Mitchell Feigenbaum, a founding father of Chaos Theory, died at age 74 on June 30.

Feigenbaum is worth remembering because Chaos Theory changed the face of scientific research, and in so doing, changed the world. As investors, you and I directly benefit from the insights of Chaos Theory to this day. Mitchell Feigenbaum helped bring those insights to light.

At the time Chaos Theory came along in the 1970s, science was heading for a crisis of specialization. The various scientific disciplines had become reinforced silos, with narrow windows of expertise applied to increasingly narrow slices of observation.

Meanwhile, the self-anointed top dog of scientific disciplines, theoretical physics, was literally questioning its own future. In 1980, the renowned Cambridge cosmologist Stephen Hawking gave a lecture titled, “Is the End in Sight for Theoretical Physics?”

In a lecture doubting the future of his own field, Hawking observed that it now took “enormous machines and a great deal of money” to find new discoveries. In terms of reducing reality to its smallest components, physics had hit a limit.

Chaos Theory reversed the narrow specialization trend by looking at phenomena rather than components. It sought to understand emergent behavior, which meant studying systems rather than particles.

So, in a manner of speaking, Chaos Theory “saved” science from itself by reversing the relentless trend of reductionism, which had all but exhausted itself, and moved in the opposite direction towards holism.

Rather than take things apart, Chaos Theory focused on putting things together, and in so doing, found whole new worlds to explore.

Think about the difference between a molecule of water and a glass of water, or a drop of water versus an ocean storm. Chaos theorists would argue the behavior of turbulence in a glass of water is a more interesting topic than a standalone water molecule; the behavior of a storm is more interesting still.

In his book “Chaos: Making a New Science,” James Gleick described the field like this:

Now that science is looking, chaos seems to be everywhere. A rising column of cigarette smoke breaks into wild swirls. A flag snaps back and forth in the wind. A dripping faucet goes from a steady pattern to a random one. Chaos appears in the behavior of the weather, the behavior of an airplane in flight, the behavior of cars clustering on an expressway, the behavior of oil flowing in underground pipes.


No matter what the medium, the behavior obeys the same newly discovered laws. That realization has begun to change the way business executives make decisions about insurance, the way astronomers look at the solar system, the way political theorists talk about the stresses leading to armed conflict.

Chaos Theory as a discipline was born in 1972, when the MIT Professor Edward Lorenz accidentally discovered a phenomenon dubbed “sensitive dependence on initial conditions” and wrote a paper on it.

Sensitive dependence on initial conditions is more commonly known as the Butterfly Effect, a nickname popularized by the Michael Crichton novel Jurassic Park (which later became a blockbuster movie).

The idea behind the Butterfly Effect is that, if a butterfly flaps its wings over Tokyo, the ripple effects can impact weather patterns over Buenos Aires or New York. Lorenz documented how tiny changes in chaotic systems compound into big differences over time; this was the birth of Chaos Theory.

Mitchell Feigenbaum was involved in Chaos Theory from almost the earliest days. He earned a doctorate in theoretical physics from MIT in 1970 and then, after a few years of postdoctoral work, went to the Los Alamos National Laboratory in 1974. The wild ideas swirling around “chaos,” brand new and utterly strange at the time, immediately gripped him.

From the earliest days, Feigenbaum was known as a wandering genius. Not only that, Feigenbaum was an actual, literal wandering genius. He was known to roam the streets of Santa Fe, lost in thought at all hours of the night. Later in life, he was awarded a MacArthur Genius Grant.

A defining feature of Feigenbaum, and a key factor in his contributions to Chaos Theory, was a relentless curiosity and a permanent sense of wonder.

As a child, Feigenbaum once said he was fascinated by the radio in the family kitchen. He found it amazing that music could suddenly come out of a box. At Los Alamos, he tried experimenting with 26-hour days, causing his work rhythms to shift in and out of phase with colleagues.

Feigenbaum was known to pose strange questions, and then drop everything to search for answers on the spot. He wanted to know the distance at which trees merge into a formless shape; he wanted to know why the moon looked larger next to the horizon; he wanted to understand the behavior of clouds. In regard to cloud studies, he spent so much research time on airplanes, his flying privileges were revoked.

Early on, Feigenbaum seemingly wanted to think about everything and work on everything. For much of his career, he spent more time and energy providing brilliant insights into other people’s projects rather than his own. He was too restless to laser-focus, but he could help with whatever you were working on.

But as it turns out, Feigenbaum’s wide-ranging polymath mind was ideally suited to Chaos Theory, a discipline that requires the bridging of thoughts and concepts from many other scientific disciplines.

To really get a handle on chaos as a researcher, for instance, you couldn’t just stay in your lane as a biologist or physicist or chemist or mathematician. You had to mix stuff together in unknown amounts, like a science-based version of experimental cooking.

Feigenbaum also found time to make real breakthroughs in the field. One of his major contributions to Chaos Theory was the discovery of the Feigenbaum Constant, an exceedingly strange number with infinite decimal places that rounds to roughly 4.6692.

The Feigenbaum Constant has useful applications across biology, physics, chemistry, and meteorology in respect to fluidity and flow measures. Like Chaos Theory itself, fluidity and flow are “go everywhere” type concepts. The Feigenbaum Constant acted as a bridge by which the disciplines could talk to each other.

Feigenbaum also liked to invent things and solve interesting problems in his spare time. For instance, he wrote computer codes to reverse the mistakes of copy machines; figured out how to accurately represent three-dimensional geography maps on a two-dimensional page; and came up with geometric designs that make it harder to counterfeit paper currency.

Chaos Theory itself, along with its sibling discipline of Complexity Science, has contributed greatly to a more realistic understanding of how markets work. Chaotic behavior within a system shows us why we need to have respect for the inherent risk in markets, and why market forces, like the ocean, cannot be controlled or tamed.

Yet at the same time, the presence of surprising universal truths — like the usefulness of Feigenbaum’s Constant across disciplines — shows how patterns exist within chaos that can be detected and exploited.

Thanks to the brilliant work of Feigenbaum and others, as investors we stand on the shoulders of giants. We can harness the forces of chaos — which is not the same as randomness — while protecting our capital through position sizing and risk management.

One way to make hay from Chaos Theory is to implement a series of logical systems for investing, while making sure to have respect for risk and uncertainty (bounded chaos) baked into the design.

At TradeSmith, this is what we do through our platform of software tools, with the aim of empowering individual investors.

We’re forever grateful to the brilliant ideas of Mitchell Feigenbaum, and many other pioneers of Chaos Theory, Behavioral Economics, and Complexity Science, for discovering the insights that enable this.

Richard Smith
Richard Smith, Ph.D.
CEO & Founder, TradeSmith