The Relationship Tension Goldilocks Zone


In every interpersonal relationship, the other person will inevitably have some habits, values, or opinions that bother you. They can crop up in every domain of the human experience. They can range anywhere from mildly irritating:


To moderately infuriating:


To absolutely intolerable:


For the most part, these incongruities aren’t complete dealbreakers. But many of these small irritations can build enough cumulative frustration to jeopardize even the most seemingly perfect relationships.

Intuitively speaking, you might think: “If I am more tolerant of my partner and more understanding about their flaws, we will be happier in our relationship.” It is a very admirable, selfless philosophy in principle, but in reality it’s hard to prevent subconscious resentment from building up. Even if you consciously say you forgive them, the anger or hurt or sadness still lingers somewhere in the back of your mind and comes back to bite you later.


A more promising philosophy is to talk frequently about the problems that arise in a relationship.

Activation Discomfort

I’m not going to lie. Talking about conflict is absolutely terrifying. Nevertheless, chemical reactions show us why gathering up your courage to talk things out is worth it.

Exothermic reactions require a little bit of free energy and brings the reaction to an unfavorable state compared to the reactants alone. However, after the reaction completes, the products end up in a favorable state, and there is a net release of energy despite the initial activation energy needed.


The discomfort you feel in a relationship follows a similar trajectory. Sure, when you hear “we need to talk” you freak out and start sweating bullets. I call this activation discomfort. However, research shows that honest communication about sources of conflict (or misunderstandings during imagined conflicts) is essential for opening up avenues to start repairing trust. Only with the honest communication can you start damage control over the conflict that has occurred, and the relationship tension curve looks kind of like this:


But hold on a sec. Sometimes arguments end really badly. Just because there is honest communication and opportunities for repairing trust arise, does that mean there’s actual long-term benefits to relationships?

Negativity Threshold

As it turns out, there has been plenty of research that shows how healthy conflict resolution improves relationship health in the long run, but one particular body of work really pinpoints the mathematical reason that it works.

In her excellent TED talk called The Mathematics of Love, Hannah Fry describes what psychologist John Gottman and mathematician James Murray call the negativity threshold. The negativity threshold is the intensity of a conflict necessary before a couple talks about that conflict. The negativity threshold stays the same regardless of cumulative relationship health. For any given conflict, there are two possible outcomes, illustrated below: if the conflict is trivial enough, it gets ignored, but if it's intense enough, it's talked about.


In their research, Gottman and Murray conclude that a lower negativity threshold leads to healthier relationships because couples with a low negativity threshold respond more immediately to conflict and thus turn more of their conflicts into net gains in relationship health. Relationships last when each partner lets the other get away with less hostility before they decide to talk about the hostility at hand. On the other hand, couples who let conflicts sit as an elephant in the room and brew under the surface are more likely to get divorced.


Not Too Hot, Not Too Cold

So we’ve established that having too high a negativity threshold is bad. But, having too low a negativity threshold turns out to be detrimental as well.

Take the extreme for example. If I’m five seconds late to a lunch appointment with a friend, should we sit down and work things out? What if the haircut I got was a quarter inch shorter than my partner would like it, do we need to talk? What if they insist the taste of green M&Ms are superior to orange M&Ms when you know they’re the same damn thing, should you argue with that? Absolutely not, that’s ridiculous. The negativity threshold is too low at this extreme. You quickly become pissed off at your partner for being too nitpicky or hard to please.

In astrobiology, there is a concept called the Goldilocks Zone, which is the region around a star with just enough atmospheric pressure (or, in turn, temperature) to form liquid water on the surface of planets in that region and therefore support life forms. You can’t be too close or too far.


Choosing the ideal negativity threshold becomes a similar optimization problem. You want to be sensitive enough to the conflicts that arise in a relationship that you talk about elephants in the room, but not so sensitive that you become incessantly nitpicky, which itself is unhealthy (because it often results in destructive criticism or hypercriticism). It's all about finding the negativity threshold where you talk about the big problems but love them in spite of the little idiosyncrasies. I call this the Relationship Tension Goldilocks Zone.

I created a simulation to replicate a typical relationship (detailed code and math in the Appendix). It randomly generates a bunch of relationship conflicts of varying intensities, and looks at how much relationship tension accumulates over time given a particular negativity threshold. You want to find a negativity threshold that keeps the relationship tension within the Relationship Tension Goldilocks Zone, like so:


The above graph shows relationship tension over time for one particular negativity threshold, changing based on the net ups and downs for each conflict described earlier.

We can see that there is a tipping point on either side of the ideal negativity threshold that quickly pushes the relationship out of the Relationship Tension Goldilocks Zone:


This model gives substance to the meaning of forgiveness, being true to yourself, and being understanding and understand how they affect relationship health.

  • Forgiveness is about how willingly you let your relationship recover after being wronged, and is represented by the net improvement in relationship health following a conflict that exceeds the negativity threshold.
  • Being true to yourself is about how readily you confront ideas and behavior that challenge your own values. This is represented by the negativity threshold. As we saw, there is a sweet spot for being true to yourself; you can be too yielding or too unyielding.
  • Lastly, being understanding means being more accepting of the fact that people have flaws at all, and often many, many flaws. This can be conceptualized as how large the acceptable Relationships Goldilocks Zone (the green stripe in the graphs) is for your relationships, and being more understanding means widening that zone.

Obviously, this model generalizes a lot of nuances that are in each relationship that make them unique. Nevertheless, it helps explain why we all know that one couple with a perfectly harmonious relationship that seems to break up out of nowhere. It also explains why we all know that couple that argues all the time but have been happily together for ages. If there’s one thing to learn from those relationship archetypes or this model, it’s that conflict handled correctly is great for relationships!


Appendix: Some unimportant math

Assume that for a given relationship, there is a probability distribution function f(x) that gives the distribution of conflicts by intensity ranging from 1 to 100. Each relationship also has a negativity threshold T. For any given conflict that arises in this relationship, if the intensity I_c exceeds T, the couple talks about it, and the relationship health sees a net gain of n% of I_c. If cumulative relationship tension exceeds I­limit, then the relationship falls apart.

Given that general framework, I use mostly anecdotal evidence to make assumptions about the probability distribution function and the net gain percentage. I use an exponential power law to model the likelihood of conflicts at different intensities (high intensity conflicts are exponentially less likely than low intensity conflicts). I also assume relationship health has a net improvement of 20% of the conflict intensity when the conflict is resolved. With those assumptions, I can solve for a negativity threshold.

It is important to note that the intensity of conflict can be operationalized through a variety of different metrics; Gottman famously uses skin conductance, verbal cues, heart rate, facial microexpressions, motor activity, and blood pressure. I use arbitrary units for simplicity’s sake.

If you don’t like the assumptions that I’ve made, I’ve written some code that you can go in and edit in your own probability distribution functions, net gain percentages, negativity thresholds, etc: github. Currently, only R is supported, but I’ll maybe eventually find time to write the same prototype in Python and Java. You can see step-by-step how the code I wrote resulted in the simulated plots at this webpage here, no local R on your machine required.

Here are some additional GIFs from my simulation. Each of these GIFs come from the same random sample, but the simulation generates a new sample each time it is run. The first set is without nitpickiness (i.e. any net gain in relationship health that drops cumulative tension below 0 is set to 0). The second set allows for nitpickiness.