem to crumble. The Greek philosophers, who shaped Western thought for millennia, found these properties particularly disturbing. Their universe was one of substance and being, not emptiness and non-being. Zeno of Elea, with his famous paradoxes about motion being impossible, demonstrated the philosophical problems that infinity and its twin, zero, posed to Greek thought. Pythagoras and later Aristotle built a worldview where the universe was full, finite, and comprehensible—a system that had no place for the void. This rejection of zero would dominate Western mathematical and philosophical thought for nearly two thousand years, even as the concept quietly developed in Eastern civilizations.

Chapter 2: East Embraces the Void: Zero's Journey through Hindu and Islamic Worlds

While Western philosophers shunned the concept of nothingness, Eastern civilizations embraced it. In India, sometime around the 5th century CE, zero underwent a profound transformation. Hindu mathematicians took the Babylonian placeholder and revolutionized it, turning zero from a mere symbol into a full-fledged number with its own place on the number line. This breakthrough was influenced by Hindu religious concepts that, unlike Greek philosophy, were comfortable with emptiness and the void. The brilliant Indian mathematician Brahmagupta, writing in the 7th century, provided the first formal rules for calculating with zero. "When zero is added to a number or subtracted from a number, the number remains unchanged," he wrote. "A number multiplied by zero becomes zero." He even attempted to handle division by zero, though he couldn't fully resolve its paradoxes. The Indian concept of zero was intrinsically linked to their religious understanding of nothingness (sunya) and infinity—two concepts that were seen not as opposing forces but as complementary aspects of the universe. As Islamic civilization expanded across Asia and into parts of Europe in the 8th and 9th centuries, Muslim scholars eagerly absorbed and developed mathematical knowledge from conquered territories. Al-Khwarizmi, whose name gives us the word "algorithm," wrote influential texts explaining the Hindu numeral system, helping spread the concept of zero throughout the Islamic world. The Arabic word for zero, "sifr" (meaning "empty"), eventually gave us the English words "zero" and "cipher." Islamic mathematicians and philosophers took a different approach to zero than their Greek counterparts. Where Aristotle had rejected the void, Islamic thinkers embraced it as compatible with their theology. The Quran itself asks, "Does man forget that We created him out of the void?" This theological comfort with nothingness allowed Islamic civilization to develop and use zero freely, creating the foundation for algebra and advanced mathematics. Zero traveled alongside Arabic numerals and Islamic mathematical concepts as trade networks expanded, eventually reaching medieval Europe through Islamic Spain and Italy. But the Western world, still in the grip of Aristotelian thought, would resist this powerful concept for centuries longer, even as it reluctantly began to adopt the practical convenience of Arabic numerals for commerce and calculation.

Chapter 3: The Renaissance Challenge: Zero and the Infinite Cosmos

By the 15th century, Europe was awakening from its medieval slumber, and zero played a crucial role in this intellectual rebirth. Renaissance artists like Filippo Brunelleschi revolutionized painting by using a vanishing point—essentially a zero-dimensional object representing infinite distance—to create realistic perspective. This technical innovation was more than just artistic; it represented a fundamental shift in how Europeans conceptualized space and infinity. The Catholic Church, which had long aligned itself with Aristotelian philosophy, initially seemed open to these new ideas. Nicholas of Cusa, a German cardinal, boldly declared "the earth is not the center of the universe" and suggested the cosmos might be infinite. These speculations laid groundwork for Copernicus, whose heliocentric model placed the sun, not Earth, at the center of our planetary system. These revolutionary ideas implicitly challenged the finite, Earth-centered Aristotelian cosmos that had dominated Western thought for millennia. However, as the Protestant Reformation threatened the Church's authority in the 16th century, Catholic authorities became increasingly hostile to ideas that challenged traditional doctrine. The Counter-Reformation saw the Church reasserting Aristotelian philosophy and rejecting the infinite cosmos and the void. Giordano Bruno was burned at the stake in 1600 for, among other heresies, suggesting an infinite universe with countless worlds. Galileo was forced to recant his Copernican views in 1616, the same year Copernicus' work was placed on the Index of forbidden books. Into this intellectual battlefield stepped René Descartes, a mathematician trained by Jesuits but drawn to the new science. His invention of Cartesian coordinates placed zero at the origin of his coordinate system, making it the central reference point for all mathematical descriptions of space. Yet Descartes himself couldn't fully embrace the void, maintaining that a vacuum was impossible. It would take the experiments of Evangelista Torricelli and Blaise Pascal in the mid-17th century to definitively prove that vacuums could exist, undermining one of the core tenets of Aristotelian physics. By the end of the Renaissance, zero had transformed from a feared concept to an essential tool for understanding the cosmos. The finite, Earth-centered universe was giving way to an infinite one, setting the stage for the scientific revolution to come. The void was no longer something to be denied—it had become something to be studied.

Chapter 4: The Calculus Revolution: Zero's Mathematical Power Unleashed

The 17th century witnessed mathematics' most significant revolution, as Isaac Newton and Gottfried Wilhelm Leibniz independently developed calculus—a breakthrough that required embracing the paradoxical properties of zero. Born prematurely on Christmas Day 1642, Newton would transform our understanding of motion and change by manipulating quantities that approached zero without quite reaching it. Newton's method of "fluxions" allowed him to determine the slope of a curve at any point by examining how quantities changed over infinitesimal intervals of time. When analyzing the curve y = x² + x + 1, Newton used a peculiar trick: he introduced an infinitesimal quantity (represented by o) that was treated sometimes as zero and sometimes as non-zero. This mathematical sleight-of-hand seemed logically dubious—dividing by a quantity that simultaneously vanished—yet it yielded correct results that perfectly described natural phenomena. Leibniz, working independently in Germany, developed a similar approach with his "differentials" (dx and dy), which represented infinitely small changes in variables. His notation, which we still use today, made the manipulations of these quantities more intuitive. Both men recognized that their methods allowed them to solve previously intractable problems: finding tangent lines to curves, calculating areas under curves, and describing rates of change in physical systems. This new calculus became the language of nature itself. Newton's famous differential equation F = ma (force equals mass times acceleration) unified terrestrial and celestial physics, showing that the same laws that governed falling apples also determined planetary orbits. For the first time, scientists possessed mathematical tools that could describe motion, change, and dynamics throughout the universe. Yet a troubling paradox remained at calculus's core. Bishop George Berkeley scathingly criticized these methods in 1734, calling infinitesimals "ghosts of departed quantities" and pointing out that Newton and Leibniz were essentially dividing by zero—an operation forbidden in normal mathematics. Berkeley was technically correct; calculus lacked logical rigor. It would take another century before mathematicians like Augustin Cauchy and Karl Weierstrass finally placed calculus on solid ground by developing the concept of limits, which allowed them to approach zero without actually dividing by it. Despite these logical difficulties, calculus proved unstoppable because it worked. Its power to describe everything from flowing water to gravitational attraction revolutionized science and engineering, demonstrating that zero's paradoxical properties weren't just philosophical curiosities—they were keys to understanding the physical world.

Chapter 5: Modern Physics: Black Holes, Quantum Mechanics and the Power of Nothing

The 20th century saw zero move from mathematical abstraction to physical reality as scientists discovered that nothingness itself has profound physical properties. In thermodynamics, absolute zero emerged as the lowest possible temperature—a point where molecular motion virtually ceases. William Thomson (Lord Kelvin) showed that this temperature, about -273.15°C, represents a fundamental limit that can be approached but never reached, creating a universal scale where zero marks a true physical boundary. Quantum mechanics, developed in the early 1900s, revealed even stranger properties of nothingness. Max Planck's solution to the "ultraviolet catastrophe" introduced the revolutionary concept that energy comes in discrete packets called quanta. Later, Werner Heisenberg's uncertainty principle demonstrated that even perfect vacuum contains energy fluctuations. This "zero-point energy" means that absolute emptiness is impossible—the vacuum constantly seethes with "virtual particles" popping in and out of existence. In 1948, Dutch physicist Hendrik Casimir predicted that this quantum vacuum could exert physical force. By placing two metal plates extremely close together in a vacuum, certain virtual particles are excluded from the space between the plates, creating a pressure difference that pushes the plates together. This "Casimir effect"—the pressure of nothing—was experimentally confirmed in 1997, proving that emptiness itself has measurable physical effects. Einstein's theory of relativity revealed zero's most dramatic manifestation: the black hole. When a massive star collapses under its own gravity, it can compress to a point of zero volume and infinite density—a singularity where space and time themselves break down. At this zero-dimensional point, the laws of physics as we know them cease to function. The event horizon surrounding this singularity marks a boundary from which nothing, not even light, can escape. Perhaps most profound is the role of zero in cosmology. The big bang theory suggests our entire universe emerged from a singularity—a point of zero size but infinite density approximately 13.8 billion years ago. Recent observations indicate that the universe's expansion is actually accelerating, possibly driven by zero-point energy of the vacuum itself. This "dark energy" may ultimately determine the fate of our cosmos, potentially leading to an eternal expansion and eventual heat death as everything approaches absolute zero.

Chapter 6: The Ultimate Zero: How Nothingness Shapes Our Universe

At the frontiers of theoretical physics, zero continues to challenge our understanding of reality. String theory, which attempts to unify quantum mechanics and general relativity, essentially tries to banish zero from physics by replacing zero-dimensional point particles with tiny one-dimensional strings. These strings, vibrating in multiple dimensions, eliminate the troublesome infinities that arise when particles are treated as mathematical points. Yet this elegant solution comes at a cost: it requires 10 or 11 dimensions, most of which must be "curled up" too small to detect with current technology. The quantum vacuum, once thought to be simply empty space, has proven to be perhaps the most complex and dynamic aspect of reality. Quantum field theory reveals it to be a seething ocean of virtual particles that continuously appear and disappear, borrowing energy according to Heisenberg's uncertainty principle. This quantum foam may be responsible for everything from the Casimir effect to the accelerating expansion of the universe. Some physicists even speculate that our entire universe might be a quantum fluctuation—a bubble of reality that emerged from the ultimate void. Zero's role extends beyond physics into information theory and computing. The binary system that powers all digital technology relies entirely on patterns of zeros and ones. Without zero, modern computers could not function. Ironically, the same division-by-zero errors that plagued ancient mathematicians continue to crash sophisticated computer systems today, as the USS Yorktown incident demonstrates. Zero remains both essential and potentially dangerous. The philosophical implications of zero continue to resonate across disciplines. The paradox of creating something from nothing connects mathematics to metaphysics, science to theology. Eastern philosophical traditions that embraced the void millennia ago find unexpected validation in quantum physics, which suggests that emptiness contains limitless potential. Meanwhile, the zero-sum thinking that dominates many economic and political models may itself be challenged by emerging understanding of complex systems and network effects. As we peer into black holes, explore quantum fields, and contemplate the birth and possible death of our universe, we find zero at every critical juncture. The concept that was once rejected by ancient philosophers as an impossibility now appears to be woven into the very fabric of reality. Our universe begins with zero, is sustained by the energy of nothing, and may ultimately end in the perfect equilibrium of absolute zero. The dangerous idea that transformed civilization continues to shape our deepest understanding of existence itself.

Summary

The story of zero reveals a profound pattern in human intellectual development: concepts initially rejected as dangerous or impossible often become essential to future progress. Zero began as a simple placeholder in Babylonian mathematics but evolved into a number with its own properties, sparking fierce resistance from Greek and early Christian thinkers who couldn't reconcile nothingness with their philosophical systems. The eventual acceptance of zero enabled revolutionary developments: from Arabic numerals and algebra to calculus, modern physics, and computing. Each advance required overcoming deep-seated fears about the void and embracing the paradoxical properties of nothing. This historical journey offers important lessons for our approach to knowledge today. First, intellectual courage often means embracing concepts that initially seem threatening or contradictory—the most transformative ideas frequently challenge existing frameworks. Second, cultural exchange proves vital to innovation, as zero's development across Babylonian, Indian, Islamic, and European civilizations demonstrates. Finally, the story reminds us that mathematics isn't merely a human invention but seems mysteriously embedded in reality itself. When Physicist Eugene Wigner noted the "unreasonable effectiveness of mathematics in the natural sciences," he might have been thinking of zero—a concept born from human abstraction that somehow captures fundamental truths about our universe, from the quantum vacuum to cosmic singularities.

About Author

Loading...

Charles Seife

CHARLES SEIFE is a Professor of Journalism at New York University. Formerly a journalist with Science magazine, has also written for New Scientist, Scientific American, The Economist, Science, Wired UK, The Sciences, and numerous other publications. He is the author of Zero: The Biography Of A Dangerous Idea, which won the PEN/Martha Albrand Award for First Nonfiction. He holds an M.S. in mathematics from Yale University and his areas of research include probability theory and artificial intelligence. He lives in Washington D.C.

Read more