Of butterflies and piranhas

John Cook writes:

The butterfly effect is the semi-serious claim that a butterfly flapping its wings can cause a tornado half way around the world. It’s a poetic way of saying that some systems show sensitive dependence on initial conditions, that the slightest change now can make an enormous difference later . . . Once you think about these things for a while, you start to see nonlinearity and potential butterfly effects everywhere. There are tipping points everywhere waiting to be tipped!

But it’s not so simple. Cook continues:

A butterfly flapping its wings usually has no effect, even in sensitive or chaotic systems. You might even say especially in sensitive or chaotic systems.

Sensitive systems are not always and everywhere sensitive to everything. They are sensitive in particular ways under particular circumstances, and can otherwise be quite resistant to influence.

And:

The lesson that many people draw from their first exposure to complex systems is that there are high leverage points, if only you can find them and manipulate them. They want to insert a butterfly to at just the right time and place to bring about a desired outcome. Instead, we should humbly evaluate to what extent it is possible to steer complex systems at all. We should evaluate what aspects can be steered and how well they can be steered. The most effective intervention may not come from tweaking the inputs but from changing the structure of the system.

Yes! That’s an excellent, Deming-esque point.

Bradley Groff pointed be to the above-linked post and noted the connection to my recent note on the piranha principle, where I wrote:

A fundamental tenet of social psychology, behavioral economics, at least how it is presented in the news media, and taught and practiced in many business schools, is that small “nudges,” often the sorts of things that we might not think would affect us at all, can have big effects on behavior. . . .

The model of the world underlying these claims is not just the “butterfly effect” that small changes can have big effects; rather, it’s that small changes can have big and predictable effects. It’s what I sometimes call the “button-pushing” model of social science, the idea that if you do X, you can expect to see Y. . . .

In response to this attitude, I sometimes present the “piranha argument,” which goes as follows: There can be some large and predictable effects on behavior, but not a lot, because, if there were, then these different effects would interfere with each other, and as a result it would be hard to see any consistent effects of anything in observational data.

I’m thinking of social science and I’m being mathematically vague (I do think there’s a theorem there somewhere, something related to random matrix theory, perhaps), whereas Cook is thinking more of physical systems with a clearer mathematical connection to nonlinear dynamics. But I think our overall points are the same, and with similar implications for thinking about interventions, causal effects, and variation in outcomes.