IELTS Academic Reading Practice Test 121

Until the early 1970s, anyone who needed to multiply two large numbers quickly reached for a slide rule: a flat ruler with a sliding central strip and a transparent cursor that ran across both. The device has no batteries and no moving parts beyond the strip and the cursor, and it was once so familiar to engineers that it acquired the affectionate nickname 'the slipstick'. Its principle, however, is not obvious. A slide rule does not multiply numbers directly; it adds lengths that represent their logarithms, and because adding logarithms has the same effect as multiplying the numbers themselves, the answer appears on the scale.

Logarithms were the invention of the Scottish mathematician John Napier, who published his description of them in 1614. Napier's aim was to simplify the tedious arithmetic of astronomy, and his tables allowed a multiplication to be performed by adding two numbers found in a book. In 1620 the English mathematician Edmund Gunter placed a logarithmic scale along a straight line, so that a length on the rule corresponded to a logarithm. To multiply, the user measured a distance with a pair of brass dividers and added it to another distance. Gunter's scale was accurate and popular, but the dividers were awkward, and a slip of the hand ruined the calculation.

The next step was to make one scale slide along another, so that distances could be added mechanically. This is usually credited to William Oughtred, an English clergyman and mathematician who devised such an instrument around 1622 and also designed a circular version in which a rotating disc carried the scales. Oughtred's priority was later disputed by others, and the earliest rules were expensive, hand-divided instruments made for wealthy scholars rather than working engineers. A generation passed before the straight rule, with two scales sliding in a groove, became a practical tool.

The accuracy of any slide rule is limited by its length, because the marks on the scale can only be spaced so far apart. On a rule 25 centimetres long, the distance between 1 and 2 occupies about 7.5 centimetres, but the gap between 8 and 9 is only a little over one centimetre. Users therefore learned to work with numbers between 1 and 10 and to keep track of the decimal point in their heads. A standard rule gave three significant figures, which was sufficient for most engineering of the period.

Several refinements followed. Glass cursors with a fine hairline allowed users to read across from one scale to another. By the middle of the nineteenth century the French artillery officer Amédée Mannheim had standardised an arrangement of scales that made the instrument quicker to use. The Mannheim layout, with its characteristic placement of the A, B, C and D scales, remained the basis of most rules for a century. Specialised versions appeared for surveyors, accountants and chemists, and rules of 50 centimetres or more were made for laboratories that needed an extra digit.

Aviation produced its own variant. The circular flight computer combined a slide rule with scales for fuel consumption and wind, allowing a pilot to calculate headings and times in the air. It was developed in the United States in the 1930s and, in various forms, is still taught in pilot training today, long after the slide rule itself vanished from the engineer's desk. Navigators used similar devices at sea, and special rules with scales for timber or for the strength of materials were sold to particular trades.

For most of the twentieth century the slide rule was standard equipment. Engineering students carried one in a leather case clipped to the belt, and examinations required it as routinely as a pen. Designers of bridges, aircraft and dams relied on it, and the astronauts of the Apollo programme took rules aboard as a backup in case their electronic systems failed. Its speed encouraged a particular style of calculation: the engineer made a rough estimate first, then used the rule to refine it, and always kept a sense of the size of the answer.

The end came quickly. In 1972 Hewlett-Packard introduced a handheld calculator that could perform the same operations electronically, and although it cost several hundred dollars, its price fell steadily. Within a few years the slide rule had been displaced in universities and design offices alike, and by the middle of the 1970s the largest American manufacturer had stopped making them. The change was so complete that a tool once used by millions became, within a generation, an object that many young engineers had never handled.

The slide rule has since acquired a second life as a collector's item and as a teaching aid. Teachers sometimes use one to show why logarithms turn multiplication into addition, and museums display the elaborate boxwood and ivory rules of the eighteenth and nineteenth centuries alongside the mass-produced plastic instruments of the 1960s. Its deeper legacy is conceptual: the rule was an analogue computer, in which a physical quantity, in this case length, stood for a number. The same idea underlies the machines that once modelled tides and flight.

None of this persuades the enthusiasts who still meet to compare collections and to demonstrate feats of mental arithmetic with a rule in hand. Their argument is simple: a slide rule never runs out of power, and it never rounds the wrong digit.

A solar sail is, in essence, an enormous mirror. Instead of burning propellant to produce a jet of gas, it relies on the pressure that light itself exerts on any surface it strikes. Light carries momentum, and when a photon bounces off a reflective film it hands over a small part of that momentum. A ball thrown at a wall rebounds, and the wall receives a push; in the same way, the departing photon leaves a push behind it. Because photons arrive in unimaginable numbers — sunlight delivers about 1,361 watts to every square metre above the atmosphere — the combined effect, though gentle, is continuous.

The numbers are worth pausing over. Sunlight falling directly on a perfectly reflecting surface produces a pressure of roughly nine micronewtons per square metre. For a sail a thousand square metres in area, that amounts to about nine millinewtons — the weight of a paperclip. On a spacecraft of a few kilograms, it would yield an acceleration of about a millimetre per second per second. Ridiculously small, one might think; yet it never stops. Left to act for a month, such an acceleration would add roughly two kilometres per second to the craft's velocity, and the only cost is sunlight, which is free.

The film itself is extraordinarily thin, typically a few micrometres — less than a tenth of the thickness of a human hair — and coated with a reflective layer of aluminium. It must be launched folded into a space the size of a shoebox and opened once in orbit, so the engineering of deployment is as demanding as the optics. Some designs extend rigid or inflatable booms from the centre, like the ribs of an umbrella; others spin the whole spacecraft so that the outward pull keeps the membrane stretched. Ripples and small tears matter, because a sail that is not flat scatters light in unhelpful directions.

The idea is old. Russian writers were discussing the pressure of light as a means of space travel in the 1920s, long before any satellite existed. Engineers returned to the idea whenever a mission required a great deal of velocity and very little payload. For decades the difficulty was practical rather than theoretical: nobody could build a film light enough and strong enough to be worth launching, and nobody could fold it into a rocket.

That changed in 2010, when the Japanese space agency launched IKAROS alongside a Venus-bound orbiter. The craft unfurled a square sail about 14 metres on each side — nearly 200 square metres of film just 7.5 micrometres thick. It used the sail not as a demonstration but as a working propulsion system, measuring a steady acceleration as it travelled outward. In December 2010 it flew past Venus. A much smaller American experiment, NanoSail-D, deployed a ten-square-metre sail in low Earth orbit a few months afterwards, but it was IKAROS that first showed that sunlight could drive a spacecraft between the planets.

The best-known recent test came from a privately funded organisation. LightSail 2, a satellite not much larger than a loaf of bread, was launched in 2019 and deployed a sail of 32 square metres. Over the following months its controllers adjusted the angle of the sail so that the push of sunlight added energy to its orbit, and they measured the resulting rise. That the orbit could be raised at all was the point. A sail is not a powerful engine but a means of gaining velocity slowly, over weeks, by tacking like a yacht.

Sails have obvious limitations. The force falls off with the square of the distance from the Sun, so beyond the inner planets the acceleration becomes negligible. Even a large sail cannot drive a heavy spacecraft quickly. Nor can a sail simply be pointed at the Sun and driven towards it, any more than a yacht can sail straight into the wind. To travel outward, the craft tilts the sail so that the thrust has a component along its direction of travel, and it follows a widening spiral; to move inward, it tilts the other way and lets the thrust brake it.

Current research follows several directions. Because a sail carries no propellant, it is attractive for long missions to small bodies. A NASA CubeSat called NEA Scout, launched in 2022, was designed to sail to a near-Earth asteroid using a sail of about 86 square metres, though contact with it was never established. Sails are also proposed as a way of dragging defunct satellites out of orbit without fuel. The most ambitious proposals would not use sunlight at all: a powerful laser on the ground, or an array of them in space, could push a very thin sail towards another star, a scheme that remains entirely theoretical but has attracted serious study.

A goal is scored in a football stadium. The crowd rises, the scorer turns away in celebration — and then everyone stops and waits. A video official is examining the build-up to see whether a player was offside forty seconds earlier. The celebration resumes, or it does not. Within a decade this pause has become part of the grammar of the game, and it has provoked a quarrel about technology in sport that is more interesting than the familiar complaint that machines are ruining everything.

The instruments are of several kinds. Goal-line technology, approved for use in matches in 2012, answers a single question — whether the whole of the ball crossed the line — and answers it in under a second. Video assistant referees, first used at a World Cup in 2018, review goals, penalties and red cards. Tennis has its own ball-tracking system, in use at major tournaments since 2006, while cricket's Decision Review System, introduced in 2008, combines ball tracking with sound recordings.

The case for such systems rests on a simple observation: some errors are not a matter of interpretation but of fact, and television makes them visible to millions of people within seconds. When a shot crosses the line by half a metre and no goal is awarded, the injustice is not a charming eccentricity of the sport but a failure that everyone can see. The same is true of a batsman given out leg-before when the ball would have missed the stumps. Such mistakes are correctable, and refusing to correct them is hard to defend.

The objections are equally serious. The first concerns time: a review can take several minutes, during which the tension that makes sport compelling leaks away. The second is subtler. Celebration depends on certainty, and a review makes every celebration provisional; players have learned to glance at the referee, or at the screen, before they dare to celebrate. Something is lost in that glance, though it is hard to say what.

The third objection concerns football's threshold for intervention. Officials may intervene only when there has been a 'clear and obvious error', a phrase that sounds precise and is not. Whether an error was clear and obvious enough to merit review turns out to be a judgement as contestable as the original decision, so the technology has added a second layer of argument without removing the first. Cricket has evolved a different and more honest compromise: 'umpire's call', under which a marginal decision stands, acknowledging that the technology cannot settle everything.

Money is a further problem. The systems are expensive to install and to staff, and only the richest competitions can afford them. A top division may have twenty cameras and a team of officials watching them; an amateur league has a referee and, if it is lucky, a linesman. Whatever else the technology achieves, it widens the distance between the elite game, where decisions are scrutinised frame by frame, and the rest, where the same mistakes pass uncorrected.

Then there is the question of who decides. A decision once made in public, by a named person on the field, is now made partly in a room by technicians the crowd cannot see. Responsibility is dispersed, yet the referee still carries the blame, and nobody has an obvious way of holding a remote official to account. If the reform was meant to make decisions more trustworthy, its effect on accountability has been the opposite.

Transparency, however, is within the organisers' control, and here some sports have done much better than others. Cricket and rugby show the evidence on the stadium screen while the decision is being made, so that spectators see what the officials see and can follow the reasoning. Football's rules on big screens vary from one competition to another, and crowds are often left watching a referee hold a finger to an earpiece. The same decision is therefore accepted in one sport and resented in another.

Against all this stands the argument that error is an essential part of sport: that the disputed goal, the argument afterwards and the shared sense of injustice are what spectators actually value. I have never found this persuasive. Error is part of sport in the way that illness is part of life — it happens, but nobody would choose it. The pleasure described in these conversations comes mostly from argument about judgement, which no machine can settle, not from argument about whether a ball crossed a line, which a machine can settle instantly.

The sensible conclusion, it seems to me, is neither to embrace the technology uncritically nor to wish it away. Systems should be confined to narrow questions of fact, and judgement calls should remain with the referee, whose authority the technology ought to support rather than erode. Above all, the evidence should be shown to the crowd as it is shown to the officials, so that a decision is explained rather than announced. The problem with refereeing technology is not the machine; it is the threshold, the cost and the silence that too often surround it.