Introduction to Complexity

The 14 wolves of Yellowstone

They reintroduced wolves to Yellowstone National Park in 1995. Just a small number. After being hunted out decades earlier, wolves had vanished from the ecosystem. In their absence, elk populations had grown too large and slowly stripped the park of vegetation—especially along rivers. The hope was simple: bring back a natural predator, and maybe the elk would stay in check.

The hope was that the wolves would at least survive. Instead... they changed the entire landscape.

Elk started avoiding the riverbanks. Vegetation returned. Willows, aspens, and cottonwoods began to thrive again. That brought back birds. Beavers too—they used the wood to build dams, which created new ponds and habitats for fish, otters, ducks, and amphibians. Even the rivers themselves changed course—flowing more steadily, with less erosion. All from the reintroduction of a few wolves.

All these big and unexpected changes as a result of a subtle change is the hallmark of what we call a complex system. Complex systems can be found anywhere, and even in anything. Bee hive, flocking birds, funghi, human societies, the internet, friendships, scientific progress, crowds, diseases.

But it does not end there. Complex systems can be found even in mathematic: equations whose behavior can all of a sudden become unpredictable and chaotic, and just like that, a moment later they return to a highly predicable state. And whether it is ants building giant structures or these strangly behaving mathematical functions, they all fall under the header of Complexity Theory.

Let's pause here for a second and talk about what scientists mean when the use the term complexity. When people hear the word complex, they tend to think complicated—like a satellite, a nuclear reactor, or tax law. But in complexity science, "complex" means something else entirely. It refers to systems made up of many simple parts, interacting in sometimes surprising ways. From those interactions, new patterns and behaviors emerge—often in ways no one predicted. This is the idea of emergence: when a system as a whole behaves in a way that can’t be traced back to any single part.

Think of a murmuration of starlings, fashion trends and cultural norms, or traffic jam. No one’s in charge. There’s no master plan. Yet somehow, coordination arises. Behavior happens. Structure appears, seemingly from nowhere.

Complexity theory aims to understand how this happens. How simple, local rules can lead to global behaviors. How feedback loops drive change. How tipping points appear, and how small interventions can cascade through a system in ways that are sometimes powerful—and sometimes catastrophic.

Over the past few decades, we've come to recognize complexity in just about everything: ecosystems, supply chains, climate systems, social networks, economic markets, immune responses, public health, political movements, financial crashes, urban planning, even the spread of fake news. We’ve built models, drawn networks, simulated agents, mapped the chaos.

But here’s the thing: complexity theory still needs a breakthrough.

We know these systems share something fundamental. There’s a deep structure they all seem to follow—common threads connecting a rainforest to your backyard, or an anthill to a megacity, or the spread of disease to the rise of an idea. We’ve gotten good at describing these systems. But the big question remains:

How do we use this knowledge?

How do we apply what we’ve learned about complexity to actually solve real-world problems? How do we design interventions that work with these systems instead of against them? How do we avoid unintended consequences? How do we embrace complexity, without trying to control it?

That’s why I’m building Umoja, a platform to explore how our deepening understanding of complex systems—combined with the tools of today, like AI, simulations, and modern modeling—can help us design better, more adaptive, more human-centered systems. Not just to explain the world we live in, but to help shape it.