Article by Carlo Rovelli: “In the institute where I used to work a few years ago, a rare non-infectious illness hit five colleagues in quick succession. There was a sense of alarm, and a hunt for the cause of the problem. In the past the building had been used as a biology lab, so we thought that there might be some sort of chemical contamination, but nothing was found. The level of apprehension grew. Some looked for work elsewhere.
One evening, at a dinner party, I mentioned these events to a friend who is a mathematician, and he burst out laughing. “There are 400 tiles on the floor of this room; if I throw 100 grains of rice into the air, will I find,” he asked us, “five grains on any one tile?” We replied in the negative: there was only one grain for every four tiles: not enough to have five on a single tile.
We were wrong. We tried numerous times, actually throwing the rice, and there was always a tile with two, three, four, even five or more grains on it. Why? Why would grains “flung randomly” not arrange themselves into good order, equidistant from each other?
Because they land, precisely, by chance, and there are always disorderly grains that fall on tiles where others have already gathered. Suddenly the strange case of the five ill colleagues seemed very different. Five grains of rice falling on the same tile does not mean that the tile possesses some kind of “rice-attracting” force. Five people falling ill in a workplace did not mean that it must be contaminated. The institute where I worked was part of a university. We, know-all professors, had fallen into a gross statistical error. We had become convinced that the “above average” number of sick people required an explanation. Some had even gone elsewhere, changing jobs for no good reason.
Life is full of stories such as this. Insufficient understanding of statistics is widespread. The current pandemic has forced us all to engage in probabilistic reasoning, from governments having to recommend behaviour on the basis of statistical predictions, to people estimating the probability of catching the virus while taking part in common activities. Our extensive statistical illiteracy is today particularly dangerous.
We use probabilistic reasoning every day, and most of us have a vague understanding of averages, variability and correlations. But we use them in an approximate fashion, often making errors. Statistics sharpen and refine these notions, giving them a precise definition, allowing us to reliably evaluate, for instance, whether a medicine or a building is dangerous or not.
Society would gain significant advantages if children were taught the fundamental ideas of probability theory and statistics: in simple form in primary school, and in greater depth in secondary school….(More)”.