Calculating The Cosmos is a book about the history and current practice of physics, astronomy, and cosmology by British mathematics professor Ian Stewart. The book gives the reader an overview of many topics, including gravitation, the solar system, spacetime, extraterrestrial life, and quantum mechanics. The book is divided into nineteen chapters, as well as a short prologue and epilogue.
The prologue begins with the mission to comet 67P/Churyumov-Gerasimenko, then gives a brief recounting of previous space missions. The role of mathematics in astronomy is discussed, followed by its role in cosmology. The first chapter takes us through the history of gravitational theories, from the ancient Greeks to Galileo, Kepler, and Newton, and onward to general relativity and quantum mechanics. More detail in the path toward relativity would have improved the book here. With the second chapter, Stewart begins discussing the solar system, starting with its formation. The nebular hypothesis of a collapsing gas cloud that forms stars and planets is the main focus, along with previous theories and why they were rejected. These are used to illustrate the importance of physics concepts like momentum and angular momentum. The chapter ends with a discussion of possible futures for the solar system, some of which involve planetary collisions and ejections.
The third chapter is devoted to the theories for the formation of the Moon. These include the giant impact hypothesis, as well as several other ideas that fail to explain the Moon’s composition, tidal locking with Earth, and angular momentum. Much of the chapter concerns the nature of constructing simulations for events like an impact between Earth and a Mars-sized object, or the formation of a solar system. In the fourth chapter, Stewart examines the Titius-Bode law, then expands to power laws in general. Their use in discovering Uranus comes next, followed by the use of perturbation techniques to find Neptune. The chapter ends with the accidental correctness of perturbation techniques concerning Pluto and their failed prediction of Vulcan, a hypothetical planet closer to the Sun than Mercury. Oddly, no mention is made here of the hypothetical Planet Nine, and Stewart does not note that Neptune is out of place by the Titius-Bode law.
The fifth chapter is called Celestial Police, in reference to a group of astronomers at the turn of the 19th century, though most pages have the chapter name “Number of Asteroids.” Stewart gives the history of discovery of the asteroids, then explains how resonances with Jupiter’s orbit explains gaps in the asteroid belt. This leads into a discussion of the 2½-body problem and the five Lagrange points of such a system. The chapter concludes with natural examples of objects in Lagrange point orbits, such as Jupiter’s Trojan asteroids and Saturn’s moons Tethys, Telesto, and Calypso. The next two chapters concern the moons and rings of Saturn and Jupiter, respectively. The discovery of Saturn’s rings and the path toward discovering their true nature comes first, then Stewart shows how resonances with Saturn’s moons explain both the gaps in its rings and how the F ring stays in place. Resonances appear once more in Chapter 7 to explain conjunctions between the moons of Jupiter and Pluto. The chapter ends with facts about some of Jupiter’s and Saturn’s major moons.
Comets are the focus of the eighth chapter. The comet 67P and the effort to land a space probe on it are examined in greater detail. Better known comets, such as Halley’s Comet, are discussed to illustrate the predictive power of mathematics. The origin of comets leads to sections on the Oort Cloud and the Kuiper Belt, then the chapter concludes with the 1994 impact of Shoemaker-Levy 9 on Jupiter. The ninth chapter gives a basic overview of chaos theory, and does a good job of clearing up common misconceptions in popular culture about the subject. After this, Stewart returns to the asteroid belt resonances to discuss a possible origin for the object that likely caused the Cretaceous extinction event.
The tenth chapter discusses various types of orbits and how they can be used to send spacecraft from one place to another with varying degrees of efficiency and travel time. In the eleventh chapter, Stewart brings optics into the discussion to write about stellar composition and classification, illustrated by the Hertzsprung-Russell diagram. The nuclear fusion reactions that power stars, as well as the ultimate fates of stars of various masses comes next. The role of stars in producing all of the heavier elements is explained, from supernovas to newer stars. The observation of sunspots is the subject of the next section, as well as a possible explanation for their cycles. The last subject of the chapter is the means of measuring cosmic distances, from the distance from Earth to the Sun to the distances of various stars. The chapter ends with a few pages of color illustrations, the only ones in the book.
Chapter 12 is devoted to galaxies. Stewart begins with the Milky Way, observed since antiquity but only explained relatively recently. Hubble’s empirical classification of galaxies is cited, then attempts to explain the various shapes are discussed. The failure of galactic rotational speeds to match predictions is left as a puzzle for a later chapter. In the thirteenth chapter, the methods for discovering exoplanets are examined, along with possibilities for extraterrestrial life both elsewhere in the solar system and elsewhere in the universe. The chapter concludes with Stewart’s inventive imagination concerning a hypothetical alien world. The fourteenth chapter begins with the historical steps toward current theories about black holes. The difference between a static black hole and a rotating black hole are explained, as well as their possible role as a link to other universes and hypothetical white holes, which function as expellers of matter and energy that cannot be entered. Alternative explanations for black hole geometry, such as gravastars, are considered at the end of the chapter. The Penrose diagrams here could use more explanation, as they can be quite confusing to a lay reader.
The fifteenth chapter is about the distribution of matter in the universe, as well as the topology of the universe. Stewart does as well as he can without resorting to complex mathematical equations, but doing so would greatly aid the reader’s understanding of the subjects involved. In the sixteenth chapter, the discoveries and interpretations leading to the Big Bang theory are discussed, as well as the various proposals for how the far future of the universe may play out. The next two chapters deal with inflation, dark matter, and dark energy, which are correctives to make the Big Bang theory agree with experimental results. Stewart criticizes this standard cosmological model for its large number of unobserved conjectures, then discusses some alternative theories. The final chapter waxes philosophical about the unlikely combination of physical constants that seem fine-tuned to produce life, then Stewart critiques some of the more outlandish claims regarding this. The epilogue recounts many subjects from the book and points out the difference in procedure between science and mathematics.
Overall, Stewart does a good job of both exploring past and present scientific theories while stressing that science is always tentative, subject to new theories and empirical evidence, unlike his native mathematics. He helpfully notes the scientific jargon so that the lay reader can look up the relevant topic to learn more. However, there is relatively little mathematics in the book, and this can be disappointing for people who cannot see physics without the mathematics. Even so, Calculating The Cosmos is a good read for an intelligent layperson who wants an introduction to cosmology.