The elusive and infinitesimal “cause” of gun violence – part 1

Despite being an advocate for serious gun law reform, I do have to say that there is one approach from my fellow advocates that often fails upon examination, and the “2A” defenders like to make hay of it. A lot of media attention is directed at “one cause” propositions like “mental health” or particular registration laws. But upon examination of any one given case, say the October, 2017, Las Vegas mass shooting that killed 58 people and wounded 422, the “one cause” gets harder to find, and it is difficult to find the single change to gun laws that would have prevented that one tragedy from occurring.

This post is a deeper dive into why that “one cause” is so illusive and why the rates of violence, such as the 40-per-day rate of non-suicide gun deaths, or the one-per-day rate of mass shootings (where four or more people are killed or wounded), remain so stubbornly consistent from year to year.

I noted in a prior post that gun violence rates show less a “cause-effect” correlation to any single measure of potential “cause” than they look mathematically more like “lottery math,” a cruel random chance where the “number of tickets sold” is simply replaced by the number of guns out in the community. In effect, guns appear to “just go off,” at eerily-predictable rates. [1]

Rattner graph on gun availability

Source: Steven Rattner – MSNBC

That said, there are some factors that do appear to have higher correlation to some gun violence, for instance the tie between child gun deaths and unsecured weapons that I noted in that earlier post.

A lesson from basic calculus

Trust me, this applies to the topic, but allow me a digression here into a mathematical concept that was so troubling to the 17th-century Catholic Church that it banned its teaching, the concept of the infinitesimal. [2] If we try to predict the path of a ball thrown into the air in a parabolic arc, its direction and velocity can be easily measured between the points on the curve intersected by the blue line below. By capturing just two moments in time, and measuring the horizontal (ΔX) and vertical (ΔY) distances traveled, we can quantify the rate of speed and “slope” of the ball as it arcs upwards.


But to get a more accurate understanding of the ball’s trajectory and eventual landing point, we need to “zoom in” closer to the red arc path itself. When we do this, ΔX and ΔY get smaller and smaller as we approach the green line, which touches the arc at just one point on the curve. This is the “tangent” point where these two values get ever closer to zero, approaching what is called an infinitesimal distance. When you get too close to that point, the ball does not appear to move, let alone indicate any determinable direction.

This is the point where the math gets creepy, because we need to divide ΔY by ΔX. However, ΔX and the distance traveled along the arc are both approaching zero. And when that point is reached, as those 17th century Catholic mathematicians knew, the conventional math of division goes to Hell, and they read nasty theological implications into that contemplation. Isaac Newton and Gottfried Leibniz got around this problem at the turn of the 18th century by inventing the “new math” of infinitesimal calculus (today usually called just calculus). [3]

Here is the gun-violence-related point: The closer you look at “the cause” of the velocity and direction of the ball, or “the cause” that initiated a specific case of gun violence, the more elusive and immeasurable they become. Millions of people have issues with mental health, but determining the decimal fraction of those who will shoot somebody today would strain your calculator with too many “point zero-zero-zeroes.” And there are well over 300 million guns in the U.S., but just one of those will likely be involved in a mass shooting incident today. “What are the odds?” somebody likely says at every incident. And the answer is always “Pretty darn tiny.”

But the ball does complete its arc (unless it reaches the velocity required to go into orbit around the earth, which Newton demonstrated using that same calculus), and over 100 people still die unnecessarily every day from gun-based murder, accident or suicide. Reality exists even when you have your nose too close to the problem to understand it.

Enter Siméon Denis Poisson

French mathematician Siméon Denis Poisson (1781–1840, pronounced “pwa-sawn”) made major contributions to understanding these types of events through describing the math of what is now called a “Poisson process.”

Think back to that imaginary lottery that averages one winner per day. In any given minute, somebody may have purchased the winning ticket, but probably not. A winning ticket is sold on the average of once every 24 hours, yet the odds of that “win” happening within the next minute are very, very tiny. And the next minute as well, and the next minute. But at some point, given enough tickets sold, there will be a winning ticket drawn. [4]

Aye, and there is the rub: “the number of tickets sold.” When it comes to guns in America, we have sold a lot of “gun tickets” to a lot of people who “push the risk level” up, each one infinitesimally. Yet in the end, our “ball in the air” reaches a “velocity” of over 100 deaths per day. In short, when you look too closely, your favored “cause” of the shooting usually disappears from view, but people still die.

Understanding the “risk force vectors”

You can systematically study what I call the “risk force vectors” that affect these gun violence rates just as forces that throw that ball into the air, but often only when you “step back” a bit from the problem.  One way to do this is to isolate the legal and cultural differences between “low-rate” countries and other “high-rate” countries. “The cause” is most likely to be found in some combination of these factors. There are many “risk force vectors” in this debate, however at this point, institutions in the United States may be prohibited by law from studying them, either by statute or by cultural resistance.

One interesting point too often forgotten is that we can eliminate some 70% of the U.S. population from “being a risk force vector,” even a small one. These are the people who don’t own guns. Thus, 70% of the population bears the weight of the problems caused by the remaining 30%. That doesn’t sound very democratic, constitutional issues aside.

And when it comes to mass gun violence, we can, with 99%-plus probability, rule out half the population from being a contributing “risk force vector,” which is people who have “XX” chromosomes in their genetic structure. Women are only very rarely perpetrators of mass gun violence. And yet, they also “bear the weight of the sins” of the other half of the population with “XY” chromosomes. This does not seem like justice to me.

Finally, about 23% of the U.S population are under 18 years of age, so they should not be a “risk vector.” If they are, it is because an adult was either negligent or criminal in providing a minor with unrestricted access to a lethal weapon.

It seems like with those numbers, we ought to be able to do a lot to narrow down the problem and reduce the rate of gun violence. But that minority fraction of “XYs” who insist that lethal weapons must remain available in unsecured circumstances still hold the political power in the U.S. That needs to change.

In part 2 of this post, which is in the queue, I will look at the math behind why these rates of gun violence change so little from year to year. You can sign up for notification of new blog posts by entering your email address in the box on the left of your screen, or click on the Facebook or Twitter icons to follow this blog.


  1. I have written several posts about how the one-per-day rate of mass gun violence looks mathematically a lot like a “one draw per day” lottery, including this post after that Las Vegas shooting about “stochastic gun violence.”
  2. I wrote more about this battle of math versus theology in this earlier post.
  3. I wrote more about the rivalry between Newton and Leibniz on credit for the “invention” of calculus in this earlier post.
  4. Counterintuitively, out of 100 games set up to average one winner per day (where, like the most common U.S. lotteries, multiple winning tickets are allowed), about 37 draws will produce zero winners, and another 37 will produce just one winner. The remaining 26 draws will have quickly-declining probabilities of two winners (about 18 times) and three winners (about six times) with larger numbers of winners still possible but increasingly unlikely. See this post for more on that phenomenon.

2 thoughts on “The elusive and infinitesimal “cause” of gun violence – part 1

  1. Bruce Lindgren

    There has been some interesting work done recently looking at the gun violence problem in terms of epidemiology, which involves a kind of “medical mathematics.” (Essentially, epidemiology applies statistical analyses to the spread of disease, and the same kind of analyses can apparently be useful in the study of gun violence.)


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