The elusive and infinitesimal “cause” of gun violence – part 2

In a prior post I looked at the “infinitesimal phenomenon” in gun violence occurrences, where the closer you look for “the one cause” of any gun event, the more it slips away. Yet, in aggregate and over time, the causes are clearly real. In this continuation, we’ll look at why gun violence statistics are so constant over time, or if changing at all, trend very slowly. As you will see, in many ways we look at this problem “backwards.”

For instance, gun deaths from causes other than suicide have hung close to a predictable 40 per day in the United States, and incidents of mass gun violence, defined as four or more killed or wounded in a single incident, have occurred at a rate close to one per day for the last few years.

In one sense this is just the nature of statistics and “random” events. But if gun violence events have some human being pulling a trigger, then how can they be random? Stay tuned, and we will get to that.

The Central Limit Theorem

Last year I wrote a post that contained a computer simulation of a “wonky” six-sided die that you can “roll” hundreds of time to demonstrate the staple of statistics called the Central Limit Theorem. In the simulation, the die has one side with six “pips” but is blank on the other five sides. Nonetheless, if you roll this die enough times and average out your scores, a pattern appears that starts to look statistically “normal,” the classic bell-shaped curve. Click here to bring up a browser tab that will simulate the roll of this “wonky die.”

2000 dice rolls

The Central Limit Theorem says that, given enough samples of any population of varying characteristics, the mean (average) of the sample will begin to approach the mean of the underlying population. In our gun violence examples as a case in point, no matter how complex or skewed are the underlying “causes” of mass gun violence, any large sample over a given period of time, say, one year, will itself show an average very close to the “population” average, which are the “baked-in rates” of gun violence in this case.

In other words, if the underlying conditions behind mass gun violence do not change significantly from year to year, even if we have no clear idea of what those conditions are, any sizable sample will give us pretty much the same answer. It’s kind of like that cynical definition of “insanity” in which you keep trying the same thing and expecting a different result. The numbers won’t change unless the underlying conditions change.

“Overdetermined” cause

I have also cited in past posts this graph of sampled heights of adult males living in the United States to demonstrate the concept of overdetermined cause:

Adult Male Height

In addition to demonstrating the Central Limit Theorem just discussed, this graph has a very smooth “normality” centered around 176 centimeters (or just over five feet, nine inches) precisely because there are so many “causes” behind adult male height, and at the same time there millions of men in the population “smoothing out” the graph. [1] Any single gene might have a strong correlation to adult male height, or socioeconomic level may have a significant correlation, or the occurrence of a childhood disease.

Any one of these alone might be sufficient to impact adult height. However, the causes are called “overdetermined” because there are more than are necessary and yet they are all impacting the situation simultaneously, and perhaps interacting with one another. A poorer socioeconomic level often goes along with poorer nutrition, for instance.

And so it goes with gun violence. There are so many causes that the rates of suicide and rates of mass violence take on this “normal curve” (indeed an unfortunate appellation) with a central, rarely changing, mean. Yet, any single cause, taken by itself, often seems to have little determinable effect on the outcome.

When dealing with time-based events like gun violence, however, there is a “hard stop” on one end, which is “time zero,” or two unrelated events happening simultaneously, say, shootings in two different cities at almost the same moment. This “squished” version of the classic normal curve is called a Poisson distribution (named after the aforementioned Siméon Denis Poisson), which compresses to “time zero” the smaller the average (mean) time gets between events, like these examples, where the mean is represented by the Greek letter lambda (λ). This is more like what incidents of gun violence graph to in real life over time.


The Poisson Distribution

This reality of overdetermined cause does not mean that you can’t “do something” about gun violence. Rather, it requires taking multiple corrective measures on those factors that are demonstrated to have the largest individual impact before you will see progress.

Think of how the rate of adult tobacco smoking has declined in the United States, going from 21% to 14% of the adult population in just the twelve years studied by the Centers for Disease Control between 2005 and 2017. It took multiple legal and societal changes over many years to start moving that rate, but it happened. And yet, to echo Part 1 of this post, if you were to ask any individual smoker why he or she smokes, it would be very difficult to “find the cause.”

“Cause” versus “randomness”

Several of my posts in the past have noted how gun violence rates, particularly for mass violence, fit the “math of randomness” far too well, which suggests that guns “just go off” at some rate, and in random circumstances. It might help to look at this backwards. In an “overdetermined” gun violence environment like the United States, it requires many “anti-causes” in order to stop guns from firing, such as keeping them securely out of the hands of “high-risk” individuals, trained operators, gun-safety features, good behavioral health assistance, and societal pressure against unsafe firearm use. Other “civilized” countries know this, and actively employ “anti-causes” which are socially (and sometimes legally) unavailable in the U.S.

When any one of these “anti-cause” factors fail, then the “tumbler” full of numbered balls that is the “gun violence lottery” has been set to spin, and where she stops, nobody knows.


  1. You can generate a very similar curve for adult women, centering around 64 inches, but layered on top of the “male” graph there is considerable overlap. Thus the “XX” versus “XY” genetic difference and its related effects are significant to final height, but it is not correct to say that “men are taller than women.”

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