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. Reasoning of a probabilistic or statistical kind is a potent tool of evaluation and analysis. Not to have it at our disposal leaves us defenceless. To be unclear about notions such as mean, variance, fluctuations and correlations is like not knowing how to do multiplication or division.
This lack of familiarity with statistics leads many to confuse probability with imprecision. Early during the pandemic, scientists mapping and modelling the spread of the virus in the UK were criticised for estimating rather than accurately depicting how severe the virus might be. Criticisms of their “dodgy predictions” proceeded from a misunderstanding: dealing in uncertainty is exactly why statistics is helpful.
Without probability and statistics, we would not have anything like the efficacy of modern medicine, quantum mechanics, weather forecasts or sociology. To take a couple of random but significant examples, it was thanks to statistics that we were able to understand that smoking is bad for us, and that asbestos kills. In fact, without knowing how to deal with probability, we would be without experimental science in its entirety, from chemistry to astronomy. We would have very little idea about how atoms, societies and galaxies operate.
What is probability? A traditional definition is based on “frequency”: if I roll a die many times, one-sixth of these times the number one will show; hence I say that the probability of rolling a one is 1/6. An alternative understanding of probability is as a “propensity”. A radioactive atom, physicists say, has a “propensity” to decay during the next half an hour, which is evaluated by expressing the probability that this could happen.
In the 1930s, the philosopher and mathematician Bruno de Finetti introduced an idea that proved to be the key to understanding probability: probability does not refer to the system as such (the dice, the decaying atom, tomorrow’s weather), but to the knowledge that I have about this system. If I claim that the probability of rain tomorrow is high, I am characterising my own degree of ignorance of the state of the atmosphere.
We know many things, but there is a great deal more that we don’t know. We don’t know whom we will encounter tomorrow in the street, we don’t know the causes of many illnesses, we don’t know the ultimate physical laws that govern the universe, we don’t know who will win the next election, we don’t know if there will be an earthquake tomorrow. If I catch the virus, I do not know if I will survive.
But lack of complete knowledge does not mean that we know nothing, and statistics is the powerful tool that guides us when we do not have complete knowledge, which is to say: virtually always. Death rates, case rates and R numbers are now a feature of everyday news coverage. A better understanding of statistics and probability would help us all not only to better understand what we know of the pandemic, but also to take wiser decisions, for instance in balancing risks and evaluating whether certain behaviours are safe. There is no certainly safe behaviour, nor a certain way to get ill.
In this uncertain world, it is foolish to ask for absolute certainty. Whoever boasts of being certain is usually the least reliable. But this doesn’t mean either that we are in the dark. Between certainty and complete uncertainty there is a precious intermediate space – and it is in this intermediate space that our lives and our decisions unfold.