Three-Body Problem of Identifying School Shooters
When are 'red flags' actual warnings that someone is going to commit a mass shooting? Astrophysics explains why this answer is impossible to know.
Just five days before the school shooting at Annunciation Catholic School in Minneapolis, Robin Westman went to Frontiersman Sports and bought a .38 special revolver. The owner said Westman did not exhibit any of the red flags his staff are trained to look for. He said Westman was friendly, smiled, laughed, and asked questions.
This behavior is a stark difference from the videos posted just before the attack, when Westman pointed a loaded .38 revolver directly at a cellphone camera being held in first-person POV (essentially pointing the gun at herself).
Why is it so difficult to tell if someone is just another customer in a gun store versus someone who is plotting a school shooting?
Three-Body Problem
Scientists know a huge amount about physics. But if you take three objects floating in space like a planet, a moon, and an asteroid, there is no formula that can perfectly predict their orientations over time.
They can easily model and predict the positions and interactions of two objects, but adding a third makes the outcomes turn into chaos. This makes the three-body problem a deceptively simple question with no general solution.
Even if you know everything about where those bodies start, a tiny error in your initial data or change to one element in the system grows exponentially over time. This same problem plays out every day as school officials and police try to predict if someone is going to commit violence.
Three Forces Behind School Shootings
For a school shooting to take place, there are three core elements that interact to predict (or prevent) a violent act:
Intent: Does the person want to cause harm?
Capability: Do they have access to firearms, ammo, and the skills to use them?
Action: Will they actually take a gun to a school and pull the trigger?
On their own, none of these three factors guarantees a school shooting will happen. But when all three are present and they begin to interact (just like planets orbiting), the ability to predict the outcome is impossible. This is because we don’t know all three elements with precision and each tiny shift or miscalculation can dramatically change the outcome.
What the Three-Body Problem Teaches Us
In astrophysics, the three-body problem shows that even a deterministic system governed by strict laws of physics becomes unpredictable. In this simulation, three orbits of planets become a chaotic mess after making a tiny change to the mass of the planets (try the simulator).
In the real world, the position and momentum of objects (or people) constantly change based on the influence of internal and external forces.
In the case of a school threat:
A student shows signs of intent with dark writings, violent fantasies, drawing maps, writing a hit list, or threats on social media.
Even with intent, they may or may not have capability through access to firearms at home, knowledge of how to use them, or connections to others who do.
Even with intent and capability, they may or may not take action by actually carrying a gun to school and pulling the trigger.
The relationship between intent, capability, and action mirrors the three-body problem because each of these three elements doesn’t exist in isolation and the influences are both mutual and nonlinear.
For example:
A student might not have strong intent at first but gaining easy access to weapons increases their confidence in taking action.
After a violent drawing is found, a teen might get connected with help and resources while the same drawing being dismissed by adults might push a teen further down the pathway to committing violence by reinforcing their feelings of being unnoticed.
Even with access to a gun, anger from being bullied, and an easy way to sneak the weapon into school, positive relationships with a small group of peers could cause a student never to take action.
This constant, three-way feedback loop between intent, capability, and action is what makes the system unstable and impossible to predict with accuracy.
Small Errors, Big Consequences
Chaos theory explains how systems that follow deterministic rules (e.g., weather patterns, planetary motion) can still behave unpredictably over time due to their extreme sensitivity to small changes in the conditions. Even tiny differences at the start can lead to dramatically different results which make long-term predictions nearly impossible. This is often called the "butterfly effect" where something as small as a butterfly flapping its wings could theoretically trigger a distant storm.
Just like in chaos theory, tiny measurement errors or changes in a planet’s orbit result in different outcomes. For example, these 20 graphics are possible orbits of three planets with the same mass. Making the smallest possible changes to starting positions, trajectory, or velocity can generate a nearly infinite number of possible orbits.
These principles of chaos theory apply to predicting threats at schools:
If we underestimate intent because a threat sounds like a joke, we might miss an early opportunity to intervene because a predictable situation escalates into mass violence (underestimating velocity).
If we assume capability is low because the student has no known weapon access, we might ignore how easy it is to steal a gun from a car, take a gun from a friend’s house, or borrow one from another student (measurement error).
If we dismiss early actions as “just a kid who is fascinated with guns” we might fail to see how they fit into a larger plan with growing intent and capability (missing the influence of gravity from other planets).
It’s not always a matter of failing to recognize red flags because the elements are always shifting and when they are constantly changing alignment, the outcomes can change rapidly. If a threat assessment team determined in October that a kid had some intent but no access to weapons and then the kid finds a gun inside a dresser drawer during Thanksgiving at grandma’s house, now the whole equation is different.
Why Some Threats Fizzle and Others Escalate
We've all seen cases where a serious-sounding threat went nowhere while others were a quiet student who was overlooked by everyone until they became a headline. That’s the chaos of the three-body problem.
Maybe the student who made serious sounding threats had no real intent. Or maybe their environment shifted because after the threat was identified, someone intervened, they got support, or their access to weapons was removed. With the quiet student, maybe all three elements—intent, capability, and action—suddenly aligned and no one saw it in time.
The inherent unpredictability of the three-body problem teaches us that knowing the pieces is not enough. We need to understand how they move together in the real world to actually determine the outcome.
Dealing with Chaotic Systems
The three-body problem reminds us that some problems and outcomes are unknowable because they are chaotic by nature. Just as astronomers cannot predict the exact orbit of three bodies in space, school officials and police cannot perfectly predict who will become a shooter. The red flags often look obvious in hindsight, but in real time they are subtle, shifting, and often indistinguishable from ordinary teenage boundary testing, pranks, harmless fascination with weapons, or attention-seeking behavior.
This does not mean prediction is hopeless, we just need to better understand its limits. Instead of looking for certainty, we have to create friction at every stage where intent, capability, and action might align. Safe storage laws, supportive interventions, attentive peers, reporting systems, and accessible mental/social services all act like little gravitational pulls that can nudge the trajectory of a teen away from violence. Inversely, without help the pull toward violence can get stronger just like an asteroid caught in Earth’s orbit.
In the end, the lesson of the three-body problem is not despair but vigilance because even tiny shifts in alignment can lead to different outcomes. If chaos makes prediction impossible, then our responsibility is to keep tilting the system toward safety and supportive services because the smallest interventions might be the butterfly wing that prevents the next category 5 hurricane from forming.
David Riedman is the creator of the K-12 School Shooting Database, Chief Data Officer at a global risk management firm, and a tenure-track professor. Listen to my weekly podcast—Back to School Shootings—or my recent interviews on Freakonomics Radio, New England Journal of Medicine, and my article on CNN about AI and school security.