When a butterfly flutters its wings in one part of the world, it can eventually cause a hurricane in another...Argh. The reference is of course to the famed "butterfly effect," in which certain dynamical systems (like the weather) exhibit what is called "sensitive dependence on initial conditions." (There's a decent explanation of the effect, and some of the misconceptions surrounding it, here.) Sensitive dependence, no problem; but the clear implication of the ad, and that of the popular use of the idea, is that the slight puff of air caused by the butterfly's wings grew and grew until it became a raging hurricane.
Like the theoretical wings of the butterfly, events on the other side of the planet (not to mention right here in the U.S.) can ripple toward you at an alarming rate of speed and brew up quite a storm in your business .... and your life.This is balderdash (not to mention flapdoodle). What grew and grew ("rippled toward you") is the difference between the states, at corresponding times, of the system sans butterfly and the one with it. There's nothing to suggest which one will end up with a hurricane, or that either will. If we picked a point in time halfway between then and now we wouldn't be able to tell which one had the butterfly and which didn't. The point is just that in such systems (and the Economist is correct to imply that the economy is one such system), a small difference in initial conditions will grow into a large difference later on: one which may even be manifested, at a particular place and time, between Katrina on one hand and complete calm on the other. It doesn't mean you should be on guard for those stormbringer butterflies across the globe. Or whatever the news-junkie analogue is. After all, even if butterflies became extinct we still wouldn't be able, in January, to predict the weather for Game 2 of the World Series (even if we did know where it was going to be).
Interestingly, the Wikipedia entry on the Ray Bradbury story "A Sound of Thunder," which refers to this effect (although before the work on chaos theory which led to the name) doesn't indicate why the story's ending is implausible; and even in the entry on the effect itself, which also mentions the story, it is not criticized in the obvious way (i.e. that the effect as described is not chaotic enough).