I’ve never before tried to figure out a creature’s life history based on their language. This is because there is no other species on Earth with which scientists could do this. Scientists have methods to infer the anatomy or lifestyle of organisms that are difficult to study because they are rare and difficult to find, like deep-sea fish or small nocturnal rodents that live in complex tropical rainforests on uninhabited islands, or because they are difficult to contain for observation, like whales. Given only a blurry video or photograph of a new species, scientists will classify its morphology, relate it to similar animals, and logic out the functions of its structures. Of course, there would never be an opportunity to use this approach with a species that has developed language and technology comparable to our own unless we encounter an alien species—which the narrator of Ted Chiang’s “Story of Your Life” does. Like scientists with only visual evidence that an organism exists, the people in Chiang’s story cannot physically interact with the aliens they would like to study.
If I were to guess at the life history of the Heptapods, I would start with their physical anatomy. They have barrel-shaped torsos supported by seven identical limbs, which, judging from the narrator’s description of their rippling movement, probably evolved from tentacles used for swimming by an aquatic ancestor. Heptapods are radially symmetric and therefore their movement is multidirectional, rather than unidirectional as is in the case of bilaterally symmetric humans (and every other land animal on Earth). This is an important part of the story, since this fact is used by the narrator to figure out that Heptapod writing is also multidirectional; it doesn’t matter what direction you turn their characters because they mean the same thing at any angle. In contrast, English letters lose meaning when they are twisted or attached to each other in odd ways.
It so happens that the vast majority of radially symmetry animals on Earth are aquatic (think sea anemones or jellyfish—which are both considered sessile during at least one stage of their life cycle), further supporting the theory that Heptapods evolved from an aquatic ancestor. One might think of Heptapods as a hypothesis of what intelligent life would look like if radially symmetry never evolved. Bilaterally symmetric animals outcompeted radially symmetric animals because they are better suited to purposeful movement (which is useful if you are a heterotroph and need to move around in order to find food). If bilaterally symmetry never arose, jellyfish-like creatures might have eventually evolved into terrestrial organisms, become social, and developed the concept of language as we know it. They might even have been more successful with higher thinking because they have a complete view of their environment (have eyes surrounding their entire head part), rather than the limited view that we have (having only two eyes on the front of our face).
If the Heptapods really do have their origins in the ocean, then that might explain their system of mathematics that has Gary the scientist so excited. The first human concept of physics that the Heptapods recognize is Fermat’s Principle of Least Time, which explains light refraction when it travels from air to water. If the Heptapods remained close to water as they evolved terrestrially (perhaps continuing to hunt aquatic prey or find mates there) then light refraction would be a very important concept to them. It would make sense that they would start their study of physics there. Motion and gravity were the first concepts explored by humans. Humans needed to know how to best manipulate projectiles in order to hunt wild animals, which involves all the basic principles of two dimensional motion that physicists like Newton were interested in. Instead of time and velocity as basic units, the Heptapods may have started out with units of fluidity or light refraction as well as the “action” that is mentioned in the story.
Similarly, their basic units of mathematics might be influenced by alternative senses. The narrator ponders “what kind of perception made a minimum or maximum readily apparent to them?” Do the Heptapods really perceive the world with senses that humans do not have and have never imagined? If so, this implies that they have sensory organs and receptors that do not exist on Earth! How cool would it be to find out how they work? And if we discovered how a new sense worked we could probably design a tool to measure whatever it detects for ourselves! That is probably the only way we could implement any sort of Heptapod mathematics to solve real-world problems. Hooray for biology!