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Chaos Theory is the branch of mathematics that deals with complex systems whose behavior is highly sensitive to slight changes
Aug. 23, 2017 02:00 PM
Why Understanding Chaos Theory Is Important to Your Business
“Chaos: When the present determines the future, but the approximate present does not approximately determine the future.”
– Edward Lorenz
We all probably remember the movie (“Jurassic Park”), even if we don’t remember this exact scene: Dr. Malcolm, played by Jeff Goldblum is explaining Chaos Theory to Dr. Ellie Sattler, played by Laura Dern.
Dr. Malcolm is explaining how random, seemingly negligible events can disrupt even the most carefully laid out plans.
Dr. Ian Malcolm: [after the T-Rex failed to appear for the tour group]. “You see a Tyrannosaur doesn’t follow a set pattern or park schedules, the essence of chaos.”
And then later in the movie…
Dr. Ian Malcolm: “Oh, yeah. Oooh, ahhh, that’s how it always starts. Then later there’s running and um, screaming.”
Yes, running and screaming. That’s what happens when even the most carefully developed plans eventually succumb to the compounding of all these “random, seemingly negligible” events. And understanding the ramifications of Chaos Theory is becoming even more relevant as we look to machines to take over increasingly complex tasks.
What Is Chaos Theory?
Chaos Theory is the branch of mathematics that deals with complex systems whose behavior is highly sensitive to slight changes in conditions, so that small alterations can give rise to unintended consequences. Chaos Theory is the science of surprises, and not always pleasant surprises. While traditional science deals with predictable phenomena like gravity, electricity, or chemical reactions, Chaos Theory deals with nonlinear things that are mostly impossible to predict, calculate, or control, like turbulence, a bar brawl, the stock market futures, debris flying out of the bed of a truck, or a child darting onto the street.
There are several underlying principles of Chaos Theory, including:
- Butterfly Effect: This is probably the most common principle; that a butterfly flapping its wings in one part of the world can eventually cause a hurricane in another part of the world. Here is a more realistic way to describe the Butterfly Effect: small changes in the initial conditions can lead to drastic changes in the results. Our lives are an ongoing demonstration of this principle.
- Unpredictability: Because we can never know all the initial conditions of a complex system in sufficient detail, we cannot hope to predict the ultimate fate of a complex system. Even slight errors in measuring the initial state of a system could be amplified dramatically, rendering any prediction useless or even wrong.
- Mixing: Turbulence describes how two adjacent points in a complex system could eventually end up in very different positions after time has elapsed. Examples: Two neighboring water molecules may end up in different parts of the ocean or even in different oceans. Or a group of helium balloons that launch together eventually landing in drastically different locations.
- Feedback: Systems often become chaotic when there is feedback. A good example is the behavior of the stock market. As the value of a stock rises or falls, people are inclined to buy or sell that stock. This in turn further affects the price of the stock, causing chaotic, unpredictable stock price movements.
Chaos Theory Meets the Autonomous Car
Complex systems (sometimes called complexity theory) are systems whose behavior is intrinsically difficult to model due to the dependencies, relationships, or interactions between their parts and its environment. Complex systems are impacted by factors such as non-linearity, emergence, spontaneous order, adaptation, and feedback loops. And while an autonomous car may not be the most complex system in the world, it is certainly more complex than playing checkers, chess or Grand Theft Auto.
So what happens when Complex Systems run into the world of Chaos Theory?
Complex or dynamical systems – that is, systems whose state evolves over time –display dynamics that are highly sensitive to initial conditions (butterfly effect). These sensitivities manifest themselves as an exponential growth of perturbations in the initial conditions over time. As a result, the behavior of these complex systems grows more and more random (unpredictable). This happens even though these systems are deterministic, meaning that their future dynamics are fully defined by their initial conditions.
So while we can’t avoid the impact of Chaos Theory, especially as we employ Machine Learning and Artificial Intelligence to a growing body of complex systems and environments, here’s what we can do to mitigate the impact of Chaos Theory:
- Build a plan for the continuous testing and refinement of the analytics. The performance of analytic models decay over time; they have a half-life because the world changes such as public sentiments driven by widening wealth gaps, corporate acts of malfeasance, government scandals, rising burden of student debt, growing ranks of the under-employed, wage stagnation, mounting populace divide on social media, legalization of marijuana, rising media sensationalism, climate change, terrorism, Cubs win the World Series, etc.
Figure 1: Half-life Calculation
Even apparently stable analytic models constantly need to be evaluated and fine-tuned. Think of it as the “Data Scientist Life-time Employment Act!” See the blog “2016 Presidential Election: Did Big Data Just Get Lazy” for more details on the analytics half-life effect.
- Create a dashboard to monitor the performance of your analytic models. A dashboard is the perfect monitoring device to ensure that business managers and the data science team are proactively monitoring the performance and state of the analytic models. Heck, maybe even integrate some data science into the dashboard to predict when a model is starting to fail (i.e., predictive maintenance). See the blog “Big Data Dashboards” for some ideas about how to transform your “monitoring” dashboard into a “predictive” dashboard.
- Understand the costs and liabilities associated with Type I and Type II errors and use those costs and liabilities to prioritize your investments in data acquisition, data quality, metadata enhancements and model tuning. See the blog “Understanding Type I and Type II Errors” for an approach for quantifying the costs and liabilities associated with Type I and Type II errors.
To borrow again from the movie “Jurassic Park”, don’t get caught with your pants down with respect to the potential ramifications of Chaos Theory on your complex analytic projects.
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