Saltway: IELTS Academic Reading practice test

Sodium chloride is the only rock that human beings eat. The body cannot manufacture it and cannot manage without it, since salt governs the fluid around every cell, and a person deprived of it altogether will eventually die. A few grams a day are enough, and people who eat a good deal of meat obtain much of what they need from it; communities living mainly on grain and vegetables need rather more. What made salt extraordinary, however, was not that everyone required it but that almost nowhere could produce it. A household could grow its own food and weave its own cloth, but it could not make salt, and so for most of recorded history salt had to be carried, bought and taxed. That combination of universal need and concentrated supply is why a plain mineral shaped roads, cities and governments.

There were three ways of winning it. The simplest was to let the sea do the work: seawater was admitted to shallow ponds and left until the salt crystallised on the floor, a method still used from Portugal to Vietnam. It costs almost nothing in fuel, but it demands a long dry summer and a steady wind, which is why the great salt coasts lie in warm climates. The second was mining. Ancient seas that dried up left thick beds of rock salt buried beneath later sediments, and where these came near the surface they could be cut like stone; the workings at Wieliczka in southern Poland have been in use since the thirteenth century. The third was boiling. Water seeping through a buried bed emerges as brine, and brine can be evaporated over a fire, which is how inland Europe made most of its salt and why the woods around the springs of Cheshire and Luneburg were felled.

Because supply was concentrated, salt travelled, and the most celebrated of its routes crossed the Sahara. At Taghaza, in what is now northern Mali, the mineral lay so close to the surface that travellers reported seeing houses built from it; the slabs were loaded onto camels and carried south to Timbuktu and the cities of the Niger, where the kingdoms of the western Sudan had gold but no salt. The often-repeated claim that the two were exchanged weight for weight is a later embellishment, and the surviving accounts describe nothing so tidy. What is clear is that the rate was good enough to keep caravans crossing one of the harshest deserts on earth for six hundred years.

Europe had salt roads of its own. One of the oldest, the Via Salaria, ran from Rome to the pans at the mouth of the Tiber, and the Latin word for the allowance paid to a soldier has left its trace in the English word salary. Further north the trade was bound up with fish. Herring spoils within a day, and the North Sea shoals lay far from the markets that wanted them, so the whole fishery depended on salt brought from Luneburg and sent on to the Baltic through Lubeck. The merchants who organised that traffic built the Hanseatic League.

A commodity that everyone must buy is also a commodity a government can tax, and few taxes have been more detested than the French gabelle. From the fourteenth century the crown held a monopoly, and across much of the country every household above the age of eight was obliged to buy a fixed quantity each year at a price the state set, whether it needed the salt or not. Rates differed sharply from province to province, which made smuggling irresistible: salt was carried across the internal customs lines on the backs of men, women, children and dogs, and thousands of those caught were sent to the galleys. The tax was swept away in 1790, restored a dozen years later, and survived in one form or another into the twentieth century.

What finally made salt cheap was not a change of heart but a change of technique. In the nineteenth century engineers learned to drill into a buried bed, pump water down the borehole and bring the brine back up, a method known as solution mining that put nobody underground at all. Boiling was transformed in turn by the vacuum pan, which lowers the pressure above the liquid so that it evaporates at a much lower temperature and burns far less fuel. Output rose and prices fell for good. At the same time refrigeration began to take away salt's oldest employment, the preservation of meat and fish, and within a century the mineral that had built cities was among the cheapest substances on the market.

It did not become less useful. Most of the salt produced today never reaches a kitchen. The largest share goes to the chemical industry, where it is split into chlorine and caustic soda, the starting points for plastics, solvents, paper and a great deal else. In countries with cold winters the next largest use is the road, since sodium chloride lowers the freezing point of water and highway authorities spread millions of tonnes of it every year. That practice carries a cost of its own. Salt does not break down, and long-term monitoring of rivers in the north-eastern United States has recorded a steady rise in salinity in catchments where the roads are treated, with consequences for the freshwater species living in them.

The history of salt is usually told as a story about a substance, but it is really a story about scarcity. Nothing about sodium chloride changed between the fourteenth century and the twentieth. What changed was the cost of getting at it and the arrival of something else that would do its job. Value is not a property a material carries about with it. It is a relationship between what a thing can do, how hard it is to obtain and what else is available, and any of the three can move.

In the late 1940s the United States Air Force was losing aircraft at a rate nobody could account for. Pilots were failing to control machines that were mechanically sound, and after faulty equipment, pilot error and inadequate training had each been investigated and found wanting as explanations, attention turned to the cockpit itself. Its dimensions, the distance to the pedals, the height of the seat, the reach to the controls, had been fixed in the 1920s from the average measurements of several hundred pilots, and the assumption behind them was so obvious that nobody had thought to examine it: that a cockpit built for the average pilot would fit almost every pilot reasonably well.

The assumption was finally tested in 1950 by a young lieutenant, Gilbert Daniels, who measured more than four thousand pilots on a long list of bodily dimensions. Taking the ten most relevant to the cockpit, he defined an average range generously, as the middle 30 per cent of the distribution on each one, and then asked a simple question: how many of the four thousand fell inside that range on all ten at once? The answer was none. Even on three dimensions taken at random, fewer than one pilot in twenty-five qualified. The average pilot, considered as a physical person, did not exist.

What Daniels concluded was not that pilots should be selected differently but that the cockpit should be changed, and the Air Force acted on the recommendation with unusual speed. Seats, pedals, helmet straps and shoulder harnesses were all made adjustable, and manufacturers who objected that it could not be done were told to do it anyway. The adjustable seat, now so ordinary as to be invisible, is a direct descendant of that decision. The episode repays attention because it illustrates something more general than aircraft design. An average is a statement about a group. The moment it is treated as a description of a member of that group, it can go quietly and badly wrong.

Part of the trouble is arithmetical. A mean is one number standing in for a whole distribution, and distributions differ in ways a mean cannot report: two towns with the same average income may be identical or violently unequal, and a lake whose average depth is a metre may still drown you. Where a distribution has two peaks rather than one, as with the heights of a mixed adult population, or the arrival times of a commuter train that is either punctual or twenty minutes late, the mean settles in the gap between them and describes nobody whatever. The statistician Ada Nkemelu puts the matter bluntly: an average is a summary, and the question to ask of any summary is what it had to throw away in order to be brief.

It would be a mistake, though, to treat averages as a species of statistical fraud. Nkemelu's own point cuts both ways, since a summary that throws nothing away is not a summary. Without aggregates there would be no way of saying that one treatment works better than another, that a policy has changed anything, or that this year differs from last; the alternative to a well-chosen average is usually not richer information but no information at all, and the demand to examine every individual case is in practice a demand that nothing be compared. What the Daniels episode shows is not that averages are useless but that they answer one kind of question, about populations, and are constantly pressed into service for a different kind, about persons.

Medicine has spent two decades learning that distinction. A clinical trial reports an average treatment effect: how much better, taken as a whole, the treated group did than the untreated one. That number is indispensable for deciding whether a drug should be licensed, and it is a poor guide to what will happen to any particular patient, because an average improvement of two points may conceal a large benefit to a minority and none at all to everybody else. The remedy usually proposed, a trial designed around a single patient who is given the treatment and a dummy in alternating periods, is genuinely useful for long-lasting conditions whose symptoms respond quickly and reversibly. Its enthusiasts, however, have been slow to say how small a share of medical questions it is capable of answering.

Education has been less fortunate. The observation that a class taught to its middle serves the middle better than the ends is sound enough, and the inference that instruction should therefore be tailored to each learner is appealing. But the most popular version of that inference, the belief that pupils have individual learning styles which teaching ought to match, has been tested repeatedly and has not survived: when learners are taught in the manner they say they prefer, they do not, on the evidence, learn any more. Rejecting the average, in other words, is no guarantee of getting the individual right, and a bad model of a person can do more harm than a crude summary of a group, because it carries the authority of having been personalised.

My own view is that the error is one of translation rather than of measurement. Nothing was wrong with the arithmetic of the men who built the 1920s cockpit; what was wrong was the sentence they wrote with it, which turned a fact about a set of pilots into a specification for a seat. The useful discipline is to ask of every average one meets what question it was built to answer, and whether that is the question now being put to it. This is less exciting than abolishing averages and less comfortable than trusting them, which may be why it is so rarely done.