How to Make the World Add Up : Ten Rules for Thinking Differently About Numbers

by Tim Harford

That’s the equivalent of comparing the total cost of buying a house with the annual cost of renting one; it’s not a trivial confusion. Net measures are put alongside gross ones – the equivalent of comparing a firm’s profit with its turnover.

First – and most important, since the visual sense can be so visceral – check your emotional response. Pause for a moment to notice how the graph makes you feel: triumphant, defensive, angry, celebratory? Take that feeling into account. Second, check that you understand the basics behind the graph. What do the axes actually mean? Do you understand what is being measured or counted? Do you have the context to understand, or is the graph showing just a few data points? If the graph reflects complex analysis or the results of an experiment, do you understand what is being done? If you’re not in a position to evaluate that personally, do you trust those who were? (Or have you, perhaps, sought a second opinion?) When you look at data visualisations, you’ll do much better if you recognise that someone may well be trying to persuade you of something. There is nothing wrong with artfully persuasive graphs, any more than with artfully persuasive words. And there is nothing wrong with being persuaded, and changing your mind. That’s our next subject.

A man with a conviction is a hard man to change. Tell him you disagree and he turns away. Show him facts or figures and he questions your sources. Appeal to logic and he fails to see your point.

Sometimes we’re interested in sizing up the current situation as a means to anticipate, and perhaps profit from, what will happen next.

We shouldn’t be too quick to judge Fisher. Even if you’re the smartest one in the room – and Irving Fisher usually was – it simply isn’t easy to change your mind.

As we saw in the first chapter, our preconceptions are powerful things. We filter new information. If it accords with what we expect, we’ll be more likely to accept it.

One of the reasons facts don’t always change our minds is that we are keen to avoid uncomfortable truths. These days, of course, we don’t need to mess around with a static-reducing button. On social media we can choose who to follow and who to block. A vast range of cable channels, podcasts and streaming video lets us decide what to watch and what to ignore. We have more such choices than ever before, and you can bet that we’ll use them.

‘Making public commitments “freezes” attitudes in place. So saying something dumb makes you a bit dumber. It becomes harder to correct yourself.’19

‘When my information changes, I alter my conclusions. What do you do, sir?’

ten statistical commandments in this book. First, we should learn to stop and notice our emotional reaction to a claim, rather than accepting or rejecting it because of how it makes us feel.

Second, we should look for ways to combine the ‘bird’s eye’ statistical perspective with the ‘worm’s eye’ view from personal experience. Third, we should look at the labels on the data we’re being given, and ask if we understand what’s really being described. Fourth, we should look for comparisons and context, putting any claim into perspective. Fifth, we should look behind the statistics at where they came from – and what other data might have vanished into obscurity. Sixth, we should ask who is missing from the data we’re being shown, and whether our conclusions might differ if they were included. Seventh, we should ask tough questions about algorithms and the big datasets that drive them, recognising that without intelligent openness they cannot be trusted.

Eighth, we should pay more attention to the bedrock of official ...

sometimes heroic statisticians who protect it. Ninth, we should look under the surface of any beautiful graph or chart. And tenth, we should keep an open mind, asking how we might...

‘Well-placed trust grows out of active inquiry rather than blind acceptance.’

Yale University researcher, Dan Kahan, showed students some footage of a protest outside an unidentified building. Some of the students were told that it was a pro-life demonstration outside an abortion clinic. Others were informed that it was a gay rights demonstration outside an army recruitment office. The students were asked some factual questions. Was it a peaceful protest? Did the protesters try to intimidate people passing by? Did they scream or shout? Did they block the entrance to the building? The answers people gave depended on the political identities they embraced. Conservative students who believed they were looking at a demonstration against abortion saw no problems with the protest: no abuse, no violence, no obstruction. Students on the left who thought they were looking at a gay rights protest reached the same conclusion: the protesters had conducted themselves with dignity and restraint. But right-wing students who thought they were looking at a gay rights demonstration reached a very different conclusion; as did left-wing students who believed they were watching an anti-abortion protest. Both these groups concluded that the protesters had been aggressive, intimidating and obstructive.

the way our political and cultural identity – our desire to belong to a community of like-minded, right-thinking people – can, on certain hot-button issues, lead us to reach the conclusions we wish to reach. Depressingly, not only do we reach politically comfortable conclusions when parsing complex statistical claims on issues such as climate change, we reach politically comfortable conclusions regardless of the evidence of our own eyes.*

expertise is no guarantee against this kind of motivated reasoning: Republicans and Democrats with high levels of scientific literacy are further apart on climate change than those with little scientific education. The same disheartening pattern holds from nuclear power to gun control to fracking: the more scientifically literate opponents are, the more they disagree. The same is true for numeracy. ‘The greater the proficiency, the more acute the polarization,’ notes Kahan.4

one of our stubborn defences against changing our minds is that we’re good at filtering out or dismissing unwelcome information.

A curious person, however, enjoys being surprised and hungers for the unexpected.

Neuroscientific studies suggest that the brain responds in much the same anxious way to facts which threaten our preconceptions as it does to wild animals which threaten our lives.6 Yet for someone in a curious frame of mind, in contrast, a surprising claim need not provoke anxiety. It can be an engaging mystery, or a puzzle to solve.

curiosity starts to glow when there’s a gap ‘between what we know and what we want to know’. There’s a sweet spot for curiosity: if we know nothing, we ask no questions; if we know everything, we ask no questions either. Curiosity is fuelled once we know enough to know that we do not know.7

Next time you’re in a politically heated argument, try asking your interlocutor not to justify herself, but simply to explain the policy in question. She wants to introduce a universal basic income, or a flat tax, or a points-based immigration system, or ‘Medicare for all’. OK: that’s interesting. So what exactly does she mean by that?

Those of us in the business of communicating ideas need to go beyond the fact-check and the statistical smackdown. Facts are valuable things, and so is fact-checking. But if we really want people to understand complex issues, we need to engage their curiosity. If people are curious, they will learn.

What’s false is interesting – but not as interesting as what’s true.

‘only boring people get bored’.

‘The cure for boredom is curiosity,’ goes an old saying. ‘There is no cure for curiosity.’

If we want to make the world add up, we need to ask questions – open-minded, genuine questions. And once we start asking them, we may find it is delightfully difficult to stop.