the butterfly and the el nino
To give a vivid image of what chaos theory refered to someone came up with the following imaginary scenario: a butterfly somewhere in Japan beats its tiny wings, setting in course a chain of events that triggers an el nino in the southern United States. (The butterfly is not the sole cause of the el nino - many other factors have to be present, but those tiny wing beats might have disturbed the air currents just enough to tip the balance and get the ball rolling.)
The scenario conveys the idea that minute differences in the initial state of a system can, over a period of time, have huge consequences. One important implication is that the behaviour of these systems turns out to be unpredictable. Meteorologists can't predict exactly when and where the next el nino will occur because, for instance, they can't gather information about the movements of all the butterflies in Asia.
Some natural systems can be predicted very accurately. The orbits of the planets, for instance, have been reduced to neat mathematical equations from which the future course of those planets can be precisely predicted. We can pinpoint their locations on every day of the following year; but we can't predict what the weather will be on those days.
In contrast to weather systems, which are difficult to grasp, a simpler system that also behaves chaotically is the game of pinball. Imagine a ball rolling across a frictionless surface and bouncing off circular obstacles. If we assume the ball sets off in a particular direction we can predict the course it will take as it bounces between the obstacles.
The problem arises when we try to actually fire the ball in exactly the same initial direction. There is bound to be some minute discrepancy between the initial conditions in the real system and the system as we described it in our mathematical model. The wing beats of a passing butterfly could be responsible for a discrepancy like this. In other systems this discrepancy would remain practically insignificant, but with the circular obstacles every time the ball bounces off them the difference between the real angle and the predicted angle is doubled. If you begin with a very small number and keep doubling it it doesn't take long before the number gets very big indeed.
In systems like this, because we don't know with perfect accuracy all the details of the system at any given moment, we can't predict its future course with any reasonable accuracy beyond a short period of time.
Does this mean that science has come up against a brick wall and that the project of reducing the whole of reality to a single unified theory has been stopped in its tracks? Not at all. There are perfectly good theories for weather systems and pinball games. They describe perfectly well what generally happens in systems like this - we know perfectly well how balls behave when they collide with circular obstacles. It's just that in practice we can't use these very neat theories to make the kind of impressive long-term predictions we can make with other systems. That's not because the theory is wrong. It is simply a consequence of our inability to get sufficiently accurate figures for all the forces at work in the system.