Through the Mandelbrot Gate : THE GHOST FROM THE GRAND BANK <i> By Arthur C. Clarke (Bantam: $19.95; 274 pp.) </i>

Arthur C. Clarke has long been fascinated with two mysterious worlds: outer space and the Earth’s oceans. His voyages beyond the stars have been more celebrated, but in works like “The Deep Range,” “Dolphin Island” and “Cradle,” he has repeatedly ventured beneath the waves as well. In “The Ghost From the Grand Banks,” Clarke puts on his diving suit again, this time to describe two rival groups in the early 21st Century attempting to raise and refurbish the Titanic in time for the 2012 centennial of its disastrous collision.

There is yet another world that interests Clarke, the world of mathematics, and one of its recent discoveries, the Mandelbrot Set, also figures prominently in this novel. Simply put, the Set is a basic mathematical relationship that generates incredible complexity--a curve that becomes more and more fantastically convoluted the more closely it is examined. The characters in “Ghost” often discuss and observe various manifestations of the Set, and one family even constructs a lake in its shape.

(The cover illustration beautifully encapsulates all of the novel’s themes, showing the Mandelbrot Lake with the Titanic sinking in it. Readers who are uncomfortable with mathematics may wish to read the final “appendix” first, since its explanation of Mandelbrot’s mathematics is clearer and more thorough than in the novel itself.)

In a sense, the Mandelbrot Set provides a cautionary tale: Something which seems so easy in the beginning quickly grows so infinitely complicated that it could not be fully appreciated in a million lifetimes. Its existence powerfully suggests that there are indeed limits to humanity’s ability to comprehend and control the universe.

Of course, the Titanic itself is the symbol of another cautionary tale, as Clarke notes: “There is no need to revisit her to be reminded of the most important lesson the Titanic can teach--the dangers of overconfidence, of technological hubris.” And in other ways, this novel indicates Clarke’s new wariness of scientific progress and its powers. An earlier Clarke novel, “Imperial Earth” (1976), casually presents a restored Titanic in New York Harbor as one element in the celebration of America’s Quincentennial in 2276; here, the task of recovering the Titanic proves surprisingly challenging and frustrating, as if Clarke now recognizes that there can be pitfalls as well as payoffs in grandiose technological projects.

One passage in “Ghost” significantly reveals this changed attitude. For 15 years, in fiction and nonfiction, Clarke tirelessly and successfully championed the building of geosynchronous satellites to achieve a superior system of worldwide communication. However, in this novel, “the latest marvel of communications technology” is “the first fiber-optic cable to be laid under the Arctic ice cap,” and “by eliminating the long haul up to the geostationary orbit, and its slight but annoying time delay, the global phone system had been noticeably improved.” Perhaps, Clarke now indicates, the most advanced scientific method is not always the best; perhaps there are cases where returning to an old and familiar method actually is better.

This novel offers many of these striking passages and small revelations--tidbits of historical trivia, anecdotes about a diver’s life, wry references to “2001” and unobtrusive in-jokes for science-fiction fans. As is usually the case in Clarke’s works, “Ghost” is filled with remarkable moments.

Such a statement, of course, implies that there are larger flaws in the novel, and by conventional standards, this is undoubtedly the case. Clarke makes unusual demands on readers: His chapters are short and fragmentary, and they tend to jump from continent to continent, from character to character, from future to past, without explanation. Like an ocean, Clarke’s writing has shallow areas as well as unexpected depths. And without revealing any of Clarke’s surprises, one can say the novel has several threads that are left undeveloped, seemingly forgotten or abruptly cut off in an inartistic manner.

To the uncharitable, these lapses will merely demonstrate that Clarke is a clumsy writer; others, noting that such problems are less evident in his previous novels, may see Clarke attempting to produce a kind of Mandelbrot novel, where unfolding intricacies cannot be satisfactorily resolved and so must simply be abandoned. To be sure, “The Ghost from the Grand Banks” never will be taught in schools of creative writing as a model of the Well Made Novel; however, as Clarke’s satisfying conclusion also suggests, there may be a deeper logic in the novel’s apparent weaknesses.

Indeed, long after Clarke’s science and predictions are obsolete and outdated, future readers who are more attuned to the intricacies of the Mandelbrot Set may better appreciate the unique insights and narrative style of this fascinating and thought-provoking writer.