The first person-narrator and protagonist, Louise Banks, begins the story in the present. She addresses her future daughter and describes to her the present moment as the most important moment in her and her daughter’s lives. It is the moment her husband asks her if she wants to make a baby with him. The couple have been married for two years and live on Ellis Avenue, in a house that they will move from when their daughter is two years old. Louise and her husband are slow-dancing on the patio when he asks her this life-changing question. Louise then relates an incident thirteen years in the future, when her daughter accuses her of having a baby just so she can be made to do chores. This future incident occurs in a different house, on Belmont Street. Louise notes that they will sell the Ellis Avenue house two years after their daughter’s “arrival” and sell the Belmont Street house shortly after their daughter’s “departure.” By the time the Belmont house is sold, Louise and her husband will be divorced and the two will have begun new relationships with different people.

Using the moment that she decides to have a baby as a reference point, Louise recounts the event that led to it. It is a few years prior and alien ships have appeared in orbit around earth. At the same time, strange objects have appeared in meadows all over the world, including nine in the United States, where Louise lives. Shortly after this, Louise receives a call from the military. They want to consult Louise, a linguist, about the aliens. Louise agrees and when she arrives, she is introduced to Colonel Weber and Dr. Gary Donnelly, a physicist. Colonel Weber asks Louise to listen to a recording. Louise assumes correctly that it has something to do with the aliens, but Weber refuses to give any information other than to show her the recording. After listening to it, Louise asks for more information on the aliens’ anatomy and behavior, in order to contextualize the sounds she is hearing. Weber is reluctant to answer, still not wanting to reveal anything to Louise. Louise then patiently explains that the only way to learn the alien language is to interact directly with the aliens themselves. Colonel Weber says he’ll get back to her about it.

Back in the present, and again addressing her future daughter, Louise notes that the phone call from the military to meet was probably the second most impactful phone call of her life. The first is the phone call she will receive from Mountain Rescue to come and identify her daughter’s dead body in the morgue. Her daughter will be twenty-five then. Louise and her husband will have been divorced many years by that time, and together they will drive to the morgue and affirmatively identify the body on the table as their daughter’s.

Sometime after her initial meeting with the military, Louise is invited to come interact with the aliens in person. She arrives at a military encampment that has been built around one of the alien objects, or “looking glass.” The looking glasses are two-way communication devices between humans and alien. Each of the looking glasses in each place on earth are assigned a linguist, like Louise Banks, and a physicist, like Gary Donnelly. The sites are all equipped with cameras so the government can monitor the scientists’ progress. Louise and Gary are asked to send daily reports, including how much English the aliens appear to understand.

Louise enters the large tent that has been erected over the looking glass. The looking glass is over ten feet high and twenty feet across. As Louise and Gary approach the looking glass, it becomes transparent, revealing a room with some furniture and a door in the back wall, but no aliens yet. Louise and Gary set up their equipment as they wait for the aliens to arrive. When they do, there are two of them, and Louise is fascinated by their appearance. The aliens, which Gary calls “heptapods,” have seven lidless eyes that ring all the way around the top of their bodies and seems to glide smoothly along the ground above rippling limbs.

Louise begins the process of learning to communicate with the heptapods. By noting the aliens’ gestures and recording their speech patterns, Louise is able to begin decoding the aliens’ spoken language. She takes notes on her computer about the sounds and gestures the heptapods make, and labels this mode of verbal communication “Heptapod A.” This will help distinguish between other languages or modes of communication the heptapods might also use. Louise then attempts to reproduce the heptapods’ speech with her own voice but is unsuccessful. The team will have to rely on recordings of the heptapods voices to communicate verbally with them. Louise tells Gary the process will take a while and require patience.

Back in the present, Louise addresses her future daughter again and relates a story about the word “kangaroo.” The story goes that when Europeans first landed in Australia, they asked an indigenous person what the animal with a pouch was called. “Kanguru” was the response. Only later did the Europeans learn that “Kanguru” meant “What did you say?” Louise notes that the story is probably not true, but that it illustrates an important point about language, and she uses it in her classes she teaches. Louise also relates a story to her future daughter about something that will happen when her daughter is five years old. The daughter hears “maid of honor” as “made of honor” and Louise will go on to use that as an example of child language acquisition in her linguistics courses.

Gary and Louise meet with Colonel Weber to brief him on the first day’s session. Louise asks Colonel Weber to approve the use of a digital camera and video screen so that they can try and communicate with the heptapods in writing. Louise hopes this will speed up progress. Colonel Weber reluctantly approves the request.

Louise relates another story involving language and her daughter. When her daughter is sixteen, Louise will be waiting for a date to arrive. She asks her daughter not to make any comments about him, lest her daughter embarrass her. Her daughter promises to make any comments in code to her friend Roxy who is also there. After Louise’s date arrives and they are ready to leave the house, Roxy asks Louise’s daughter what the weather will be like tonight. Louise’s daughter responds, “I think it’s going to be really hot.” The comment goes over Louise’s date’s head, but Louise and Roxy know exactly what the comment means.

At the next looking glass session, Louise elicits writing from the heptapods. Their writing is logographic, as opposed to alphabetic, which means it will be more difficult for Louise to decode it. Louise learns the heptapods’ written “words” for various heptapod body parts. Louise and Gary cannot pronounce the heptapods’ names, so they call them Flapper and Raspberry. The following day, Gary acts out some basic physical movements in front of the heptapods, such as running and jumping, while Louise displays the English word for each movement. The heptapods catch on to what Louise is trying to do and do the same thing for the humans. Raspberry mimics Gary’s movements and Flapper displays the heptapods’ written word for each movement. 

Louise begins to perceive the way the heptapods’ written language works. Instead of displaying multiple characters or “words” as their sentences become more complex, the heptapods display a single pattern containing different variations, such as extra strokes or flourishes. In other words, rather than adding words in a certain order to create sentences, the heptapods’ written language layers each concept within an expression on top of one another. Louise realizes that the order of the “words” doesn’t matter. A heptapod sentence is presented as one symbol and the way each constituent stroke in any given symbol is oriented provides the context for understanding the nuance of each expression. Gary hypothesizes that this way of expressing all ideas simultaneously, rather than linearly as in human languages, is a result of the radial symmetry of the heptapods’ physiology. If their bodies have no “forward” or “backward” then perhaps their language doesn’t either.

In the following days and sessions, Louise and Gary focus on learning the basics of the heptapod language. They want to ask deeper questions, such as “Why are you here?”, but need a better understanding of the language to get there. The heptapods continue to be cooperative and patient with them. The difficulty in learning the heptapod written language is that it appears to be nonlinear. This is a kind of writing that no culture in humankind has ever produced.

Louise relates another “memory” about her daughter, from the future. Louise and her daughter, now sixteen, are having breakfast together. Louise’s daughter is complaining of her hangover from a party the previous night. The conversation reminds Louise of the fact that her daughter is not a clone of herself. She is her own person, totally unique, and Louise could not have made her on her own.

Back at the looking glass site, Louise arrives one morning and announces a breakthrough realization: the heptapod written language is semasiographic. Rather than conveying speech sounds and patterns in their writing, a hallmark of all human writing systems, the heptapod writing conveys meaning without reference to speech. Louise uses the example of a circle bisected by a diagonal line, which humans all over recognize as meaning “not allowed.” It conveys meaning, but without referencing spoken language. The heptapods’ symbols are similar, but far more complex. Instead of characters (e.g., letters and word parts) representing a series of speech sounds and patterns, heptapod writing has a visual syntax. The way the strokes in a given symbol are arranged visually provide the context for understanding how all the parts of the symbol fit together and thus its meaning. Because heptapod written language has no relationship to heptapod speech patterns, Louise dubs their spoken language Heptapod A and their written language Heptapod B. One implication of this is that the scientists will need to learn Heptapod A and Heptapod B separately. It will require time and patience before Gary can ask the heptapods about their mathematics and physics.

Louise relates another anecdote about her future daughter, which also relates to patience. Her daughter will be six and she and Louise will be preparing to travel to Hawaii with her father. The trip is in a week, but Louise’s daughter is impatient. She wants to be in Hawaii already. Louise tells her the anticipation will make the experience better.

Louise also reflects on another “memory” of the future, when her daughter will graduate from high school. Louise marvels that this beautiful woman is the same little girl she will raise. There is so much about her daughter that Louise will never understand, like her fascination and aptitude with money and finances. But Louise knows her daughter will always do what makes her happy, and this gives Louise great satisfaction. 

As the sessions with the heptapods progress, the scientists begin learning the heptapods’ concepts of mathematics and science. Some modes, like arithmetic, are successfully communicated between the two species, but others, like algebra and geometry, are not. Physics also proves to be a challenge. The weeks drag on and the scientists become disillusioned. Louise and the other linguists, on the other hand, continue making progress in learning, understanding, and using both Heptapod A and Heptapod B. Louise begins to grasp the visual grammar of Heptapod B. When the linguists ask the heptapods why they have come, the heptapods consistently answer that they are here to observe. Indeed, they often don’t answer questions and simply watch the humans on the other side of the glass.

Louise recollects a time in the future when her daughter will be thirteen and they’ll be at the mall together. Her daughter wants money to shop with but doesn’t want to be seen with her mother by her friends. Louise refuses to pretend she isn’t there and her daughter becomes exasperated with her. Louise marvels at how quickly her daughter moves through different phases of her life, always seemingly one step ahead of her.

Louise continues to make progress with heptapod writing. She continues to improve in writing it herself and begins to “think” in the semagrams of Heptapod B. Meanwhile, Gary and the other physicists have finally found common ground between themselves and the heptapods. The breakthrough comes when the heptapods appear to understand what humans call Fermat’s Principle of Least Time. This principle dictates that light always follows the most extreme path to its destination, either the longest path possible or the shortest path possible. Fermat’s Principle applies to many areas of study, but the mathematics that underlie and describe the principle is the same no matter the area of study. Therefore, Gary hopes that the heptapods can show him their underlying mathematics, because this could provide the two species with a common language to talk about and share all scientific principles.

Louise thinks about the asymmetric relationship she will have with her future daughter. Every time her daughter runs into something or scrapes her knee, Louise will feel the pain as if it were her own. Yet she has no control over this apparent physical extension of herself in the form of a daughter. Similarly, when her daughter laughs, Louise will feel like the laughter is inside of her. Louise then laments her daughter’s disregard for self-preservation.

Progress with the heptapods accelerates after the Ferment’s Principal breakthrough. Gary discovers that concepts that are exceedingly complex for humans seem elementary to the heptapods. Conversely, the heptapods use “highly weird” math, in Gary’s parlance to describe concepts that are simple to humans. It seems that heptapod mathematics and human mathematics are the reverse of one another. But importantly, both heptapods and humans use a system of mathematics to describe the same universe. Louise wonders what the heptapods’ perception is like that would lead to such a difference in the two species.

Louise recalls a time, sixteen or so years in the future, when her teenage daughter will come home from her father’s, exasperated. At fifteen, she is becoming a beautiful young woman, with black hair and blue eyes like her father. She complains that her father has interrogated her over her new boyfriend. Louise explains patiently that that’s just how fathers are.

One of the scientists, Cisneros, poses a question at another looking glass sites. He has noticed that when asked the same question a second time, the heptapods often verbally answer using the same words they used the first time, but in a different order. Does Heptapod B operate the same way, in which the order the strokes are made doesn’t matter? Louise decides to test the question. Rather than having the heptapods write their answer and then display it, Louise asks Flapper if she can watch as they write their symbol, in real time. Flapper agrees and the result reveals that the heptapods know how the entire sentence will lay out before writing the first stroke. The heptapods do not write as we do, one element at a time, one following the other. Rather, everything happens at once, with each semagram totally dependent on the rest of the “sentence.” Louise notes that no human could do this as quickly and fluidly as the heptapods do.

Louise remembers a joke. The punchline is that there’s no need to worry whether or not your kids will blame you for everything that’s wrong with their lives, because of course they will. It’s inevitable.

Gary and Louise are having dinner at a Chinese restaurant. Louise asks Gary how he’s progressing with Heptapod B and Gary confesses he’s given up because he’s no good at languages. Louise has likewise given up on trying to learn the mathematics. Louise is intrigued by Fermat’s Principle, however, and asks Gary to elaborate on it. Gary explains the principle in more detail to Louise. What strikes Louise about Fermat’s Principle is that it seems to suggest that light has to “know” where it is going to end up before it begins traveling there, in order to always take the most extreme route. This reminds Louise of Heptapod B. It is an entirely different kind of thinking from human thinking, which proceeds linearly.

Louise remembers a future moment where her fourteen-year-old daughter asks for help with her homework. Her daughter needs help remembering the phrase that means both sides can win.  Louise suggests “win-win situation” but her daughter says there’s another term, a math term. Louise tells her daughter to call her father, the mathematician, but she doesn’t want to.

Louise continues to practice Heptapod B and the process has a profound effect on her way of thinking. She begins to be able to do it without planning every stroke of a semagram ahead of time, just as the heptapods are able to do. She begins to think in Heptapod B, “seeing” ideas form in her mind’s eye as semagrams, rather than “hearing” them in English. Louise begins to think multi-directionally about her ideas, recognizing when premises and conclusions are interchangeable.

A State Department representative comes to the looking glass site and presses the scientists about the question of why the heptapods have come to Earth. The official stresses that while the U.S. government wants to understand why they are here, it does not have to be an adversarial relationship. Gary describes this as “non-zero-sum game” and a remarkable thing happens to Louise. She “remembers” the incident with her daughter, fourteen years in the future, when her daughter can’t remember the phrase. Louise seems to be drifting through time nonlinearly or experiencing time in a nonlinear fashion. 

Louise recalls a moment in the future when her daughter is three years old. Her daughter asks her why she has to go to bed, and Louise says, “Because I’m the mom and I said so.” Louise laments that she will turn into her mother. Despite all her promises to herself that this would never happen, it is inevitable.

Louise begins to wonder if it really was possible to know the future, simply by changing the way one perceives the world. She does a thought experiment in which she imagines a Book of Ages that contains everything that ever happened or will happen. Louise imagines someone turning to the page that says what will happen to them tomorrow and reading that they will win a lot of money on a racehorse. But if the person has free will, then they can choose whether or not to actually go place the bet. Thus, the existence of a Book of Ages and free will simultaneously is a contradiction. Or is it? Louise ponders this. She proposes the possibility to herself that knowing the future might create a sense of urgency and an obligation to do the things that bring about that very future.

Gary invites Louise to his place for dinner and they stop at a store on the way to pick up a few things. Louise sees a salad bowl at the store. This triggers a “memory” of the future when her three-year-old daughter will pull that exact salad bowl off of the table and onto her head, requiring a trip to the hospital for stitches. Louise decides to buy the salad bowl. Her knowledge of the future makes this action feel like the right thing to do.

Louise considers the sentence “The rabbit is ready to eat.” The sentence can mean two very different things, depending on the context. Similarly, a ray of light’s path to its destination can be viewed in two equally valid ways. Humans would say the ray of light travelled along a straight line until it hit the water which refracts its path in a different direction. Heptapods would say the light “knew” its destination before moving and took the fastest route. Both are equally valid ways of describing the behavior of light. Louise concludes that humans developed a linear way of perceiving the world, whereas heptapods perceive everything simultaneously.  

Louise has a recurring dream about her daughter’s death. When she wakes up from one of these dreams, she is in Gary’s bed with him. Her daughter has not even been conceived yet.

Louise remembers the future when her daughter is three and climbing a flight of stairs. Louise reflects that her daughter’s love of climbing began at this early age and carried all the way through her truncated life.

Louise begins to grasp the advantages of Heptapod B. It allows for more flexibility of thought. The linear grammar of English is too constraining for a species with a simultaneous mode of consciousness, like the heptapods. This realization also helps illuminate the usefulness of Heptapod A’s seemingly random grammar.

Louise remembers her future daughter’s infancy. She reflects on how her daughter will perceive the world at this time in her life. It is not a linear perception of cause-and-effect relationships. There is no future and there is no past. An infant lives its life in the present tense only. Now is all that matters. Louise envies this worldview.

Louise contemplates the heptapods’ mode of consciousness and free will. It seems that if heptapods know the future and always act in a way that will lead to that future, then they do not have free will. But Louise explains that “free will” or “coercion” don’t mean anything to a being like the heptapod, which has a simultaneous consciousness. Louise understands this because of her newfound perspective and ability to know the future. Now that she knows the future, she would never act contrary to that future. Louise also realizes that for heptapods, all language is performative. As in the English phrase “I promise,” saying equals doing. Heptapods know how every conversation will go, but if they don’t perform the conversation, their knowledge of it wouldn’t be true.

Louise remembers reading a story to her future daughter. Her daughter has heard the story dozens of times and knows how it will go. But she wants to hear it performed again anyway.

Louise explains how her memory works now that she can think in Heptapod B. She sees the approximately five decades between learning Heptapod B and her death in blocks of time each encompassing years. They did not fall into place in any particular order. But Heptapod B has only affected her memory. Her consciousness still moves along linearly, from moment to moment. When Heptapod B reigns in her mind, Louise has glimpses of the totality of the rest of her life. These glimpses are her new “memory.”

The scientists at the looking glass attempt a sort of gift-giving ritual with the heptapods. The humans are offering a presentation of the Lascaux cave paintings. Louise speaks with another scientist, Burghart, who has also become proficient in Heptapod B. Both know the future, know that the other also knows, and neither says anything about it. They simply go about performing the actions they know will manifest the future they can already see. At one point in the session, the heptapods announce that they are leaving, all of them. And they do. The looking glass goes blank. It is the last humans will ever see of the heptapods.

Louise remembers when her daughter will be a day old. As Louise holds her, her daughter makes a movement that Louise recognizes as one her daughter made, or will make, inside of her womb.

The heptapods never return. Louise wishes she could fully experience the heptapods’ worldview. Perhaps then she could know exactly way the heptapods visited earth. Nonetheless, Louise reflects on how profoundly her meeting the heptapods changed her life. It set in motion the events that result in the birth of her daughter and Gary’s daughter. It allows her, in this present moment on the patio in the moonlight with Gary, to “know” her daughter, nine months or so before she has even been born. Louise wonders whether her current actions are leading her to the most extreme pain or the most extreme joy, in a variation on Fermat’s Principle. Regardless of the answer to this question, Louise answers Gary’s proposition to make a baby in the affirmative. The two retire to the bedroom to make love and to create their future daughter.

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