Living in a Nonlinear World

After my Systems Engineering class last Friday, I kept reflecting on our discussions with the students about various dimensions of integrating renewable energy, especially photovoltaic (PV) systems, into the electric grid. The concept of nonlinearity continued to stir my thoughts. Today, as I listened to George Harrison’s Living in a Material World, I felt the desire to write a post on Living in a Nonlinear World.

Economists focus on the economic world, religious practitioners on the spiritual world, psychologists on the emotional world, ecologists on the environmental world, philosophers on the ethical or moral world, digital experts on the cybernetic and digital world, and so forth. But where do engineers fit in?

Though engineers often rely on linear, cause-and-effect thinking, we live in a nonlinear world where systems frequently surprise us with unpredictable responses. Nonlinearity—where outcomes are not proportional to inputs—is a defining feature of many natural, technological, and social systems. In this context, engineers face profound challenges as they work to understand and manage systems that defy simple rules.

In linear thinking, actions and consequences align predictably: a small action results in a small effect, and a large action in a large effect. However, nonlinear systems do not behave in this straightforward way. In such systems, a minor change might trigger a massive impact, while a significant effort may yield minimal results. These nonlinear responses are among the primary challenges of our modern world, where vast networks of interconnected, dynamic systems shape our environments and experiences.

Take the electric grid, for example: what happens when millions of inverter-based devices (like solar panels) are integrated into it? This aggregation of devices could lead to emergent phenomena—unexpected patterns and behaviors not evident from individual components. Will their combined effect be additive and predictable, or might they amplify, saturate, or destabilize the grid in ways we cannot fully foresee? These questions highlight the complexities of managing nonlinearity within engineered systems.

Nonlinearities challenge us precisely because they defy our expectations of how systems "should" behave. In nonlinear systems, an entire system’s behavior can shift or even reverse due to changes in feedback loops, altering the balance between reinforcing and stabilizing dynamics. These feedback loops—mechanisms that either reinforce or dampen certain behaviors—are at the heart of nonlinear dynamics. A small disturbance in one loop can ripple through the system, causing disproportionately large changes elsewhere.

So, where is the limit? Just because systems lack obvious boundaries does not mean they lack constraints. Every system has thresholds or limits—often hidden or complex—that define its capacity to operate. Our challenge is to identify these limits and recognize how growth or external stressors can push us closer to them. In a nonlinear world, growth does not continue indefinitely; it eventually encounters resistance, saturates, and may even create new constraints.

When one factor in a system is freed from a limiting constraint, growth occurs, affecting other interconnected elements. This shift can make resources either more abundant or scarcer, until another component becomes the new limiting factor. Growth is thus self-limiting, bound by the system’s internal dynamics and the interplay of its factors.

Beyond the nonlinear aspect, our world is also a multi-layered, multidimensional, chaotic, and complex reality where economic, social, environmental, and technological realms are deeply interconnected.

In such a complex environment, reductionism, the attempt to isolate and simplify phenomena without considering their context—must be avoided. Reductionism risks blinding us to the intricate, often hidden interactions that drive real-world behavior. Instead, an integrative, system-thinking approach is essential, enabling us to appreciate the full depth and intricacy of the nonlinear world we inhabit.

Cheers,

Paulo

Ref.: Rutherford, Albert. The Systems Thinker: Essential Thinking Skills For Solving Problems, Managing Chaos, and Creating Lasting Solutions in a Complex World, 2018.

https://www.youtube.com/watch?v=4Ta3wCAMlvI&list=PLOYTeA2BoRTb0iLjfS1OigtRN9F87L5fa&index=6