The previous article I wrote about randomness proved quite controversial. After all, random processes are used all the time to model things in science. How can I say randomness is not a scientific explanation?

Let me first make a distinction between a model and an explanation. A model shows us how some physical thing operates, but it does not explain the cause of the thing. An explanation, on the other hand, tries to explain the cause.

But surely if we can effectively model something with randomness, then randomness must also be part of the causal explanation for the thing? Well, not so fast.

Let’s look at how we model randomness with computers. Computers themselves are not random in the slightest. Computer code is entirely deterministic. So, how can we model randomness with a computer? We use what is known as a pseudorandom number generator. The “pseudo” means the numbers are not really random. But, why do we call them random?

This brings us to the notion of randomness. Randomness is an elusive concept to pin down exactly, but we do know some things about randomness. In particular, when an event is perfectly random, it is completely impossible to predict the event’s outcome. Say a fair coin is flipped in a completely random manner, then regardless of how much we know about the initial conditions of the coin flip, and however much computer power we have, we can never predict the outcome of the flip better than 50/50 odds. This fundamental unpredictability is one of the standard ways that mathematicians define randomness. Which, by the way, makes sense given that the study of randomness often received its practical motivation from gambling. For example, Pascal developed his theory of probability in order to figure out how to fairly divide the winnings of an interrupted game of gambling.

When we test a sequence of numbers for randomness, we are essentially testing how easy it is to predict the sequence of numbers. One of the simplest tests is to measure how frequently heads and tails occur during a series of coin flips. If the distribution is heavily skewed one way or the other after a large number of flips, then we can be pretty certain the coin is not fair. We cannot be absolutely certain, since there is always a small probability for a really long run of heads, but as the run lengthens, the probability of achieving the run with a fair coin drops exponentially. If we cannot find any predictable patterns in a series of numbers, then we say the series is at least pseudo random.

However – and this is the really important point, so pay attention – we can never say a series is truly random just by examining it, since we would have to run an infinite number of randomness tests to look for all conceivable patterns. Thus, without actually knowing the original cause of a number sequence, the best we can ever say is a sequence is pseudo random with regard to the set of randomness tests that we have run. This conclusion is mathematically provable with Kolmogorov complexity.

Now we come to the second really important point, so don’t switch to YouTube just yet! Observe that the reverse is not true. Once we have detected a predictable pattern in a number sequence, then we are able to say, at least with some confidence, the sequence is not random. And the longer the sequence and higher the predictability, the greater our confidence grows.

Back to the pseudo random number generator, this is why we say a sequence of numbers generated by a completely deterministic algorithm is in some sense “random.” It is not truly random, since anyone with the algorithm can predict the sequence. However, if all one has is the sequence of numbers, it is extremely difficult to find the predictive pattern. This makes the sequence of numbers useful for modeling a random process on a computer.

Now here is where we get back to the discussion of whether randomness can be a scientific explanation. As we can see with the pseudo random number generator, we can effectively model processes with randomness on a computer. So, the notion of randomness poses no problem when it comes to modeling. Random models are used all the time.

The problem comes when we try to move from model to causal explanation. Say someone used a pseudo random number generator to model a physical thing, and the model turned out to be really accurate. Can we say this is good evidence the thing is really random? Well, how can we when the very process we used for modeling is entirely deterministic? Such a statement would be a self-contradiction: “I perfectly modeled this process with a deterministic cause, therefore the process is caused by something that is truly random.”

So, we can see that while the concept of randomness does great work in science as a model, it is still impossible for science to conclude that anything is in actuality random. On the other hand, science has no such obstacle when it attributes deterministic causality. Such an attribution can be made, at least with high confidence if not with certainty, because even though we cannot determine when things are random, we can determine when they are not random.

And that, my friends, is why I claim randomness can never be a scientific explanation. It is just humanly impossible to identify true randomness.