Good morning, afternoon, and evening!
We're doing some database and other light server maintenance this weekend (upgrading the version of MySQL we use in particular, but also probably doing some CDN work.)
I expect all of this to be pretty invisible except for some small "couple of minute" blips as we switch between machines, but there's a chance you will notice something untoward. I'll keep an eye on comments as per usual.
Ta for now!
An amateurish burglary in 1950s London ends in murder. One of the men involved is a 19-year-old named Derek Bentley. Bentley has the understanding of a child – and he wasn’t the killer. But the British justice system seems determined to deliver the death penalty. The fate of capital punishment lies in the balance, and so too does the fate of Derek Bentley.
This episode was previously released to subscribers only – for bonus episodes, behind-the-scenes conversations, our monthly newsletter and ad-free listening, please take a look at the Cautionary Club.
Further reading
On Derek Bentley:
“Bentley: The Hangman’s Account.” By Albert Pierrepoint. The Guardian. 31 July 1998.
https://www.derekbentley.com/pierrepoint/wnJUL98.html
“Efforts to save Bentley Fail” The Guardian. 28 Jan 1953.
Regina v. Derek William BENTLEY (Deceased) [1998] EWCA Crim 2516. 30 July 1998.
“Efforts to save Bentley Fail” The Guardian. 28 Jan 1953.
PEELERS PROGRESS Policing Waltham Abbey since 1840 By Bryn Elliott. 2001.
“Let him Have it!” By David Morgan. Inside Croydon. 26 March 2023.
“1953: Derek Bentley hanged for murder.” BBC News.
“A Close up of the notice board, its glass front smashed” Associated Press Photo. 28 Jan 1953.
“Derek Bentley Hanged.” Australian Associated Press. 28 January 1953.
On Crime and Capital Punishment:
Firearms (Amendment) Bill. House of Commons. 11 June 1997.
“Long-Term Historical Trends in Violent Crime” by Manuel Eisner. Crime and Justice. University of Cambridge. 2003
“The Secret Executioner“. By Marcel Berlins. The Guardian. 31 March 2006
The Abolition of the Death Penalty in the United Kingdom. By Julian Knowles QC. 2015
On Lord Goddard:
Crimes of Violence. Hansard. House of Lords. 23 March 1950.
“The Last of the Tiger” Time. 1 September 1958.
“Bentley Judge Attacked” BBC News. 30 July 1998.
“A Chief Justice got away with murder” by Marcel Berlins. The Independent. 2 August 1998.
The first term of my master’s degree in economics was an alarming experience. The econometrics was bewildering. The macroeconomics was even more mysterious. Everything was drenched in incomprehensible mathematics — or, to be more honest, maths that I could not comprehend.
Most worrying of all was the microeconomics: this was a subject that had felt so natural and so enjoyable as an undergraduate, but now, it, too, had retreated into an austere stronghold of calculus. Some relief came with a lecture on Kenneth Arrow’s general possibility theorem, which relies on a different type of mathematics: formal logic.
Why had economists become so enamoured of mathematics — and was any of it useful?
It may be worth winding the clock back to 1960, when the physicist Eugene Wigner published an article with the title “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”. Physics and mathematics had been bedfellows for so long that their partnership seemed inevitable, but Wigner took a step back and asked why.
Take Newton’s law of gravity. Wigner noted that it was based on some commonalities between the orbit of the moon and the parabolic path a stone takes when hurled through the air. Scientists could observe cannonballs dropped from the Tower of Pisa all they liked, but lacking vacuum chambers, stop-motion photography and precise clocks, all their observations were inevitably vague. And yet based on “a single, and at that time very approximate, numerical coincidence” Newton constructed a mathematical law of great precision and generality.
Wigner’s next example was the application of matrix algebra in quantum mechanics. It proved successful, despite the fact that the mathematicians who developed matrix algebra had done so long before the scientific ideas in question had arisen. Time and again, purely mathematical ideas were unleashed upon the natural sciences and, against any reasonable expectation, had conquered all.
Wigner’s essay was influential and widely emulated. One author flipped the title to explore the unreasonable effectiveness of physics in mathematics. The era of Big Data was heralded by three researchers at Google with their article “The Unreasonable Effectiveness of Data”. Economist Vela Velupillai took a swipe at mathematical economics with “The Unreasonable Ineffectiveness of Mathematics in Economics”.
Velupillai’s piece made a surprising attack. Instead of the usual criticism that economics uses unrealistic assumptions, he focused on some of the deep foundations of the most complex theorems in mathematical economics. Velupillai argued that those foundations were built on disputed mathematical territory, and so the proofs were mathematically unsound.
I’m not enough of a mathematician to adjudicate, but I certainly agree with Velupillai this far: if mathematics is to be useful in economics, much depends on choosing the right kind of mathematics. The formal logic I loved so much delivers some delightful insights about the nature of infinity, or whether we can ever coherently talk about “what society prefers” rather than the preference of an individual. But I’m not sure how useful it is for practical policy.
(I have some evidence for this. More than three decades ago, I had the privilege of taking a term of formal logic tutorials with Liz Truss as my tutorial partner. She seemed to acquire a reasonable grasp of Peano arithmetic and Cantor’s diagonalisation argument, and yet somehow these insights did not spare her — or us — from an economic train-wreck. We have just passed the third anniversary of Liz Truss becoming the prime minister, meaning the third anniversary of her no longer being prime minister will be on us before we know it.)
Mainstream economics continues to rely on what we might call Newtonian mathematics: using calculus to optimise, subject to constraints. What is the most profitable combination of price and output for a manufacturer? Which basket of goods maximises consumer utility while staying within a budget?
All useful enough, and yet not really suited to understanding the behaviour of macroeconomic cycles, or weak points in a financial system, or how consumers are persuaded to act against their own interests by sleazy app-designers and conmen.
A variety of alternatives have emerged. Behavioural economists favour a more psychologically realistic description of human behaviour. This is obviously appealing, but the problem is that psychologically realistic humans are not mathematically predictable. Behavioural public-policy wonks thus have to resort to testing promising ideas to see what works. The mathematics required for these experiments was developed by statistician Ronald Fisher and (sadly less famous) the head brewer of Guinness, William Sealy Gosset. The cheerful Gosset was a man who well understood the power of small but rigorous experiments.
I am all in favour of this experimental approach, but we need to be realistic about what can be achieved. Behavioural economics can tell us a bit about the psychology of bubbles, but rather less about why the bursting of the dotcom bubble was mostly confined to the stock market, while the US housing bubble of a few years later developed into the largest financial crisis for decades. That’s not a question about the madness of crowds, but about the deep structure of financial markets. Recommended James Fergusson What are the limits of the AI mathematician?
Another approach, then, is to introduce ideas of economic complexity, borrowing mathematical tools from ecology and late 20th-century physics, used to study networks, chaotic systems and emergent behaviour. Over the years this column has described insights from complexity science ranging from the economics of solar panels to how to prevent a housing bubble.
All this suggests that maybe the problem economics faces isn’t that it is too mathematical, but that the mathematics it has used for decades — one heavily based on classical physics — is needlessly narrow.
A modern economy can be studied in many ways. Historians, anthropologists and even psychiatrists might have something useful to say. But let’s not turn our backs on mathematics. As long as we are broad-minded about what kind of maths might help, and as long as we don’t expect maths to be as unreasonably effective as it is in physics, the mathematicians might still have something to teach us.
Written for and first published in the Financial Times on 25 Sep 2025.
I’m running the London Marathon in April in support of a very good cause. If you felt able to contribute something, I’d be extremely grateful.
![[syndicated profile]](https://www.dreamwidth.org/img/silk/identity/feed.png){kind=small}
tim_harford_feedIn 1983, a plane takes off from Ottawa with less than half the required fuel on board. As the engines cut out one by one, the pilot is left with a ticking clock and an impossible task. But what does a tale of an unusual plane crash have in common with one about a disappearing canal?
For this special episode, Tim is joined by colleagues from across Pushkin’s podcast network. Heavyweight’s Jonathan Goldstein stops by to muse on the cost of mistakes and whether we’re really in control of how many we make. Plus, Nate Silver and Maria Konnikova from the podcast Risky Business have a gambler’s take on the strange science of regret.
Please check out our new Cautionary Club and consider joining for bonus episodes, ad-free listening, monthly video conversations and our behind-the-scenes newsletter.
Further Reading
On the Chesterfield Canal
The Day they pulled the Plug, Nigel Blundell The World’s Greatest Mistakes and Stephen Pile The Book of Heroic Failures.
On the Gimli Glider
Humble Pi by Matt Parker. Freefall by William and Marilyn Hoffer, the official investigation report and reporting in Flight Safety Australia, Soaring Magazine and The Ottowa Citizen.
In 1799, the German adventurer-scientist Alexander von Humboldt set out on what would prove to be a five-year exploration of South America. Young, independently wealthy and almost absurdly energetic, Humboldt took a vast array of instruments with him. A one-man harbinger of the age of big data, he measured the circumferences of cacti, the air pressure and ground temperature near the summit of Mount Chimborazo, and even had time to correct the positioning of Havana on the maps of the Spanish navy.
Humboldt was also deeply curious about the wonders of the new world. He was an exciting writer and a sensitive painter, and would have been puzzled at the suggestion that anyone should have to choose between scientific data and personal experience.
I’ve been thinking about Humboldt as I tried to make sense of YouGov’s recent polling. Since 2011, YouGov have asked survey respondents to pick up to three issues they feel are the most important facing the UK. A few weeks ago, “Immigration and Asylum” became the most popular choice.
This is slightly unnerving, since the last time that was true was the summer of 2016, just before the issue was eclipsed by four glorious years of the most important issue being “Britain leaving the EU”. We don’t necessarily make our smartest decisions when our brains are awash in anxiety about immigration.
It is also slightly puzzling. Why is this suddenly now the issue of the day — rather than the economy (slow growth, persistent inflation, high taxes) or health (widespread chronic illness, long waiting lists for the NHS)?
What would Humboldt make of all this? Does either the data or personal experience suggest that the UK’s most pressing problem is something to do with immigrants?
Start with personal experience. We all have problems in our lives, and some of those problems feel like the kind of things our political leaders should be dealing with. Maybe you’re looking for a job and can’t find one. Maybe you’ve recently been burgled or robbed. Maybe you can’t afford a decent house, have been waiting too long for a medical appointment, or are aghast at how much tax you have to pay.
Any of us can make such a list — a sort of satanic inversion of the gratitude journal. But when I look at my own list I’m quite struck by how hard it is to connect any of my actual, real-world, everyday problems to immigrants in general or asylum seekers in particular.
One possible retort is that migrants actually are lengthening NHS waiting lists and raising my tax bill, I just don’t realise it. Maybe. My impression is the NHS needs as many immigrants as it can hire, but nothing on my tax bill tells me whether asylum seekers are responsible for any significant part of it. Maybe they are.
Another retort is that my experiences don’t represent those of the ordinary UK resident. Fair enough. There are nearly 70 million of us and we’re all entitled to our own headaches. No one person’s experience can come close to reflecting everyone else’s.
Personal experience may not even reflect the truth of what is right in front of us. Just ask MP Rupert Lowe, who a few weeks ago tweeted a photograph with the text “Dinghies coming into Great Yarmouth, RIGHT NOW. Authorities alerted, and I am urgently chasing. If these are illegal migrants, I will be using every tool at my disposal to ensure these individuals are deported.” Lowe also called for “mass deportations. NOW.”
The boat was in fact being rowed from Land’s End to John O’Groats by a team raising money for a motor neurone disease charity. It’s easy to chuckle at Rupert Lowe, but we are all at risk of seeing only what we expect to see.
The economists Alberto Alesina, Armando Miano and Stefanie Stantcheva have conducted some fascinating surveys of public perceptions of a variety of policy issues, and the results on immigration are sobering. UK respondents dramatically overestimate how many immigrants there are and how many of them are Muslim. They overestimate what proportion of immigrants are from north Africa by a factor of 10, and from the Middle East by a factor of two, and underestimate how many are from North America. Respondents underestimate how many are Christian, and also underestimate the education levels and employment status of immigrants relative to the UK-born population. These misperceptions are not unique to the UK — they are common in rich countries.
We should, like Humboldt, pay a bit more attention to the data. Oxford university’s Migration Observatory has curated a useful collection of evidence about migration and the asylum system in the UK. We can see, for example, that the cost of the entire asylum system has soared in recent years, from less than £500mn in 2013/14 to more than £5bn in 2023/24. That is still a small sum relative to the cost of the NHS, which spends £5bn every 10 days or so. But it’s not trivial, and it has grown quickly. The issue has not simply been dreamt up by tabloid editors.
Yet just because the system for processing asylum claims has become overwhelmed does not mean the UK itself has too. Foreign-born UK residents are much more likely to be of working age than the UK-born — and thus less of a fiscal burden. They tend to be healthier than the UK-born, and are much more likely to have a university degree. Seventy-five per cent of them have lived in the UK for more than five years and 90 per cent speak good English. None of this suggests that immigration is likely to usher in any sort of financial, social or cultural calamity.
It is not hard to see how so many people came to worry about immigration. We are surrounded by apocalyptic social media messages and news headlines. But the hard data suggests that the largest of the UK’s very real problems are no more being caused by mass immigration than they are by a group of charity fundraisers rowing past Great Yarmouth.
Then again, the hard data is never as eloquent as a good story. That is why the voraciously curious Alexander von Humboldt sets us such a good example. He’d measure the cactus but he’d also sketch it; drag his barometer up a volcano, but be sure to spin a yarn about the epic climb.
In short: respect the data, but also look carefully at what you see all around you. Above all, think for yourself.
Written for and first published in the Financial Times on 18 Sep 2025.
I’m running the London Marathon in April in support of a very good cause. If you felt able to contribute something, I’d be extremely grateful.
It’s D-Day and the Allies are about to invade Nazi-occupied France. For the landings to succeed, American soldiers on Omaha Beach will have to break through some formidable coastal defences – Hitler’s Atlantic Wall. Sherman tanks will come in very handy – and the Allies have come up with a novel solution for getting them to the beach. These tanks will swim. Everyone from Winston Churchill down thought swimming tanks were a great idea… but were they?
This episode is available exclusively to members of the Cautionary Club, and Pushkin+ subscribers.
Further Reading
The Second World War. Vol II. W Churchill.
Normandy 44 by James Holland
Overlord by Max Hastings
Beyond the Beachhead by Joseph Balkoski
The Maritime Archaeology of Duplex Drive Tanks in the United Kingdom by Thomas Cousins, Thomas Harrison and Dave Parham. Bournemouth University, UK
The Design of Everyday Things by Don Norman
Clay Christensen’s Milkshake Marketing by Carmen Nobel (Harvard Business School)
Don’t Solve the Wrong Problem by Prashant Verma
What is Workplace Innovation? By The European Workplace Innovation Network
Interview with D-Day veterans – D-Day I Was There. BBC News.
![[staff profile]](https://www.dreamwidth.org/img/silk/identity/user_staff.png){kind=small}
mark in ![[site community profile]](https://www.dreamwidth.org/img/comm_staff.png){kind=small}
dw_maintenance - Database maintenancetim_harford_feed - Cautionary Tales – Derek Bentley Must Hangtim_harford_feed - The wrong kind of maths![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
alierak in dw_maintenance - AWS outagetim_harford_feed - Cautionary Tales – The Canal, the Crash and the Ketamine (Pushkin’s Reign of Error)tim_harford_feed - The UK’s problems aren’t caused by immigrationtim_harford_feed - Cautionary Tales – Can You Make A Sherman Tank Float?chimingchiming
