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Butterflies surround a glowing ball of energy

At the level of our lives, the famous butterfly effect is largely an urban myth. (Image: Thomas Cotterill)

These days we are all familiar with the concept of the “butterfly effect.” The usual formulation goes something like this: when a butterfly flaps its wings in one part of the world (often the Amazon jungle) it can cause a hurricane in another part of the world. The colossal disparity in magnitude between cause and effect embodied in the idea has fired the collective imagination around the globe.

The butterfly effect was “discovered” in 1961 by MIT meteorologist Edward Lorenz. He was working at the time as an assistant professor in MIT’s department of meteorology where one of his projects involved an early computer program designed to simulate weather. As so often happens in science, his discovery was accidental. Looking to save some input time, he rounded one of a dozen numbers representing atmospheric conditions from .506127 down to .506. To his amazement, the tiny reduction utterly transformed his long-term forecast. Lorenz wrote about the experience in a 1972 paper titled, “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?” The title was imaginative, intriguing, and provocative. A completely new idea was born. Vast opportunities for exciting scientific speculation suddenly sprang into being.

It does not seem to have occurred to Lorenz to look for some savage and inappropriate multiplier effects in his crude weather model. Such models represent nonlinear systems where small changes in input can result in large changes in output, so his results, while startling, may have seemed plausible. However, the quality of long-term weather forecasts in the sixties and early seventies left much to be desired, a warning sign, surely, that all was not as it should be.

Fast-forward to contemporary chaos theory. This new science has happily embraced the butterfly effect and made it a centrepiece of the struggle to understand randomness. Chaos is a kind of deterministic nonlinear system, so once again we see the sensitive dependence on initial conditions. A small change at one location can provoke large differences in a later state. Lorenz has a precise, yet at the same time approximate definition. “Chaos: When the present determines the future, but the approximate present does not approximately determine the future.”

This is fine, but humans always want to find new uses for things. If something looks good over there, why not try it out over here? Nuclear power can generate electricity, but it also comes in handy when you need to obliterate a city. Explosives work wonders loosening things up in mines, but artillery shells are just as efficient at thinning folks out on the battlefield.

Thus, we are treated to such gems as “If you change the smallest of life’s details then you change its outcome.”

Sniff! Sniff! Can you smell the science?

At the personal level, we all know how hard it is to alter our lives in significant ways. Big changes usually require sustained effort over long stretches of time. Why is this so? The answer is simple: our lives, while difficult to predict in their precise details, are not really nonlinear systems. They are subject to the usual kinds of cause and effect, and as a species, we are built deliberately to ignore the inconsequential.

At the ecosystem level, life is subject to endless dampening effects that limit the impact of changes. There are checks and balances. No virus or bacterium can run amok completely. Organisms have immune systems. No species multiplies endlessly. Predator numbers increase to exploit the increased food supply. Life forms are limited to specific environments. Nothing lives forever. Localized damage may occur, but the web of life is resilient and adapts. It is capable, not only of resisting change, but of repairing itself, re-establishing a pre-existing status quo.

Many bad analogies have been advanced to sustain a false impression of how widely the butterfly effect may be applied. “Although the butterfly effect may appear to be an esoteric and unlikely behavior, it is exhibited by very simple systems: for example, a ball placed at the crest of a hill may roll into any of several valleys depending on, among other things, slight differences in initial position” (Wikipedia). This is a rigged example with a fixed number of easily attainable, divergent, yet rigid and repeatable outcomes. There is no process of transformation here; once the ball starts rolling, the system is closed and the outcome is assured. The widely spaced end positions of the ball are determined entirely by the valley shapes and the directions in which they lie and not by the passive ball. It is really a simple cause and effect setup where the initial position of the ball (on a slope that leans slightly towards a particular valley or valleys), and perhaps wind direction, determine which way it starts rolling.

The butterfly effect is a common theme in time-travel fiction. The usual presentation has the storyline diverge in the event of a seemingly minor occurrence resulting in two radically different outcomes. The key words here are “seemingly minor.” There is often confusion over magnitude. That is, the “insignificant” event may have far more ramifications than are suggested up front. Such tales depend heavily on rigging the game to get the desired outcome. They ignore factors that might mitigate the divergence and stress those that accentuate it. Those familiar with the repeated timeline meddling in the film “The Butterfly Effect” know how huge the impacts of the timeline-changing events actually are. Far from minor occurrences, they are all emotionally charged life-changing disasters. However, like the ball example above, each scenario is really just regular (albeit sometimes psychological) cause and effect. This must be so or the story would make no sense.

In love with the idea, we have exaggerated the impact and prevalence of the butterfly effect. Most systems, including those that branch, work by familiar cause and effect. Those that do not are lacking in interest for the simple reason that they are unintelligible.