How to make a breakthrough

The title is a bit tongue-in-cheek, because I am not actually providing a recipe. It is more of an inkling, a dinner-napkin doodle. But there’s something interesting here, still half-submerged, so I am writing it down. Perhaps future me – or you! – will help make it the next step forward.

Ever since my parents bought me an MK 54, I knew that programming was my calling. I dove into the world of computers headfirst. It was only years later when I had my formal introduction to the science of it all. One of the bigger moments was the discovery of the big O notation. I still remember how the figurative sky opened up and the angels started singing: so that’s how I talk about that thing that I kept bumping into all this time! The clarity of the framing was profound. Fast programs run in sublinear time. Slow programs run in superlinear time. If I designed an algorithm that turns an exponential-time function to constant time, I found a solution to a massive performance problem – even if I didn’t realize it existed in the first place. I’ve made a breakthrough. Suddenly, my code runs dramatically faster, consuming less power. Throughout my software engineering career, I’ve been learning to spot places in code where superlinearity rules and exorcizing it. And curiously, most of them will hide a loop that compounds computational bandwidth in one way or another. 

I wonder if this framing can be useful outside of computer science. Considered very broadly, The Big O notation highlights the idea that behind every phenomenon we view as a “problem” is a superlinear growth of undesired effects. If we understand the nature of that phenomenon, we can spot the compounding loop that leads to the superlinearity. A “breakthrough” then is a change that somehow takes the compounding loop out of the equation.

For example, let’s reflect briefly on Alex Komoroske’s excellent articulation of coordination headwinds. In that deck, he provides a crystal clear view of the superlinear growth of coordination effort that happens in any organization that aims to remain fluid and adaptable in the face of a challenging environment. He also sketches out the factors of the compounding loop underneath – and the undesired effects it generates. Applied to this context, a breakthrough might be an introduction of a novel way to organize, in which an increase in uncertainty, team size, or culture of self-empowerment result in meager, sublinear increases in coordination effort. Barring such an invention, we’re stuck with rate-limiting: managing nonlinearity by constraining the parameters that fuel the compounding loop of coordination headwinds.

Though we can remain sad about not yet having invented a cure to coordination headwinds, we can also sense a distinct progression. With Alex’s help, we moved from simply experiencing a problem to seeing the compounding loop that’s causing it. We now know where to look for a breakthrough – and how to best manage until we find it. Just like software engineers do in code, we can move from “omg why this is so slow” to “here’s the spot where the nonlinear growth manifests.”

It is my guess that breakthroughs are mostly about finding that self-consistent, resonant framing that captures the nature of a phenomenon in terms of a compounding loop. Once we are able to point at it and describe it, we can begin doing something about it. So whether you’re struggling with an engineering challenge or an organizational one, try to see if you can express its nature in terms of big O notation. If it keeps coming up linear or sublinear, you probably don’t have the framing right. Linear phenomena tend to be boring and predictable. But once you zero in on a framing that lights up that superlinear growth, it might be worth spending some time sketching out the underlying compounding loop, causality and factors and all. When you have them, you might be close to making a breakthrough. 

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