In a few days after publication for this article, I will be giving my proposal defense to share initial progress on my PhD research with my doctoral advisory committee. In preparing for this defense, a key part of my research involves mathematical inequalities. More precisely, I am trying to derive novel upper bounds on functions that measure the error that arises from implementing a certain computer algorithm; this would allow me to ensure that the result this algorithm gives is trustworthy, and not just some nonsensical set of outputs.
In the time away from this preparation, I have thought about the inequalities people more usually use the word to describe, referring to parts of society, or the economy, that are greater than or less than others.
I will say at the outset that precisely measuring these inequalities is quite challenging, since societies and economies cannot be anywhere close to fully described by mathematical quantities (at least for the research I’m doing, I can write down what the error functions are). Of course, there are quantities that can be measured to showcase inequality — differences in personal wealth or income, grades in school and on tests, access to services and comforts that improve the quality of life.
But how people feel also plays a role in shaping narratives about social or economic inequality, allowing these imbalances to persist, or at least adding many more complex layers to the picture. One recent example I have thought of a lot is how the infrastructure and manufacturing legislation passed during Joe Biden’s presidency sent higher proportions of government money to heavily Republican areas struggling with long-term economic decline. And yet, Republicans remained staunchly in favor of now-President Donald Trump, whose tariffs and “government efficiency” efforts may well end up harming (or already have harmed) those very voters.
Humankind has long justified inequality of this sort with several different arguments over the millennia. The political or religious arguments in this realm—that some people deserve or have earned more than others; that those with the most expertise or ability should have the greatest say; that God has deemed certain people worthy of an afterlife in paradise and others worthy of an eternity in damnation—are all specious. Indeed, they flagrantly contradict the basic doctrine of human rights, and the teachings of religion to love one’s neighbor as oneself, or care for and protect those in need.
But what is so scary to me is that a much harder argument to break is the mathematical reasons for the existence of inequalities in society and the economy. It is virtually impossible to find a way to optimally construct such overwhelmingly complex systems so that everyone gets the same slice of the pie. And the way societies and economies grow is by naturally having short-term (or even long-term) winners and losers, before things settle into a brief Nash equilibrium until another shock or chaotic event occurs to throw everything topsy-turvy again. How can we beat the logic of mathematics in this case? Are the odds eternally stacked against us?
These questions may also be virtually impossible to answer, and I don’t claim to have any special knowledge that would make some answers I write carry much weight at all. What I will say: in complex systems, actions that may seem very small can nevertheless play an outsize role in the larger picture. We do not always have the freedom to make any choice possible, but when we do, we should make the choice to heed life’s call to connect with others over the call to solely protect ourselves. Then the system may come to have a new feature, yielding new mathematics that might turn those greater than or less than symbols into something looking more like an equals sign.
