IELTS Academic Reading — Practice Test 22

Traffic congestion is one of the most visible failures of modern urban life, and one of the most expensive. In large cities, drivers routinely lose the equivalent of several working days each year sitting in stationary traffic, and the costs ripple outward: goods arrive late, buses run behind schedule, and exhaust fumes gather over crowded streets. As populations concentrate in cities and car ownership rises, the problem grows rather than eases. For most of the twentieth century, the standard response was to build — wider roads, new ring roads, extra lanes — on the assumption that congestion was simply a shortage of capacity. That assumption has proved stubbornly, and expensively, wrong.

The reason is a phenomenon that transport researchers call induced demand. When a congested road is widened, the extra space is soon filled by journeys that were previously not made, or were made at other times or by other routes. Drivers who once avoided the rush hour return to it; some who took the train switch back to the car. Within a few years the new road is as clogged as the old one, and the city has spent heavily for little lasting gain. Studies of American cities have found an almost one-to-one relationship between the number of lane-miles added and the number of miles subsequently driven — a regularity so consistent that some economists refer to it as a fundamental law of road congestion. Building alone, in short, cannot solve the problem it is meant to cure.

To many economists the underlying difficulty is not a lack of tarmac but a mistake in pricing. A busy road at rush hour is a scarce resource, yet drivers pay nothing for the delay each additional car imposes on all the others. Because the true cost of a peak-time journey is hidden, too many people choose to travel then. The remedy, first set out in detail by the American economist William Vickrey in the 1950s, is to charge for road use directly, and to charge more when demand is highest. Faced with a price, the argument goes, some drivers will travel at off-peak times, share a vehicle or use public transport, leaving the road to those who value the journey most. The point of the charge is not to raise money but to change behaviour.

For decades the idea remained largely theoretical, until a handful of cities put it into practice. Singapore led the way in 1975 with a simple scheme requiring a paper permit to enter the centre, later replaced by an automatic electronic system that deducts a fee as vehicles pass overhead gantries, adjusting the price by the hour. London introduced a flat daily 'congestion charge' for its central area in 2003; traffic entering the zone fell sharply in the first years, and the revenue was directed by law into the city's buses and other public transport. Stockholm followed with a scheme that voters, initially hostile, approved in a referendum once a trial had shown them the benefits. In each case the pattern was similar: predictions of chaos gave way, after a difficult start, to measurably freer-flowing streets.

None of this has made road pricing popular. The most persistent objection is that it is unfair. A flat charge takes a far larger share of a low earner's income than of a wealthy driver's, so the rich can carry on much as before while the poor are priced off the road. Critics also resent being asked to pay for something that was, within living memory, free. There is a deeper unease, too, about turning access to public space into a commodity, available in effect to whoever can afford it. For politicians, the result is a proposal that is easy to attack and hard to defend, however sound its economic logic.

Defenders of pricing answer these charges on several fronts. Much depends, they argue, on what is done with the money. If the revenue is returned to the public — spent on better buses, cheaper fares or lower taxes elsewhere — the overall effect on poorer households can be positive, since many of them do not own cars and gain most from improved public transport. Exemptions and discounts can shield residents, disabled drivers and essential workers. And congestion itself, they point out, is hardly fair: it wastes the time of bus passengers and delivery drivers alongside that of the wealthy. Whether pricing helps or harms the worse-off, in this view, is not fixed in advance but depends on the design of the scheme.

The next stage of the debate is already taking shape around technology. Satellite positioning makes it possible to charge drivers precisely for each kilometre travelled, varying the rate by place and time far more finely than any network of gantries. Such systems could replace fuel taxes, which are dwindling as vehicles turn electric. But they raise a new worry: a charging scheme that tracks every journey is also, potentially, a record of everywhere a person goes. Reconciling the economic case for pricing with a legitimate concern for privacy may prove as difficult as winning the original argument. The technical means to price the roads now exist; the political and ethical means are still being worked out.

Infinity is one of those ideas that everyone feels they understand until they are asked to explain it. A child who realises that numbers never run out — that however high you count, you can always add one more — has grasped something genuine about the infinite. Yet this everyday intuition conceals difficulties that have troubled thinkers for more than two thousand years. Is infinity merely a way of speaking about processes that never stop, or is it a thing in its own right, a quantity larger than any finite number? Can there be different sizes of the infinite, or is 'endless' simply endless? Questions of this kind seem at first like idle wordplay, but the attempt to answer them rigorously has reshaped mathematics and continues to unsettle its foundations.

The ancient Greeks were the first to confront the problem squarely, and their most influential answer came from Aristotle. He drew a distinction that would dominate thought for the next two millennia, between what he called potential and actual infinity. A potential infinity is a process that can be continued without end: one can always add another number, divide a line again, or extend a sequence a step further, but at no moment is an infinite total actually reached. An actual infinity, by contrast, would be a completed infinite whole — the entire endless sequence of numbers considered all at once, as a finished object. Aristotle accepted the first and firmly rejected the second, regarding a completed infinity as incoherent. For centuries mathematicians followed him, treating the infinite as something one approached but never arrived at.

This cautious consensus was overturned almost single-handedly in the late nineteenth century by the German mathematician Georg Cantor. Cantor took the daring step of treating infinite collections as completed objects that could be handled and compared, exactly the move Aristotle had forbidden. His key tool was disarmingly simple. Two collections are the same size, he proposed, if their members can be paired off one to one, with none left over — the principle a shepherd uses in counting sheep against pebbles, without needing numbers at all. Applied to the infinite, this idea produces startling results. The even numbers can be matched perfectly with all the whole numbers, since each whole number doubles to give exactly one even number; by Cantor's criterion, therefore, there are just as many even numbers as numbers altogether, even though the even numbers are only 'half' of them. A part, it turns out, can equal the whole.

Cantor might have stopped at the reassuring conclusion that all infinities are the same size. Instead he proved something far stranger: that some infinities are bigger than others. Using an ingenious method now known as the diagonal argument, he showed that the points on a line — the so-called real numbers, including all the endless decimals — cannot be paired off with the whole numbers, however cleverly one tries. There are simply too many of them. The real numbers form an infinity of a higher order than the counting numbers, and the argument can be repeated to generate an unending tower of ever larger infinities, each dwarfing the last. Infinity, far from being a single unreachable horizon, turned out to have an intricate internal structure of its own.

Such conclusions were not welcomed by everyone. Cantor's former teacher, Leopold Kronecker, regarded the whole enterprise as a dangerous fantasy, insisting that only the whole numbers had any real existence and that the rest of mathematics should be built from them alone. He used his considerable influence to block Cantor's work and to frustrate his career, a campaign that contributed to the younger man's recurrent bouts of depression. Others, however, saw at once what had been achieved. The great mathematician David Hilbert declared that no one should ever be able to drive mathematicians out of the paradise that Cantor had created for them. The dispute was not merely technical; it turned on what mathematical objects are, and whether the mind is free to bring them into being.

The new theory of infinite sets soon revealed unsettling cracks. If any collection whatever can form a set, one may consider the set of all sets that do not contain themselves — and then ask whether it contains itself, a question that leads straight to contradiction. This puzzle, identified by Bertrand Russell, forced mathematicians to rebuild set theory on more careful foundations. One question in particular resisted every effort. Cantor had conjectured that there is no size of infinity lying strictly between that of the whole numbers and that of the real numbers — a claim called the continuum hypothesis. Decades of work failed to settle it, and for good reason. It was eventually shown, through the combined results of Kurt Gödel and Paul Cohen, that the hypothesis can neither be proved nor disproved from the standard axioms of set theory. Both it and its denial are consistent with everything else mathematics assumes.

What, then, is the status of the infinite? On one view, the objects Cantor described are as real as any in mathematics, discovered rather than invented, and the fact that the continuum hypothesis cannot be settled by current axioms merely shows that those axioms are incomplete; the truth is out there, waiting for a richer theory to capture it. On another, the infinite is a useful fiction, a set of rules for manipulating symbols that need answer to nothing beyond itself, so that asking whether the continuum hypothesis is 'really' true is a confusion. Between these positions the argument continues, unresolved after a century. That mathematics can prove, with complete rigour, that one of its own oldest questions has no answer within its accepted rules is perhaps the strangest legacy of the attempt to count the uncountable.