David Adger on Arrival in Inference:
IN THE ORIGINAL short story, ideas from physics and mathematics are crucial to the plot. Among them is Fermat’s principle of least time. This states that light traveling between two points traverses the shortest possible path. The refraction of light can be understood in terms of this principle. Upon coming into contact with water, a beam of light changes direction because the index of refraction of water is different from that of air. Because light travels more slowly through water than air, the amount of time light spends travelling through water is minimized. The overall length of the path is also minimized. Understanding the behavior of a beam of light at the interface between air and water seems to require knowledge of both its starting and end points—a notion that is counterintuitive.
Fermat’s principle describes behavior in the physical world in terms of how the system works globally. The difference between the immediate agent of change and some final result that the system aims to achieve has been the subject of study for centuries, going back as far as the time of Aristotle and the distinction he made between effective (efficient) cause and final cause. In 1744, Leonhard Euler wrote that “there is absolutely no doubt that every effect in the universe can be explained as satisfactorily from final causes … as it can from the effective causes.”
In the original short story, not just light, but the whole universe is depicted as being susceptible to explanation from two distinct standpoints. Human language and physics are shaped by an inclination to see the world in terms of cause and effect. It is for this reason that Fermat’s principle seems unintuitive. The aliens in Arrival understand the universe as involving final, not efficient, causes. Humans think of refraction as being caused by the differing densities of air and water—in effect, a succession of causal chains. The aliens would see it as a point of equilibrium of the system, and the system as an atemporal whole.
Chiang’s short story interweaves ideas from both linguistics and physics, but the latter are largely absent from the film. Fermat’s principle featured in early versions of the script, but did not make the final cut. This is a shame because the notion that the world can be perceived and understood from two distinct perspectives, local and causal versus global and atemporal, helps to explain the effects that learning the alien language has on Banks. In the original story, the physics and linguistics reinforce one another. In the film, more has to be taken on trust.