Clearwater: IELTS Academic Reading practice test

Before machinery could make cold, cold had to be collected. The apparatus for doing so was ancient and simple: a deep pit, walls thick enough to keep the summer out, a layer of straw packed around and between the blocks to stop them freezing into a single mass, and drainage at the bottom so that meltwater ran away instead of standing and accelerating the loss. An ice house of this kind, filled from a frozen lake in January, would still hold usable ice the following October, with perhaps a quarter of it gone. The principle had been understood for two thousand years. What changed in the nineteenth century was that somebody thought of selling it.

That somebody was a young Bostonian named Frederic Tudor, who in 1806 loaded a brig with ice cut from a pond near his family's estate and sent it to the island of Martinique. The venture failed comprehensively. There was no ice house at the other end, nobody had any idea what to do with the cargo, and he lost several thousand dollars. He spent the next twenty years failing more intelligently: building storage at the destinations before the ice arrived, and, most importantly, creating the demand. In each new port he gave ice away to bar owners on condition that they served cold drinks at the usual price, until customers came to expect them and would not accept anything else. By the 1830s the business was profitable and Tudor was rich.

The technical breakthrough came from an employee. Nathaniel Wyeth devised a horse-drawn cutter which scored the surface of a frozen lake into a grid of parallel lines, so that uniform rectangular blocks could be levered out instead of being sawn by hand into whatever shapes the saw produced. Uniform blocks could be stacked tightly with no air gaps between them, and ice stacked with no air gaps melts far more slowly. The invention therefore cut the cost of harvesting and the losses in transit at the same time, and it is the reason the trade became large rather than merely ingenious.

At its height the business was astonishing in its reach. Ice cut in Massachusetts in February was carried round the Cape of Good Hope to Calcutta, a voyage of about four months, packed in sawdust that the timber mills had previously thrown away; something like two thirds of each cargo survived, which was enough. The British community in India built ice houses to receive it, and the arrangement lasted until local manufacture displaced it. Norway developed a substantial export trade to Britain from its own lakes, and a particular Massachusetts pond acquired a brand reputation of the kind now associated with mineral water.

What the trade made possible mattered more than the trade itself. The domestic ice box, an insulated cabinet with a compartment for a block delivered every few days, changed what a household could keep. The refrigerated railway wagon, which was simply an ice box on wheels, allowed meat to be slaughtered and dressed in one place and eaten a thousand miles away, which is why the American meat industry concentrated itself in a handful of cities near the railheads rather than remaining beside every market town. Fresh milk, fish and fruit began to travel. A great deal of what people in industrial countries ate by 1900 depended on a pond in New England having frozen.

The end came from three directions at once. Cities had grown, and ice cut from rivers downstream of a city was carrying what the city had put into the river; typhoid was traced to it, and public health authorities began to restrict the sources. A series of unusually warm winters, in which the crop simply did not form, produced what the newspapers of the time called ice famines, with prices multiplying and no supply at any price. And mechanical refrigeration, which had existed since the 1850s and had been too expensive and too unreliable to compete, crossed over.

The shape of that crossover is worth attention, because it is a pattern that recurs. For roughly fifty years the machine was the inferior product: it cost more per ton, broke down, and used ammonia, which is poisonous. Natural ice held the market throughout. Then, within about fifteen years, the position reversed completely, and by the 1920s the natural trade was finished except in remote places. Nothing dramatic happened in 1910 that had not been happening gradually since 1870; the machine improved steadily and the natural product did not, and a steady improvement in one of two competitors produces a sudden change in the market rather than a gradual one.

Almost nothing of this remains except the words. People who have never seen a block of ice still call the appliance an ice box, and the buildings survive here and there in the grounds of country houses, usually mistaken by visitors for wells or for follies. What is worth keeping is the recognition that an entire industry, employing tens of thousands and reshaping world diets, existed to move a substance that is worthless where it is found and available free to anyone with a saw and a cold January.

In 2007 a group of physicists and economists published an analysis of data from thousands of cities in several countries, arguing that a number of quantities vary with a city's population in a regular mathematical way. The claim had two halves. Infrastructure, measured as the length of road surface, the number of petrol stations or the kilometres of electrical cable, grows more slowly than population: double the number of people and you need about eighty-five per cent more of these things, not a hundred per cent more. Socioeconomic quantities, including wages, patents, economic output and also crime and the transmission of disease, grow faster than population, by something in the region of fifteen per cent above proportionality for each doubling.

What made the paper influential was not the numbers themselves but their consistency. The same two exponents, roughly 0.85 for infrastructure and roughly 1.15 for social output, appeared in data from the United States, from China, from Germany and from Brazil, and in data from different decades, which is not the kind of thing that usually happens in the study of human settlements. If it holds, it implies something important: that cities of different sizes are not merely larger and smaller versions of the same thing but are systematically different, and that size itself does some of the work usually attributed to policy, history or culture.

A mechanism was proposed for each half. Infrastructure forms a network that has to reach every point in a space, and networks of this kind enjoy economies of scale for geometrical reasons: a longer trunk serves a larger area, and the additional branches needed grow more slowly than the area does. Social output depends not on the number of people but on the number of interactions between them, and in a larger city people are also closer together, so the interactions available to each person rise as the city grows. The two mechanisms are independent and they predict exponents on either side of one, which is what is observed.

The critics have concentrated, correctly, on a question that sounds procedural and is not: what is a city? The published exponents depend on treating a city as a particular kind of object, and there are at least three candidates. One may take the administrative boundary, which is a political artefact and in many countries excludes most of the suburbs. One may take the built-up area, defined by where the buildings are. Or one may take the functional area defined by where people travel to work. Reanalyses that hold the data constant and vary this definition find that the superlinear exponent moves considerably, and under some reasonable definitions it falls close to one, meaning that output per person does not rise with size at all.

There is a second and more technical objection. Fitting a straight line through a cloud of points on logarithmic axes will always produce a slope, and the slope will always look convincing, which is why a great deal of the literature on power laws in the social sciences has had to be revisited. Confidence intervals were frequently not reported in the early papers, alternative functional forms were not tested against the same data, and when they have been, several datasets fit a curve rather than a straight line at least as well. None of this shows the claim to be false. It shows that the evidence was presented with more confidence than it could carry.

Ana Seferi, who works on urban measurement, has put the position as sharply as anybody: the robust result and the famous result are not the same result. The sublinear scaling of infrastructure survives every change of definition anybody has tried, in every country with usable data, and it is not seriously contested by the critics. The superlinear scaling of output is real in most specifications but substantially smaller than first claimed, sensitive to definition, and absent in some. It is also, unfortunately, the half that appears in policy documents and conference keynotes.

The leap that is made from the famous half is the part that concerns me most. From the observation that output per person rises with city size, it does not follow that cities should be made larger, for two reasons that the literature itself supplies. The costs also scale superlinearly, and by a similar amount: housing costs, congestion delay, certain categories of crime and the transmission of infectious disease all rise faster than population in the same datasets. And an average says nothing about distribution, so a city where output per head has risen by fifteen per cent may be one in which a quarter of residents are worse off. The scaling relations describe what happens. They contain no recommendation whatever.

What survives is worth having, and it is the unfashionable half. If a city of two million genuinely requires only about eighty-five per cent more road, pipe and cable than two cities of one million, then density is not merely a preference of planners but the single most consistent empirical result in the economics of urban form, with direct consequences for emissions, for the cost of public services and for what a government can afford to provide. That finding is robust, replicated and almost never quoted, while the contested half has become a slogan. It is a reasonably typical outcome, and it suggests that what determines which part of a result travels is not how well established it is but how quotable.