Thomas Pynchon is the apostle of imperfection, so it is arguably some sort of commendation to say that his new novel, “Against the Day” (Penguin; $35), is a very imperfect book. Imperfect not in the sense of “Ambitious but flawed.” Imperfect in the sense of “What was he thinking?”

The book is set in the period between 1893 and around 1920, and this is the plot: An anarchist named Webb Traverse, who employs dynamite as a weapon against the mining and railroad interests out West, is killed by two gunmen, Deuce Kindred and Sloat Fresno, who were hired by the wicked arch-plutocrat Scarsdale Vibe. Traverse’s sons—Kit, a mathematician; Frank, an engineer; and Reef, a cardsharp and ladies’ man—set out to avenge their father’s murder. (Webb also has a daughter, Lake, but she takes up with one of the killers.) This story requires a thousand and eighty-five pages to get told, or roughly the number of pages it took for Napoleon to invade Russia and be driven back by General Kutuzov. Of course, there are a zillion other things going on in “Against the Day,” but the Traverse-family revenge drama is the only one that resembles a plot—that is, in Aristotle’s helpful definition, an action that has a beginning, a middle, and an end.

The rest of the novel is shapeless, just yards and yards of Pynchonian wallpaper: fantastic invention, arcane reference, virtuosic prose. Elaborately imagined characters and incidents, from a man who may or may not be transformed into a jelly doughnut to a city beneath the desert and a near-death experience in a mayonnaise factory, pop up and disappear after a few pages, so many raisins in the enormous loaf. The World’s Columbian Exposition of 1893; the mysterious collapse of the Campanile in the Piazza San Marco, in Venice, in 1902; the equally mysterious Tunguska Event, in 1908, in which roughly eight hundred square miles of Siberian forest was flattened, evidently by an exploding asteroid; the Mexican Revolution; and the troubles in the Balkans leading to the First World War all figure in the book’s pages. Longer-running characters include the eternally youthful crew of a sometimes invisible airship, Inconvenience, who style themselves the Chums of Chance; initiates of a British spiritualist society called T.W.I.T.; a private eye named Lew Basnight; a glamorous mathematician named Yashmeen Halfcourt; and an itinerant photographer called Merle Rideout, his daughter, Dahlia, and his ex-wife, Erlys, who has run off with a magician named Zombini. Scenes are set in (among other places) Colorado, New York, Venice, Paris, Croatia, Macedonia, Mexico, various points in Asia, and Hollywood. Characters are given names like Alonzo Meatman, Ruperta Chirpingdon-Groin, Professor Heino Vanderjuice, the Reverend Lube Carnal, and Wolfe Tone O’Rooney. Pig Bodine, a recurring avatar who appeared in Pynchon’s first novel, “V.” (1963), puts in his ritual appearance. There is a literate dog, a machine for time travel, a “subdesertine frigate” for voyaging beneath desert sand, and assorted mad inventors, shamans, clairvoyants, terrorists, drop-dead-gorgeous women, and drug abusers. The whole thing sloshes along, alternately farcical and magniloquent, with threads left dangling everywhere, sometimes for hundreds of pages, ultimately forever. The novel doesn’t conclude; it just, more or less arbitrarily, stops.

So what was Pynchon thinking? To begin with, he was apparently thinking what he usually thinks, which is that modern history is a war between utopianism and totalitarianism, counterculture and hegemony, anarchism and corporatism, nature and techne, Eros and the death drive, slaves and masters, entropy and order, and that the only reasonably good place to be in such a world, given that you cannot be outside of it, is between the extremes. “Those whose enduring object is power in this world are only too happy to use without remorse the others, whose aim is of course to transcend all questions of power. Each regards the other as a pack of deluded fools,” as one of the book’s innumerable walk-ons, a Professor Svegli of the University of Pisa, puts it. Authorial sympathy in Pynchon’s novels always lies on the “transcend all questions of power,” countercultural side of the struggle; that’s where the good guys—the oddballs, dropouts, and hapless dreamers—tend to gather. But his books also dramatize the perception that resistance to domination can develop into its own regime of domination. The tendency of extremes is to meet, and perfection in life is a false Grail, a foreclosure of possibility, a kind of death. Of binaries beware.

Pynchon has an interest in military and political history (also in sexual practices that are more fun to read about than one imagines they would be, for most of his audience, to engage in). His special interest, though, is science, about which he knows a great deal—whether what he knows is accurate or not doesn’t matter: he’s a novelist—and toward which he maintains the ambivalence implied by his over-all view of history. Science is either a method of disenchantment and control or it is a window onto possible worlds: it all depends on the application. In Pynchon’s last novel, “Mason & Dixon” (1997), in which the protagonists were eighteenth-century surveyors, the relevant science was astronomy. In “Against the Day,” it is mathematics, specifically, the mathematics associated with electromagnetism, mechanics, and optics—with electric light, the movies, and, eventually, weapons of mass destruction. In “Against the Day,” as in “Gravity’s Rainbow” (1973), there are hints, throughout the book, of apocalypse, end-of-the-species images of masses crowding toward their doom.

Thus readers will encounter many references to, and, frequently, extended disquisitions on, such matters as Hamilton’s Quaternions, Gibbsian vector analysis,Riemann spheres, Prandtl’s discovery of the boundary layer, the Hilbert Pólya Conjecture, the Minkowskian space-time track, and Zermelo’s Axiom of Choice. Inserting this stuff into novelistic situations produces passages like this one, describing a meeting of an outfit known as the Transnoctial Discussion Group (which never appears again in the book):

**{: .break one} ** “Time moves on but one axis,” advised Dr. Blope, “past to future—the only turnings possible being turns of a hundred and eighty degrees. In the Quaternions, a ninety-degree direction would correspond to an additional axis whose unit is √-1. A turn through any other angle would require for its unit a complex number.” “Yet mappings in which a linear axis becomes curvilinear—functions of a complex variable such as w=ez, where a straight line in the z-plane maps to a circle in the w-plane,” said Dr. Rao, “do suggest the possibility of linear time becoming circular, and so achieving eternal return as simply, or should I say complexly, as that.”. . . As if the hour itself in growing later had exposed some obscure fatality, the discussion moved to the subject of the luminiferous Æther, as to which exchanges of opinion—relying, like Quaternions, largely on faith—often failed to avoid a certain vehemence. “Bloody idiots!” screamed Dr. Blope, who belonged to that British school, arisen in the wake of the Michelson-Morley Experiment, of belief in some secret Agency in Nature which was conspiring to prevent all measurement of the Earth’s velocity through the Æther. If such velocity produced, as Fitzgerald maintained, a shrinkage of dimension in the same direction, it was impossible to measure it, because the measuring device would shrink as well. “It’s obvious Something doesn’t want us to know!” **