Patricia Wall / The New York TimesThe cover of "The Rise and Fall of Great Powers," written by Tom Rachman and published by Dial Press. Rachman zigzags from 1988 to 1999-2000 to 2011 as he tells the story of a woman who bears witness to decades of rapid cultural, political and technological changes.

“The Rise & Fall of Great Powers”by Tom Rachman (The Dial Press, 384 pgs., $27)

Tom Rachman’s ingenious second novel, “The Rise and Fall of Great Powers,” is harder to describe than “The Imperfectionists,” his sensational first. So here is some sample dialogue, by way of introduction. Humphrey, an older man with a heavy Russian accent, is explaining Russian history to Tooly, an eager 10-year-old girl who will grow up to become the book’s tough, quick-witted main character and the most important person in Humphrey’s life.

“There is long tradition,” Humphrey begins. “First, we must have bald leader. After, hairy leader. Bald, then hairy. Czar Alexander II, he is bald. Then, Nicholas II. He got hair. Next comes Lvov. Bald like cucumber. Then Kerensky. Lots of hair. Lenin is very bald. Who must come next? Stalin.”

“He was hairy?” the girl asks.

“This is reason he wins leadership battle. Trotsky also has fool head of hair, so it is close race. But Stalin has more. Also, he is more idiot. So he wins. After hairy Stalin, they need bald. They look around Politburo and see Khrushchev — perfect! Then Brezhnev, also fool head of hair. Then Andropov: Bald. Chernenko: hair. Gorbachev: bald.”

“With the stain on his head?”

“Yes, but you don’t make fun of. It’s not nice.”

That conversation is held in 1988. Rachman zigzags from that year to 1999-2000 to 2011, as he tells the story of a woman who bears witness to decades of rapid cultural, political and technological changes. She is also someone who, by all rights, should not be able to get out of bed in the morning. Her own story is one of having no real home, being abandoned by parents and being passed from one companion to another. By having Tooly call all the adults in the book by their first names — since she is a conversational match for any of them — Rachman succeeds in keeping readers almost as baffled about her origins as she is.

Besides, this novel is more ambitious than a mere family story. As in “The Imperfectionists,” Rachman needs only a few well-drawn characters to fill a large canvas and an impressive swath of history. That book was about the life of a newspaper (with a strong resemblance to what was then called The International Herald Tribune) but also about a changing world. This one reaches from the eras of Humphrey’s “friends” — all authors, including John Stuart Mill and Sir Isaac Newton (“we are like two peas in a pond”) — to the age in which kids sit at the dinner table, watching videos, not having to know anything they can’t Google.

The richness of this book is more apparent once the reading is over. In other words, “The Rise and Fall of Great Powers” is knottier than “The Imperfectionists,” and more deliberately confusing. Tooly has no home, and she moves through the world with different traveling companions.

First there is Paul, who takes her to Thailand from Australia and enrolls her in an odious international school. She has a fourth-grade teacher, Mr. Priddles, who heartily dislikes her and makes pronouncements like, “To say that someone called W.B. Yeats is ‘better’ than someone called Sting is a construct, basically.” Luckily, Tooly is smart enough to educate herself.

In 1999, she has just moved to New York with Humphrey, who has taken on the role of parent or companion to her. But at 21, Tooly is old enough to fend for herself. She is in the thrall of a smooth operator whose name, Venn, can’t be coincidental; a set of Venn diagrams of how the book’s characters overlap would reveal many secrets about its story. Venn protects Tooly, notably at the downtown haven for nerd geniuses he seems to be running; the place has a school bus as a fun bit of décor and has spawned many terrible startup ideas and one that could be worth a fortune.

Venn also teaches Tooly to check out college students’ apartments by ringing doorbells, pretending each apartment was the one in which she grew up and then casing the place. This gives the book a set of glib students who get their opinions from cable news and whose superficial political debates give Rachman much to skewer. For all its serious points, this book is never too busy for hilarity. When someone insists on playing Prince’s “1999” in that very year, one kid says: “If you party like it’s 1999, we all leave, and you log on to a chat room with people from Finland.”

The Tooly of 2011 has settled down enough to own a small, failing but lovingly maintained bookstore on the Welsh side of the Welsh-English border. The place is lucky to sell a used copy of “Land Snails of Britain,” as it does on the book’s opening page. And it has only one employee, who declaims at Tooly when she’s trying to read and revels “in pronouncing on grand issues, like the man of consequence he most certainly was not.” She is a true bibliophile, a free spirit and a content Luddite when it comes to the computer age, and she seems to accept rootlessness as her natural state.

But during the later parts of the novel, when it touches back down in 2011 and shows Tooly the true nature of all the adults she has known, there are scenes of breathtaking cruelty. Rachman doesn’t milk them. He doesn’t have to. This would be a much less potent book if it collapsed into a sob story.

And Rachman means to balance the individual characters in this story with the ways the world changes them. As Humphrey, who instills Tooly with a sense of world history, puts it: “I know what the 20th century has for breakfast. It is too much work getting to know new century.”

For a character who is more cynical, we now live a cyberhell that not even science fiction could have anticipated. “You can’t blame yourself for having been swallowed by your times,” this person tells Tooly. “They eat nearly everyone.”