No-one ever thinks they're cured

Posted by Tim Harford

https://timharford.com/2025/04/how-to-cure-premature-enumeration/

https://timharford.com/?p=9193

John von Neumann — the man who created game theory, advanced many branches of mathematics and physics, and did more than anyone to design the modern computer — was someone who attracted a certain amount of mythology.

One story about von Neumann has a colleague setting him a fun puzzle. In this puzzle, two trains, 20 miles apart, chug slowly towards each other down a single track. A fly starts at the front of one train and zips off towards the other, then instantly turns around and zips back again. Back and forth goes the fly, until the trains smash into each other, squashing it between them.

The fly travels at 15mph, and each train puffs along at 10mph. How far does the fly travel before being squashed?

“15 miles,” says von Neumann, instantly.

“Oh, you spotted the trick,” says the colleague, disheartened.

“What trick? I just summed the converging infinite series,” von Neumann replies.

Von Neumann’s biographer Ananyo Bhattacharya — author of The Man from the Future — suspects this tale of blazingly quick calculation is both apocryphal and overblown, since for a mathematician such as von Neumann summing the converging infinite series is less of a feat than we might imagine. But there is a simpler way: notice that the trains will crash after an hour, and the fly is travelling at 15mph.

I almost hope the story is true, because if it is, it suggests that even the great von Neumann engaged in the curious practice of “mindless maths” — plunging into a calculation when calculation is beside the point.

For an example, consider this question: how much dirt is there in an empty hole, 3ft by 3ft by 3ft? If you answered “27 cubic feet”, congratulations: that’s the correct figure for the capacity of the hole. Unfortunately, it’s the wrong answer; the hole is empty.

Here’s another example, from business school researchers Asher Lawson, Richard Larrick and Jack Soll: “Joey went to the store and bought a pack of chips. A bottle of water costs $3, a pack of chips costs $1 and a pack of gum costs $2. How much did he spend in total?”

In their survey, a quarter of respondents answered $6. These people presumably saw the numbers and the word “total” and were too busy calculating an answer to read the question.

“The presence of numbers in a problem tempts people to perform mathematical operations,” write Lawson and his colleagues, “even when the correct answer requires no math.”

Mindless maths is an example of what the psychologists Abraham and Edith Luchins called the Einstellung effect. This German word for “setting” or “attitude” may be best translated here as “set-up”. The Luchinses gave experimental participants a series of problems to solve in which a particular approach always delivered a solution. After that set-up, they were given further problems with much simpler solutions, but cranked through the well-established method instead, missing those easy shortcuts. Metaphorically speaking, they kept reaching for their trusty hammer even when the situation called for a screwdriver.

One lesson, then, is to stop and think. It is no surprise that people who tend to fall for trick puzzles also tend to fall for disinformation. The good news is that spotting fake news doesn’t require vast expertise; the habit of slowing down and calming down usually suffices.

But this is not just a question of spotting fake news. Mindless maths is closely related to what I have termed “premature enumeration”. This sad affliction often affects people who feel comfortable with numbers, and has them leaping to calculate and analyse a numerical claim they see in the news before they have asked some basic questions.

Such questions include “What’s the source of this claim?” and “What definition are they using?”

Sources matter. Some surveys are vast and expensive scientific endeavours; others are clickbait designed to sell ice cream. Some claims are made by independent analysts, others by partisans.

Definitions matter too. Whether you’re pondering a statistic about gun violence or binge drinking, teen mental health or extreme weather events, there is no equation you can solve, no graph you can plot, that will compensate for misunderstanding how these categories have been defined and measured.

So, again: stop and think. Students sitting exams the world over are advised to take their time and read the question properly, and that is sound advice. But even those of us whose last exam was decades ago would do well to reflect for a moment on the claims or the questions in front of us. It is difficult to reach the correct destination without first establishing the starting point.

As for von Neumann and the fly, I’m with Bhattacharya. Von Neumann wouldn’t have fallen for it: part of his brilliance was his unerring eye for the simplest solution to any problem.

In the early 1950s, scientists at the Rand think-tank approached von Neumann for his advice on how to design a cutting-edge computer to tackle a formidable piece of mathematical analysis. Von Neumann asked for more details about the problem, and was treated to a two-hour presentation of every intricacy, with his colleagues scribbling on blackboards and pulling out tables and charts.

Having listened to everything with his head in his hands, von Neumann stared blankly for a while. He looked like “his mind had slipped his face out of gear”, recalled one witness.

Then von Neumann spoke. “Gentlemen, you do not need the computer. I have the answer.”

Written for and first published in the Financial Times on 21 March 2025.

The paperback of “The Next 50 Things That Made The Modern Economy” is now out in the UK.

“Endlessly insightful and full of surprises — exactly what you would expect from Tim Harford.”- Bill Bryson

“Witty, informative and endlessly entertaining, this is popular economics at its most engaging.”- The Daily Mail

I’ve set up a storefront on Bookshop in the United States and the United Kingdom – have a look and see all my recommendations; Bookshop is set up to support local independent retailers. Links to Bookshop and Amazon may generate referral fees.

https://timharford.com/2025/04/how-to-cure-premature-enumeration/

https://timharford.com/?p=9193

Posted by Tim Harford

https://timharford.com/2025/04/the-tao-of-bad-buildings/

https://timharford.com/?p=9181

The most interesting architecture story of recent months is neither Adrien Brody’s Oscar for playing an architect, nor Donald Trump’s executive order “Promoting Beautiful Federal Civic Architecture”. It was the revelation, late last year, that the first building to win the prestigious Stirling Prize is now scheduled to be demolished.

The building, the University of Salford’s Centenary Building, was only completed in 1995 and for nearly a decade it has been largely vacant. The plans to knock it down have frustrated those who argue that it is greener to repurpose a building than to replace it. Former Riba president Jack Pringle has suggested that all Stirling Prize winners should be “listed”, introducing more regulatory barriers to changing or replacing them. But if architects did a better job of making beautiful, practical and adaptable buildings, would such protections really be needed?

About the same time as the Centenary Building was receiving its plaudits from the architectural establishment, the iconoclastic thinker Stewart Brand published a book and presented a BBC television series, both titled How Buildings Learn. Brand was unsparingly critical of much contemporary architecture, but his work was much more than a grumble about carbuncles. Instead, he made a striking and powerful argument: all buildings are predictions, and all predictions are wrong.

Sometimes the errors are obvious and blameworthy. Flat roofs often leak, large windows trap the sun’s heat, hard surfaces reflect noise. No matter how pretty your award-winning library looks on Instagram, such failings will make it unloved if not unusable.

But often the predictions are wrong because they could never have been right. Inventions from air conditioning to the car, the shopping mall to the internet, have reshaped what we can do with buildings and what we need from them. Nobody can reasonably blame the Victorian architect of a quayside warehouse for not anticipating the rise of the shipping container, nor the designer of a fine Georgian townhouse for failing to foresee the coming of the safety elevator. For Brand, then, the mark of a good building is that it gracefully adapts in the face of change.

Building on the work of the architect Frank Duffy, Brand outlined six different layers of a building, from the site to the structure (which can last decades) to the skin and services (cladding and wiring may be changed every decade or so) to the space plan (which may change every few years) and the “stuff” (furniture and appliances in frequent motion). Buildings adapt well when the slow layers such as the structure do not prevent changes to faster layers.

So what sort of buildings age gracefully? Brand outlines three approaches.

First, the “High Road”: build something so staggeringly beautiful that the world will contort itself to preserve it, such as Rouen Cathedral, Chatsworth House or the Parthenon. More practical, however, is the “Low Road”, relying on simple and unpretentious shapes and structures. Old warehouses and terraces endure because they are easy to amend or extend.

Absolutely to be avoided is the third way, which Brand disdains as “Magazine Architecture” — clever exteriors that look good in photographs but are impractical and inflexible for those unfortunate enough to have to inhabit them. A geodesic dome looks amazing, until you want to soundproof it, insulate it, extend it or even put up a set of shelves.

All buildings are predictions, then. But useful as that perspective might be, why stop there? Many other things are also predictions. A marriage is a prediction. So is a new business. So is an institution such as the UK parliament or Nato. And since all predictions are wrong, marriages, businesses and institutions also have to change, whether gracefully or not.

Insert your own metaphor here: strong foundations, expensive renovations, endless leaks. One can push the analogy too far. But Brand’s idea remains insightful. Our lives are shaped by relationships and organisations that must keep adapting to changing circumstances.

Airport bookshops are full of books about corporate adaptability. What is a start-up if not a Low-Road institution, simple, spare and ready to pivot? Marriages and institutions, in contrast, lean heavily on the High-Road idea that nothing will, should or can change. Or perhaps they are more like Magazine Architecture, designed to be photogenic but rotten under the surface.

In fact, marriages often adapt just fine. Step beyond the wedding vows and the impractical dress, and a good marriage is a Low-Road structure after all: unpretentious, unflashy and practical. It is built of timeworn elements, to be adjusted as needed. It is not made for show.

Institutional change is not so easy. Many institutions are High Road at best, and Magazine Architecture at worst. Much of their dignity and their power comes from their pretence at permanence. Nato needs to be flexible, sure — but isn’t the whole point of Nato a certain unyielding constancy? One might say the same for the US constitution.

These institutions have committed themselves to the High Road: grand, noble and often expensive. But they also need to serve a practical function, which means they must adapt. If not, we can all see that the wrecking crews grow ever bolder.

Written for and first published in the Financial Times on 14 March 2025.

Loyal readers might enjoy the book that started it all, The Undercover Economist.

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.

https://timharford.com/2025/04/the-tao-of-bad-buildings/

https://timharford.com/?p=9181