Perhaps the way we start out the day, even a tiny decision or practice, could change the course of one’s life. Nonlinear science—chaos theory to be specific—identifies the butterfly effect, which has become a popular if misunderstood buzzword. The concept originated with MIT meteorology professor Edward Lorenz, who serendipitously discovered the phenomenon while running some weather simulations. He noted that in theory, the flapping of a butterfly’s wings in one part of the world could cause a typhoon somewhere far distant.

Little decisions we make can reverberate profoundly. Movies and books are full of this kind of story, but we often get locked into predictable patterns in our everyday lives. Jump to the last paragraph if you don't want to go through the fun mathy stuff.

The scientific name for the butterfly effect is “sensitive dependence on initial conditions”. Lorenz was running computer simulations to work on weather predictions, using the same modelling equation and, he thought, essentially the same starting points. The first time he ran the simulation, he used 0.506127. The second time he rounded it off to 0.506, assuming it wouldn’t matter.

He expected the simulations to match, but many hours later, when he checked the results, they were totally different. At first he didn't see why. Looking back, he saw that the initial values entered were ever so slightly different, by a tiny fraction. Tiny events—the movement of a butterfly's wings—could create dramatic effects.

The graph below shows this kind of simulation. We can see that very quickly, the red and blue lines, which at first track together, diverge. Like identical twins, they start very close to the same point but may end up very different.

In real-world terms, this means that complex systems—unfortunately including the weather—are hard to........

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