n a short foreword, author Stewart, a noted mathematician and science popularizer (and as of last year's publication of the novel Wheelers with co-author Jack Cohen, a science-fiction writer as well), tells of his long fascination with Edwin Abbott's Victorian classic Flatland (1884) and his own inspiration to write a sequel. In this impulse, Stewart joins such predecessors as Dionys Burger with Sphereland (1965) and A.K. Dewdney with The Planiverse (1984). After this brief orientation, the narrative begins.
In Flatland, 100 years have passed since A. Square's 3-D visitor, the Sphere, appeared. Square's bright, curious granddaughter, Victoria "Vikki" Line, encounters a copy of her grandfather's manuscript for the first time and sees fit to invoke a return visit from the Sphere. But, instead, her summons is answered by an even weirder creature, the Space Hopper, a horned, grinning, irreverent version of the Sphere. Almost before she knows what's happening, Vikki is raised up above her normal plane of existence and taken on a guided tour of the Mathiverse. (Occasional shifts in viewpoint back to the lamenting family in Flatland set the stage for Vikki's eventual emotional reunion with her parents and brothers at the finish of the narrative.)
Vikki's adventures occur in a generally ascendant order of complexity. She starts out by learning about our familiar spacetime, and some of the mathematical quirks associated with 3-D objects. But then she's off to a number of new dimensions: a fractal universe, a land called Topologica, the Projective Plain, Platterland, Cat Country and the Domain of the Hawk King. Each of these realms has its eccentric inhabitants who interact with Vikki and the Space Hopper in both obstructive and helpful ways. Concluding with a descent into quantum realms, Vikki emerges as a changed young line, and re-enters her own thin universe ready to spread the gospel of higher dimensions.
Lewis Carroll would be proud
Don't pick up this book expecting Rudy Rucker's The Sex Sphere (1984). Like the illustrious Martin Gardner, Stewart is not a novelist who knows and uses mathematics as subtext; he's a mathematician who knows and uses fiction as a vehicle. Therein lie both his powers and his deficiencies.
The primary rationale for the existence of Flatterland is the introduction and elucidation of complicated ideas and theories and history. This is the charge frequently leveled against science fiction in general, and a book like this shows how hollow such a charge usually is. For the most part, science fiction really only cares about cool adventures, weird aliens, bizarre landscapes, college-sophomore-level philosophizing, sense of wonder and wish fulfillment, and that's the glorious way it should be. If SF writers really were obsessive academic experts, all SF would end up sounding like Stewart's sometimes dry but overall engaging book.
Although he devotes some wordage to building up the personalities of Vikki Line and the Space Hopper, and detailing the social problems of Flatland, Stewart is really only concerned with concretizing the most counterintuitive aspects of modern mathematics and physics. And at this he does a fine job, coming up with angles and examples new to the pop-math canon. Particularly in the lands of Topologica and Platterland, the stuff of equations and theorems comes alive. (Platterland, a hyperbolic universe, will remind readers of Christopher Priest's The Inverted World [1974].) And when Vikki and the Space Hopper enter a paradox-filled sequence of time-travel in Chapter 14, Stewart produces a mini-adventure to rival Robert Heinlein's "All You Zombies."
Spiritual ancestors invoked by Stewart are Lewis Carroll and L. Frank Baum, and readers will enjoy encountering allusions to Oz and Wonderland. Stewart's propensity for puns and sometimes too-fey verbal constructions (our world is consistently referred to as "Planiturth") might jar. But on the whole, using large amounts of well-constructed dialogue and some useful diagrams, Stewart manages to hold our interest through what could have been merely an exercise in pedantry.
