Butterfly Effects

Continuing a consideration of the “Zoology of Surprise,” –from the Hummingbird Effect, Black Swans, and Hippo Paradoxes–it is time now to confront the much-misunderstood “Butterfly effect.”  As I have learned, this phrase is not so much a metaphor about butterflies as it is about the nonlinear, unpredictable, and yet chaotically “orderly” behavior of hurricanes, epidemics, and (potentially even) stock markets!  Perhaps it is possible to tease out some implications for dealing with surprises by understanding a bit more about this metaphorical creature of surprise.  When looking into the matter, it is easy to see why people have become confused. Yet, it is also is apparent that understanding this concept is increasingly important to making sense of our past, present, and future wherever we are…

Traditionally the “butterfly effect” is discussed in phrases such as “as a butterfly flapping its wings in Tokyo could cause tornadoes in California” but this is a misconception of the meaning of the term. The concept of the “Butterfly Effect” comes from the research and mathematical literature (which generally has little to do with butterflies) of chaos theory.  This in turn is a subset of the currently rapidly evolving “complexity theory” (which will be addressed at much greater length in future posts on this blog). Chaos theory is applied in many scientific disciplines, including: geology, mathematics, microbiology, biology, computer science, economics, engineering, finance, meteorology, philosophy, physics, politics, population dynamics, psychology, and robotics.

Image:  Gouache, charcoal and ink by Black Elephant Blog author

Image: Gouache, charcoal and ink by Black Elephant Blog author

As the Wikipedia explains: In chaos theory, the butterfly effect refers to “the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.”

The Wikipedia entry continues: “The name of the effect, coined by Edward Lorenz, [an American mathematician (23 May 1917 – 16 April 2008)],  is derived from the metaphorical example of the details of a hurricane (exact time of formation, exact path taken) being influenced by minor perturbations such as the flapping of the wings of a distant butterfly several weeks earlier. Lorenz discovered the effect when he observed that runs of his weather model with initial condition data that was rounded in a seemingly inconsequential manner would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome.”  In this important sense, the phrase “butterfly effect” is not a metaphor, as mathematician and statistician Dr. David Hand explains in his new book, The Improbability Principle, discussed here on this blog.

What scientists painstakingly emphasize is that they are not talking literally about butterflies flapping their wings and causing hurricanes.   Instead, they are talking about nonlinear systems which demonstrate disproportionality (outcomes are not directly proportional to inputs) and, in particular, the relatively recent (made in the last century or so; see “Henri Poincare“) scientific observations that such systems are complex, dynamic, and exhibit sensitivity to initial conditions.  These systems include many natural systems such as weather, climate, and population growth in ecology.  (Nonlinear systems–of which chaotic systems are a subset–also include most systems, such as ICT (Internet, etc.) and social media, energy grids, finance and banking, food and water, transportation, and medical and health systems, upon which our modern societies rely to function.)

These chaotic systems, paradoxically for those of us educated to see mainly directly connected causes and effects, demonstrate a strange sort of “order”:  they are deterministic but not predictable.  Even though there are no random elements involved in their iterations,they are characterized by irregularity.  This behavior is known as “deterministic chaos” or “chaotic systems.”

Image:  Wikipedia

Image: Wikipedia

It appears that some disagree whether chaotic systems are really a subset of complex systems.  This is because, while chaotic systems are deterministic, truly complex systems aren’t.  According to one of the early proponents of complexity theory, Ilya Prigogine  (known for pioneering research in “self-organizing systems”), complexity is non-deterministic, and gives no way whatsoever to precisely produce the future.  Therefore, some say (also here and here, for instance) that there is a dividing line between a “complicated” deterministic order that is “chaos” and an order in which randomness prevails that is “complex.”   Some maintain that complexity is the opposite of chaos. Chaotic systems are sensitive to initial conditions whereas complex systems (such as social systems) evolve “far from equilibrium at the edge of chaos.”  Complex systems evolve at a critical state “built up by a history of irreversible and unexpected events,” also known as an “accumulation of frozen accidents,” by physicist Murray Gell-Mann.

What’s important about all this for a blog on surprise, change, and abrupt change, arguably, is that irregularity and unpredictability are inherent parts of the complex systems that make up our world. Apparently, we have known this (to varying degrees) scientifically for about a century.

It’s worth asking if standard analytic and planning processes have caught up to the science? We can forecast the weather but within time-limited bounds.    If we consider that these natural systems, such as weather and climate–while complex–are less complex than those involving human interactions (and, especially, human interactions with natural and digital systems!!), there seems to be a need for an abundance of caution when attempting to predict what individuals or social groups will do in the future.  As the head of the New England Institute for Complex Systems, Dr. Yaneer Bar-Yam, says, “No empirical observation is ever useful as a direct measure of a future observation.”  He adds:  “It is only through generalization motivated by some form of model/theory that we can use past information to address future circumstances.”

Unpacking what all this means for more standard approaches to planning, investing, predicting, forecasting, hiring, and organizing and managing work is a daunting task.   Butterflies and frozen accidents…what are we to make of it all?  As we move beyond the tenets of the Industrial Age into a digital, hyperconnected age, delving into these matters, arcane as they seem, may be an unavoidable task.  As this blog matures, I’ll link to some seemingly great work in this area, and welcome suggestions for the same.  (This post may be updated.)