You should spend about 20 minutes on Questions 1–13, which are based on Reading Passage 1 below.
The Machine That Refused to Be Built
Charles Babbage, his Difference Engine and the limits of Victorian engineering
By the beginning of the nineteenth century, navigation, astronomy, insurance and engineering all depended on printed tables of numbers: logarithms, sines, and the positions of the stars. These tables were compiled by hand, and every figure had to be calculated and then copied by a clerk, sometimes several times over. Errors were common and could be costly. A mistake in a table of lunar distances might put a ship hundreds of miles off course; a mistake in a table used by bankers might ruin a business. Charles Babbage, a young Cambridge-trained mathematician, was convinced that the whole process could be mechanised.
In 1822 Babbage presented a short paper to the Royal Astronomical Society describing a machine he called the Difference Engine. Its purpose was not merely to calculate faster than a clerk but to remove the possibility of human error altogether. The engine would work by the method of finite differences, a technique that allows any reasonably smooth mathematical function to be tabulated using addition alone, with no need for multiplication or division. If the first values in a series are known, each successive value can be obtained by repeated addition of a constant difference.
This was a crucial insight for a mechanical designer. Addition is far easier to build into brass and steel than multiplication, because it requires only wheels that turn and a mechanism that carries a digit into the next column when a wheel passes nine. Babbage's engine stacked a series of vertical columns of figure wheels, one for each order of difference, and each turn of the handle advanced the calculation by one step. A separate mechanism would then stamp the results onto a soft metal plate, so that printed tables could be produced without any typesetter reading the numbers.
Persuaded by the value of accurate tables, the government began to provide money for the project in 1823, and Babbage engaged Joseph Clement, one of the finest precision engineers in London, to build it. The work pushed the engineering of the day to its limits. To cut the thousands of identical parts required, Clement designed and built special machine tools, including improved lathes and dividing engines, and his workshop became famous among engineers. Progress was slow and extremely expensive, but the by-products of the project, in the form of more accurate machine tools, were themselves significant.
By 1832 a demonstration section had been assembled. It was only about one seventh of the complete engine, which would have required some twenty-five thousand parts, yet it worked flawlessly, calculating results to six figures. Visitors were invited to watch it operate, and among those who came in 1833 was the seventeen-year-old Ada Byron, daughter of the poet, who was captivated by the machine and would later write the most influential account of Babbage's ideas.
The full engine was never finished. Clement's costs rose, and a dispute over payment led him to stop work and refuse to hand over the completed parts. Babbage's relations with the government deteriorated too, particularly after he published a fierce attack on the scientific establishment. By 1842 the Treasury had spent roughly seventeen thousand pounds and had nothing to show that could be sold, and the project was abandoned. Babbage himself had contributed several thousand pounds of his own money.
He did not give up. Between 1847 and 1849 he designed a second machine, the Difference Engine No. 2, which was simpler and far more elegant than the first and needed only about eight thousand parts; it would have calculated to thirty-one digits. The government declined to fund it. Meanwhile Babbage had conceived something far more ambitious. From 1834 he had been working on the Analytical Engine, a general-purpose machine whose instructions could be changed, and in 1843 Ada Lovelace published a set of notes explaining how it might be programmed, including a method for computing a sequence known as the Bernoulli numbers.
Others carried the simpler idea forward. In Sweden the engineer Georg Scheutz and his son Edvard completed a working difference engine in the 1850s, and machines of this kind were used for a time to produce printed tables. Babbage, meanwhile, became a celebrated and somewhat cantankerous public figure, campaigning against street musicians and publishing an autobiography in 1864. He continued to refine his designs for the rest of his life, filling notebooks with improvements that no workshop was ever asked to build. He died in 1871, his engines unbuilt, and for decades his designs were treated as an intriguing failure.
That judgement changed at the end of the twentieth century. To mark the bicentenary of Babbage's birth, the Science Museum in London decided to build Difference Engine No. 2 exactly as he had designed it, using only materials and techniques available in the nineteenth century. Construction began in 1989 and the machine was completed in 1991. It contains some eight thousand parts and weighs about five tonnes. When the handle is turned it performs exactly as Babbage predicted, and the printer completed in 2000 produces tables with no errors at all.
The experiment settled a long-running argument. Babbage's design was not a fantasy but a workable machine, and the reason it was never built was not technical impossibility but money, temperament and the absence of a market for tables that a machine could produce more cheaply than clerks.
You should spend about 20 minutes on Questions 14–26, which are based on Reading Passage 2 below.
Building with Living Cells
Three-dimensional printing, in which an object is built up layer by layer from a digital design, has been used since the 1980s to make plastic parts. Bioprinting applies the same logic to living tissue. Instead of molten polymer, the printer is loaded with a bioink: a gel, usually water-based, in which living cells are suspended. The print head lays down the ink in fine lines, one thin layer at a time, and the gel is then set, or crosslinked, so that it holds its shape. The word is used loosely; strictly, bioprinting means the automated deposition of living cells, not merely the printing of a scaffold for them to grow on. The term covers a family of techniques rather than a single method. The ambition is large — replacement organs grown from a patient's own cells — but the reality so far is more modest.
Bioprinting is usually divided into three stages. In the first, images from a scanner or an MRI machine are converted into a computer model of the tissue required. The second is the printing itself: software divides the model into thin slices, and each slice becomes a path for the print head. The third, and often the longest, is maturation: the printed construct is kept in a bioreactor, a vessel that supplies nutrients at the right temperature, so that the cells can multiply, connect with one another and begin to behave like real tissue. Without this period of cultivation a printed patch of skin is merely a shape containing cells.
Several printing methods are in use. Extrusion, the most common, pushes the bioink through a nozzle in a continuous filament, much as a baker pipes icing. It is quick, works with viscous gels and can deposit a high density of cells, but the pressure involved damages some of them and the filament is relatively coarse. Inkjet printers fire tiny droplets from a cartridge; they are gentler on cells, but the inks must be very runny, and the droplets tend to splatter. In laser-assisted printing, a pulse of light transfers a small patch of bioink from a film onto the target. It offers fine resolution, but the equipment is expensive and the process slow.
The choice of bioink is a compromise between conflicting requirements. It must be liquid enough to flow through the nozzle, yet set quickly enough to support the layers printed above it. It must not be toxic, and it must allow cells to move, stretch and communicate. Natural materials dominate. Alginate, extracted from brown seaweed, sets when calcium ions are added. Gelatin and collagen, both derived from animal tissue, provide sites where cells can attach, while fibrin, a protein involved in blood clotting, is used in some of the most demanding work. Synthetic polymers are also used, often as a scaffold that slowly breaks down as the cells produce their own supporting matrix.
The greatest obstacle is blood supply. In the body no cell lies more than a fraction of a millimetre from a capillary, because oxygen and nutrients will not diffuse much further. A printed block of tissue thicker than about two hundred micrometres therefore dies in the middle, which is why bioprinted skin and cartilage, both of which survive with very little blood, have advanced furthest. Researchers are trying to print the vessels themselves. One approach uses a sacrificial ink, printed as a network of fine threads and then dissolved away, leaving hollow channels that can be lined with the cells that form blood vessels.
Some products have already reached patients or the laboratory bench. Sheets of printed skin are being developed for burns and for testing cosmetics, and printed cartilage is being studied for damaged joints and for the discs of the spine. In 2018 researchers at Newcastle University in the United Kingdom printed human corneas, the transparent front of the eye, using a bioink containing corneal cells. Companies now print small pieces of liver tissue that pharmaceutical firms use to screen drugs for toxicity, since damage to the liver is one of the commonest reasons for a medicine to be withdrawn from the market.
Whole organs remain far off. A printed kidney or heart would need millions of cells, a network of vessels and a structure fine enough to filter blood or to beat; the tissue must also mature for weeks before it is useful, and it must not provoke an immune reaction. Printing speed is another constraint: a structure large enough to be useful takes hours, during which the cells in the earliest layers are sitting in conditions that no cell in the body would tolerate. Regulation and cost add further barriers, since any implantable product must meet the same standards as a conventional device, and a printed organ would be effectively unique to one patient.
Current research is therefore directed at intermediate goals. Printed patches of heart muscle are being tested for repairing damage after a heart attack, and organ-on-a-chip devices, in which tiny printed tissues sit in channels on a plastic slide, allow drugs to be tested on human cells rather than on animals. Some groups are working towards printing directly into the body, using a robotic arm to deposit material in a surgical cavity; this would avoid the difficulty of keeping a fragile construct alive outside the body, though it raises questions of its own about infection and control. For now, the aim is to repair tissue rather than to replace it.
You should spend about 20 minutes on Questions 27–40, which are based on Reading Passage 3 below.
Can We Trust Online Reviews?
Why star ratings tell us less than we think
Before buying almost anything online, most of us now do the same thing: we look at what other people have said. Word-of-mouth recommendation, once limited to friends and neighbours, has been industrialised. Reviews have become the infrastructure of online commerce. A restaurant with a four-star average will fill its tables; the same restaurant with three stars may not survive. Because a single number now carries so much commercial weight, it is worth asking how that number is produced, and whether it deserves the trust we place in it.
The case for reviews is strong. They solve a problem that advertising cannot: a seller has an interest in exaggerating, whereas a customer who has already paid has little reason to lie and, in aggregate, reports experience that no single buyer could obtain. A hundred accounts of a hotel's breakfast, a laptop's battery life or a courier's reliability amount to a form of distributed evidence. This is the familiar logic of the crowd, and it works well when the crowd is large, independent and honest.
Those conditions are rarely all met, and the first casualty is the star average itself. Ratings are not normally distributed. Most customers who bother to write do so at the extremes, after a delight or an outrage, which produces a mass of top marks, a smaller mass of bottom marks and very few in between. Averaging such a distribution throws away almost everything that matters. The difference between 4.3 and 4.5 stars is usually noise, an artefact of a handful of reviews and of the platform's own rounding, yet customers and algorithms alike treat it as a meaningful judgement.
Then there is outright deception. Fake reviews can be bought in bulk, exchanged between sellers or generated by automated accounts, and some businesses offer rewards to customers who remove an unfavourable rating. Platforms have become much better at detecting this, using patterns in timing, wording and the relationships between accounts, and regulators have begun to act: America's Federal Trade Commission has adopted rules against buying, selling or promoting fake reviews. Detection is a continuous contest, because those who sell reviews change their methods whenever a pattern is identified. The scale of the problem, however, is genuinely unknown. Platforms publish figures for the reviews they remove, but nobody can measure the fakes that are never caught, and estimates produced by academics vary enormously.
Even where no money changes hands, incentives distort the picture. A business that asks every satisfied customer for a review while saying nothing to the rest is not fabricating anything, yet it manufactures an impression. The same is true of verified-purchase badges, which are a genuine improvement because they tie a review to a transaction, but which also persuade readers that the reviewer is an expert on the product when all that person has done is buy it. Over time most platforms appear to drift towards inflation, because the pressure to solicit reviews is felt most keenly by businesses that are struggling.
Readers, too, bring their own weaknesses. A long line of research in consumer psychology suggests that people are influenced by the number of reviews as much as by their content, and that a flawless record can arouse suspicion. A hotel with a hundred perfect scores and not a single complaint reads, to an experienced eye, like a hotel where complaints have been removed. An accumulation of mildly positive reviews, each written quickly after a purchase, can be less informative than a single long account by someone who has used the product for a year. A lower average containing a detailed, specific complaint about noise, or a reply from the owner explaining what has changed, may tell a reader far more.
My own view is that reviews remain the best source of information ordinary buyers have, and that abandoning them would leave us entirely in the hands of advertising. But they should be read as evidence rather than as verdicts. That means looking at how many reviews there are, how recent they are, and whether the negative ones are specific and consistent rather than generic. Two reviewers complaining independently about the same problem is far more informative than a single one-star score, and a review written two years ago may describe a different business altogether.
Platforms could help more than they do. They could show the distribution of ratings rather than a single average, and weight recent reviews more heavily. They could also make it easy to see whether a review was invited. A simple change would be to show a histogram beside the score, so that a cluster of one-star ratings cannot be hidden inside a respectable total. None of this would eliminate fraud, but it would make the system slightly harder to game. Regulation has a role too, though it will always lag behind the techniques used by those who profit from deception.
The honest answer to the question is therefore conditional. We can trust reviews in the way we trust any testimony: not because they are guaranteed to be true, but because, taken together and read with care, they are more likely to be true than anything the seller tells us, and because a system in which customers compare notes is, for all its flaws, more honest than one in which only the seller speaks.
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