Stephen K. Bannon has read the book three times. He still keeps a copy of it — one that’s creased and copiously underlined — in a library with the rest of his favorites at his father’s house in Richmond, Va.

The book, “The Fourth Turning,” a 1997 work by two amateur historians, Neil Howe and William Strauss, lays out a theory that American history unfurls in predictable, 80-year cycles of prosperity and catastrophe. And it foresees catastrophe right around the corner.

The book delineates history into four seasonal cycles, or “turnings”: growth, maturation, decay and destruction. It is the kind of wild, provocative idea that Mr. Bannon loves. But it is also just the kind of thinking that his opponents see as evidence that he is too Machiavellian and idiosyncratic for the job of President Trump’s chief strategist.