What sort of mathematics would Vonnegut's Tralfamadorean's like to do? Or,
alternatively, what sort of worldview would a sentient species have if their idea of simple mathematics was the calculus of variations? Those are the mathematical questions addressed by this clever story. Of course, much more goes on here than just that. We meet an interesting character who is a linguist hired by the government to help us communicate with a new alien species. In addition to learning about her progress in
this difficult task, we see how she is courted by, marries, and eventually divorces her partner in the project who is a
physicist. In fact, the "your life" of the title is the life of the
daughter from that marriage.
At first, the physicists and linguists are both having trouble
communicating with the aliens. The linguists are bothered by their
nonlinear writing system which seems to require thinking of the sentence as
a whole rather than as a string of words stretched out in time. The
physicists start making headway when they try to talk to the aliens about
the refraction of light. Somehow the aliens make it clear that they think
about this phenomenon along the lines of Fermat's principle: that light
takes the path from point A to point B which will get it there in the least
time. Of course, this statement requires that you imagine the light
knowing where it will be going before it gets there (sort of like the
problem with the sentences, eh?)
In fact, Fermat's principle is just an example of the application of
variational mathematics to physics. If you've had some calculus you can
probably get a vague idea of what the calculus of variations is. Remember
how some points were "critical points" because the slope of the tangent
line was zero there? The idea is the same but replace x (the
variable) with a function itself and you get a sort of infinite dimensional
generalization in which some FUNCTIONS are critical points because some
sort of derivative of a function of the function is zero. Sounds weird, I
know. In fact, we do not resort to using it too often because it does seem
a bit too abstract. But the fact is, as this story relates, much of
physics can be stated in these terms in a way that completely
eliminates the notion of time passing or events causing other events.
The idea of this story is to explore a different mindset in which the
calculus of variations, rather than algebra, is the most elementary form of
mathematics.
Contributed by
Kevin
"I think that here the physics (for Chiang is really using Calculus of
Variations as a physical law rather than mathematical principle) as an
example rather than as the focus of the story. The story focuses more on
how language itself can alter your way of thinking, and seeing the Universe
as a maximization/minimization problem is one of the ways in which your
mindset changes. Regardless, this is one of the most thoughtproviking
(and enjoyable) stories I have red in a long time." 
