Does butterfly affect?

Can a butterfly really cause a hurricane?


Having been working in complexity science, I realize that I have a problem with the conventional understanding of the butterfly effect. Sure, in ideal deterministic chaotic systems, the butterfly effect does a great job illustrating the quasi-stochastic nature of chaos and sensitivity to small perturbations. But in the real complex world, far from a mathematically idealized deterministic model, there is no reasonable sense in which we can say that a butterfly’s wings can cause a hurricane. Even if this isn’t surprising, as intuitively people won’t attribute a hurricane to a butterfly, I would argue that causally attributing World War I to the assassination of Archduke Ferdinand follows the same fallacy.


Consider a pot of supercooled water. Any minúte impurity in it can seed the freezing transition of the entire pot. But can we really say that this impurity “caused” the transition? This seems to depend on the counterfactual world: what would have happened otherwise? If the pot is sitting in an isolated clean room where there would not typically be any dust other perturbations, then this one particular impurity may be to blame for the phase-transition. But out in the messy “real world,” abundant with impurities of all kinds, supercooled water would not survive long anyhow — if not this impurity, then another would have seeded the transition a moment later.


Now, this counterfactual definition of causality, formalized by Judea Pearl using tools information theory, similarly gives problems for the classic interpretation of the butterfly effect. Would the hurricane have happened if not for the butterfly? To answer this question carefully, it isn’t enough to look at what the world would look like if we removed the butterfly, but held everything else fixed. Instead, we must consider the full statistical ensemble of possible world, and quantify to what extent the butterfly shifts that ensemble. To model this in a mathematically idealized setting, we could take some deterministic chaotic system, add some small stochastic noise to it at all times t to generate the statistical ensemble of possibilities, and then consider the effect of some slight “butterfly” perturbation at a given time t*. In the typical scenario, the impact of this single perturbation will not rise above the impact of the persistent background noise inherent to any complex real-world system. As such, the impact of butterfly’s wings will typically not rise above the persistent stochastic inputs affecting the Earth (such as from quantum noise or outer space).


This reasoning also undermines some of the reductionist mechanistic perspective we often have on the world (especially in the proverbial “West”). Roughly speaking, it may often be quite difficult to cleanly attribute a real-world outcome to one particular cause. For example, regretful thinking like “if only I had…” often relies on holding the world fixed and only changing that one past decision — which is just as problematic as for butterflies and hurricanes. And so, perhaps indeed, “the devil is in the details” — it isn’t the one-time events that truly determine our lives, but rather it is how we guide their continual unfolding.

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