As a math major, reading this book prior to class often came with the burden of disclaiming, "It's not about math." And that's a little disappointing, actually, because I don't read enough books about math, especially fiction books. And The Integral Trees would make a damn good title for a math novel.
But no, Larry Niven had to go and steal the title for his own nefarious purposes. It actually took me longer than it should have taken to realize why the integral trees were named as such—I admit I did not scrutinize the diagrams very closely. They're shaped like integral signs. That's … not very impressive.
Fortunately, most of the book's worldbuilding is impressive and pretty much what I expect from the person who wrote Ringworld. I'd go so far as to declare the worldbuilding in The Integral Trees superior to Ringworld's. Although Niven's concept of a ringworld is better-known and more portable than the Gas Torus and Smoke Ring of this novel, the latter environment results in far weirder inhabitants and habitations. Getting used to how one moves around in an environment consisting of constant freefall is a bit of a challenge. But this gives Niven the opportunity to construct wonderful scenes that would usually be more at home in a fantasy story rather than a work of science fiction.
Now, I'm not one who visualizes events, even the most mundane ones, so scenes like the flight of the CARM don't fill my mind with cinematic wonder. Nevertheless, there's still plenty about the unique environment of the Smoke Ring that intrigues me, such as the changes in physiology undergone by the descendants of the original Discipline crew-members. These are people, humans with the same foibles as the rest of us, yet they are biologically somewhat different. Not only are their bodies longer, slimmer, their feet almost as skillful at manipulating objects as their hands, but their society, having developed in a ring of translucent gas, has radically different conceptions of "ground" and "sky." Science and their history prior to arriving at the Smoke Ring is more mythological than archaeological; some tribes are lucky enough to have a Scientist who has access to tapes and readers with the data of the Discipline expedition.
Although the inhabitants of the Smoke Ring have largely forgotten Discipline, Discipline has not forgotten them. The ship is controlled by the recorded personality of Sharls Davis Kendy. Niven steps away from a true "artificial intelligence" by using recorded personalities; these, along with the concepts of "storage space" and "tapes" and "readers" make for a very analog vision of the future. As a recorded personality, however, Kendy is a very interesting character. Unlike an AI, who would presumably be extremely clever and patient, Kendy is a fallible being who makes a lot of mistakes (including letting the Discipline anywhere near the Smoke Ring, though he claims he has erased that part of the mutiny from his memory). Kendy is also our only connection to Niven's distant State, a somewhat totalitarian, surveillance-based system of distributed governance. As such, the duty to recover crew for the Discipline and continue its mission is vital.
This sense of urgency and necessity runs through all the plots of The Integral Trees. This is a survival story, actually multiple survival stories, set in a fantastic environment. The protagonists are refugees who survived the destruction of their tuft more from luck than any skill on their parts; as the only remaining members of the tribe, they have to start anew somewhere. But subsequent events make this very difficult. At first the refugees have to struggle to survive in the open air of the Smoke Ring, living on little more than some bark that splintered from their fractured, forlorn tree. Soon they have to deal with other inhabitants of the Smoke Ring, another tribe that has no compunctions about capturing slaves.
Many of the main characters experience a test of loyalty as they weigh the options for survival. Minya, once a member of the Dalton-Quinn Tuft and now married to one of the Quinn refugees, enters the story as an antagonist. With the destruction of the tree, she is stranded far from her tuft with the rest of the refugees, and out of pure practicality she marries one of the two available males. After becoming a slave, Minya learns she's pregnant, though she's not sure who the father is. Nevertheless, she strives to escape and reunite with her husband, whom she has known for only a few weeks.
Grad Jeffer, apprentice to the Scientist of the Quinn Tribe, finds himself apprenticed to the Scientist of the tribe that captures and enslaves the refugees. He is in that delicate position of collaborator: still a slave, but trusted and accorded with privileges beyond an ordinary slave's position; liked, essentially, by no one. Jeffer, as a Scientist, has the corrupted remnants of the Discipline crew's knowledge, as well as the tapes and reader to go with it. But this doesn't preclude his own crises of conscience, first when he is plotting and initiating a rebellion that results in the murder of a Scientist, and then later when he is conversing with Kendy aboard the CARM. Jeffer may not be the leader of Quinn Tribe, but he is an authority figure, and for much of the book he functions as a leader while the tribe tries to escape from the slaver tree.
And finally, we come back to Kendy, for whom the question of survival is twofold. Firstly, on a personal level, he wants to continue his mission. Babysitting the Smoke Ring civilization until it reaches a level that he can jumpstart and control must be boring. And as we learn early in the book, his memory capacity is severely limited, so he is constantly editing old memories to make room for new ones. How long can this go on before he is no longer himself? Or has that already happened? Secondly, Kendy needs to fulfil one of his missions: ensure the survival of the State. Although the Discipline's primary mission was to seed planets with the materials that would form complex life, every such ship is also a little pocket of the State, completely able to refound the State should it cease to exist elsewhere. The fact that the crew has so thoroughly mutinied and abandoned the values of the State must be incredibly galling for Kendy.
Or at least, that's the sense I get from his chapters. Reading The Integral Trees takes effort, and not just because of the odd setting. Niven teases us by offering very little exposition; almost everything about the Smoke Ring society is explained through action and a little dialogue. Once in a while, particularly during Kendy's chapters, we'll get longer infodumps, but they never go into the detail I'd like. We don't learn that much about the State, just enough to suggest a totalitarian government. The result is a very tight book focused only on telling a story about these characters and not concerning itself with other, secondary characters. Indeed, I can count on one hand the characters who feel real or three-dimensional to me, and even that might be a stretch.
This is the same problem I experienced in reading Ringworld. Niven is a very clever, creative writer with a fertile imagination. His characters, however, are flat, almost set pieces at times. And sometimes the interactions between them just don't feel real at all. Minya and Gavving's marriage really irked me at first; they've known each other for a day, and she proposes to him. I suppose this is justifiable by pointing out that this society has evolved for five hundred years, and so customs are bound to be different from our own. But it's not just the stark pragmatism at work here—that's a quality I really do see as emerging from the evolution of a society in free-fall. It's a question of loyalties, of dependencies and relationships. Some of the other characters also have a quick change of heart, convenient for Niven and the plot but problematic from the reader's perspective. Consequences for being an antagonist are almost invariably a slap on the wrist and, if you're lucky, marriage! By the time the refugees escape, with some now-converted antagonists and some allies in tow, it seems like there are lots of loose ends that Niven simply decides to truncate rather than resolve. This mutability in the dynamics between characters makes it very difficult to become invested in one character or another's survival, and that sort of pathos is essential to a good survival story. And since The Integral Trees is a survival story….
There are some brilliant things about this book, not the least of which is its superiority to Ringworld when it comes to worldbuilding. I thought that part of the back cover summary was an editor's hyperbole; it's not. Alas, that's not enough, not even for Niven. The story is basic, well-structured, but short when it comes to an emotional connection. It's stunted. Ringworld suffers from similar shortcomings, but it's still superior in that respect. Fortunately, they are both on the shorter side for science fiction, so you can easily make that decision for yourself.