Tim Harford's Blog, page 19

The rights and wrongs of copying

Should we worry that Rachel Reeves, who is likely to become the UK’s first female chancellor of the exchequer, will be a “cut-and-paste chancellor”? When my colleague Soumaya Keynes reviewed Reeves’s book, The Women Who Made Modern Economics, she stumbled upon a sentence that copied an uncredited source almost verbatim. It wasn’t hard to find several other examples of what most people would regard as plagiarism.

This is embarrassing for Reeves, but then again it would have also been embarrassing if she had instead been caught paying a stingy tip in a restaurant, or not returning a book to a library. Moments of carelessness or disregard for others are unbecoming. Although: he that is without sin among you, let him first cast a stone.

I am more interested in what the kerfuffle teaches us about copying and creativity in an age of information abundance. Let’s start with this sentence: “Laurencina was the daughter of a Liverpool merchant, Lawrence Heyworth, whose own family had been weavers at Bacup in Lancashire.” This sentence appeared on a website, Rethinking Poverty, before migrating — with only a different spelling of Lawrencina — to Reeves’s book.

That’s awkward. Yet it is hardly the theft of a significant idea. The biographical detail about the father of the mother of the economist Beatrice Webb is trivial. It is exactly the kind of thing most researchers would happily learn from a single credible source. A wiser writer (or research assistant) would have simultaneously concealed the borrowing in the text and acknowledged it in the endnotes. But this quickstep is a defensive manoeuvre aimed at protecting the author’s reputation for integrity (a reputation which, in the case of Reeves, has rightly been tarnished). The Rethinking Poverty website would earn no traffic either way, and the reader simply does not care.

The whole game of intellectual ownership here has been so stylised that it is hard to discern the purpose, even if we all recognise the rules. For example, when the second paragraph of this column lifted 13 words verbatim from the King James Bible, was that plagiarism? Obviously not. But only because everyone knows that I was quoting from the Bible. If the copying is blatant enough, it is no longer plagiarism but homage.

It feels like there should be a simple rule that we could apply, for example, “don’t copy other people’s work”. But as Kirby Ferguson argues in his glorious video essay, “Everything is a Remix”, “copying is at the core of creativity and the core of learning”. Star Wars uses ideas from Fritz Lang’s Metropolis, Akira Kurosawa’s The Hidden Fortress and even Stravinsky’s The Rite of Spring, but it would be fatuous to suggest that either a creative or an economic sin had thereby been committed.

Our confusion about the rights and wrongs of copying is partly because there are so many different ingredients in our soup of intuitions. If I were to print 10,000 copies of Reeves’s book, sell them and keep the revenue, I would be committing one form of intellectual property theft, indirectly stealing money from her and her publisher. If instead I printed “by Tim Harford” on the cover, I would be committing a different form of mischief.

In cases of academic plagiarism, the concern is different again. Teachers are not worried about student plagiarism because they fear someone will be deprived of royalties, but because plagiarism undermines the education process: it tempts the student not to bother studying and makes it hard for the teacher to assess the student’s accomplishments.

For these reasons, it is hazardous to offer a blanket opinion about the rights and wrongs of copying, but let me unwisely do so anyway: I think we fuss too much about it. In the long run, student plagiarists are mostly harming themselves, and so we should discourage them from plagiarism for the same reason that we discourage them from binge drinking or unprotected sex: for their own good.

Copyright exists for a good reason, and it is not to maximise the income of anyone who owns the rights to an act of creation: it is to balance the incentive to create ideas against the right to enjoy or build on the ideas of others. As I’ve argued before, copyright protection is needlessly broad and long, favouring a tiny minority of wealthy creators at the expense of our broader creative culture.

As for the kind of authorial plagiarism of which Reeves is so plausibly accused, we fuss too much about that too. Isn’t it odd that a book can be shallow and derivative without plagiarising — and that a book can also contain plagiarism while being deep and original? It suggests that the kind of plagiarism you can detect with software or a keen eye on Wikipedia might not be the kind of imitation that really matters.

As Malcolm Gladwell argued nearly 20 years ago in The New Yorker, it is absurd to pretend that writing or any other creative act is an act of solitary inspiration, in which no other influences are present. Given that writers will always build on the words of other writers, it is also slightly silly to insist that what matters most is to plaster over the building blocks so they cannot be discerned behind a shallow facade of new phrases. (Gladwell was subsequently accused of plagiarism in later pieces for The New Yorker.)

It is both wise and polite to acknowledge your sources of inspiration, but neither foolishness nor rudeness is a hanging offence. I think a little less of Reeves now, but only a little. And as for the “cut and paste chancellor”? Spare us. Running the finances of the British state is a challenging job, which calls for many qualities. The ability to fake originality isn’t one of them.  

Written for and first published in the Financial Times on 26 January 2023.

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What makes a good prophecy?

A couple of years ago, taking questions on stage in front of a live audience, I was asked to do my duty as an economist and make an economic forecast. But the questioner had a demanding benchmark for what made a good prediction, informing me that the previous keynote speaker at this conference had been a prominent scientist, who warned of a deadly global pandemic. That was in the autumn of 2019. Would my forecast be as good?

I parried the question with two questions of my own: my interlocutor would never hear a more consequential forecast than what he was told in 2019, but had he done anything differently? I knew the answer was no. Why, then, was he so interested in hearing another prediction?

My non-answer was weaselly, yes. But the exchange points to a problem: producers of forecasts frequently give people warnings they ignore, and unless consumers of forecasts are honest with themselves about what they plan to use them for, their demand for a glimpse of the future seems fatuous. Or, to quote George Eliot, “Among all forms of mistake, prophecy is the most gratuitous.”

A reliable forecast can be an invaluable guide to action. Weather forecasts are an example. A prediction that it will rain tomorrow is less certain than a prediction that the sun will rise, but as an aid to planning our day they fall into the same category.

But my questioner wasn’t asking for a weather forecast or anything like it. He wanted me to spin an interesting story about an uncertain future, much as the scientist had spun an interesting story. (His story came true, but let’s not be too awestruck by that.) There are many such stories: about the dangers of artificial intelligence, or the possibility of a Chinese invasion of Taiwan. They are often useless, not because they are wrong (although they often are) but because we have no idea what to do with them.

Tolstoy was quipping about this problem in regards to the war of 1812 when, 50 years later, he wrote War and Peace: “Nothing was ready for the war which everyone expected.” (Dominic Cummings, special adviser to Boris Johnson as the pandemic arrived, quoted these lines in his recent witness statement to the UK’s Covid-19 inquiry.)

To pick a case from the 20th century, the US Naval War College undertook a war gaming exercise in 1932, which made plain the risk that US military bases might be bombed in an aerial attack originating from across the Pacific. As Steven Johnson describes in his 2018 book Farsighted, America’s naval strategists had been given a glimpse of the risk of catastrophe at Pearl Harbor. But they did not respond; instead they hoped for the best.

It is easy to see why some forecasters liken themselves to Cassandra, the Trojan princess cursed with the ability to see the future — and to be ignored. If we are to avoid Cassandra’s fate, there are steps we can take to make our prophecies useful. First, they must be clear and vivid. Cassandra’s warnings were vivid but cryptic: “Keep the bull away from the heifer! She’s caught him in her dress, her engine, on her black horn, striking.”

With hindsight, that was a premonition that King Agamemnon was about to be murdered by his wife, Clytemnestra. But only with hindsight. Better, says Jane McGonigal in her recent book Imaginable, is to visualise specific scenes from a future life. (This practice, sometimes called “episodic future thinking”, is essentially mental time-travel.) A warning in 2019 about a pandemic would have felt more real if it had encouraged people to picture themselves in that pandemic-affected future, each day starting with a Joe Wicks workout and the fortunate few having a cupboard full of face masks, toilet paper and spaghetti.

I can’t promise that episodic future thinking really will unlock the future. I doubt we could have imagined April 2020 from the perspective of October 2019, even if we were certain a pandemic was coming. But any attempt to imagine the future in concrete, everyday terms can be surprisingly insightful.

Second — and this might seem paradoxical — a good prophecy must recognise that the future is unknowable. War and Peace had a line about this, too: “What science can there be in a matter in which, as in every practical matter, nothing can be determined and everything depends on innumerable conditions, the significance of which becomes manifest at a particular moment, and no one can tell when that moment will come?”

That is why I would rather have two vivid, plausible, contradictory scenarios to consider than one. A single forecast offers false certainty, assuming we believe it at all. But two compelling explorations of mutually exclusive futures? Now we are starting to move away from the sterile question “what will happen?” and towards the fertile question “what would we do if it did?”

Third, forecasts need to be crafted with a particular audience in mind. Ideally, that audience would actively participate in the process rather than passively consume the result. War games, role-playing exercises and scenario workshops can all help. If a forecast doesn’t address the concerns and the blind spots of its audience, it will be ignored.

For a forecast to be useful, it is neither necessary nor sufficient that it be accurate. That might seem a bizarre claim, but we only know whether a forecast was accurate when it is too late. In advance, what we can hope for from our prophets is that they open our eyes to different plausible futures, motivate us to anticipate threats and opportunities and remind us that, in the end, the future cannot be known. It can only be imagined.

Written for and first published in the Financial Times on 8 December 2023.

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Cautionary Tales – DANGER: Rocks Ahead! (Classic)

Torrey Canyon was one of the biggest and best ships in the world – but its captain and crew still needlessly steered it towards a deadly reef known as The Seven Stones. This course seemed like madness. But the type of thinking that resulted in such a risky manœuvre is something we’re all prone to…

We have a treasure chest of Cautionary Tales to bring you in 2024, but first we need to take a short rest. This week we’re taking you all the way back to the start, with a classic episode from our Cautionary Tales vault.

[Apple] [Spotify] [Stitcher]

Further reading

Two authoritative books were written about Torrey Canyon shortly after the events described in the podcast, and I’ve relied on both of them.

One is Oil and Water by Edward Cowan, and the other is The Black Tide by Richard Petrow. Both excellent, both long out of print.

For a more contemporary discussion of plan continuation bias I strongly recommend Meltdown by Chris Clearfield and Andras Tilcik.

This book also contains a good description of Marlys Christianson’s study of plan continuation bias in emergency rooms, “More and less effective updating” in Administrative Science Quarterly 2018.

The study of landings at Hartsfield-Jackson airport is Chris A. West’s “The Barn Door Effect“.

The dark tale of Sir Cloudesley Shovell is told in Dava Sobel’s hugely enjoyable book Longitude, although I am sceptical Sir Cloudesley actually survived long enough for anyone to murder him.

Cautionary Tales – When Stalin killed the weekend

What if you could never have the same day off as your friends and family? Would you quit your job? What if it was the murderous dictator Joseph Stalin giving you the order?

The Soviet Union wanted its factories to run every day, all year long. And so in 1929, Stalin killed the weekend: workers were prevented from all taking the same day off at the same time.

In this crossover episode of Cautionary Tales and The Happiness Lab, Tim Harford and Yale professor Dr Laurie Santos tell the story of Stalin’s curious, calendar-reshaping experiment. They explore what it can teach us about time off even today and why the holidays matter so very much.

[Apple] [Spotify] [Stitcher]

Further Reading

Dan Lewis, The Soviet Plan to End the Weekend Now I Know

EG Richards, Mapping Time

Judith Shulevitz Why You Never See Your Friends Any More The Atlantic

Jodi Kantor “As Shifts Vary, Family’s Only Constant Is Chaos” – New York Times 14 August 2014 and Jodi Kantor “Starbucks to Revise Policies to End Irregular Schedules for its 130,000 Baristas” New York Times 15 August 2014

Oliver Burkeman Four Thousand Weeks

Terry Hartig et al. Vacation, Collective Restoration and Mental Health in a Population

Thomas Schelling Micromotives and Macrobehavior

Heather Boushey Finding Time

Why the breakdown of the 9-5 job is making us lonelier

Why does nobody have spontaneous fun any more? You can blame the economists for this one, if you like. Specifically, blame the Soviet economist Yuri Larin, who in May 1929 proposed the idea of nepreryvka, the “continuous work week”.

At the time, most people in the Soviet Union lived according to the rhythm of a traditional seven-day week, with Sunday a day of rest for all and Saturday a second day off for some. Larin’s plan, enthusiastically backed by the Soviet leader Joseph Stalin, would change all that. Larin’s idea was to move to a five-day cycle, with four days working and one day of rest. Workers were handed a slip of paper, yellow, orange, red, purple or green. On this arbitrary basis, their rest days were allocated. Yellow workers all got one day off at the same time; green workers all had a different rest day. The yellows and the greens would never again take the same day off.

You can see why an economist proposed this idea: as long as you don’t think too hard about real people, it has much to recommend it. Many workers would get a day off more often, and everyone would get an equal allocation of time off. Valuable resources from machines to roads to shops would no longer stand idle for one or two days a week but would be used all year round. Since your rest day was shared only with a few, it would be easier to access services on your day off — anything from a haircut to a doctor’s appointment.

But the problem was obvious enough. How could a sports team meet to play on a rest day morning? Or a choir get together to sing? What if one spouse was a yellow and another spouse a green? “What is there for us to do at home if our wives are in the factory, our children at school, and nobody can visit us?” complained one worker. (His complaint is recorded in Mapping Time, a history of calendars by EG Richards.)

And while some Soviet officials rather liked the disruption to people’s ability to gather together, the system was soon regarded as a failure. A collective day of rest was reintroduced in 1931 and, as Stalinist excesses go, nepreryvka is little more than a curiosity.

Yet it is a curiosity that has attracted the attention of contemporary writers. Writing in The Atlantic magazine in 2019, Judith Shulevitz pointed out that many low-income workers had their hours set unpredictably, and at short notice, by a capricious-seeming algorithm. The hours might be too short to pay the bills, or exhaustingly long, but they might also be nepreryvka hours: reasonable enough when viewed in isolation, but desynchronised. This desynchronisation makes it impossible for people to socialise with friends, to join clubs or participate in community activities, or even to see their own partners.

A couple of years later, Oliver Burkeman’s book Four Thousand Weeks pointed out that people at the other end of the economic ladder might be trapped in a nepreryvka of their own making: the hybrid workers, the freelancers and, above all, the digital nomads of Instagram. All had unprecedented control over where and when they worked. They could write code in a Bermuda beach-house. They could handle their emails from a Scottish glen. Or, on a mundane level, they could take a yoga class instead of the morning commute. All very pleasant, but one risk is that they end up doing all these things alone.

When we all worked 9-to-5 at the office, we could bond together in the canteen, meet up for a drink after work on Friday, and feel confident that not only would we be free on Sunday but that all of our friends would be free too. Now everything is out of step: you can do what you want, but good luck finding someone who happens to be free at the same time to do it with you.

The hybrid knowledge worker is in a vastly more privileged position than the zero-hours contractor who could have their social life, education or childcare thrown into chaos by sudden, random demands to show up and start working. Still, both problems are real.

Even Stalin only let the nepreryvka disaster last for a couple of years. Is there any prospect that modern capitalist societies can fix their own problems too? For workers in precarious positions, there is some hope that enlightened self-interest will prevail. For most jobs, it’s surely preferable for a large employer to deal with the cost and hassle of fluctuating business requirements than it is for employees to cope with relentless uncertainty.

As MIT professor Zeynep Ton argued in her book The Good Jobs Strategy, employers who figure this out will get better, more experienced and more committed staff than employers who offload all the costs of uncertainty on to their workforce.

The rest of us may have to rely on some time-honoured traditions. A decade ago, a team of researchers led by the psychology professor Terry Hartig examined the effect of vacation on people’s demand for antidepressants — but they took an unusual approach. As well as asking whether taking a vacation made people feel less in need of antidepressant medication — it does — they also found that the more people were on holiday simultaneously, the happier everyone was.

As Burkeman explains, there’s nothing strange about this: it’s easier to enjoy your holiday if you have other people to enjoy it with.

Which brings me to Christmas. For the Harford family, figuring out who would be where over Christmas and New Year started in July and hit overdrive in October. Such long-range diary planning seems onerous and absurd. Why can’t we be a bit more spontaneous? But if advance planning the Christmas get-togethers is what it takes to escape our self-inflicted nepreryvka, advance planning it shall be. There is a season for spontaneity; Christmas isn’t it.

Written for and first published in the Financial Times on 24 November 2023.

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Have yourself an atelic little Christmas

A strange thing happened to me one Christmas Day afternoon. I was a young adolescent, certainly not too old to enjoy sweets and gifts and the inevitable Bond movie on the telly. Yet after the presents had been unwrapped, and the turkey and pudding consumed, I found myself feeling deflated. I took to my bedroom and lay down in the December dark. When my father found me, I tearfully complained: Christmas was already over, but it wasn’t even four o’clock.

It was all a little juvenile, but then, so was I. Yet perhaps my bout of sadness reflected something more universal. Did not Alexander weep because there were no more worlds to conquer? (Possibly not.) We busy humans are always looking ahead to the moment our goals are achieved. And then what? The feeling of emptiness often stalks the feeling of accomplishment like a shadow.

What distinguishes the teenage me from the adult me — and from many other adults — is that the adult me has far more projects, with far more goals to achieve. When I tick something off the list, I don’t flop in my bedroom; I’m too busy for that. The to-do list is long. I’m not sure the adult me is really wiser than the teenager, though. There is nothing wrong with having goals but — with apologies for the cliché — life must be about the journey as well as the destination.

Oliver Burkeman, in his splendid book Four Thousand Weeks, reflects on the distinction between “telic” and “atelic” projects. (The terms originate, of course, with a philosopher, Kieran Setiya.) Telic projects have a goal, an end state; atelic projects do not. The telic runner works towards the achievement of completing an iconic marathon; the atelic runner enjoys the experience of running and the immediate consequence of feeling fit from day to day. The telic reader hopes to sharpen their skills, impress people with their insight at dinner parties, or pick up some followers on GoodReads. The atelic reader likes books.

As Burkeman ruefully observes, instead of “atelic activity” we could say “hobby”, but that word has “come to signify something slightly pathetic.” Our culture tells us that hobbies are for losers.

A project can be partly telic and partly atelic — both a means to an end and an end in itself. But in that ambiguity lies a trap, because the goal has a tendency to obscure the activity itself. For example, loyal readers may know that I love role-playing games. (The most famous example is Dungeons & Dragons.) They are utterly atelic: a joy to prepare for, a joy to experience with a group of old friends, a joy to remember. They are never complete; you never win or lose.

But recently I found myself starting to plan a game, and before long I was dreaming of relaunching an old gaming fanzine, maybe fundraising on Patreon. A hobby wasn’t enough; somehow it had to become a publication, even a side-hustle. Madness! So if I sound harsh about telic projects, the harshness is directed at myself: too little of my time is spent doing things for their own sake.

Christmas offers an opportunity to observe the struggle between the telic and the atelic. When we haul out the Christmas-card list and churn through it, we are in the world of the telic. When we spend time and thought writing to old friends (or phoning them, or even being so bold as to visit them), we are in the realm of the atelic. One completes a Christmas card list; one does not complete a friendship.

Or consider the venerable tradition of gift-giving. Last year I noted the work of the behavioural scientists Jeff Galak, Elanor Williams and Julian Givi. They argued that we often choose gifts with the moment of unwrapping in mind, even though this is just the beginning of the story as far as the recipient is concerned. As a result we are too focused on surprises, on “humorous” gifts (although even the best punchline soon passes) and on stuff that can be wrapped rather than experiences, which cannot. Another way to see this is that, again, we are obsessed with the moment at which a goal is achieved (present delivered!) even though many of the best gifts endure in someone’s life. If we thought more about the ongoing role a gift might play for the recipient, and less about achieving our own short-term objectives, we’d do a better job of choosing good presents.

Even Santa Claus makes a list and checks it twice, and I cannot imagine preparing for Christmas without a thick wad of checklists. But I’ve come to realise, over the years, that my rather elaborate Christmas preparations no longer have a particular goal; Christmas has become a seasonal hobby of mine. The list is long: decant treats from kitchen cupboards into an old picnic hamper; curate a Christmas playlist; write letters to old friends. Some of it happens, some of it doesn’t, most of it is great fun — and somehow or other, Christmas comes just the same. It is a state of mind I would do well to cultivate all year round.

Written for and first published in the Financial Times on 16 December 2022.

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What the data shows about the UK’s public services doom loop

Everyone in the UK will have their own stories of crumbling public services, but indulge me for a moment while I share mine. A couple of years ago, I applied for power of attorney on behalf of my ageing father, in case it became necessary. The Office of the Public Guardian bungled the paperwork; months later nothing had been done, but my father had died. I was told the fee would be refunded but, more than a year later, that hasn’t happened and the OPG is ignoring my emails.

Here’s another one. A year ago, we contacted the NHS’s Child and Adolescent Mental Health Service, CAMHS, for help with my teenage daughter. CAMHS sent over a stack of questionnaires for her, us and her school to fill out, which all of us duly did. For months, nothing happened. Nearly a year later, CAMHS sent us much the same stack of questionnaires and asked us to start again.

Or another. In May, my son was referred to an NHS orthodontist for treatment, but we heard nothing for months. When my wife popped in to ask whether any paperwork had gone missing, she was told that my son was in the system, but that they were still dealing with referrals from May 2020. The waiting list was more than three years long.

I don’t tell you these tales to gain sympathy. My daughter is fine, my son is fine and I don’t need that refund. And why would you sympathise? I fear that most British readers of this column will be channelling the “Four Yorkshiremen” sketch: “Oh, we used to dream of waiting for three years — it would have been an honour just to know we were on a waiting list” . . . “You were lucky to have your emails ignored. The OPG printed out our emails, soaked them in kerosene and used them to set fire to our house . . . ”

Anyway, one man’s anecdotes mean little enough. To find out whether the problem is real, we need to turn to the data. That data has been gathered in a joint effort by the Institute for Government (IFG) think-tank and the Chartered Institute of Public Finance and Accountancy (Cipfa). Each year they publish a public-services performance tracker, following the state of healthcare, social care, prisons, courts, schools and other services. Each year the story seems to get worse. This year the IFG has been using the less-than-encouraging phrase “doom loop”.

This doom loop encompasses most services you can think of. The crown court backlog has risen more than 50 per cent since March 2020, to about 65,000 cases — a number the IFG claims understates the true problem, since the backlog is now stuffed with more complex cases. The waiting list for elective hospital procedures has increased by almost 70 per cent since the start of the pandemic.

As for emergency cases, there was a longstanding target that fewer than 5 per cent of people would wait longer than four hours to be admitted, transferred or discharged after attending an A&E unit. Four hours is a long “emergency”, so this target never struck me as much of a stretch. Still, on the eve of the pandemic the four-hour benchmark was being missed in 25 per cent of cases. In 2022-23, nearly 45 per cent of cases were missing the four-hour target (unsurprisingly now abandoned). One of those cases was my father, shortly before he died.

The government points to the pandemic and the cluster of public-sector strikes to explain why things are going so badly, but the origins of this doom loop are much older. Take healthcare: according to the IFG, the UK has invested less than the average rich country on capital spending (medical scanners, hospital buildings and the like) and it’s done this almost every year since 1970. The two exceptions, both years under New Labour, can hardly compensate for half a century of scrimping.

The austerity of the decade from 2010, during which healthcare investment was well below typical OECD levels, made matters worse, but it piled pressure on 40 years’ worth of weak foundations.

In the case of St Mary’s Hospital in London, these weak foundations are all too literal. The Financial Times recently reported that the hospital had rotting floor joists, frequent flooding, a hole in one lavatory floor that led to a car park, a ward closed due to a collapsed ceiling, and sewage backing up out of the drains and into the outpatient department. Yet St Mary’s is no longer regarded as an urgent priority for investment, because five other hospitals appear to be in more imminent danger of falling down.

Most public services deteriorated in the decade from 2010 under the pressure of austerity, and then deteriorated again during the pandemic. It is not easy to see how they will recover, since many years of weak economic growth have left the UK somehow achieving the trifecta of high taxes, chronic budget deficits and inadequate public services.

In case you’re still feeling optimistic, another think-tank, the Resolution Foundation, recently launched a report on infrastructure which pointed out that given the likelihood of more extreme weather, the challenges of decarbonising the energy system and the constrictions of Victorian sewers and railways, “a huge increase in investment” would be needed: “some household bills could double”. And I haven’t even mentioned potholes.

What can be done? The IFG argues for less churn in both personnel and policies, better industrial relations and more forward planning for recruiting new public-sector workers and retaining experienced staff — all reasonable ideas, but not the first time they have been raised. Money is clearly also needed — not an emergency splurge, but a stable and sustained plan for investment over decades. It’s hard to see where that money will come from.

The next government — almost certainly with Keir Starmer as prime minister — will start from an unenviable position. Yet they will have one advantage: everyone can see that something must change.

Written for and first published in the Financial Times on 10 November 2023.

My first children’s book, The Truth Detective is now available (not US or Canada yet – sorry).

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Cautionary Tales – How the Radium Girls Fought Back

Mollie Maggia’s dentist planned to remove a painful abscess from her mouth. But to his horror, her jawbone disintegrated at his touch, crumbling and splintering until it resembled ash. Like hundreds of her colleagues, Mollie had been slowly poisoned by her work with glowing radium dust. Eight months after her first toothache, she was dead.

In our previous episode, Cautionary Tales told the story of the “Radium Girls”. Their employers ignored the horrific side effects of the women’s work, resorting to obfuscation and even outright lies to deny their claims that they were getting sick.

In this follow-up interview Tim Harford sits down with Kate Moore, the author of Radium Girls: The Dark Story of America’s Shining Women. Tim and Kate discuss how the women banded together and worked out what was happening to them, as well as how they fought back against their powerful bosses and their monumental legacy.

The simple maths puzzle that shows us how to separate fact from fiction

For certain kinds of questions, there are answers that are simple, elegant and wrong. Take the most famous example of the genre, the “bat and ball” question: if a bat and a ball together cost $1.10, and the bat costs a dollar more than the ball, how much does the ball cost?

This is known as a cognitive reflection problem, because it’s designed to be a test of your ability to stop and think rather than a test of sophisticated maths. There’s a tempting wrong answer: 10 cents. But a moment’s reflection says that can’t be right: if the ball costs 10 cents, then the bat costs $1.10 and the two together don’t cost $1.10. Something doesn’t add up.

The bat and ball problem was developed by the behavioural economist Shane Frederick of Yale University and made famous by Nobel laureate Daniel Kahneman in his book Thinking, Fast and Slow. It’s an elegant illustration of Kahneman’s model of the human mind, which is that we have two modes of thinking. There’s a fast, intuitive processing system, which solves many problems with graceful ease but can also be lured into error, and there’s a slower, more effortful logic module, which can grind out the right answer when it must.

Frederick’s bat and ball problem offers an obvious decoy for the fast-thinking system to grab, while also having a correct answer that can be worked out using simple algebra or even trial and error. Most people consider the decoy answer of 10 cents even if they eventually produce the correct answer. The decoy answer is more popular when people are distracted or rushed and the correct answer takes longer to produce. (Have you got it yet?)

Frederick’s poser is not merely a curiosity: research by the Cornell psychologist Gordon Pennycook and others has found that people who score well on problems such as the bat and ball do a better job of distinguishing truth from partisan fake news.

The problem also raises some intriguing questions about the dual-system model of the mind. For example, when people get the answer wrong, what intuitive shortcut is leading them astray? And are they really wrong because they are careless? Or is it because the puzzle is beyond their capabilities?

In a fascinating new article in the journal Cognition, Andrew Meyer and Shane Frederick unleash a barrage of new studies, many of them subtle tweaks of the bat and ball problem. These tweaks enable Frederick and Meyer to distinguish between people who err because they subtly misread the question and those who thoughtlessly subtract the smaller number from the larger one. The truth is murkier than the fast- and slow-thinking model: there are different intuitions and different ways to be wrong.

I suppose that shouldn’t be a surprise. Pennycook reminds me that “the bat and ball question is just a single problem and if you think about the way we think in the real world, it’s obvious that our intuitions are varied and complicated”.

What blew my mind about Meyer and Frederick’s article was the way they painstakingly undermined the idea that made the bat and ball question famous — which is that many people can figure out the right answer if only they slow down for long enough to avoid the decoy. Meyer and Frederick suggest that this is not the case. They try variants on the question: in one case people are told, “HINT: 10 cents is not the answer”; in another they are offered the bold prompt, “Before responding, consider whether the answer could be five cents”. Both prompts help people find the right answer — which is, yes, five cents — but in many cases, people still don’t figure it out.

Some experimental subjects were given the question, followed by the bold and explicit statement: “The answer is five cents. Please enter the number five in the blank below: ___ cents.” More than 20 per cent of people did not give the correct answer despite being told exactly what they should write. Are they just not paying attention at all? Surely not.

“They definitely ARE paying attention,” Frederick tells me in an email. More likely, he says, they are stubbornly clinging to their intuitive first guess and are fearful of being tricked by a malevolent experimenter.

Pennycook agrees. “There’s always 20 per cent,” he offers, somewhat tongue in cheek. “Twenty per cent of people have crazy beliefs, 20 per cent of people are highly authoritarian.” And 20 per cent of people will not write down the right answer to a maths problem even when it’s handed to them on a plate, because they trust their gut more than they trust some tricksy experimenter.

Meyer and Frederick propose that we could sort the responses to the bat and ball question into three buckets: the reflective (taking the time to get it right the first time), the careless (who succeed only when given a prompt to think harder) and the hopeless (who cannot solve the problem even with heavy hints).

If this was just about funny logic puzzles, it would all be good clean fun. But the stakes are higher: remember Pennycook drew a clear connection between the ability to solve such puzzles and the ability to spot fake news. I argued in my book How to Make the World Add Up that a few simple mental tools would help everyone think more clearly about the numbers that swirl around us. If we calmed down, slowed down, looked for helpful comparisons and asked a couple of basic questions, we’d get to the truth.

I didn’t have the vocabulary at the time, but implicitly I was arguing that we were careless, not hopeless. I hope I was right. After some reflection, I am not so sure.

Written for and first published in the Financial Times on 3 November 2023.

My first children’s book, The Truth Detective is now available (not US or Canada yet – sorry).

I’ve set up a storefront on Bookshop in the United States and the United Kingdom. Links to Bookshop and Amazon may generate referral fees.

The simple maths puzzle that shows us how to seperate fact from fiction

For certain kinds of questions, there are answers that are simple, elegant and wrong. Take the most famous example of the genre, the “bat and ball” question: if a bat and a ball together cost $1.10, and the bat costs a dollar more than the ball, how much does the ball cost?

This is known as a cognitive reflection problem, because it’s designed to be a test of your ability to stop and think rather than a test of sophisticated maths. There’s a tempting wrong answer: 10 cents. But a moment’s reflection says that can’t be right: if the ball costs 10 cents, then the bat costs $1.10 and the two together don’t cost $1.10. Something doesn’t add up.

The bat and ball problem was developed by the behavioural economist Shane Frederick of Yale University and made famous by Nobel laureate Daniel Kahneman in his book Thinking, Fast and Slow. It’s an elegant illustration of Kahneman’s model of the human mind, which is that we have two modes of thinking. There’s a fast, intuitive processing system, which solves many problems with graceful ease but can also be lured into error, and there’s a slower, more effortful logic module, which can grind out the right answer when it must.

Frederick’s bat and ball problem offers an obvious decoy for the fast-thinking system to grab, while also having a correct answer that can be worked out using simple algebra or even trial and error. Most people consider the decoy answer of 10 cents even if they eventually produce the correct answer. The decoy answer is more popular when people are distracted or rushed and the correct answer takes longer to produce. (Have you got it yet?)

Frederick’s poser is not merely a curiosity: research by the Cornell psychologist Gordon Pennycook and others has found that people who score well on problems such as the bat and ball do a better job of distinguishing truth from partisan fake news.

The problem also raises some intriguing questions about the dual-system model of the mind. For example, when people get the answer wrong, what intuitive shortcut is leading them astray? And are they really wrong because they are careless? Or is it because the puzzle is beyond their capabilities?

In a fascinating new article in the journal Cognition, Andrew Meyer and Shane Frederick unleash a barrage of new studies, many of them subtle tweaks of the bat and ball problem. These tweaks enable Frederick and Meyer to distinguish between people who err because they subtly misread the question and those who thoughtlessly subtract the smaller number from the larger one. The truth is murkier than the fast- and slow-thinking model: there are different intuitions and different ways to be wrong.

I suppose that shouldn’t be a surprise. Pennycook reminds me that “the bat and ball question is just a single problem and if you think about the way we think in the real world, it’s obvious that our intuitions are varied and complicated”.

What blew my mind about Meyer and Frederick’s article was the way they painstakingly undermined the idea that made the bat and ball question famous — which is that many people can figure out the right answer if only they slow down for long enough to avoid the decoy. Meyer and Frederick suggest that this is not the case. They try variants on the question: in one case people are told, “HINT: 10 cents is not the answer”; in another they are offered the bold prompt, “Before responding, consider whether the answer could be five cents”. Both prompts help people find the right answer — which is, yes, five cents — but in many cases, people still don’t figure it out.

Some experimental subjects were given the question, followed by the bold and explicit statement: “The answer is five cents. Please enter the number five in the blank below: ___ cents.” More than 20 per cent of people did not give the correct answer despite being told exactly what they should write. Are they just not paying attention at all? Surely not.

“They definitely ARE paying attention,” Frederick tells me in an email. More likely, he says, they are stubbornly clinging to their intuitive first guess and are fearful of being tricked by a malevolent experimenter.

Pennycook agrees. “There’s always 20 per cent,” he offers, somewhat tongue in cheek. “Twenty per cent of people have crazy beliefs, 20 per cent of people are highly authoritarian.” And 20 per cent of people will not write down the right answer to a maths problem even when it’s handed to them on a plate, because they trust their gut more than they trust some tricksy experimenter.

Meyer and Frederick propose that we could sort the responses to the bat and ball question into three buckets: the reflective (taking the time to get it right the first time), the careless (who succeed only when given a prompt to think harder) and the hopeless (who cannot solve the problem even with heavy hints).

If this was just about funny logic puzzles, it would all be good clean fun. But the stakes are higher: remember Pennycook drew a clear connection between the ability to solve such puzzles and the ability to spot fake news. I argued in my book How to Make the World Add Up that a few simple mental tools would help everyone think more clearly about the numbers that swirl around us. If we calmed down, slowed down, looked for helpful comparisons and asked a couple of basic questions, we’d get to the truth.

I didn’t have the vocabulary at the time, but implicitly I was arguing that we were careless, not hopeless. I hope I was right. After some reflection, I am not so sure.

Written for and first published in the Financial Times on 3 November 2023.

My first children’s book, The Truth Detective is now available (not US or Canada yet – sorry).

I’ve set up a storefront on Bookshop in the United States and the United Kingdom. Links to Bookshop and Amazon may generate referral fees.