38 pages • 1 hour read
Charles SeifeZero: The Biography of a Dangerous Idea
Nonfiction | Book | Adult | Published in 2000A modern alternative to SparkNotes and CliffsNotes, SuperSummary offers high-quality Study Guides with detailed chapter summaries and analysis of major themes, characters, and more.
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The Peril of Zero
Seife’s first words in Zero recount how a single overlooked zero in a missile cruiser’s code caused the ship’s engines to fail. This sets the tone for the rest of the book, throughout which Seife attempts to impress upon readers the perilous nature of zero. “No other number can do such damage” (2), he asserts, and its dangers come in many forms.
Zero is dangerous to mathematicians: “When you have infinity in an expression, or when you divide by zero, all the mathematical operations—even those as simple as addition, subtraction, multiplication, and division—go out the window. Nothing makes sense any longer” (129). Seife guides readers through the math to demonstrate this, and in Appendix A he emphasizes the illogical results of division by zero with a comical proof that Winston Churchill is a carrot, probably anticipating that many readers will not otherwise appreciate why “1/0” is dangerous.
Zero is dangerous to physicists. Zero baffled their attempts to understand elementary particles by confronting them with zero-point energy and confounded their inquiries into space-time and gravity with the enigma of the black hole. However, Seife explains that zero did even worse damage than this. As physicists scrambled to account for these phenomena, zero brought their theories into conflict with each other: “Zero dwells at the juxtaposition of quantum mechanics and relativity; zero lives where the two theories meet, and zero causes the two theories to clash” (192).
Zero is dangerous to philosophers. Seife states that ancient people feared zero as a symbol of the “emptiness and chaos [that were] present before the universe came to be” (19). Seife describes how zero defied Pythagoras’s mystical belief in the unity of shapes and numbers. He explains that Zeno’s paradox puzzled and frightened the Greeks because its solution lay in zero. He establishes that the West’s cherished Aristotelianism, with its apparently sensible arrangement of the cosmos and its proof of God’s existence, depended upon the absence of the void.
These individuals resisted zero for different reasons. Zero is a threat because it is illogical: Dividing by zero leads to absurd conclusions. Zero is a threat because it is unpredictable: It appears in unexpected places, producing unexpected paradoxes. Zero is a threat because it is unmanageable: It resists easy assimilation into preexisting theories and beliefs or outright contradicts them. Above all, Seife suggests, zero is a threat because it is incomprehensible: It is a transcendent truth, always lying just beyond the control of human reasoning.
The Revelation of Zero
Seife does not argue that zero is powerful and significant only because it is dangerous. Zero has another side: It is revelatory. A revelation, in religious contexts, is knowledge imparted by a supernatural agent. It is a divine visitation unanticipated by the recipient, and it radically transforms the recipient’s perspective. Furthermore, a revelation authenticates itself; the recipient’s confidence in the revelation is grounded in faith, not reason. Throughout the ages thinkers have reasoned and experimented toward a better understanding of the universe. Seife indicates that zero has played an important yet unique role in this process, expanding human knowledge in a way that often seems more mystical than logical.
Zero’s revelations range in subject and scope. Zero reveals the solution to Zeno’s paradox, a philosophical problem. Zero reveals the preferability of belief in God in Pascal’s wager, which involves theology. Accepting zero was integral to the invention of calculus, which unlocked the mysteries of how nature works. Zero-point energy, the ground zero of the black hole, and the zero hour of the Big Bang are further manifestations of zero—in this case, scientific. Finally, Seife explains how zero-point energy plays a role in the ultimate fate of the universe: eternal expansion. Zero is an eternal, transcendent reality providing answers to the most important questions.
Seife juxtaposes such discoveries with the more traditional forms of knowledge-seeking favored in Europe—even in the realm of theology. Aristotle did not base his philosophy upon divine revelation, though his philosophy sought to prove the existence of God. Aristotle reasoned upward, subjugating (Seife implies) the most transcendental truths to his own human reasoning. He rejected zero because it was incomprehensible. By contrast, Seife repeatedly argues that Hindu, Islamic, and Jewish thought embraced the ineffable. These philosophies were grounded on holy texts received by faith—supernatural revelations that were never expected to fit neatly within human understanding. By emphasizing the paradoxical nature of zero, Seife intentionally gives the concept the mystical flavor commonly associated with non-Western philosophy and religion (arguably embracing an Orientalist stereotype).
Seife never says that zero is God, but he carries the comparison far. He remarks on the association between the void and the Hindu god Shiva and explains how God was identified with infinity and the void in the Jewish mystical tradition of Kabbalah. He states, “Humanity could never force zero to fit its philosophies. Instead, zero shaped humanity’s view of the universe—and of God” (3). Zero, like God, is dangerous but also potentially a source of ultimate truths. Zero, like God, is a mystery that must be grasped by faith, not mere reason. Zero, like God, creates (the Big Bang) and destroys (black holes, the heat death of the universe). Zero, like God, survives opposition and is revealed—not, presumably, manufactured—by human thought.
The Dualism of Zero and Infinity
Seife relies on various pairs of ideas to structure his discussion: East and West, philosophy and science, numbers and shapes, math and physics, etc. These pairs are not always simple dichotomies; often the relationships of the components are more complex. The components are intertwined and interdependent, not merely antagonistic. Seife sees such a dualism in zero itself, which is dangerous and confusing but also empowering and enlightening. He also sees such a dualism between zero and infinity.
Seife shows that zero and infinity often go together. They concur in the mystical conceptions of God in Hinduism and Kabbalah. They concur in the solution to Zeno’s paradox: an infinite series approaching zero. They concur in the Riemann sphere, on which they are almost interchangeable: Their powers are identical, though oriented opposite each other. They concur in Pascal’s wager, where even if the probability of God’s existence approaches zero, the expected value of believing in God remains infinite. They concur in zero-point energy: Infinite energy spews from the vacuum, even at an infinitesimal, zero-dimensional scale. They concur in black holes, in which finite mass is packed infinitely dense in a zero-dimensional singularity. They even concur in the ultimate fate of the universe: expanding into an infinite void.
Infinity also has properties that render it similar to zero. Most obviously, both are difficult for the human mind to comprehend: Both the eternal universe envisioned by Aristotle and the nothingness before the Big Bang strain conceptualization. Seife suggests that the paradoxes only accumulate the deeper one digs. The idea that one infinite set could exceed another infinite sense seems as nonsensical as the results of dividing by zero.
Seife underscores the dualism of zero by associating it with Eastern philosophy, which he says is often dualistic; for example, Seife mentions the balanced conflict between good and evil in Zoroastrianism and the intermingled powers of creation and destruction in Hinduism. Seife also repeatedly associates zero and infinity with yin and yang, beginning in Chapter 0: “Zero is powerful because it is infinity’s twin. They are equal and opposite, yin and yang. They are equally paradoxical and troubling” (2). Yin and yang appear together, each containing a portion of the other, making them choice descriptors for infinity and zero; they are distinct but never entirely isolated from each other.
