As we begin a new semester following a hopefully restful winter break, I have been thinking about the various concepts of stability, a term often used in mathematics and invoked to describe many aspects of life more generally. With this more meditative column, I hope to challenge some notions of what it means to be “stable,” and argue for a reflection on promoting stability in unstable times.
I think it helps to start with definitions of mathematical stability. In one meaning, stability refers to the relationship between the solution to a problem, and the additional input parameters of that problem. For example, we may want to study an equation y = f(x): let’s say we know some values of x, and the function f. In this simple example, we can apply f(x) to obtain y. However, there may be additional flexibility in how we choose values of x — this flexibility is what we call problem parameters, or problem data. Stability in this setting is the idea that, for small changes in the problem parameters, changes in y should also be reasonably small.
Alternatively, one could speak of the stability of mathematical algorithms. Let’s start again with the notation y = f(x), but this time, x represents inputs to a computer program, f represents the algorithm, and y represents the output. Again, we could imagine tweaking the inputs x slightly: for the algorithm f to be stable, these slight tweaks should result in only slight differences in the output y.
I admit that this all seems very abstract, but I think the power of this stability concept is its generality. We could imagine any equation or algorithm, and study whether or not it is stable. Going beyond the mathematical binary, in life we use the words “stable” and “unstable” to describe many situations, and additionally assign levels of stability. Situations could become more stable or devolve into instability over time. There is some analogy with the mathematical definition—stable situations may better absorb or adapt to perturbations to the status quo—but in life, stability has a decidedly more general and flexible notion.
Let me now be very concrete. The United States currently faces deep questions of its stability: the aggressive and deadly incursions of ICE to cities across the country, or the military in Latin America, matched with insensitive, dangerous, and erroneous rhetoric from the Trump Administration and its allies, has stoked a national and global foment. This country has not been immune to such moments, as some may suggest — the Civil Rights Movement, the Progressive Era, Reconstruction, and the Civil War, all occurred within the 250 years of the USA, a nation formed through revolutionary bloodshed and turmoil.
So in that sense, have we ever been a stable country? I would argue yes in many respects, but no in many others. This answer, while perhaps unsatisfactory, I think should give us immense hope: we are not consigned to a state of permanent instability, and can focus on specific issues we are passionate about to improve multiple aspects of the situation at once.
We may not ever reach the ideal of stability, either, but this is also not a terrible thing in my view. One person’s stability may very well be another’s injustice, and countries need to evolve as new challenges arise. A strategy of hope amid uncertainty, perseverance amid intransigence, and creativity amid instability yields novel approaches and paradigms that can bring about continued prosperity, if only we are courageous enough to see it through.
But as a final thought, I think we all are — the bravery of those protesting in Minneapolis, Portland, even across the Hudson River in New York, is present in all of us, waiting to showcase itself in the pursuit of a more stable world. This pursuit is a long, messy, nonlinear, and, yes, unstable one; but the difficulty of subjects like mathematics or political affairs makes them all the more worthwhile to pursue, and the results we develop in the face of such difficulty are a true testament to human ingenuity and courage.
Per aspera ad astra.
