From Ian Stewart
Stuart Leslie’s letter makes several correct statements about the butterfly effect (4 April). But it is more informative to understand the sense in which this metaphor is true, instead of demolishing one interpretation in which it is false. It is not true that events of the magnitude of a butterfly flapping its wings do not affect major events such as hurricanes. Indeed, weather forecasters have had to grapple with this problem since they became aware of chaos theory. Very tiny changes to the current state of the weather, put into the equations that predict future weather, lead to large-scale changes in the forecast.
The “butterfly effect” in this sense is what we mathematicians call “sensitive dependence on initial conditions”. The physical laws that govern the weather are such that, if we could run the Earth’s weather twice with the only initial difference being flap or no flap, the results would diverge exponentially.
Even though in reality there are innumerable “butterflies”, each causes the end result to vary unpredictably. What one flap really causes is the difference between the two “runs”, in the context of the rest of the weather system. A different flap, in this sense, might “cause” a tornado in the Philippines, compensated for by snowstorms over Siberia. It is impossible in practice to cause a specific hurricane by employing suitably trained butterflies. Nevertheless, in other contexts, such as electrically nudging heartbeats, such “chaotic control” provides an efficient route to desired dynamic behaviour.
Coventry, West Midlands, UK
