Did We Forget About Chaos?

The Butterfly Effect Is Still Here

We don’t hear much about chaos theory these days. Have we relegated chaos theory to the dustbin of 1980s/1990s academia and popular culture (James Gleick, 1987: Chaos: Making a New Science, Jurassic Park, 1993)? Have we forgotten about the power of the butterfly effect and unintended consequences? 

Chaos is ever-present 

Chaos is a natural phenomenon described and formalised by the mathematical field known as chaos theory. Chaos theory explains how very small differences in initial conditions can lead to vastly different outcomes in dynamic systems - even deterministic ones! 

The Mathematics of Chaos

Mathematically, chaos arises from non-linear differential equations, where feedback loops can magnify tiny variations over time. These systems are simple and deterministic — governed by fixed and understandable laws — but unpredictable in practice because precise initial measurements are not possible in real life.

One of the simplest mathematical models that exhibits chaotic behaviour is the double pendulum. A double pendulum consists of one pendulum arm attached to another, with each arm having a mass at its end and a rod connecting them. This simple structure exhibits complex, chaotic motion, meaning its future behaviour is highly sensitive to minute changes in its starting position, leading to unpredictable but deterministic paths. This is known as sensitive dependence on initial conditions, and in fact, we can never measure initial conditions well enough to predict outcomes accurately beyond a certain time frame.

Fig 1. Illustration of a double pendulum

Fig 2. Simulated path of a double pendulum

In this figure, two sequences start with values differing by just 0.000001. Over iterations, their paths diverge dramatically, illustrating the essence of chaos.

Economics - ‘the Dismal Science’

If chaos shapes physical systems, what about social and economic ones? Traditional Economics relies on over-simplified, equilibrium-based models that fail to explain crises. Agent-based models can improve economic theory (Doyne Farmer: Making Sense of Chaos). But more fundamentally, Economics is not easily testable in a scientific laboratory sense. If you choose a set of policies or parameters, you cannot go back and rerun the experiment (except perhaps in computational simulations). Hence, it prevents real progress in mathematical understanding. 

Chaos and Stability

Chaos theory shows that many systems are highly sensitive to initial conditions (the "butterfly effect"). But that doesn’t mean everything is always unpredictable. Chaos is characterised by dynamical instability—small changes amplify—but stability emerges due to other counterbalancing forces.

Even chaotic systems often settle into "strange attractors," patterns that constrain possible outcomes. These provide a kind of bounded unpredictability—things vary, but within a structure. For example, you know the pendulum can only swing in one plane and within a certain maximum radius, so you can predict something about it with confidence!

Our World is Actually Quite Stable

Natural systems have feedback mechanisms (negative feedback, damping, conservation laws) that keep them within stable ranges. Example: your body temperature regulation, or ecosystems stabilising via predator–prey balances, or stabilising climate feedback loops such as the CO2 fertilisation effect, in which more carbon drives more greening, which in turn increases carbon uptake (however, there are also destabilising carbon feedback loops).

So, despite the underlying complexity of our world, we often see stability because countless feedback loops, institutions, and norms act as shock absorbers. This creates the illusion of order, even though, beneath the surface, myriad small fluctuations are constantly being resolved before they escalate. What we perceive as “stable” is, in reality, a continuous process of micro-adjustments that keeps chaos at bay. That is, until those mechanisms are sometimes overwhelmed.

Resilience in Chaos

The world is both chaotic and stable. Chaos drives unpredictability in detail, while feedback and constraints create robustness in form. For humans, this duality is a source of resilience: by embracing uncertainty, we can adapt, innovate, and thrive — just as Dr. Ian Malcolm reminded us in Jurassic Park, ‘Life finds a way’.