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.
Summary
Background
Chapter Summaries & Analyses
Key Figures
Themes
Index of Terms
Important Quotes
Essay Topics
Tools
BetaChapter 7-AppendicesChapter Summaries & Analyses
Chapter 7 Summary: “Absolute Zeros: The Physics of Zero”
“Zero Heat” explains how William Thompson discovered absolute zero, the lowest possible (but practically unattainable) temperature. The discovery of absolute zero to helped launch the study of thermodynamics, a branch of physics. Thermodynamics in turn spawned statistical mechanics, which helped physicists begin to understand the nature of light. Eventually, two physicists, building on the Stefan-Boltzmann equation’s description of the relationship between temperature and light radiation, arrived without apparent error at the seemingly absurd conclusion that ordinary objects emit infinite-energy radiation at wavelength zero. The discovery—the “ultraviolet catastrophe”—forced physicists to backtrack to find where their theories were in error.
“The Quantum Zero: Infinite Energy” describes two ideas proposed by Max Planck and Einstein that resolved the “ultraviolet catastrophe” but turned physics upside down. Planck theorized limits on molecular movement: “They vibrate only with certain acceptable energies, called quanta” (166). Seife explains how counterintuitive this notion is, as qualities in nature seem to have continuous rather than discreet values. Nevertheless, Einstein’s explanation of the photoelectric effect—describing light as photon particles rather than as waves—revealed that light was quantized.
Seife then explains the Heisenberg uncertainty principle, which alleges that the velocity and position of a particle cannot be simultaneously known with perfect precision. Every place in the universe, even the vacuum, is brimming with the energy of particles blinking in and out of existence at the smallest scale—unlimited energy, in fact. Physicists discovered that this zero-point energy exerts force through the Casimir effect, making a surprising connection to Pythagoras’s musical discoveries.
“The Relativistic Zero: The Black Hole” details the strange implications of Einstein’s general and special theories of relativity: that time, length, and mass change with speed, that at the speed of light mass becomes infinite and time stops, and that gravity is the result of objects making indentations in the space-time fabric of the universe. He then describes “the ultimate zero and the worst infinity of them all: the black hole” (178), emphasizing its paradoxical and extreme qualities, such as its ability to trap light. The black hole is a zero because it occupies no space and an infinity because it bends space-time further and further until it punctures it.
“Something for Nothing?” explores late 20th-century scientific speculations concerning new methods of space travel—specifically, warping through wormholes in black holes and extracting energy from the diffusive zero-point energy of the vacuum through the Casimir effect.
Chapter 8 Summary: “Zero Hour at Ground Zero: Zero at the Edge of Space and Time”
“Zero Banished: String Theory” shows that both general relativity and quantum mechanics struggle against the zero-dimensional singularities of black holes and elementary particles, respectively. String theory eliminates the difficulties of singularities by regarding black holes and elementary particles as loops rather than points. However, string theory requires the existence of many dimensions, and although the theory is elegant and resolves problematic zeroes and infinities, it is unverifiable as of the book’s publication—more like philosophical speculation than scientific experimentation.
“The Zeroth Hour: The Big Bang” positions zero as central to the universe’s origins: “The universe was born in zero” (200). Referring to Aristotle’s belief in an eternal universe, Seife recounts how scientists were gradually forced to concede that the universe had a beginning—the Big Bang, ground zero of the universe. Einstein loathed the idea of such a beginning so much he simply invented a force to keep the universe stable, but later developments lent credence to the idea. Edwin Hubble, for example, discovered via the Doppler effect that galaxies are speeding away from each other, while the discovery of cosmic background radiation finally confirmed the Big Bang. Seife concludes by recounting how zero-point energy factors into physicists’ speculations about the extreme conditions of the universe’s first moments and the origin of the universe itself—perhaps even of infinite universes.
Chapter ꝏ Summary: “Zero’s Final Victory: End Time”
Seife argues that owing to the zero-point energy of the vacuum, the universe’s fate will be one of eternal expansion. “To Infinity and Beyond” summarizes the history of zero, emphasizing how it so often troubled philosophers and scientists but just as often concealed the mysteries of mathematics and the cosmos behind its infinite veil.
Appendices Summary
The appendices are brief demonstrations of miscellaneous concepts mentioned in earlier chapters. Appendix A explores how division by zero leads to illogical conclusions: Careless division can result in zero equaling one or even “prove” that Winston Churchill is a carrot. Appendix B explains the equation that gives the value of the golden ratio. Appendix C offers a modern example of solving a function with a derivative using the concept of the limit. Appendix D is a demonstration of Cantor’s proof that the set of all rational numbers is the same size as the set of all natural numbers. Finally, Appendix E is a simplified illustration of how wormholes make time travel possible.
Chapter 7-Appendices Analysis
These chapters primarily explore zero’s impact on modern physics. Sometimes, mathematicians study things that have no apparent real-world correlative or application. In explaining that that physicists hoped zero and infinity were among those things, Seife underscores The Peril of Zero: “For physicists, however, zero and infinity seemed utterly irrelevant to the workings of the universe. Adding infinities and dividing by zeros might be a part of mathematics, but it is not the way of nature. Or so scientists had hoped” (157). Seife argues that zero is in fact everywhere—an omnipresent, transcendental reality encountered in all areas of human thought and inquiry, but one that frequently disrupts long-held beliefs and systems.
The work Seife has done to establish the troublesome nature of zero in prior chapters positions readers to appreciate why zero’s appearances throughout these chapters are significant. The subject matter of the book’s later chapters is highly complex and abstract; without a deep understanding of quantum mechanics, readers might not understand why zero and infinity are distinct problems for such fields as opposed to mere complexities. By positioning thinkers like Einstein and Planck as the “successors” of Zeno and Aristotle, Seife renders the science secondary to the overarching point: that the brightest minds have wrestled with zero for millennia, even as the field of study has shifted.
The zero of physics—the vacuum or the singularity—dominates Seife’s discussion in these chapters. The vacuum is the scientific analog of the philosopher’s void, and the singularity is the scientific analog of the mathematical point: a zero-dimensional space. For Seife, both zeros are intertwined with each other and with infinity. The vacuum is infinite thanks to the expansion of the universe, but even a zero-dimensional sample of the vacuum contains infinite energy—zero-point energy. Similarly, the singularity of a black hole is infinitely dense, and physicists speculate that within it, infinite universes may be spawned just as ours was from the Big Bang.
Seife’s titling of chapters underscores this point about The Dualism of Zero and Infinity. His use of the infinity symbol as the “number” for his final chapter anticipates one of its key points—that the universe’s fate is one of infinite expansion—while also nodding to its summation of the book’s content. Its subject is “everything” (at least, everything in the book). Similarly, the first chapter, titled “0,” not only introduces the book’s main subject but previews its contents. In other words, it too contains “everything,” but an everything that is about “nothing.” The two chapters mirror one another, highlighting the relationship between the two seemingly opposing concepts.
With this final section’s emphasis on how zero and infinity intersect, zero is here at its most paradoxical. Repeatedly Seife describes the most counterintuitive results of modern physics’ engagements with zero and infinity: the theory that elementary particles are quantized; the impossibility of knowing a particle’s position and velocity precisely simultaneously and the result (that empty space overflows with infinite zero-point energy); the theory that time, length, and mass change with speed; and the fact that black holes might enable time travel. Seife’s word choice stresses the seeming irrationality of these discoveries; for instance, he says of the conceptualization of light as both a particle and a wave that “this mathematical description has no intuitive meaning” (169). Nevertheless, Seife urges patience in order to benefit from The Revelation of Zero, saying of string theory’s requirement of many dimensions, “Like imaginary numbers, we can’t see them or feel them or smell them, even though they are necessary for doing calculations. […] it is the predictive power of the equations that interests scientists, rather than their comprehensibility […]” (197). Even some of the appendices illustrate paradoxes: Appendix A demonstrates the illogicality of division by zero, and Appendix E explores the possibility of time travel through black holes.
