Trying to “popularize” mathematics or science is by no means easy. Any author who sets out to write a book on these subjects for laypeople must overcome several daunting hurdles. One, of course, is finding the right level of sophistication: make the book too easy and you risk “dumbing down” the material to a point where the discussion may even become misleading; don’t make it easy enough, and you run the obvious risk of making it incomprehensible. And, of course, another daunting challenge for an author is to make the material interesting to an audience that does not instinctively find it so.
One possible approach to this latter challenge is to tie the material in to some aspect of popular culture that people do seem to have some instinctive interest in. There are a number of books that have been written with this idea in mind; two that I have looked at previously are The Physics of Superheroes by Kakalios and The Physics of Star Trek by Krauss. Both are very good books, but the former, I have always thought, represents the gold standard of popular science exposition for laypeople; it is beautifully and entertainingly written with an ideal mixture of actual science and laugh-out-loud humor. It also doesn’t hurt, I must admit, that I spent a great deal of time from about 1958 to 1966 voraciously reading the very silver-age comic books that are lovingly discussed in detail here, slowing down only when I discovered other things (i.e., girls) that were more interesting.
I had assumed, from the title of the book under review, that it would be like the Kakalios and Krauss books, but this assumption turned out to be not completely correct. The Adler book is similar in spirit and motivation to, but somewhat different in execution than, the two books cited above. Like Kakalios and Krauss, the author here is a physicist, and therefore all three books are largely concerned with that discipline. Also like the two previous books, this one does so by reference to aspects of popular culture. While Kakalios limited himself to comic book superheroes and Krauss used Star Trek as primary motivation for discussion, this book is somewhat more wide-ranging, and cuts a large swath through both science fiction and fantasy. (What’s the difference? Roughly speaking, the latter isn’t bound by any rules of physics and allows the use of magic.) So, for example, in this book, the author references not only Star Trek but also Harry Potter, the Dresden Files, 2001: A Space Odyssey, and a host of science fiction authors, including, but by no means limited to, Larry Niven, Robert Heinlein, Jerry Pournelle, and Ursula K. LeGuin.
Although I was a voracious comic book reader in my childhood and also watched every episode of Star Trek (both original and Next Generation) several times, I somehow never developed any real passion for science fiction novels or short stories. I read some, but only occasionally, and have never to this day read a Harry Potter book or seen one of the movies. Nevertheless, I found that this wasn’t any real impediment to my enjoyment of the book under review: the author does a very good job of summarizing the relevant background, so even someone without a great deal of experience with this literature will not be at a disadvantage. In fact, one benefit of this book is that it might instill interest not only in physics but also in science fiction. As I read I occasionally found myself making mental notes of things I might want to take a look at it in the future.
Another distinction between this book and the ones by Krauss and Kakalios (particularly the latter) is that this one is pitched at a somewhat higher (and less jocular) level. Kakalios seems to apologize whenever he is forced to use mathematics; in this book, by contrast, the author does not shy away from using not only equations involving trigonometric functions and the natural logarithm, but also, on occasion, calculus. Page 78, for example, contains the sentence “We can use Newton’s second law to write down a differential equation for the speed, v, of the rocket…”, followed by the differential equation itself, the statement that it can be solved “by elementary calculus”, and the solution, an equation involving the natural logarithm function. Kakalios rarely gets much more complicated than F= ma; here we are exposed (page 223) to “the Stefan-Boltzmann formula for a black body emitter in normalized units”. Adler assumes at least some prior exposure to physics; Newton’s laws are, however, summarized and reviewed in an Appendix (using calculus). So, this book is clearly not intended for a completely unsophisticated audience, and reading it at times required some real thought (which, I hasten to point out, is not a bad thing). Nevertheless, the book is not so intimidating that it should scare away anyone who doesn’t have a Ph.D. in mathematics or physics. The author has made a real effort to make this point comprehensible to any serious, reasonably well-educated reader, and he has succeeded in this goal.
This book is divided into four main parts, each part further subdivided into several chapters. The title of the first part, “Potter Physics”, refers, of course, to Harry Potter, but the chapters in this part are not limited to this character; also discussed, for example, are the Dresden Files books by Jim Butcher, all of which chronicle the adventures of Harry Dresden, a private detective in contemporary Chicago who also happens to be a wizard. The chapters in this part of the book address issues like shape-shifting (in connection with conservation of mass), the significance of magic spells with regard to entropy (the author concludes that the Harry Potter books seem to have less regard for magic being constrained by any rules whatsoever than do the Dresden books), the reason why Hogwarts is dark, and the use of strange animals in these books.
Part II, which at 9 chapters and about 150 pages of text is by far the longest part of the book, addresses a host of issues relating to space travel, which has obviously always been a mainstay of science fiction. Chapters in this part discuss, among other things: why space flight and exploration today is not as common as predicted by decades-old science fiction; the physics behind the idea of an “elevator” to the moon; the use of matter-antimatter reactions (as in Star Trek) as a means of propulsion; and the implications of the theory of relativity for faster-than-light motion and time travel.
The last part of the book (“Year Googol”) looks to the far future, including the likelihood of there actually being one: nuclear war and global warming, for example, are discussed in a chapter on the short-term survival of humanity, and subsequent chapters address advanced civilizations of the future and what they would (theoretically, if not practically) be capable of, at least based on our current understanding of physics.
The chapters in this book seem to be quite independent of one another, a fact which facilitates flexibility in its use. In addition to serving as a good book for self-study by any intellectually curious reader, this book could, I think, be used with considerable profit as a supplemental text in a regular undergraduate physics course or as a text for an honors seminar, perhaps supplemented by some of the actual science fiction stories mentioned here. In this regard, it should be mentioned that, in addition to an extensive bibliography of more than 250 entries, the book promises that a collection of exercises, along with hints and solutions, will appear on the publisher’s webpage for the book. (There are, as of this writing, none there yet, but presumably this will occur at some time in the future). Whether as a text for a course or as a vehicle for self-study, this book makes for interesting, educational and thought-provoking reading.
Mark Hunacek (firstname.lastname@example.org) teaches mathematics at Iowa State University.