Book Review: Imaginary Numbers: an Anthology of Marvelous
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rev-kasman.qxp 6/13/00 4:16 PM Page 775 Book Review Imaginary Numbers: An Anthology of Marvelous Mathematical Stories, Diversions, Poems, and Musings Reviewed by Alex Kasman Imaginary Numbers: An Anthology of examples of “mathe- Marvelous Mathematical Stories, Diversions, matical fiction”. Since Poems, and Musings the review appeared I William Frucht, editor have received several John Wiley & Sons new suggestions each ISBN 0-471-33244-5 week, and the list 1999, $27.95 cloth (http://math. cofc. edu/faculty/kasman/ In 1958 a collection of short stories and book MATHFICT/) has grown excerpts was published under the name Fantasia larger in a few months Mathematica. What tied these previously published than I ever thought it works of fiction together was that they all had would become. Many of something to do with mathematics. The editor of the works on this list, that book, Clifton Fadiman, later remarked, “I had like the movie Pi, were been storing away these wisps of mathematical so successful that it is thistledown in the untidy nest of my files, with hard to imagine that hardly any expectation that others might take plea- anyone with an interest in mathematics would not have noticed them. Oth- sure in them. But, to my surprise, and I believe also ers are so rare, like the books The Sinister Researches to the publisher’s, the little book assembled entirely of C. P. Ransom and The Curve of the Snowflake, that as a labor of love attracted not a vast audience, of it is difficult now to find any trace of them. Since course, but at least an inappropriately large one, many of the mathematical stories, books, and movies when one considers the esoteric nature of the sub- on the list appeared for the first time only after the ject.” Fadiman edited another collection that publication of Mathenauts, it might seem that it is appeared in 1962 as Mathematical Magpie. Then about time for someone to attempt a new collec- in 1987 author and self-proclaimed “world-class tion—and someone has. mathematician” Rudy Rucker edited a collection of Imaginary Numbers: An Anthology of Marvelous mathematically oriented science fiction stories Mathematical Stories, Diversions, Poems, and called Mathenauts. For many years these three Musings, edited by William Frucht, was published volumes remained the only published collections by John Wiley & Sons in the fall of 1999. As Frucht of mathematical fiction. explains in the acknowledgments, he successfully Who would have thought that there were so arranged for a small reissue of Fadiman’s two vol- many mathematical stories published? In fact, umes, which was to be followed by a new collection there are many more. When I reviewed the novel edited by Martin Gardner. When this plan did not Cryptonomicon for the Notices (December 1999, seem to be working out, Frucht himself collected pages 1407–1410), I included a request for more the thirty-one works that make up this book. Alex Kasman is professor of mathematics at the College Among my favorite entries in the book is the of Charleston. His e-mail address is kasman@ short story “A New Golden Age” by Rudy Rucker math.cofc.edu. (which also appeared in Mathenauts). Only this AUGUST 2000 NOTICES OF THE AMS 775 rev-kasman.qxp 6/13/00 4:16 PM Page 776 story, of all the stories in these collections, leaves discussed. For example, the discussion of the red me with the impression that it was written with shift of light from distant stars is echoed in the professional mathematicians as its intended soldier’s treatment with an eye ointment that adds audience. (In fact, Fadiman explicitly insists that a red tint to everything he sees. The inability of his collections are not for mathematicians at all.) information to leave from within the Schwarzschild In this story, and in our world as well, mathe- radius of a black hole seems somehow to explain maticians lament the fact that legislators cannot the fact that the soldiers’ families are not receiving sufficiently appreciate mathematics and that this the letters and requests they write from the front adversely affects the funding of their science. To line. In the end we are left with the impression that address this problem, one of the mathematicians even the disease that eventually claims Schwarz- in the story creates a device called the Moddler. It schild’s life was a consequence of the singular can be used to experience the thoughts of great solutions he found to Einstein’s equations. mathematicians while considering their greatest Let me briefly mention some other works theorems, giving the user the momentary feeling appearing in Imaginary Numbers. “The Church of of understanding and appreciating the results. An the Fourth Dimension” describes Martin Gardner’s attempt to read the original papers after using the (fictional) visit to an unusual church where he Moddler confirms that it does not actually give one considers theology in dimension n>3 and learns any real understanding of the concepts. Still, the some topological magic tricks. The excerpt from mathematicians find that they love using it to get Edwin Abbott’s classic Flatland is an unusual some appreciation of results that were always choice, as this passage seems to have more to do beyond them. Finally, the legislators are convinced with the sociology of the famous two-dimensional to try the Moddler, but the consequences are not world than with its mathematical elements. A chap- exactly what the mathematicians had wished. I ter from A. K. Dewdney’s Flatland-inspired novel think the moral of the story is that perhaps we Planiverse describes a one-dimensional ocean should be glad that legislators do not appreciate surface in a two-dimensional virtual universe. mathematics, because if they did, we might find Though interesting, this story left me wishing that we do not agree with their taste. the author had included more mathematics, since Another interesting story is “The Extraordinary the two-dimensional air turbulence in the boat Hotel, or the Thousand and First Journey of Ion the sails and the uniformly shallow one-dimensional Quiet” by Stanislaw Lem. Here the famous Polish sea he describes would have been ideal starting author toys with the counterintuitive nature of points for a discussion of Kelvin-Helmholz the countably infinite by postulating the existence instabilities and KdV solitons! “A Serpent with of an intergalactic hotel with rooms indexed by the Corners” is an elementary word problem disguised positive integers. For instance, the narrator of the as a story by Lewis Carroll. story arrives at the hotel to find that there are no One of the few entries in the book to be vacancies. However, as a favor the management accompanied by any comments from the editor is makes room for him by simply asking each of the the short excerpt from Alan Lightman’s book other guests to move to the next room. It goes Einstein’s Dreams. This passage, describing Einstein’s dreams of a universe in which entropy on from there, discussing ideas that we have all decreases as time passes, is preceded by histori- encountered before, but probably not in such an cal notes that may be of use to some readers and entertaining context.1 that help to “set the mood” even for those who Connie Willis’s short story “Schwarzschild already know the background. Generally, the Radius” is based on events in the life of Karl editor’s comments are helpful and appropriate. Schwarzschild, who gave the first exact solutions In fact, the book would have benefited from more. to the equations of general relativity. The historical For instance, the book includes the dialogue aspects of the story here are enhanced by cleverly “Prelude…” by Douglas Hofstadter from his self-referential fictional details. Told in flashback Pulitzer Prize-winning Gödel, Escher, Bach. form, the events are recalled by a soldier who Rereading this excerpt merely served to remind happened to intercept a letter from Einstein to me what an intricate and amazing work of art Lieutenant Schwarzschild at the front line during that book was, for it truly fulfills its promise of World War I. As the story develops, haunting analo- interweaving the spirit of the mathematics, art, gies are made between the situation of the soldiers and music of these three people. Yet I am afraid in the trenches and the scientific theories being that in isolation the excerpt might just seem like 1Or perhaps you have. George Gamow in “One, Two, nonsense. Some comments regarding the goals of Three…Infinity” attributes the hotel analogy to David Hofstadter’s book and its connection to this excerpt Hilbert, and Allyn Jackson points out to me that the arti- would be helpful. Otherwise, how is the reader cle “Hilbert’s Hotel”, by Ian Stewart (New Scientist, 19/26 unfamiliar with Gödel’s work to know that the December 1998 to 2 January 1999, pages 59–61) also pre- discussion of Fermat’s Last Theorem is not merely sents this idea in the form of a story. a joke but a clever foreshadowing of the sort of 776 NOTICES OF THE AMS VOLUME 47, NUMBER 7 rev-kasman.qxp 6/13/00 4:16 PM Page 777 logical paradox that underlies Gödel’s proof? (Let part of everyday life and typical science fiction me explain. In this dialogue a character devises a stories that I cannot see referring to a story as formal logical calculus to attempt to prove Fermat’s mathematical simply because of its connection Last Theorem. In this notation the proof of the to computers.