Once the notion of a problem is sufficiently semantically disambiguated, we can proceed toward the next marker on our map: the concept of “understanding”. Ambitious, right?! There will be two definitions in this piece, one building on another. I’ll start with the first one. Understanding of a phenomenon refers to our ability to construct a mental model of it, and that model makes reasonably accurate predictions about this phenomenon’s future state.

This definition places the presence of a mental model at the core of understanding. When we say that we understand something, we are conveying that a) we have a mental model of this something and b) more often than not, this model behaves like that actual something. The more accurate our predictions, the better we understand a phenomenon. At the extreme end of the spectrum of understanding is a model that is so good at making predictions that we literally don’t need to ever observe the phenomenon itself – the model acts as a perfect substitute. Though this particular scenario is likely impossible, there are many things around us that come pretty close. I don’t have to look at the stairs when I am climbing them. If I want to scratch my chin, I don’t need to carefully examine it: I just do it, sometimes automatically. In these situations, the rate at which the model makes prediction errors is low enough for us to assume that we understand the phenomenon. Of course, that makes rare prediction errors much more surprising, casting doubt on such assumptions.

Conversely, when we keep failing to predict what’s going to happen next with a thing we’re observing, we say that we don’t understand it. Our mental model of it is too incorrect, incomplete, or both, producing a high prediction error rate. Another related notion here is “legibility”. When we say something is legible, we tend to imply that we find it understandable, and vice versa, when we say that something is illegible, our confidence in understanding it is low. Think of legibility as a first-order derivative of understanding: it is our prediction of whether we can construct a low-prediction error rate model of the phenomenon.

Rolling along with this idea of predicting predictability of a mental model, I’d like to bring another definition to this story and define “understanding of a problem.”  I will do this in a way that may seem like sleight of hand, but my hope here is to both provide a usable definition and illuminate a tiny bit more of the abyssal depths of the nature of understanding. Here goes. Understanding a problem is understanding a phenomenon which includes us, the phenomenon that is the subject of our intention, and our intention imposed on it. See what I did there? It’s a definition turducken. Instead of producing something uniquely artisanal and hand-crafted, I just took my previous definition and stuffed it with new parameters! Worse yet, these parameters are just components of my previous definition of a problem: me, my intention, and the thing on which I impose that intention. However,  I believe this is, as we say in software engineering, “working as intended”.

First, the definition provides a useful mental model of how we understand problems. We need to understand the problematic phenomenon and we need to understand the different ways we can influence it to make it less problematic. If I want a tennis ball to smack into a tree in my backyard to scare away the bunny eating my carrots — obviously I don’t want to harm the cute bunny! — I need to know how I can make that happen. Just like we’ve seen with legibility, understanding of a problem is a first-order derivative of understanding of a phenomenon. It’s the understanding of agency: how do I and the darned thing interact and what are my options for shifting it toward some future state that I intend for it?

Second, this definition exposes something quite interesting: once we see something as a problem, we entangle ourselves with it. If something is a problem, our understanding of it always includes understanding – a predictive model! – of ourselves. This model doesn’t have to be complete. For example, to throw a ball at a tree, I don’t need to have a deep understanding of my inner psyche. I just need to understand how my arm throws a ball, as well as how far and how accurately I can throw it.

Third, we can see that, under the influence of our intention, phenomena appear to form systems: interlinked clusters of mental models that are entangled with each other. And it’s usually the mental models of ourselves at the center of entanglements, holding all of these clusters together and forming the network of the mental models that I mentioned a few articles back. This might not seem profound to you, but it was a pretty revelatory learning for me. Our intentions are what establishes our ever-complex network of mental models. Put differently, without us having preferences to some outcomes and not others, there is no need for mental modeling.

There’s probably another force at play. Intention could also be our models influencing us. When we construct the model, we have two ways to interpret prediction errors. One is to treat them as information to incorporate into the model. Another is to treat them as a manifestation of a problem, a misalignment between the environment (mistaking the environment for our model of it) and our intention. Can we reliably tell these apart? It is possible that many of our intentions are just our unwillingness to incorporate the prediction error.

Finally, the “incomplete model” bit earlier is a hint that understanding is a paradox. The pervasive interconnectedness that we encounter in trying to understand the world around us reveals that there’s rarely such a thing as a single phenomenon of which to construct a mental model. If we attempt to model the whole thing, we run into the situation that I call the Sagan’s Pie: “If you wish to make an apple pie from scratch, you must first invent the universe.” A recognition that we ourselves are part of this universe flings us toward the asymptote of understanding. So, our ability to understand some things depends on us choosing not to understand other things, by drawing distinctions and breaking phenomena down into parts of the whole — and intentionally remaining ignorant of some. We strive to understand by choosing not to.

To clear the fog of philosophy somewhat, let’s distill this all into a couple of takeaways that we’ll stash for later use in this adventure:

  • Understanding is iterative mental modeling, informed by prediction errors
  • Problem understanding is about modeling ourselves in relation to the problem
  • Problem understanding is also — and perhaps more so — about what we choose not to understand.

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