When we ask mathematicians if the sequence of dice rolls “666666666” is less random than the sequence “152635224”, they answer no, since both have exactly the same probability of happening. However, one can doubt that these same mathematicians will show themselves impassive if they obtain the first continuation during a game of dice! We all have a certain intuition of chance, which tells us that getting a 6 nine times in a row is more amazing than getting 1, then 5, then 2, etc. Researchers have long tried to understand where this mistaken intuition comes from and what it is based on.
Imagine figures formed by grids of 16 squares, some of which are black, others white (see opposite). Are these patterns the result of chance, or does their construction obey certain rules? This is the question psychologists have asked many participants for decades.
It has long been noticed that some figures seem more random than others to almost everyone. The first grid at the top left, for example, seems to you intuitively not very random, while the one at the bottom right seems to be the result of chance. Psychologists first looked for clues to predict this intuition. What do participants use to judge the degree of hazard? Several clues were put forward, such as the number of boxes of each color or the spread of black boxes, but that did not explain everything.
The idea of many researchers at the time was that the question is just absurd. From a mathematical point of view, each of these figures has exactly the same probability. Also, if one of them seems more “random” than another to almost everyone, it is because we have a biased view of chance.
Yet another idea has emerged more recently: there may be something rational behind this perception of chance.
When you ask yourself if a figure is random, you are not looking to estimate the probability of obtaining it by chance, but rather to determine the probability that this figure was produced by a random process. Although the two statements are alike, they do not mean the same thing. In the mathematical sense, the second question appeals to the notion of algorithmic complexity. Briefly said, a figure is “complex” if there is no simple procedure for producing it.
It actually appeared that we tend to consider a figure as all the more random the more complex it is in the mathematical sense. So we have an intuitive sense of complexity. Where does it come from?
To find out, Anne Hsu, from Queen Mary University in London, and her collaborators studied in 2010 the frequency of appearance of the different patterns opposite in photos of natural scenes (at the scale of one box = one pixel ). Photographs often have large dark areas and large light areas, such as all-black or white grids, appear frequently. The researchers have thus shown that the perception of the randomness of a pattern is correlated with its frequency of appearance: the grids that appear the least in natural scenes are those considered to be the most random. Conversely, uniform grids, which often appear, are judged to be not very random … However, they have low complexity.
Thus, the probability of the appearance of a pattern in the real world, its algorithmic complexity and the impression of chance it gives rise to in us are linked. We have recently shown that the frequency of appearance of patterns in the real world can explain a large part of our perception of complexity. It is therefore partly through the confrontation with the real world that we develop a certain idea of chance, consistent with the mathematical notion.
