Statisticians know we cannot rely on personal impressions alone

One way to understand China is to look at the statistics. Real income per person has increased nearly tenfold since 1990. Since the early 1980s, the number of extremely poor people in China has fallen by more than three-quarters of a billion people, more than half the population of the country. China consumed more cement in a recent three-year period than the US used in the entire 20th century.

Even on paper, it is the most dramatic explosion of economic activity in human history. Seeing it with your own eyes is another experience entirely.

Nothing in the statistics truly prepared me for a journey across Guangdong, the southern province of China that has been at the forefront of this growth. Start at Hong Kong — the ultimate high-rise city — and walk into its mainland twin, Shenzhen. Then in the shadow of the Ping An skyscraper, which dwarfs the Empire State building, catch a bullet train across the province.

Where London might have a single big block like Trellick Tower, Shenzhen will have a cluster of a dozen identical monoliths, crammed with apartments. Next to that cluster, another dozen of a different design. Then another, and another. Here and there, in the distance across the haze, would be a Manhattan-esque cluster of skyscrapers. The towers marched on and on, all the way — or so it seemed to me — to the city of Guangzhou: 45 minutes or so of high-speed travel through what seemed an infinite vista of concrete.

That night, tucked into bed in the picture-postcard landscape of Yangshuo, I couldn’t sleep. The endless tower blocks scrolled through my mind. What if we had lost our six-year-old son in the middle of Guangdong? So many people. So much concrete.

There was nothing in this experience to contradict the economic data; in fact, the two perspectives on China’s growth were perfectly complementary. But they felt very different. To borrow the terminology made famous by Daniel Kahneman’s book Thinking, Fast and Slow, the statistics spoke to my mental “system 2” — the deliberate, effortful processing of logical or mathematical information. The train journey tapped into “system 1”, a swift and automatic forming of impressions, making of comparisons and recognising of dangers. This was statistics, fast and slow.

Some will be tempted to dismiss the statistics as irrelevant book-learning, and declare that only personal experience matters. There is certainly something in that, especially when a situation is fast-moving or contains soft, hard-to-quantify details. As the Nobel laureate economist Friedrich Hayek remarked, the “knowledge of the particular circumstances of time and place” is important and often neglected.

HR McMaster — who before he was US president Donald Trump’s former national security adviser, was a counterinsurgency pioneer in Iraq — had a similar concern. He once told me the army used to wrongly believe that “situational understanding could be delivered on a computer screen”. It would be convenient if that was possible, but as Gen McMaster and his colleagues learnt the hard way, it is not. Sometimes you have to be there to understand.

But while there is a lot to be said for the rich and vivid lessons of personal experience, they have an obvious limitation: we cannot be everywhere and see everything. And what we do see may be as unrepresentative as the sloppiest of surveys. My trip to China took in tourist spots and high-speed rail links. As a result, I formed an indelible impression of a very particular slice of China.

The skew in our personal experience affects us when at home almost as much as when travelling. We are surprised when an election goes against us: all our friends agreed with us, so why did the nation vote otherwise? Newspapers and television carry tales of lottery wins and fairytale romances, terrorist atrocities or gruesome assaults by strangers. None of these stories reflect everyday life; all of them are viscerally memorable and seem to take place in our living rooms.

And there are more subtle ways in which personal experience can mislead. For example, most of us who ride on London buses will attest that they are packed. Yet the average occupancy of a London bus is just 17 people. How so? Most people witness the full buses — that is why they are full — while empty buses are observed only by their drivers.

It is not quite fair to say that our fast-and-loose “system 1” impression is a lie. It really is true that most people travel on busy buses. But if we want to understand emissions per passenger, we need a statistical perspective.

A new book by the late Hans Rosling and his family, Factfulness, advocates the merits of understanding the world both through the data and through personal experience — not of news stories or tourist traps, but of the everyday lives being lived all over the world.

“Numbers will never tell the full story of what life on Earth is all about,” wrote Rosling, despite being the world’s most famous statistical guru. But the story they do tell matters. In statistics, as elsewhere, hard logic and personal impressions work best when they reinforce and correct each other.

tim.harford@ft.com