How Well Can We Predict The Future?

Suppose you solve a mathematical equation in which you happen to mistake a negative sign for a positive sign, or vice versa, landing an answer horrifyingly different from your peers. Such occurrences are scientifically the sensitive dependence of complex systems on initial conditions. This idea is explored in the famous phenomenon: The Butterfly effect.

The butterfly effect is an intriguing model that stems from the chaos theory. Ironically, the butterfly effect spreads its wings into the meteorological, philosophical, psychological and mathematical world. Though the model seems ambiguous, it has a simple idea. A butterfly could flap its wings in one part of the world, causing a hurricane in another part of the world.

The idea first came to be when meteorologist, Edward Lorenz, ran his weather model with initial condition data. Hence, creating an attractor based on three ordinary differential equations: The Lorenz attractor.

Initially, an arbitrary point is plotted on a three-dimensional plane. Calculated based on preceding points, each successive point is located by stepping forward in time. These points unexpectedly change directions and don’t occur at the same point twice; this forms an attractor. Considered strange, two points seemingly close at one moment are arbitrarily far in the next moment. This is because the attractor diverges all points to separate paths that never cross.

Every possible condition that could be chosen leads to a separate trajectory, and essentially, a disparate future. No matter how minute and insignificant the condition may seem, be it the flap of a butterfly’s wing, it has the power to change the future indefinitely.

“It used to be thought that the events that changed the world were things like big bombs, maniac politicians, huge earthquakes, or vast population movements, but it has now been realized that this is a very old-fashioned view held by people totally out of touch with modern thought. The things that change the world, according to Chaos theory, are the tiny things. A butterfly flaps its wings in the Amazonian jungle, and subsequently a storm ravages half of Europe.”

— from Good Omens, by Terry Pratchett and Neil Gaiman

The theory has its virtues. For example, small changes with positive environmental impacts could have adverse effects on climate change. However, this theory also means predicting future events cannot be accurate, as any unpredictable change leads to an alternate result. For this reason, innumerable scientific and technological predictions turn out to be incorrect.

So why is it that we continue trying to predict things? Maybe it's the unforeseeable nature of the universe. In a place where both the imaginable and unimaginable are possible, perhaps we find comfort in predicting what the future may hold.