[In the following review, Smith discusses the long-lived appeal of Flatland and Thomas Banchoff's introduction to the novel.]

Edwin Abbott was one of Victorian Britain's most fascinating and wide-ranging figures. Appointed headmaster of the City of London School in 1865 at the age of twenty-six, he quickly developed a reputation as a leading educational reformer, championing the introduction throughout the curriculum of such subjects as natural science and English literature. During his quarter-century at the CLS, Abbott published, in addition to Flatland (1884), textbooks on writing, Latin, and Shakespeare; scholarly works on Bacon and theology; and several Christian historical novels. When he retired in 1889, it was to devote the remainder of his life to the development of his theological system, the multi-volume Diatessarica. Yet it is Flatland, the clever little mathematical “Romance in Many Dimensions,” that survives.

That survival has been due in large part to the interest of scientists and mathematicians (who use the book to introduce students to concepts of dimensionality and space-curvature) and science-fiction lovers (who see it as an early example of that genre). Neither of these groups, however, has shown much concern for Abbott or for the cultural background out of which the book arose. Yet the literary critics and historians who have directed attention over the last decade to these areas have tended to ignore Flatland's specific relevance to nineteenth- and twentieth-century mathematics. As a result, none of the many recent paperback editions of Flatland includes a truly complete introduction to the text. But that gap has now been filled by Thomas Banchoff's edition for the Princeton Science Library, an edition that will serve students of all disciplines well.

Banchoff, a Brown University mathematician who specializes in computer graphics and the visualization of higher dimensions, is also the world's leading authority on Abbott. He organized a centenary conference on Flatland at Brown in 1984 and has long been collecting materials for a biography of Abbott. His introduction is, not surprisingly, unique in combining information on Abbott with both Flatland's social and historical context and the curious fascination it has exerted—and continues to exert, in this age of hypergraphics—on mathematicians and physicists in our century.

Banchoff locates Flatland at the curious intersection of late-nineteenth-century mathematics, philosophy, and theology by presenting Flatland as both a response to, and a part of, the popularization of non-Euclidean geometry and the corresponding endeavors to visualize higher dimensions. As a vehicle for empiricist attacks on Kantian conceptions of space on the one hand, and for mystical Christian efforts to identify the fourth dimension with God or a spiritual realm on the other, non-Euclideanism had a diverse and significant cultural impact. By linking Flatland to Abbott's own religious and scientific views, Banchoff makes it clear that this jeu d'esprit is also seriously engaged with social and intellectual issues, many of them directly connected to higher mathematics.

Packing such diverse information into a small space inevitably makes the various sections of the introduction tantalizingly cursory (especially the interesting section suggesting connections between Flatland and Gulliver's Travels, Alice in Wonderland, and Huckleberry Finn), but Banchoff's biography of Abbott will no doubt develop these at greater length and thereby provide a useful companion to this new edition. In the meantime, readers who reject Banchoff's claim here that “the major reason for our interest in Flatland is that for the first time we can achieve some of the dreams of our ancestors a century ago and obtain direct visual experience of phenomena in a dimension higher than our own” (xxvi), may want to consult Banchoff's more balanced “From Flatland to Hypergraphics” (Interdisciplinary Science Reviews [1990]), Rosemary Jann's “Abbott's Flatland: Scientific Imagination and ‘Natural Christianity’” (Victorian Studies [1985]), and Elliot Gilbert's “Flatland and the Quest for the New” (ELT [1991]). Indeed, as the rest of Banchoff's introduction shows, Flatland has remained of interest for over a century precisely because of its ability to engage its readers on so many different planes in so many different dimensions.