The butterfly effect and A sound of thunder: chaotic cinema

Aston Kutcher had the chance of going back to the past and changing little things there to alter the future in the movie The butterfly effect. A sound of thunder, on the other hand, dealt with millionaires who travelled to the past to amuse themselves hunting dinosaurs. They were seriously warned, though, not to modify anything they could find or see in prehistory, since the consequences of their actions were unpredictable. Putting aside what Einstein’s theory of relativity has to say about time travelling, which is something we will talk about later, the question is: can a little change in the past really modify the future in a significant way?

We mentioned, when dealing with the problem of scale in King Kong, that the human mind thinks in a linear way but reality doesn’t always work like that. Machines usually do, as they are human inventions: if we get out of Madrid by car and set our speed at a hundred kilometres per hour, after six hours we will have travelled 600 km, so that we could be reaching Barcelona. What if we don’t start at Madrid exactly, but at Alcorcon, which is a few kilometres away? This is what the mathematicians call a change in initial conditions. Human logic would say that a slight change in initial conditions should result in a slight change in the final result: instead of Barcelona, we would reach some nearby town. It works this way with cars because they are human inventions and they are therefore linear, but in nature we could find that planning a trip Madrid – Barcelona and starting at Alcorcon instead of Madrid can lead us to Sevilla, Rome, Paris or Moscow.

It seems illogical but this is what a researcher named Lorentz found. Trying to predict the weather for the next few days, he measured all the variables he thought could have an influence, like temperature, air pressure, wind speed, etc., and he found out that tiny errors of measurement altered the final result completely. That’s why it is considered impossible at present to predict the weather, even in a rough way, with more than three days in advance. Measuring instruments are never perfectly precise. Measuring a 12 ºC temperature instead of a precise temperature of 12,00000000000034 ºC seems to be an insignificant error, but it can make our calculations predict rain instead of sun for tomorrow. These systems in which the results of changes in initial conditions are unpredictable, instead of proportional, are called chaotic systems, and chaos theory studies them.

Lorentz explained his theory with his famous metaphore that a butterfly shaking his wings could produce a hurricane. He was proving something that had come to other people’s minds before, the well-known science-fiction writer Ray Bradbury being one of them: he wrote the short story which inspired the film A sound of thunder. The butterfly doesn’t actually produce a hurricane by itself, but, in order to study a chaotic system, even the least important variables must be taken into account: ignoring the little butterfly can lead us to serious calculation errors.

How can nature be so anarchic? The answer is because systems are more stable this way, as paradoxical as it might sound. Any natural system, as a river, a mountain or an ocean, is under the influence of countless little changes at every moment: stones falling, rain, animal action, etc. If the river or the mountain reacted in a linear way to every single disturbance, the river would change course and the mountain would fall down. But chaos provides systems with flexibility: a flexible framework may bend easier than a rigid one, but it is nevertheless much more difficult to break.