A For more than four thousand years the Great Pyramid at Giza has prompted a deceptively simple question: how was it done? Built for the pharaoh Khufu around 2560 BC, the monument originally rose to roughly 146 metres and contains an estimated 2.3 million blocks of stone, with an average weight of around two and a half tonnes. No ancient Egyptian text describing its construction has ever been found. The Egyptians, it seems, saw no need to record techniques that every builder already knew, and so modern explanations have had to be pieced together from archaeology, experiment and a good deal of informed guesswork.

B The earliest surviving account comes from the Greek historian Herodotus, who visited Egypt in the fifth century BC, some two thousand years after the pyramid was completed. He was told by local priests that 100,000 men had laboured in three-month shifts for twenty years, and that the stones had been lifted from tier to tier by machines made from short pieces of timber. Herodotus portrayed the project as forced labour imposed by a harsh king, a picture that popular culture, Hollywood included, later turned into armies of whipped slaves. Most Egyptologists now regard both his figures and his account of the workforce as unreliable, although his lifting devices still have a handful of supporters.

C The case against slavery rests largely on discoveries made since 1990, when a tourist's horse stumbled over a low mud-brick wall south of the plateau and exposed a cemetery belonging to the workers themselves. The tombs, positioned within sight of the king's monument, contained bread and beer for the afterlife, and many skeletons showed fractures that had healed cleanly, implying that injured labourers received medical care. Nearby, a team led by the American archaeologist Mark Lehner excavated a settlement with bakeries, storehouses and long dormitory-like halls, along with enough cattle, sheep and goat bones to suggest that the workforce ate meat regularly. Current estimates put the number of people involved at any one time at somewhere between 10,000 and 30,000: a permanent core of skilled craftsmen supported by rotating teams of conscripted farmers, many of whom would have been free during the months when the Nile flood covered their fields.

D Transporting the stone was a separate challenge. Most of the core blocks were cut from quarries on the Giza plateau itself, but the fine white limestone of the outer casing came from Tura, on the opposite bank of the Nile, and the enormous granite beams above the burial chamber, some of them weighing as much as 80 tonnes, were brought from Aswan, more than 800 kilometres upstream. In 2013 the French Egyptologist Pierre Tallet unearthed a collection of papyri at Wadi al-Jarf, an ancient harbour on the Red Sea coast. Among them was the logbook of an official named Merer, who recorded several months spent shipping limestone from Tura to Giza along canals and basins fed by the river. The documents, the oldest inscribed papyri yet discovered, confirmed that boats did much of the heavy work.

E Over land, blocks were almost certainly dragged on wooden sledges. A wall painting in the tomb of Djehutihotep, a provincial governor who lived several centuries after Khufu, shows a colossal statue being hauled on a sledge while a figure at the front pours liquid onto the sand. For many years this detail was interpreted as a ritual gesture. In 2014, however, physicists at the University of Amsterdam showed that sand dampened to the right degree becomes stiff enough to stop a sledge from ploughing into it, roughly halving the pulling force required. Too much water, they found, has the opposite effect, so the workers must have learned the correct proportion through experience.

F The most contested question is how the blocks were raised once the structure grew tall. A single straight ramp running up one side would have needed to be extraordinarily long and, near the summit, almost as massive as the pyramid itself, which most engineers consider impractical. Alternatives include a ramp that spiralled around the outside of the monument, a series of zigzagging ramps on one face, and, most controversially, a corridor built inside the pyramid, proposed by the French architect Jean-Pierre Houdin in 2007. None has been proved, and some researchers suspect that different methods were combined at different stages. A discovery in 2018 at Hatnub, an alabaster quarry in use during Khufu's reign, added a new possibility: a steep ramp flanked by staircases and rows of post holes, suggesting that teams used wooden posts to help haul loads up slopes far steeper than earlier theories had allowed.

G More speculative explanations continue to attract public attention. In 1979 the French materials scientist Joseph Davidovits argued that some blocks were not carved at all but cast in moulds from a limestone paste, a claim that most geologists reject, partly because the stones contain fossil shells lying in their natural positions. Theories involving lost civilisations or visitors from other worlds have no scientific support whatsoever. What the evidence does reveal is arguably more impressive: a state capable of feeding, housing and organising tens of thousands of people, and of coordinating quarries, boats and building sites hundreds of kilometres apart, for the better part of two decades.

A On 10 May 1752, in the village of Marly-la-Ville near Paris, an iron rod some twelve metres tall stood waiting for a storm. It had been erected by the naturalist Thomas-François Dalibard, who was testing a proposal recently published by Benjamin Franklin: that the flash in the sky and the spark from a charged jar were one and the same. When a thundercloud passed overhead, Dalibard’s assistant drew crackling sparks from the base of the rod, and within weeks the experiment had been repeated across Europe. Not every repetition ended well. In St Petersburg the following summer, the physicist Georg Wilhelm Richmann was struck and killed while attempting to measure the electricity gathered by a similar apparatus, becoming the first person known to have died while conducting electrical research. Franklin’s conductor, which offered a safe path to the ground, soon appeared on church towers and public buildings, but the deeper question of how a cloud becomes electrified in the first place would occupy physicists for the next two and a half centuries.

B The broad answer now accepted lies in the turbulent interior of a storm cloud, where soft pellets of hail known as graupel fall through rising crystals of ice in the presence of supercooled water droplets. When the two collide and bounce apart, a small amount of charge passes between them. In a series of laboratory experiments published in 1978, the Japanese physicist Tsutomu Takahashi showed that whether the graupel ended up positive or negative depended on the temperature and on how much liquid water was present, with the sign typically reversing at around −10°C. Because the heavier pellets sink while the lighter crystals are carried upwards, the cloud gradually separates into layers of opposite charge, commonly with a positive region near the top and a negative one lower down.

C This model, however, leaves a notable gap. For a spark to jump through ordinary air at sea level requires an electric field of roughly three million volts per metre, yet instruments flown into thunderclouds by balloon and aircraft have seldom recorded fields more than a tenth as strong. In 1992 the Russian physicist Alexander Gurevich and his colleagues offered a possible way round the difficulty. Energetic particles arriving from space, they argued, constantly knock fast-moving electrons free in the atmosphere; even a modest field could accelerate these electrons to almost the speed of light, and each would liberate others in an expanding avalanche. Support for the idea came two years later from an unexpected direction, when an orbiting observatory designed to study violent events in distant galaxies detected brief bursts of gamma rays rising from thunderstorms below it, radiation that could only be produced by particles moving at tremendous speed.

D Storms, it turned out, were also producing light where nobody had thought to look. For decades, airline pilots had described faint flashes shooting upwards from the tops of storms, but in the absence of photographs such accounts were generally dismissed as optical illusions. Then, in July 1989, a team led by John Winckler of the University of Minnesota, while checking a sensitive low-light camera before a rocket launch, inadvertently filmed two columns of light extending high above a distant storm. The phenomena, now known as ‘sprites’, are reddish discharges that appear between about 50 and 90 kilometres above the ground, lasting only a few thousandths of a second. They have since been joined by a growing list of related events, including upward-moving ‘blue jets’ and expanding rings of light called ‘elves’.

E Satellites have also transformed our sense of how often lightning occurs. Data gathered by an optical sensor launched by NASA in 1995 indicated that the planet experiences roughly 44 flashes every second, the great majority of them over land rather than sea. The single most active location is Lake Maracaibo in Venezuela, where storms form on most nights of the year and the density of flashes exceeds that of anywhere else on Earth. Whether a warmer climate will bring more lightning remains disputed. A 2014 study led by David Romps projected that strikes in the United States could increase by about 12 per cent for every degree Celsius of warming, whereas a 2018 analysis led by Declan Finney concluded that global lightning might instead decline by around 15 per cent by 2100, because warming is expected to reduce the amount of ice in the upper parts of storm clouds.

F Perhaps the most persistent mystery is ball lightning, a glowing sphere said to drift slowly through the air for several seconds, occasionally even entering buildings. For centuries the evidence consisted almost entirely of eyewitness reports, and many scientists doubted that it existed at all. In 2000 John Abrahamson and James Dinniss of the University of Canterbury in New Zealand proposed that when lightning strikes the ground, it may release a cloud of vaporised soil which burns slowly as it combines with oxygen in the air. Then, in 2012, researchers studying ordinary lightning on the Qinghai Plateau in China happened to capture a ball forming just after a strike. Their spectrometers recorded its light for about 1.6 seconds and revealed the signatures of silicon, iron and calcium, elements typical of soil. A single observation cannot settle the question, but it has given one of the longest-standing puzzles in atmospheric science its first measurable data.

A Nudge, the 2008 book co-written by the economist Richard Thaler and the legal scholar Cass Sunstein, argued that the people who design forms, menus and websites are ‘choice architects’ whose decisions inevitably shape what others select. A nudge alters behaviour in a predictable way without forbidding any option or significantly changing financial incentives: moving fruit to the front of a school canteen counter qualifies, whereas removing sweets from sale does not. To ministers weary of unpopular taxes and costly programmes, the prospect was irresistible. Britain established its Behavioural Insights Team, soon known as the ‘Nudge Unit’, in 2010; by the end of the decade the OECD had identified some two hundred public bodies around the world applying behavioural insights to policy. The British team itself was later spun out of government as a company, a sign of how marketable the approach had become.

B The most celebrated successes involve defaults, the option that takes effect if a person does nothing. In a 2001 study, the economists Brigitte Madrian and Dennis Shea examined an American company that had begun enrolling new staff in its retirement savings plan automatically, while leaving them free to withdraw. Among employees hired under the new rule, participation stood at 86 per cent, against 37 per cent among comparable colleagues who had had to sign up themselves. It would be hard to find clearer evidence that inertia, rather than any considered preference, governs a great many financial decisions. Britain applied the same logic nationally from 2012, obliging employers to enrol eligible workers in a pension unless they opted out. Membership among eligible private-sector employees, well under half when the policy began, exceeded four in five by the end of the decade, even though every one of them could have walked away at any time.

C Organ donation became the emblematic case. In 2003 the decision scientists Eric Johnson and Daniel Goldstein compared European countries in which citizens are presumed to consent unless they register an objection with those in which they must record their agreement. The gap was enormous: in Austria, which presumes consent, virtually everyone counted as a potential donor, whereas in neighbouring Germany, where people must opt in, the figure was about one in eight. Yet consent on paper is not the same as organs in operating theatres. Spain, often cited as proof that such laws work, has had one since 1979, but its donation rate climbed only after 1989, when it created a national transplant organisation that placed trained coordinators in hospitals; the doctor who founded it, Rafael Matesanz, has long credited the organisation, not the law.

D Even where nudges work, they may work less well than their reputation suggests. In 2022 the economists Stefano DellaVigna and Elizabeth Linos compared trials reported in academic journals with more than a hundred conducted by two large nudge units in the United States. The published studies implied an average improvement of almost nine percentage points; the units’ own trials, run at scale, produced about 1.4. Part of the difference, the authors concluded, arises because academic studies with disappointing results are less likely to be published at all. That shrinkage should not, however, be mistaken for failure. An improvement of a point or two, obtained for the price of rewording a letter, may still compare favourably with programmes that cost millions.

E A different objection concerns legitimacy. Critics argue that nudges work by exploiting mental shortcuts, and that influence operating beneath awareness sits uneasily with treating citizens as reasoning adults. The Berlin psychologist Ralph Hertwig has proposed an alternative he calls ‘boosting’: rather than redesigning the environment around people’s limitations, governments should strengthen the competences people bring to it, for instance by teaching patients to interpret medical risks expressed as simple frequencies. A boost, he argues, can leave lasting benefits once it is withdrawn. Sunstein’s reply is that there is no neutral way to present a choice: a form must list its options in some order, so the only question is whether such design is done thoughtfully or carelessly. The charge of manipulation seems to me weakest when it is aimed at defaults, since some default must always exist; it carries more weight against techniques that rely on guilt or social pressure.

F The most searching criticism has come from within the field. In 2023 two behavioural scientists who had once promoted nudging, Nick Chater and George Loewenstein, argued that the discipline’s focus on the individual had led public policy astray. Problems such as obesity, poverty in old age and climate change, they contended, are rooted in systems, and treating them as failures of personal willpower risks letting those systems off the hook. Some industries, they noted, have welcomed such interventions precisely because they offer an alternative to tougher rules. Sunstein himself has turned to what he calls ‘sludge’: the paperwork, queues and confusing forms that deter people from claiming benefits to which they are entitled, and which he believes governments should audit and strip away.

G My own view is that both the enthusiasts and the sceptics are partly right. Where inertia is the main obstacle, as with pensions, a well-chosen default is cheap, effective and respectful of freedom. But the deeper risk is not manipulation. It is that the nudge becomes a substitute for decisions that cost governments money or political capital, such as taxing sugar or regulating emissions, allowing them to appear active while the underlying causes remain untouched. The gentle push is a useful instrument; it is not a policy in itself.