I just got through watching the movie “The Butterfly Effect.” (decent movie, I could probably form a religion from its basic plot.) The name of the movie comes from a statement you sometimes hear from those who work in chaos theory:
The flapping of a single butterfly’s wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month’s time, a tornado that would have devastated the Indonesian coast doesn’t happen. Or maybe one that wasn’t going to happen, does. (Ian Stewart, “Does God Play Dice? The Mathematics of Chaos”)
And I have to say that I’ve never understood what I’m supposed to take from this statement. Sure many systems are chaotic and we can have large differences in behavior from seemingly small changes in the initial conditions. But I sometimes get the feeling that a causal relationship is being made in this statement: if it weren’t for the butterfly, the people in the path of the tornado would be fine, i.e. the butterfly caused the tornado. But this clearly isn’t true. There are plenty of other effects which are also casually necessary for the tornado. Do I get to blame the butterfly if an even smaller change in the wavefunction of single proton somewhere in the upper atmosphere changes the initial conditions by even a smaller amount than the butterfly and this in turn changes the entire outcome of whether there is a tornado? In fact, I would argue that we can only blame the butterfly if other changes in initial conditions of comparable size do not change the outcome of whether there is a tornado or not. Chaos may be ubiquitous, but I wish we’d all stop blaming the butterfly.
Spoken like a true bayesian.
Interesting point! And anyway, given that the theory is chaotic, can we ever truly know that the butterfly was at fault?!
Somewhat unrelated comment, and I _am_ ashamed to admit this, but I wound up half-watching one of those crime scene investigation shows while cleaning my apartment this evening. Wow, the Las Vegas police department forensic scientists can do everything. A DNA comparison takes less than an hour and every computer is fitted with a special “image enhancement” function that takes a 640×480 BW security camera image and turns it into a color 1600×1280 Smithsonian-worthy photograph. They can also simulate a river and compute the exact location that evidence can be found given that it was dumped in the water at an uncertain location (LVPD has solved this silly chaos problem you mentioned). I wonder how many viewers think its all real.
It’s worth tracking down the old “Annals of Improbable Research” paper in which they identify the specific butterfly responsible for the bad weather. It’s written as a spoof but I think accidentally says something about the whole use of this fable, in line with your comments.