Free will is considered a hallmark of humanity. The ultimate exercise in free will is to create true randomness: You decide when and nobody can predict you. Can humans be random if they want to?
Mathematically randomness is defined as a process with some degree of unpredictability. The simplest random process being so-called white noise processes in which there is no information in the present state about the future: Prob( future | past )= Prob( future ). The statement reads: The probability of the future given the past is equal to the probability of the future.
In physics true randomness only takes place at the quantum level, where e.g. the decay of an unstable isotope is modeled as a random process. So-called deterministic chaos ‘looks unpredictable’; except if you happen to know the underlying dynamics and can compute with very high precision. High-dimensional chaotic processes, e.g., systems at a temperature, are best approximated as random, although the unpredictability here may really be a result of limited memory or computer power. When we physically flip a coin the assumption is that the dynamics is so complicated and high-dimensional (requires massive computation) that we can rely on the outcome being unpredictable.
Randomness is often used to simulate complex processes in computers. So-called Monte Carlo processes are getting more and more popular for evaluation of important high-dimensional integrals in Bayesian statistics. In the computer pseudo-random numbers are typically created by deterministic chaos-like algorithms.
Why would a human aim for randomness? Well, unpredictability can be useful in certain types of games like in poker – when to bluff? Or in football – where to place the penalty kick? Generally speaking, whenever we want keep our intensions secret to opponents, we would like to be random. Although useful when there is a conflict of interest, there is nothing inherently un-ethical about randomness, c.f., the most ethical deed of all, the ‘random act of kindness’. But the problem facing when we want benefit a random good cause is that mostly there is no possibility to flip a coin. So the question is: Can humans flip a mental coin and exercise ultimate free will? The short answer is no!
Humans are not really good at randomness. In a 1972 meta-analysis by carried out by Wagenaar, 14 out of 15 studies report significant deviations from randomness in human generated random sequences. A typical problem facing the free willing human is the so-called negative recency effect. Our random sequences are too regular. Imagine that you are asked to place ten points at random positions in an interval. Your solution would show negative recency if you choose to put them at roughly equal distance. It is like you want them to be too random. But in a real random Poisson point process, some points should be quite close and other more distant. Another problem for human randomness, is lack of memory and boredom which both lead to an over abundance of repeated patterns.
It seems it takes a superhuman effort to produce true randomness. In Daniel Dennett’s book ‘Freedom Evolves’ free will is based on un-consciuous randomness and unequivocally denounced as an illusion. While human freedom is indeed rapidly evolving, Dennett can only allow the notion of a free will to be considered a useful metaphor or model of human behavior. Our in-ability to actively produce randomness can be seen as another manifestation of Dennett’s insight.