This story builds on the one I wrote a while ago, and adds one more leg for this stool. This third leg came as a result of examining the solution loop with the question of “What are the limits to finding a solution?”

This question has been on my mind ever since I wrote about infinity. Infinity and something very large, yet finite can be very hard to tell apart. I needed a way to make sense of that, so this additional module for problem understanding framework was born.

Looking at the edges of the loop one by one, I can see that our mental *capacity* is the limit for the number of possible solutions. In other words, the diversity of our mental models is limited by our capacity to hold them. The example of trying to explain calculus to a three-year old or adding yet another project to the overworked leader’s plate still works quite well here.

The limit of attachment becomes evident when we look at the rate of interesting updates to the model (aka flux). I will define *attachment* as our resistance to incorporate model updates. This one is a bit more tricky. When we’ve developed a model that works reasonably well, we start exerting effort to reduce outlier updates to the model to preserve the model’s stability. Often, we apply a comforting word like “noise” to these outlier signals and learn to filter them out. It is not a surprise that in doing so, we develop blindspots: places where the real signal is coming in only to be discarded as “noise”.

Limit of attachment naturally develops from having an intention. The strength of our intention influences how firmly we want to hold the “what should be” model. Some leaders have such strength of intention that it creates “reality distortion fields” around them, attracting devout followers. This can work quite well if the leader’s model of environment doesn’t need significant adjustments. However, high intention strength hides the limit of attachment. The mental model remains constant and the growing disconfirming evidence is ignored until it is too late.

The third limit is obvious and I am surprised I haven’t noticed it in retrospect. The edge between solution and outcome (what I called effectiveness) is limited by *time*. To understand how effective my solution is, I must invest some time to apply it and observe the outcome.

These three limits — capacity, attachment, and time – appear to interact with infinity in fascinating ways. When we say that the adversaries are evenly matched, we implicitly state that their limits are nearly the same. In such cases, the infinity asserts itself. While limits play a role, it is the drowning in recursive mental models that never reach a stable state that takes the center stage.

However, adversarial adaptation is no longer an infinity-problem if your capacity is significantly higher than mine. You can easily *outwit* me. Similarly, if you are able to let go of your old models with less fuss than I, you are bound to *outmaneuver* me. Finally, if you are just plain faster than me, you can *outrun* me. For you, it’s a solvable problem. I, on the other hand, will still be in the midst of an unsolvable problem.

Maybe this is why superior speed, smarts, and agility are much sought-after traits in conflicts. As an aside, capacity advantage seems to come in two forms in adversarial adaptation: both being smarter and just being more numerous. Both require the opponent to have significant mental model diversity, which pushes them against the wall of their limits. This quantity trick is something that we’ve all observed with insects. A couple of ants in the house is not a big deal, but once you see a tiny rivulet of them streaming out of a crack in the kitchen window, the problem class swings toward unsolvable.

Similarly, the presence of limits can give us an impression of facing an infinity-problem when the problem is indeed solvable, but beyond our limits to reach an effective solution. In the organization that is caught in the “reality distortion field” of their leader, continuing to push forward might seem like fighting an invisible foe (which is a marker of perceiving an adversarial adaptation), but in reality be a matter of hitting the limit of attachment. In such situations, the outside observers might classify the problem as solvable, but from inside, it will come across as unsolvable.

Put differently, limits create even more opportunities for problem class confusion. We may mischaracterize unsolvable problems as solvable – and then be surprised when the infinity shows up. We may mischaracterize solvable problems as unsolvable – and fight impossible beasts to exhaustion.

Ronald Heifetz and Marty Linsky have this lens of *technical and adaptive challenges*. To describe the distinction in terms of the problem classes, technical challenges would belong in the class of solvable problems, and adaptive challenges would situate in the unsolvable problem class. One of the key things the authors emphasize is how often the confusion of one kind of challenge with another is at the core of all leadership problems. It is my hunch that the interplay of infinity-problems and limits has a lot to do with why that happens.

Oh! Also. While you weren’t looking, I re-derived the project management triangle. If we look at the capacity, attachment, and time, we can see that they match this triangle’s corners. Time is time, of course – as in “how much time do I have?” Capacity is cost, with the question of “how much of your capacity would you like to invest?” And last but not least, attachment is scope, with the respective “how attached are you to the outcomes you desire?” This is pretty cool, right?