Problem Statement
-
What we are trying to do? Illustrate the Butterfly Effect using the example of effect of the covid pandemic on air traffic, game streaming, air pollution, and suicide rates.
-
The butterfly effect With the advances in science in recent times, it feels like we are advancing towards a society where we have enough resources to predict everything that can happen and maybe also explain how and why of it. For example, we can make accurate hourly weather forecasts up to a few days in the future. Feats like this were not even dreamt of a few centuries ago. This success is also seen in looking into the past. Science enables us to solve uncountable mysteries of the past on a daily basis (yet many more seem to pop up every day).
Given all this, it is possible to think of the future as deterministic and as something we just have to wait for to manifest itself. But here is the catch - every system is deterministic only if you know the current state of the system to infinite precision. This is called sensitive dependence on initial conditions, i.e, any slight difference in the current state could lead us to a completely different future. Why is this the case? This is a characteristic of a chaotic system. The classic examples of a chaotic system are: two-body pendulum and water flow in a pipe. But these are not the only chaotic systems. The more and more we study different systems, we realize that most of the worldly systems are chaotic. Even the earth going around the sun is a chaotic system.
What does it mean to be in a chaotic system? We can never predict anything beyond a small time frame in the future to a decent precision. Take the example of the weather forecast systems. The reason the forecasts are limited to a week in the future is because any prediction we might make beyond that would be just bad. Weather being chaotic in nature, a butterfly’s flapping in Mexico could cause a Hurricane in Florida. Anything could effect anything.
This brings us to the question: Then, how do we determine the chain of causality in a system? The simple answer is: we can’t. All we can do is use domain knowledge and data to give most probable reasons for an event. One might argue that causality could be determined in a Randomized Controlled Test. This is not possible as we would require infinite trails, perfect data (in terms of precision), and zero errors to make any claims of perfect determinism (This is the reason we report significance of our results in an RCT).
Inspiration Our experiment and explanation were inspired from a Youtube video by Veritasium - Chaos: The Science of the Butterfly Effect - YouTube. https://www.youtube.com/watch?v=NTaZGFQNKns