Fractal Thinking: A Lens for a Chaotic World

In 1950, the first numerical weather forecast was produced on the ENIAC, a computer built to calculate artillery firing tables for the US military. Computing revolutionized meteorology by enabling more precise and long-term weather forecasts.

And so goes the story of the twentieth century. Military funding flowed into both science and industry, and advancements in each field fed into the other. Through this symbiotic relationship, we gained power, knowledge, and a feeling of control. Both scientists and the public began to believe that “the messiness of [all] systems would be clarified and accurate predictions could be made about their behavior if we could only amass enough information to pinpoint the multitude of their interlinked causes and effects.”^[1] It seemed that nature’s logic could be exposed, and thus exploited.

Formidable advances in science and computing gave rise to a new paradigm: computational thinking. James Bridle describes it as “the belief that any given problem can be solved by the application of computation.”^[2] In the realm of weather, advances in meteorology granted us unprecedented predictive capabilities, creating an illusion of complete insight into nature’s mysteries. As computational thinking gained influence, nature's chaos was erased from our collective understanding of the world.

Chaos remains in plain sight to the careful observer. For example, the field of meteorology is hopelessly limited by it. While our current predictive capabilities for weather are impressive, its chaotic nature precludes perfect knowledge. As MIT meteorologist Edward Lorenz discovered in 1961^[3]:

[Getting] more information about such variables as wind speeds, air pressures, humidity, temperature, and sunspots won’t help increase the accuracy of long-range weather forecast. Lorenz ascertained that no matter how much information a meteorologist piled up, his weather prediction would quickly go awry […] So nature is dominated by chaos, but it is not a superficial chaos that theoretically can be reduced to order once we gain enough information. Rather, nature’s chaos is profound.

Weather has — and will always have — a hard predictability limit. Weather is a dynamical system; its state continuously evolves over time. Such systems exhibit extreme sensitivity to initial conditions. This means that with each time step, a small difference between two similar states could get dramatically amplified. In weather prediction, unavoidable uncertainty in atmospheric measurements means that the data used in forecasting models never perfectly matches the real world. This uncertainty is unavoidable because our measurement devices can only be so accurate; we simply can't construct a thermometer that can measure temperature to an infinite number of decimal places. Over time, the delta between weather in the real world and the prediction model grows. In weather models, it takes just fourteen days worth of time for initial measurements to lose utility. At that point, the state of similar but not identical starting conditions lose all resemblance.

Another property of dynamical systems is that they are subject to feedback loops. Feedback occurs when outputs of a system are fed back in as inputs. Consequently, they do not follow the logic of linear systems, in which small inputs predictably lead to small effects. Rather, even miniscule inputs can produce outputs that re-enter the system, triggering a cascade of ever-larger outputs. While dynamical systems sometimes behave in an orderly, stable, and cyclical way, they “are so webbed with positive feedback that the slightest twitch anywhere may become amplified into an unexpected convulsion or transformation.”^[4] Dynamical systems thus wear two masks: chaos and stability.

Weather's chaos defies attempts at total control. Despite technological advances, weather is becoming more unpredictable, in both short and long time horizons. Research suggests that warmer temperatures have created conditions that make errors propagate faster in weather models, shortening the two-week predictability window. Rising temperatures have also transfigured larger-scale weather patterns, so the specific climatological knowledge we’ve accumulated in the past few decades is losing utility. Our default growth-centric ways of thinking struggle to compute regressions in power or knowledge like this. We thus need a new mode of thinking to comprehend the world around us, one that is colored by chaos.

Computational thinking falls short because it does not grasp that the data we can know is limited. Since we can never have perfect data, our world will forever be shrouded in uncertainty. The failure to see data as fundamentally incomplete results in a failure to see. To better grasp reality, we must perceive the otherworldly traces that chaos leaves in its wake.

As David Peat explains, "fractals [are] the traces, tracks, marks, and forms made by the action of chaotic dynamical systems"^[5]. They can be seen in every scale of our natural world: in the jaggedness of a mountain ridge, the branching of arteries, and the swirl of water in a river. Due to nature’s chaos, comprehending the world is not a static act of knowledge acquisition. Rather, it is a commitment to engage with it again and again and again, and to look upon it with fresh eyes. The most seasoned fisherman must apprehend the ocean as it is at this moment to secure food. Likewise, the fractal thinker recognizes that the patterns of chaos are the very fabric with which the world is woven.

Fractal thinking illuminates phenomena that computational thinking obscures in both the physical and digital realm. The properties of social media platforms readily follow when they are understood as dynamical systems. The recommendation algorithms are highly sensitive to initial starting conditions, such as a user’s initial social graph. Social media also has a mechanism for rapid cycles of positive feedback: users can amplify posts by interacting with them. Like a pebble that starts an avalanche, an unassuming post can go viral. While today virality is an obvious possibility, it was unanticipated in the early days of chronological and finite feeds. With fractal thinking, we see virality for what it is: a chaotic convulsion in a complex, dynamical system.

Furthermore, interactions between the physical and technological realm sometimes create complex and unanticipated feedback loops. These feedback loops create fractal patterns. For example, the automobile radically transformed the physical landscape of America. It enabled large portions of the population to migrate away from cities and into suburbs, and led to the development of highways and associated infrastructure.

The rise of the automobile was far from a linear process. Cars triggered a cascade of changes that further drove their adoption. Kenneth Hess describes the complex interplay amongst various technologies that drove the second wave of car adoption^[6]:

"[It] was brought about by a complex package of innovations and changes in living and purchasing patterns of which supermarkets, suburbs, and shopping centers are representative examples ... The supermarket itself was the culmination of numerous innovations ... Another development was the drive-in market (one with large amounts of parking space) which drew people from a wider area than other stores. Finally, the growth of home refrigeration allowed people to buy in greater quantities which often required the automobile for transport home ... On one hand, complex innovations like supermarkets were made possible by the existence of the automobile, on the other hand their growth (by replacing the nearby corner grocery) made the automobile more of a necessity. The relationship was tightly intertwined."

We can see the traces of a feedback loop: the effects of car use reinforced their necessity. The adoption of cars was a chaotic process, acting on the world through a multitude of feedback loops. The current shape of suburbia, and its attendant infrastructure, is thus a fractal footprint.

The lens of fractal thinking reveals that we can't know exactly how new innovations will interact with our physical and digital worlds. Most likely, Henry Ford could not have envisioned the contours of a post-car world. With the release of each invention, we are venturing into the unknown. In our highly leveraged and abstracted world, actively reckoning with this fact is absolutely essential for any type of visionary thinking. We'd be wise to understand that our world rests on the threshold of chaos; our attempts to purposely re-shape the world is not as straightforward as computational thinking might suggest.

Our civilization can be likened to a youth in their prime, newly awakened to their physical prowess, and their ability to re-shape the natural world. With the guidance of their elders, however, the youth might realize that to preserve the population of nearby prey for years to come, they must exercise restraint. To survive over the long term, even the fiercest hunters must cultivate the wisdom to listen to the fractal heartbeat of nature.

Our ancestors were constantly humbled by chaos, and used stories to make sense of the occasional senselessness of the world. As John Briggs describes in Fractals: The Patterns of Chaos, "most cultures have wrestled with the idea that order and chaos are a primordial duality… Many tribal peoples around the world include a trickster character among their pantheons, a figure who undercuts order by representing reality’s perpetual ironies and deceptions.” Our modern pantheon — science, industry, and computation — lacks a trickster, and only tells the story of how man conquered nature. Chaos, the missing deity, rounds out our conception of observable phenomenon.

Whether we acknowledge it or not, chaos rules our world at every level. We see its fractal calling card everywhere: in the patterns of weather to the effects of new technologies. At its own peril, computational thinking ignores chaos, blinding us to our limitations. To truly grapple with the complexity of our world — and thus to have any chance of meaningful stewardship of it — we must instead embrace fractal thinking. Fractal thinkers have an open mind and sharp eyes: through their steady gaze, they are able to discern the swirling fingerprints of chaos. Moreover, they are prepared to see something that challenges their neat abstractions and predictions.

In its infancy, meteorology was marked by a curse, that the intricacies of weather's movements would forever remain a mystery more than a handful of days into the future. The corollary to the curse deals a fatal blow to computational thinking: we are not masters of the sky, and because of chaos, we never will be.

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^[1] "Fractals: The Patterns of Chaos", John Briggs

^[2] "New Dark Age", James Bridle

^[3] "Fractals: The Patterns of Chaos", John Briggs

^[4] "Fractals: The Patterns of Chaos", John Briggs

^[5] "The Seven Life Lessons of Chaos", David Peat

^[6] "The Growth of Automotive Transportation", Kenneth Hess