## Randomness

07/05/2012This post is about thoughts I had on randomness and indeterminism. Inspired by "God doesn't play dice" - Einstein

### School

In school, I often solved problems assuming that certain events was intrinsically indeterminable. In signal processing you may assume there is some unknown noise, in economics you plan for uncertainty of markets, and in stats classes you *begin* with the assumption random variables exist and take on different values with various likelihoods. We're then taught to manipulate these objects, defining and deriving different properties of random variables. Finally, we use this knowledge in "practical" applications like finance or engineering.

All this time I never questioned the existence of incalculable events. After all, consider a dice roll or a coin flip. In class these were quintessential examples of real world randomness.

### "Randomness" because of Information Incompleteness

If we look more closely at our coin, I argue that *we only model a coin flip as random because we can't calculate it exactly*. Similarly, *we only model a dice roll as random because we can't calculate all the rotations and collisions associate with a dice roll*. There is in fact nothing random at all about either a dice roll or a coin flip. If your statistics exam gave you more details on exactly how the coin was tossed or dice was rolled, you could solve the problem without any randomness. But then it would probably be a physics exam.

In less words, we *fall back* on modeling outcomes as random whenever we have incomplete information.

### Living by the beach

To drive home the point, imagine if we didn't understand the concept of buoyancy. We live by the ocean, and some objects we throw in sink and some float. We can't actually figure out why, so we run 1000 experiments. In each experiment we throw in some object into the water and note down whether it floats or sinks. At the end of the this very complicated experiment, we come to the conclusion that floating is a Bernoulli random variable with 74.3% of objects sinking and 25.7% floating. Wow! Sounds right to me! In actuality, if we just had a better understanding of the world, we would be able to exactly calculate whether an object will sink or float and remove randomness entirely. Same goes for coin tosses, dice rolls, the weather tomorrow, and ... humans.

### Indeterminism and lack of free will

Here's where it starts getting controversial. Most people would agree that^{[1]}, if you had a computer and physics genius, you could exactly calculate how everything will unfold in a Rube Goldberg machine.

Cartoon of a complicated Goldberg machine

Now, if we had a electro-chemistry/biology/neuroscience genius and a computer, can we calculate exactly how a living cell will behave? Or how about a human? The same type of particles which make up a mechanical Rube Goldberg make up biological humans. If the behavior of the particles of the former can be predicted, why can't humans? Is consciousness and thinking anything more than the effects of neurons firing? A rolling ball which triggers a gear turning is analogous to a neuron firing triggering a muscle flex. Remember that we're not actually concerned about actually predicting human behavior, but rather about knowing whether or not it is predictable at all.

From this, we can look at life as a whole as a big Rube Goldberg which is just unfolding itself; everything is pre-determined and just waiting to happen. Furthermore, if our model of physics (how the world works) was perfect, it would even be calculable!

### Take away

Outcomes are often modeled as random because of incomplete information, not because of genuine randomness. It is within the realm of possibility that *all outcomes* are calculable with an accurate enough model of the world, eliminating the need for random modeling.

Does this mean we should stop teaching how to find the standard deviation of a random variable? Probably not. Random models are a great practical backup plan that have provided tremendous value. So kids, until you come up with an exact deterministic calculus for all outcomes, you can't use this as an excuse for unfinished stat homework.

[1] From my embarrassingly little knowledge of Quantum Mechanics, the latest theories say that there is in fact genuine randomness and incalculability in how matter behaves at this level. If this is true, then randomness has been introduced into the world and so the whole determinism argument falls apart. However, if the current theory simply introduces randomness to satisfy discrepancies between the theory and observed experiments and there exists an accurate deterministic theory, then determinism still holds.