Is the world random?

This may sound to you like a pretty philosophical question, but I would like to go mathematical for a minute (bear with me)…then yeah, let’s get philosophical (because observation can only take you so far…let us reason through it too).

Any intro to statistics or probability courses will start with a coin being thrown up in the air…that’s right, the classic Heads or Tails, the “fair coin” discussion and etc. But here is the thing: the probability of Heads or Tails only exists before the coin has been tossed. In principle, given all initial conditions – force, angle, gravity, air resistance, so on and so forth – you can technically predict with certainty which face up the coin will have. But how many of you could say with conviction, even if I did provide you with all the parameters, what would be the outcome of this little experiment? I bet none of you (no, I am not doubting your intellectual capabilities. I have a friend who is getting his PhD in Physics and he had a good laugh from the mere suggestion of such computation). And I am in principle talking about the simplest of experiments – a one shot coin toss with two possible outcomes. What’s happening here?

Well, in Economics we have a concept of “bounded rationality”, which essentially recognizes in the human person the desire to make decisions rationally (i.e. given all the available information, to choose among the options the optimal one); however due to limitations of our own human nature, we are incapable of processing it to the fullest – sometimes because we make computational mistakes, sometimes because we fail to foresee all the links a complex system entails. In other words, even if I gave you all the initial conditions and laws of motion for the coin, chances are you still wouldn’t be certain of whatever computation you came up with to predict the outcome, because you don’t know what to do with all this information, or how they interact with each other. So what do we do with it? Well, we try to understand the Data Generating Process (DGP) as well as we possibly can. So in other words – I may not know if this coin will be Heads up or Tails up once it hits the ground, but I can get pretty close to understanding how this outcome will be determined.

In case you were wondering, or never quite understood the point behind all of those Stats and Probability, or even Econometrics for my fellow economists…that’s it, an eternal attempt to gather data and develop new techniques to get closer to understanding the DGP for the most various things.

So suppose I estimated a DGP for a particular event. So I can use this estimated DGP to predict the world around me…but due to bounded rationality, it won’t be a 100% accurate. The difference between the outcome of the real DGP and my estimated DGP is the error term. Ideally, we want this error term to be as small as possible, and to be oscillating between positive and negative values (if they are consistently positive or consistently negative, there is a clear bias I can fix on my estimation). So in other words, now I know with certainty a bigger chunk of what determines the things that happen in the world, but they are still random because there is this error term, the portion I still can’t explain (maybe because of a determinant variable I can’t observe, maybe because of a relationship between different variables that are relevant but I am yet to realize, maybe even because I measured somes things wrong).

So the world itself isn’t random. Everything has an underlying cause, everything is connected, and every truth you find isn’t but a fragment of the complete and unique Truth of the universe. But the world we observe is random, the world as we understand it is uncertain, because we are incapable of uncovering all the layers and connections of this amazingly complex system.