Review by Linda P. Rothschild

Cosmic numbers are those constants that are intrinsically connected to the physical laws of our 
universe. Not all numbers that are associated with the natural world are “cosmic” in this sense. 
The number 10, the base of our modern decimal number system, is a human artifice, presumably 
chosen because it is the number of fingers on our two hands. The choice of seven as the number 
of days in a week is arbitrary, though it does date back to biblical times. In contrast, the number
 365 of days in a year does represent a cosmological fact: the approximate number of rotations
 of the earth on its axis during one revolution around the sun. However, the number 365 is not
 related to a universal physical law, but is a mere accident of the present state of the planet we
 inhabit and its relationship to its star, the sun.

To find an example of an actual cosmic number, one need only think of light. Learning that light 
travels 186,000 miles per second (and that cosmic distances are measured by light years, the
 distance light can travel in a year) has astonished and delighted school children for decades. The book under review is intended to enlighten and entertain adults through the discussion of a dozen cosmic numbers, including the history of the experiments and the scientists who were involved
 in their discovery.

The book is mainly historical, but not organized along a timeline. Rather, it’s organized as a 
series of chapters, each of which is devoted to a particular cosmic question or phenomenon. The 
author, James D. Stein, is a mathematics professor whose own research is distant from the
 topics he discusses here. He endeavors to invite the reader to join him in wonder as he relates 
the history of the experiments that led to the discovery of these “cosmic numbers.” Peppered
 throughout the discussion are entertaining anecdotes about the scientists themselves. We learn, for example, that the great 17th-century astronomer Kepler not only discovered the laws of
 motion of the planets but also won an acquittal for his mother, who was accused of witchcraft.

The author cajoles the reader to enjoy the spirit of discovery with him, keeping a light style of
 narrative. Nevertheless, Stein does not shy away from introducing mathematical formulae
 as well as precise descriptions of the science involved, sometimes in a rather condensed form.

The nonscientific reader need not be intimidated by these. Indeed, a difficult and dense page that 
seems to be chock full of equations that can generally be skimmed over with little serious loss 
of continuity. (Even this reviewer, also a mathematician, could not resist skipping a few equations.) The heavy scientific arguments are often accompanied by colorful analogies,
 for example, “chemical reactions are the result of electrons pirouetting happily from one atomic dance partner to another …” Some of the analogies the author presents might seem a bit far-fetched, such as his comparison of stars in the sky to stars in Hollywood. This is all in the spirit of keeping the reader entertained.

Several of the phenomena discussed in Cosmic Numbers are known to the educated public, 
such as the existence of a relationship between the pressure, volume and temperature of a gas. 
Others might come as a surprise. For example, it might seem reasonable that heat and coldness 
are both properties that are brought about by “sources.” However, it was not until the early 18th 
century that scientists attempted to show that cold is simply the absence of heat and to prove that 
an “absolute zero” exists, below which temperature can never fall. Stein devotes an entire
 chapter to this fascinating story, including the experiments that led to determining the value of
 minus 273 degrees centigrade for absolute zero and the significance of low-temperature physics 
in modern technology.

Many striking examples in the last few chapters come from astrophysics, including discoveries
 made possible by 20th-century science and technology. For instance, the reader will learn 
that a white dwarf star will explode in a supernova, casting out heavy elements, if its mass 
increases beyond a certain point, the Chandrasekhar limit, named after the Indian astrophysicist
 who discovered it. Such explosions are integral parts of the life cycle of the universe. Of these 
the author writes: “Every airplane has a take-off speed: the speed necessary for it to become
 safely airborne. The Chandrasekhar limit is not just a number that tolls the death knell for a massive star, it is the take-off speed for the formation of planets ― and life.”

The jocular tone used by the author may put off some readers, but many will find that the casual 
style encourages them to read on, even when the science becomes hard. The author intersperses 
anecdotes about himself throughout, which give the narrative a personal touch.

This book will appeal to a wide audience of readers who are curious to know more about the 
discovery of the laws that govern our universe. The reader might find it useful to keep the 
Internet source Wikipedia at hand to look up scientific terms and names to complement the
 information given in the book. Such occasional interruptions will not detract from an enjoyable
 and informative read.

Linda P. Rothschild is a Distinguished Professor of Mathematics at the University of California, San Diego. She is a member of the American Academy of Arts and Sciences.