Sting Like a Butterfly
I’ve been following, and sometimes participating in, a debate over Lorentz’s celebrated “butterfly effect” – the notion that because chaotic systems exhibit sensitive dependence on initial conditions, a butterfly flapping its wings in Tokyo could cause a tornado in Texas. Blog participants in the debate include William Connolley of Stoat, Colorado State’s Roger Pielke Sr. , as well as Arun, an occasional commenter here(among many other places).
Let me start by stipulating that it’s extremely improbable that any given butterfly wing flap will cause, or even affect, any given tornado. No one is claiming that butterfly aerodynamics have any useful predictive value for tornadoes. On the contrary, what is claimed is that the details, and even large scale features, of weather phenomena have an inherent long term unpredictability driven by sensitive dependence on initial conditions.
After a ritual obeisance to what he calls the second "law" of thermodynamics (his quotes), Professor Pielke offers up the following:
My first thought on reading this was that it seemed about as germane as those arguments fundamentalists offer up about evolution being wrong because they have never seen a “half-man, half-fish” creature. On second thought though, it does embody some central fallacies of the anti-Lorentzian argument. First, he is looking for a direct effect, and second, he is considering a highly damped system.
Consider the following somewhat fanciful indirect scenario: You shake or jiggle your end of the rope and it disturbs a mouse which takes off running, is spotted by a hawk, and killed. An infected flea on the mouse transfers to the hawk, infecting and ultimately killing it after it has flown to somewhere near the other end of the rope (some days later). A coyote spots the dead bird, which perished entangled in the rope, and drags it away, thereby moving the other end of the rope. Hence, indirect effects can move the other end of the rope even with the purely damped system.
If we don’t want to depend on biological interventions, we need a dynamically unstable system. As Dr. Pielke very well knows, these are common in the atmosphere. On a calm sunny summer day a warm layer of air often forms in contact with the surface. If the surface is quite flat, such a layer might become quite a bit warmer than the overlying air before some slight perturbation, possibly even the flight of a butterfly, pushes a little bit of the warm air up into the cooler and denser air above. Once the bubble of air starts moving up, its buoyancy carries it on up, and more of the warm air on the surface drains into the upward moving bubble, forming a typical summer dust devil.
The big dynamic instability in the atmosphere is the differential heating of the equator and the poles. This generates a pole ward heat transfer, which, in combination with the rotation of the Earth and inhomogeneities in the Earth’s surface produce the Rossby waves that drive much of terrestrial weather. Because of the dynamical instability that drives the atmospheric circulation and Rossby waves, quite small disturbances can, in principle, be dramatically amplified. I'm not sure I want to stretch that amplification down to the butterfly scale, but it seems conceivable at least.
Dissipation (and the second law) always win in the end, but organized motions in the atmosphere are driven by the dynamic instabilities of the system.
Let me start by stipulating that it’s extremely improbable that any given butterfly wing flap will cause, or even affect, any given tornado. No one is claiming that butterfly aerodynamics have any useful predictive value for tornadoes. On the contrary, what is claimed is that the details, and even large scale features, of weather phenomena have an inherent long term unpredictability driven by sensitive dependence on initial conditions.
After a ritual obeisance to what he calls the second "law" of thermodynamics (his quotes), Professor Pielke offers up the following:
As an additional illustration of the inability for a very small perturbation from making a large scale change, consider the following example. You lay a rope from your location to a town 10 km away. Jiggle the rope (or even vigorously shake it!). No matter now many times that you shake the rope, the rope will not move in the town. The energy that you impose will be dissipated into heat long before the motions influence the rope at that distance.
My first thought on reading this was that it seemed about as germane as those arguments fundamentalists offer up about evolution being wrong because they have never seen a “half-man, half-fish” creature. On second thought though, it does embody some central fallacies of the anti-Lorentzian argument. First, he is looking for a direct effect, and second, he is considering a highly damped system.
Consider the following somewhat fanciful indirect scenario: You shake or jiggle your end of the rope and it disturbs a mouse which takes off running, is spotted by a hawk, and killed. An infected flea on the mouse transfers to the hawk, infecting and ultimately killing it after it has flown to somewhere near the other end of the rope (some days later). A coyote spots the dead bird, which perished entangled in the rope, and drags it away, thereby moving the other end of the rope. Hence, indirect effects can move the other end of the rope even with the purely damped system.
If we don’t want to depend on biological interventions, we need a dynamically unstable system. As Dr. Pielke very well knows, these are common in the atmosphere. On a calm sunny summer day a warm layer of air often forms in contact with the surface. If the surface is quite flat, such a layer might become quite a bit warmer than the overlying air before some slight perturbation, possibly even the flight of a butterfly, pushes a little bit of the warm air up into the cooler and denser air above. Once the bubble of air starts moving up, its buoyancy carries it on up, and more of the warm air on the surface drains into the upward moving bubble, forming a typical summer dust devil.
The big dynamic instability in the atmosphere is the differential heating of the equator and the poles. This generates a pole ward heat transfer, which, in combination with the rotation of the Earth and inhomogeneities in the Earth’s surface produce the Rossby waves that drive much of terrestrial weather. Because of the dynamical instability that drives the atmospheric circulation and Rossby waves, quite small disturbances can, in principle, be dramatically amplified. I'm not sure I want to stretch that amplification down to the butterfly scale, but it seems conceivable at least.
Dissipation (and the second law) always win in the end, but organized motions in the atmosphere are driven by the dynamic instabilities of the system.
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