A Every society that has farmed land, collected taxes or held religious festivals has needed a way of dividing time into predictable units. The raw materials are supplied by the sky: the day, produced by the rotation of the Earth; the month, marked by the changing phases of the Moon; and the year, defined by the Earth's journey around the Sun. The difficulty is that these three cycles do not fit neatly inside one another. A year contains neither a whole number of days nor a whole number of lunar months, and every calendar ever devised is, in effect, a compromise between them.

B The Moon offered the most obvious starting point. The interval from one new moon to the next averages about 29.5 days. Twelve such months, however, add up to roughly 354 days, which is approximately eleven days shorter than the solar year. A purely lunar calendar therefore slips steadily out of step with the seasons. The Islamic calendar accepts this drift deliberately: the fasting month of Ramadan moves gradually backwards through the seasons, returning to the same point after roughly 33 years. Other peoples, including the Babylonians and the ancient Hebrews, preferred to keep their months tied to the Moon while inserting an additional month every two or three years, producing what is known as a lunisolar calendar.

C The Egyptians took a different path. Their civil calendar ignored the Moon altogether and consisted of twelve months of thirty days each, followed by five additional days set aside for festivals, giving a year of exactly 365 days. Its starting point was traditionally associated with the first appearance of the star Sirius on the eastern horizon shortly before dawn, an event that coincided roughly with the annual flooding of the Nile, on which Egyptian agriculture depended. Because the true solar year is nearly a quarter of a day longer than 365 days, however, the civil calendar crept forward by one day every four years, so that over the centuries its new year wandered through all the seasons. A decree issued in 238 BC under Ptolemy III proposed adding a sixth extra day every fourth year, but the reform was largely ignored, and the old system persisted.

D Rome's calendar was less orderly. By the late Republic, responsibility for keeping the calendar aligned with the seasons lay with a group of priests known as pontiffs, who could insert an extra month whenever they judged it necessary. In practice, these decisions were often shaped by politics: a year might be lengthened to extend the term of a friendly magistrate, or left short to curtail that of a rival. By the 40s BC, the official calendar had drifted around three months away from the seasons it was supposed to reflect. Julius Caesar, who had recently spent time in Egypt, resolved to end the confusion and consulted Sosigenes, an astronomer from Alexandria. The year 46 BC was extended to 445 days to bring the calendar back into line — a year later writers called 'the last year of confusion' — and from 45 BC onwards the Roman year had 365 days, with an additional day inserted every fourth year.

E The Julian calendar was a remarkable improvement, but it rested on a slight overestimate. Its average year of 365.25 days is about eleven minutes longer than the time the Earth actually takes to complete its cycle of seasons. The discrepancy is tiny, yet it accumulates to a full day roughly every 128 years, and for the Christian Church it became a growing embarrassment. The date of Easter depends on the spring equinox, which, following the Council of Nicaea in AD 325, was conventionally fixed at 21 March. As the centuries passed, the real equinox arrived progressively earlier in the calendar, and by the sixteenth century it was occurring around 11 March, so that Easter was being calculated from a date that no longer matched the sky.

F Pope Gregory XIII finally acted after generations of debate. The scheme he adopted was based largely on the work of Aloysius Lilius, a Calabrian physician with a keen interest in astronomy, who had died before it could be implemented; it was then refined and defended by the Jesuit mathematician Christopher Clavius. Announced in a papal bull of February 1582, the reform had two parts. First, ten days were removed from the calendar, so that Thursday 4 October 1582 was followed directly by Friday 15 October. Second, to prevent the error from reappearing, the rule for leap years was modified: years marking the end of a century would be leap years only if they were divisible by 400. The result is an average year of 365.2425 days, accurate enough that it will take more than three thousand years to drift by a single day.

G Adoption, however, was anything but uniform. Catholic states such as Spain and Portugal made the change almost immediately, but many Protestant governments were reluctant to follow an instruction issued by Rome. Britain and its American colonies held out until 1752, by which time the gap had grown to eleven days; Wednesday 2 September was followed by Thursday 14 September, and the official start of the year was moved from 25 March to 1 January. Stories of crowds rioting over their 'stolen' days have little historical support. Russia did not switch until 1918, after the revolution, which is why the 'October Revolution' of 1917 is commemorated in November. Today the Gregorian system is the international civil standard, though many societies still consult lunar calendars to fix their festivals.

A Few events have inspired as much dread, or as many written records, as the arrival of a locust swarm. Of the various locust species found around the world, the desert locust, Schistocerca gregaria, is generally regarded as the most destructive. In quiet periods, known as recessions, it lives at low densities across the deserts of North Africa, the Middle East and south-west Asia, an area of some 16 million square kilometres spanning about 30 countries. During a major plague, however, swarms can invade around 29 million square kilometres in more than 60 countries — roughly a fifth of the Earth's land surface.

B For much of the nineteenth century, naturalists believed that the solitary insects occasionally found in desert scrub and the gregarious ones that formed swarms belonged to different species. They look and behave so differently that the error is understandable. Solitarious individuals are green or sandy brown, avoid one another, and fly mainly at night. Gregarious ones, by contrast, are attracted to each other; their young, wingless nymphs, known as hoppers, are conspicuously black and yellow and move together in marching bands, while the adults fly by day in vast, cohesive swarms. It was the Russian-born entomologist Boris Uvarov who, in 1921, proposed that such forms were not separate species but alternative 'phases' of the same insect, and that an individual could shift from one to the other depending on how crowded it was. His phase theory remains the foundation of locust science.

C How crowding produces this transformation was clarified only recently. In a series of experiments around the turn of the millennium, Stephen Simpson and colleagues at the University of Oxford showed that the critical stimulus is touch. When solitarious locusts were repeatedly stroked on the hind legs with a fine paintbrush, simulating the jostling that occurs in a dense group, they began to behave gregariously within a few hours. The sight and smell of other locusts, by comparison, had a considerably weaker effect. A 2009 study by Michael Anstey and colleagues, published in the journal Science, identified the substance responsible: crowding triggers a sharp rise in serotonin, a messenger molecule in the nervous system, and locusts treated with drugs that block serotonin failed to become gregarious even when crowded. Behaviour, then, can switch rapidly. Changes in colour and body proportions take far longer, developing over successive moults, and there is evidence that gregarious females pass a predisposition to swarm on to their offspring through a chemical added to the foam that surrounds their eggs.

D Swarms do not appear at random; their origins lie in the ecology of the desert itself. Unusually heavy rain allows females to lay their eggs in moist sandy soil and produces the green vegetation on which the hatchlings feed. When the vegetation subsequently dries out, the expanding population is squeezed into the shrinking patches of green that remain, and it is in these crowded refuges that gregarisation begins. The upsurge that devastated East Africa between 2019 and 2021 illustrates the process. Two cyclones in 2018 dropped exceptional rain on the Empty Quarter of the Arabian Peninsula, a region so remote that breeding there went largely undetected for several generations, and Kenya later suffered its worst invasion in seventy years.

E The scale of a mature swarm is difficult to grasp. A single square kilometre may contain between 40 and 80 million adults. Each locust weighs about two grams and can consume roughly its own weight in fresh vegetation every day, which means that a swarm covering just one square kilometre eats as much in a day as around 35,000 people. Swarms can also cross formidable barriers: in October 1988, swarms from West Africa flew across the Atlantic and reached the Caribbean, a journey of roughly 5,000 kilometres that took about ten days.

F Because swarms are so hard to stop once they have formed, the emphasis today is on early warning. The Desert Locust Information Service of the UN Food and Agriculture Organization (FAO), based in Rome, gathers reports from national survey teams across the recession area, combines them with satellite estimates of rainfall and vegetation, and issues bulletins that can forecast developments up to six weeks ahead. Field officers now record their observations on a rugged handheld system called eLocust, which transmits the data by satellite to national centres and to Rome, eliminating the delays of handwritten forms. The weakest link is often access: in parts of Yemen, Somalia and the Sahel, armed conflict has at times made it too dangerous for survey teams to visit potential breeding grounds.

G Control has traditionally relied on chemical insecticides, sprayed from vehicles or aircraft over hopper bands and settled swarms. Such campaigns can be enormously expensive: the response to the 2003–2005 upsurge in West and North Africa cost more than US$400 million. Chemicals also pose risks to human health and to other species, including the natural predators of locusts. An alternative emerged in the 1990s from an international research programme known as LUBILOSA, which developed a biological pesticide based on the fungus Metarhizium acridum. Because it takes between one and three weeks to kill, it is better suited to treating hopper bands early in an outbreak than to halting swarms already on the move. Specialists broadly agree that prevention — detecting and treating outbreaks in the recession area before swarms can form — is far cheaper than responding to a plague. Yet the long quiet intervals between upsurges tend to erode both funding and expertise, so that each new crisis risks finding governments less prepared than the last.

A For most of the twentieth century, the rhythm of the modern city was set by the commute. Every weekday morning, millions of people poured into central business districts, and every evening they poured out again. The pandemic of 2020 interrupted that rhythm abruptly, in what has been called the largest unplanned experiment in working life. Several years on, the experiment has not entirely ended. Offices have reopened, and many employers now insist on a minimum number of days on site, yet in a large number of major cities weekday attendance remains noticeably below its pre-pandemic level, with buildings busiest from Tuesday to Thursday and conspicuously quiet on Mondays and Fridays. Whether that is good or bad for cities is a question on which economists, planners and commentators remain sharply divided.

B The most alarming forecast comes from the finance economists Arpit Gupta, Vrinda Mittal and Stijn Van Nieuwerburgh, who have warned of a possible 'urban doom loop'. Lower demand for office space reduces the value of commercial buildings; since taxes on those buildings make up a significant share of many city budgets, falling values eventually mean less revenue; less revenue forces cuts to public transport, policing and maintenance; and a shabbier, less safe city centre drives away still more workers and businesses. Each step, on its own, is plausible, and the logic of the chain is difficult to fault. What I find unconvincing is its unstated premise: that a city centre is, at heart, a place for offices, and that once office workers leave, nothing of equal value can take their place.

C Not everyone shares this gloom. The Stanford economist Nicholas Bloom has documented what he and his co-author Arjun Ramani called the 'donut effect': the movement of residents, spending and business activity out of large city centres and into the surrounding suburbs. Seen from the suburbs, this looks less like decline than redistribution, as local high streets that once emptied during the working day now support cafés, gyms and shops. Bloom's earlier research also suggested that remote work can benefit employers. In a well-known experiment at a Chinese travel company, call-centre staff who were randomly assigned to work from home improved their performance by around 13 per cent and were considerably less likely to quit. These are striking findings, but caution is needed in generalising from them: the work of a call centre is routine and easily measured, and the experience of employees whose jobs depend on collaboration may be quite different.

D A more fundamental objection comes from Edward Glaeser of Harvard, who has spent much of his career arguing that the defining advantage of cities is the speed with which ideas pass between people in close proximity. Much valuable knowledge, in his view, is tacit: it is absorbed by watching how an experienced colleague handles a difficult client or recovers from a mistake, rather than learned from a manual or a video call. Junior employees, who have the most to gain from such informal learning, are therefore the people most disadvantaged by a largely remote workplace. I find this the most persuasive of the arguments against remote working, although it seems to me to concern the development of individual careers more than the fate of cities as such; a firm could, in principle, bring its staff together in a suburban office park and capture many of the same benefits.

E There is also a question of fairness that enthusiasts for remote working tend to overlook. In an influential 2020 analysis, Jonathan Dingel and Brent Neiman of the University of Chicago estimated that only around 37 per cent of jobs in the United States could plausibly be performed entirely at home, and that these were disproportionately well paid. The cleaners, guards and shop assistants whose livelihoods depended on the daily influx of commuters have no such option. Remote working, I would suggest, is less a universal freedom than a privilege of the professional classes, and its costs are borne largely by those least able to absorb them.

F Environmental arguments, which are frequently made in favour of remote work, are similarly less clear-cut than they first appear. Fewer journeys to the office certainly reduce emissions from transport on the days people stay at home. But heating or cooling thousands of individual homes during the day can offset part of that saving, and workers who use their new flexibility to move further from the city may end up driving longer distances on the days they do commute. The net effect varies with climate, housing and travel patterns, and claims that remote working is unambiguously green should be treated with some scepticism.

G If remote working is to benefit cities, I would argue, it will be because cities adapt to it rather than wait for it to go away. The most frequently proposed remedy is to convert surplus offices into housing, which would bring residents, and with them shops and evening life, back to central districts. The idea is attractive but technically demanding: many modern office blocks have deep floor plates that leave interior space far from any window, and installing kitchens and bathrooms on every floor can be prohibitively expensive. Some cities have chosen to share the burden; Calgary, in Canada, has offered developers grants to convert vacant downtown towers. The centres most likely to thrive are those that diversify, adding universities, cultural venues and green space to the offices that remain. Remote working is neither the salvation of cities nor their ruin; it is a test of whether they can reinvent themselves.