So how is it different in the book?
The differences between Arrival and Ted Chiang's "Story of Your Life" are largely the kinds of changes one expects to see when a short story gets adapted into a big-budget sci-fi film -- the military angle gets pumped up, the aliens' names change from Flapper and Raspberry to Abbott and Costello, and there's more conventionally suspenseful sequences -- but most of the important details are there, albeit often explained in more technical terms. (Words like "glotto-graphic," "logogram," "semasiographic," and "ideogram" boggle the mind.) Even some of the movie's odd moments that might feel like Hollywood conventions -- like the awkward "Do you want to make a baby?" -- are straight from the text.
Obviously, a short story and a movie are two totally different art forms with separate narrative (and commercial) demands. The way the story subtly conveys shifts in time comes from verb tenses -- sentences like "I remember once we'll be driving to the mall to buy some new clothes for you" make the brain reel -- but the visual vocabulary of cinema can often be hazier and more impressionistic. Arrival is elliptical, which allows Villeneuve to toy with audience expectations in compelling ways.
Through decades of watching movies, we've all internalized certain ideas about what a "flashback" or a "flash-forward" (or, in the case of Lost, a "flash-sideways") looks like, but clever filmmakers have long played with our sense of time, destabilizing viewers by using editing, music, and voice-over to tell non-linear stories. Think of Terrence Malick's Tree of Life, Shane Carruth's Upstream Color, Michel Gondry's Eternal Sunshine of the Spotless Mind, or Christopher Nolan's many po-faced puzzle films.
I currently spend a lot of my time thinking about HBO's Westworld, which appears to be building to a finale that will involve a similarly time-bending reveal, but, sitting in the theater watching Arrival, I admired the specifically cinematic elegance of Arrival 's big twist. It's perfectly scaled to its brisk two-hour run time. It's not a launch pad for a potential series -- it's a movie. A very good one.