The Statistics of Lovers’ Quarrels
This is not a graph of my quarrels with “Emily.” It is a graph from Statistics of Deadly Quarrels by Lewis Fry Richardson. The graph shows that deadly quarrels follow an inverse power law. The vertical axis represents the number of quarrels and the horizontal axis the number of dead per quarrel; the scales are logarithmic. Many quarrels cause a single death (dots top left); and relatively few quarrels, notably world wars, cause many deaths (horizontal dashes). Question: can this type of analysis help us end war?
Cape May, New Jersey. March 23, 2024. [See “Note on Dateline” below.]
I’m in a candy shop with my girlfriend, “Emily.” I buy fudge, she buys taffy. As the cashier rings us up, I notice a basket of multi-colored gummies beside the register. Smirking, I ask the young, unsmiling cashier, Are those pot gummies?
As the cashier, still unsmiling, shakes her head, Emily, also unsmiling, looks at me and says, Don’t be an idiot, this is a candy story, of course they’re not selling pot gummies. Why would you ask that?
I don’t want to argue in front of the cashier. But after we leave the store, I tell Emily that her reaction to my gummy remark was inappropriate, I was just making a little joke. She doubles down. You weren’t funny, she says, you were offensive. For the rest of the afternoon, I sulk, while Emily seems to have moved on. Typical. [See Postscript for Emily’s reaction to this account.]
I write about the gummy incident the next morning in my journal. Writing gives me distance, which can be therapeutic. I reflect on how my long-term, romantic relationships have been defined by quarrels, quibbles, squabbles as much as by moments of mutual happiness.
Quarrels, it occurs to me, are quantifiable; you can represent them by breaking them down into variables. These include amplitude, as measured by yelling, scowling, elevated blood pressure and so on; duration, how long we yell or, conversely, go without speaking, smiling, kissing, hugging; and frequency, how often we quarrel.
Self-reports could complement behavioral and physiological data, because subjectively we might still be mad even though we appear objectively to be over the spat. If the fight is serious, Emily and I might not see each other, speak over the phone or exchange emails for days.
If you plot quarrels over time, what sort of pattern would emerge? You’d see some clustering, because one quarrel makes subsequent quarrels more likely. But a big quarrel might be followed by a period during which we try to avoid conflict by appeasing each other. In other words, quarrels beget quarrels unless they don’t.
The quarrels would probably show a Poisson distribution. That means they tend to occur at a certain rate over time, but the timing of individual quarrels is random, unpredictable. I’m guessing that if you plot amplitude and frequency, you’d get an inverse power law, meaning that little quarrels happen often, big ones seldom.
Depending on how you map them, quarrels might display fractal properties, which means the dynamics of quarrels, the way they unfold, are similar at all scales. Although each quarrel is in some sense unique, each also resembles other quarrels, big and small.
Question: can this sort of mathematical analysis help lovers avoid quarrels? I doubt it. Speaking for myself, the analytic part of my brain seems to run parallel to the emotional part. Veteran lovers know the feeling of having a fight so familiar that it seems silly to have it once again. You know how the fight ends, but you still go through the motions, with all the attendant emotions, you can’t stop yourself.
Wry self-awareness doesn’t necessarily help. Emily and I like watching comedians on Netflix. If a comedian tells a story about a fight with a romantic partner, Emily and I might smile at each other, because we’ve had that fight. But our recognition doesn’t keep us from having that same fight in the future.
Mathematical analysis, which is the basis of science, has helped humanity understand and manipulate nature in countless beneficial ways. But I fear mathematical analysis can’t help lovers avoid quarrels.
And that brings me to British mathematician Lewis Fry Richardson (1881-1953) and Statistics of Deadly Quarrels. Richardson, whose work anticipated fractals and other elements of chaos theory, pioneered numerical modeling of weather. A pacifist, he quit working on meteorological models when he realized they could be used to carry out chemical-weapons attacks.
Richardson thereafter devoted himself to mathematical analysis of war, which he hoped would help us identify causes of war and find ways to avoid it. Richardson compiled a massive database of deadly conflicts—ranging from homicides to world wars--occurring between 1820 and 1945.
Richardson’s work was published posthumously in 1960 as Statistics of Deadly Quarrels. In the book, Richardson shows that war cannot be traced to any single cause. Not resource scarcity, as Malthus hypothesized; nor class divisions, as Marx surmised; nor religious, cultural or linguistic differences.
Countries tend to fight countries with which they share a border, but countries also fight non-neighbors. War in one region makes subsequent wars in that region more likely, until it doesn’t. Overall, Richardson says, outbreaks of war seem to form a Poisson distribution or “random scatter”—like radioactive decay.
In The End of War, I argue that we choose to fight wars, and we can choose not to fight them; we can end war if we have the will. But Richardson’s analysis implies that wars are a natural phenomenon, like storms or earthquakes, rather than the actions of self-aware, intelligent beings with the capacity to understand and alter their behavior.
I loathe determinism, the idea that free will is an illusion. But contemplating the statistics of quarrels, between lovers and nations, makes me fear that the determinists are right. Emily and I are both pretty smart and self-aware—and we care for each other! We nonetheless quarrel over and over. If we can’t avoid quarrels, how can nations do so?
Maybe free-will deniers like Robert Sapolsky, the biologist, and Leo Tolstoy, the novelist, are right. Maybe when it comes to the things that matter most, like love and war, we lack free will. Maybe the best we can do is reflect on the absurdity of our behavior and smile grimly as we submit to our fate.
Postscript: What my account omits, Emily says, is that the candy store was old and family-owned, and the cashier seemed visibly annoyed by my gummies remark.
Further Reading:
Free Will, War and the Tolstoy Paradox
Free Will and the Sapolsky Paradox
Free Will and the Could-You-Have-Chosen-Otherwise Gambit
Is Killing Children Ever Justified?
You’re Not Free If You’re Dead: The Case Against Giving Ukraine F-16s
Dear Feminists, Please Help End War!
Confessions of a Woke, Antiwar, Hockey-Playing Demonic Male
Note on Dateline: A reader complained that the dates heading my columns don’t include year of publication. Squarespace, my website software, requires coding to automatically add the year. That’s a hassle, so I figured I’d just manually add a dateline specifying place and date of publication to each column. Datelines are cool in a retro way. For a full, dated list of all my past columns, see About Cross-Check.