Countless experiments show that around 10 per cent of the public don’t understand simple percentages.

MRI studies of the brains of humans (and monkeys!) indicate that we have an inbuilt ‘number sense’, but we are particularly attuned to the numbers one, two and three, and, beyond that, to detecting large (not small) differences in comparing numbers of an object. We often fall back on these evolutionary number skills. But much of life involves calculations that are more complex than comparing the relative size of small numbers. A century ago the great science fiction writer H. G. Wells said: … endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when… for complete initiation as an efficient citizen of one of the new great complex world-wide States that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write. Wells’s reference to how important mathematical understanding is to ‘endless social and political problems’ seems made for our times, but we’ve got a long way to go before we’ll completely satisfy his vision. Countless experiments show that around 10 per cent of the public don’t understand simple percentages.

For example, if you spin a coin twice, what’s the probability of getting two heads? The answer is 25 per cent, because there are four equal-probability outcomes: two heads, two tails, heads then tails and tails then heads. Worryingly, only one in four people in a nationally representative survey got this right

B. Duffy, The perils of perception (2018), loc. 325 & 340

It is not every one who has the courage to bring dogs into an expensive private hotel

It is not every one who has the courage to bring dogs into an expensive private hotel; to bring one dog indicates that you are not accustomed to deny yourself small pleasures for the sake of a few extra shillings; to bring two indicates that you have no fear of hotel-managers and that you are in the habit of regarding your own whim as nature's law.

A. Bennett, The old wives' tale (1908), 422

Chirac, like most men who have once found a woman weak, imagined that he understood women profoundly

Chirac, like most men who have once found a woman weak, imagined that he understood women profoundly. He thought of women as the Occidental thinks of the Chinese, as a race apart, mysterious but capable of being infallibly comprehended by the application of a few leading principles of psychology. Moreover he was in earnest; he was hard driven, and he was honest. He continued, respectfully obedient in withdrawing his arm:

A. Bennett, The old wives' tale (1908), 334

In pastry-making everything can be taught except the "hand,"

Constance could make good pastry, but it was not her mother's pastry. In pastry-making everything can be taught except the "hand," light and firm, which wields the roller. One is born with this hand, or without it. And if one is born without it, the highest flights of pastry are impossible. Constance was born without it. There were days when Sophia seemed to possess it; but there were other days when Sophia's pastry was uneatable by any one except Maggie. Thus Mrs. Baines, though intensely proud and fond of her daughters, had justifiably preserved a certain condescension towards them. She honestly doubted whether either of them would develop into the equal of their mother

A. Bennett, The old wives' tale (1908), 28

You cannot eat a meal in decency without the aid of the Five Towns

They are unique and indispensable. From the north of the county right down to the south they alone stand for civilization, applied science, organized manufacture, and the century—until you come to Wolverhampton. They are unique and indispensable because you cannot drink tea out of a teacup without the aid of the Five Towns; because you cannot eat a meal in decency without the aid of the Five Towns.

A. Bennett, The old wives' tale (1908), 2

And if you have no word for blue, how can you see it?

Since then a more sober explanation has taken hold as the orthodoxy. Analysis of the way in which languages produce words for different colours has revealed that the process is surprisingly consistent, throughout the world and throughout history. In 1969, linguist Paul Kay and anthropologist Brent Berlin published Basic Color Terms: Their Universality and Evolution. It offered, among others, one pertinent hypothesis. If a language had only three basic colour categories, they were almost always words for black/dark, white/light and red. If it had four or five categories, then the additional words tended to refer to green or yellow. Only once a language had six or more basic colour categories did you begin to see more complex colours given their own word. Among those was the colour that we would call blue. In the view of Kay and Berlin, Homer’s Greek didn’t have a word for blue. Colour exists on a spectrum; what isn’t obvious is how you break that spectrum down into different categories. Where does one colour stop, if you don’t have words to describe the two colours either side of the barrier? And if you have no word for blue, how can you see it?

N. Leamon & B. Jones, Hitting Against the Spin: How Cricket Really Works (2021), loc.4,454

Standard deviation ... has fallen steadily year on year and decade on decade

You can see a very clear example of this in baseball. Scoring levels have stayed relatively constant in baseball for 100 years. A good batting average in the 1930s is still a good batting average. But if you look at the standard deviation (a measure of variance, of how spread out the individual scores are) of players’ batting averages by season, it has fallen steadily year on year and decade on decade. Players have collectively averaged the same, but the averages of the best and the averages of the worst each year have got closer and closer together.

N. Leamon & B. Jones, Hitting Against the Spin: How Cricket Really Works (2021), loc.2,338