You should spend about 20 minutes on Questions 1–13, which are based on Reading Passage 1 below.
The Tyranny of Numbers
The transistor, invented at Bell Laboratories in 1947, was a small, cheap and reliable replacement for the fragile vacuum tube, and by the middle of the 1950s it was transforming electronics. Yet the transistor brought a problem of its own. Each one was a separate object which had to be wired by hand to the resistors, capacitors and other components around it, and every wire was a possible failure. As circuits grew larger, the number of connections grew faster than the number of parts, a difficulty that the Bell Labs engineer Jack Morton called the 'tyranny of numbers'. By the late 1950s the cost of assembling a large circuit could exceed the cost of its parts.
The first person to act on the idea was Jack Kilby, a new employee at Texas Instruments. Kilby had joined the company in May 1958 and had not yet earned a holiday, so he was almost alone in the laboratory that July. His answer was to form every component in a wafer of germanium, a semiconductor already used for transistors, so that the resistors, the capacitor and the transistor itself were simply different regions of the same crystal. Connections between them were made with fine gold wires. On 12 September 1958 Kilby demonstrated a working oscillator built in this way, and in February 1959 he filed a patent for a 'miniaturised electronic circuit'.
Kilby's circuit worked, but it was awkward to manufacture. The gold wires still had to be attached by hand. At Fairchild Semiconductor in California, a different group found a more elegant solution. In 1959 Jean Hoerni developed a process in which a layer of silicon dioxide, effectively glass, was grown on the surface of a silicon wafer and used to protect the delicate junctions beneath from contamination.
Robert Noyce, a co-founder of the company, saw that this oxide layer could also serve as insulation: instead of wires, narrow strips of aluminium could be evaporated onto the glass and etched into a pattern that joined the components below, on a whole wafer at once. Noyce filed his patent in July 1959.
The two firms soon found themselves in dispute. Kilby had built the first working circuit, but Noyce's method was the one that could be made in quantity, and for several years Texas Instruments and Fairchild contested priority. The matter was settled only in 1966, when the companies agreed to cross-license their patents. Kilby received the Nobel Prize in Physics in 2000. Noyce, who had gone on to co-found Intel, had died a decade earlier, and the prize is not awarded posthumously.
For the first few years the new devices were expensive curiosities. A single integrated circuit cost far more than the equivalent collection of separate components, and manufacturing yields were low, because one speck of dust could ruin an entire chip. Fairchild's planar process, as it became known, allowed many identical circuits to be made on one wafer, which was then cut into individual chips. The company's Micrologic family, introduced in 1961, was among the first ranges of integrated circuits offered for sale. Early customers were not consumers but governments: the American missile and space programmes needed small, light and reliable electronics, and for several years they were the industry's most important market.
Two further inventions shaped the chip's future. The first was the metal-oxide-semiconductor transistor, proposed by Dawon Kahng and Martin Atalla at Bell Labs in 1959. The second was complementary metal-oxide-semiconductor logic, or CMOS, in which pairs of transistors of opposite type are arranged so that current flows only at the moment a circuit switches. Frank Wanlass demonstrated such a circuit at Fairchild in 1963. Its advantage was not speed but frugality: a CMOS chip at rest draws almost no power, which suited battery-operated devices such as watches and pocket calculators.
As circuits became more complex, Gordon Moore, a chemist at Fairchild, was asked to predict how far the trend could go. In 1965, writing in the magazine Electronics, he observed that the number of components that could be squeezed onto a single chip had been doubling roughly every year since the first devices, and he predicted that the pattern would continue for at least another decade. In 1975 he revised the interval to about two years. The observation became known as Moore's law, and although it was never a law of physics, the industry treated it as a target and kept pace with it for half a century.
The most consequential development came in 1971, when Intel, the company Moore had founded with Noyce three years earlier, produced the 4004. It had been commissioned by a Japanese calculator manufacturer, Busicom. The team of Federico Faggin, Ted Hoff and Stanley Mazor designed a single chip that could be programmed to perform many different tasks. The 4004 contained about 2,300 transistors and did the work of a small computer. The microprocessor, as it came to be called, was the beginning of the general-purpose chip on which modern computing rests.
Today the phrase 'integrated circuit' is rarely heard outside textbooks; people speak instead of chips, microchips or silicon. Kilby's oscillator contained a handful of components, while a modern processor contains tens of billions of transistors. What has not changed is the principle he established in an almost empty laboratory in the summer of 1958: that the cheapest and most reliable way to join a great many electronic parts is not to connect them at all, but to build them together.
You should spend about 20 minutes on Questions 14–26, which are based on Reading Passage 2 below.
Printing with Drops of Ink
The printer in an office is usually a laser machine, but most home printers, and a growing number of machines in factories, form images by throwing tiny drops of liquid ink at paper — a method known as inkjet printing. A device using the underlying principle was patented by Lord Kelvin in 1867, but making it reliable took a century of work on nozzles, fluids and electronics. Nothing touches the paper except the ink: the image is built up dot by dot as a print head passes across it.
The commonest way to make a drop is to boil it. In a thermal print head, each nozzle contains a tiny resistor. A pulse of current raises its temperature by several hundred degrees Celsius in microseconds, and a thin layer of ink in contact with it flash-vaporises. A bubble of vapour forms and expands, forcing a droplet out of the nozzle. The current is switched off, the bubble collapses, and surface tension draws fresh ink in for the next pulse. Canon and Hewlett-Packard reached this principle independently in the late 1970s.
The alternative is to squeeze the ink mechanically. A piezoelectric head contains a chamber whose wall is made from a ceramic that changes shape under an electric field; lead zirconate titanate is the material usually chosen. A voltage makes the crystal bend, and the movement sends a pressure wave through the ink that ejects a drop. Because nothing is heated, the method tolerates liquids that boiling would damage, and the head lasts longer. Epson built its business on the approach.
Not every head makes drops only when it needs them. In continuous inkjet, used mainly for stamping dates and batch codes onto packaging, a jet of ink breaks into an even stream of drops which pass through a charging electrode. In one common arrangement, drops that are not wanted receive an electric charge and are deflected into a catcher, from which the ink returns to the tank; the rest fly straight on. The method is fast but wastes ink.
The amount of ink in a drop is measured in picolitres, trillionths of a litre, and a drop of a few picolitres is only ten to twenty micrometres across. Resolution is stated as dots per linear inch, and machines commonly claim several hundred to several thousand. Such figures mean little alone, since a head may fire several drops at one spot. Many photo printers vary the volume of each drop, using a small one for a pale area and a larger one for a dark tone, which gives the impression of continuous tone.
Colour printing needs at least four inks, not three. Cyan, magenta and yellow can in principle be combined to make any hue, but all three together give a muddy brown rather than a true black, so a black ink is added. It also saves ink and sharpens text, since one black dot has crisper edges than three overlapping ones. The eye is easily deceived: dots lie on a grid, and by varying how many of each colour fall in a cell, and how large they are, the printer suggests a smooth range of shades. This technique, halftoning, makes the dots disappear at normal viewing distance.
Ink is a chemical balancing act. Desktop inks are mostly water, with colorant and various additives. Dye-based inks dissolve completely and give bright colours, but they fade in sunlight. Pigment inks, made from suspended solid particles, are more durable, but the particles must be milled to a fraction of a micrometre and kept apart by dispersants, or they clog the nozzles. Humectants hold water in the ink so that an idle nozzle does not dry out, while surfactants adjust surface tension so that a drop wets the paper evenly. On coated paper the coating draws the water away by capillary action, leaving colorant at the surface.
Given how ordinary the ink is, why do replacement cartridges cost so much? Printers are priced close to the cost of manufacture, sometimes below it, and the profit comes from consumables — what economists call the razor-and-blades model. In many thermal printers the heaters and nozzles wear out, so they are built into the cartridge: every refill carries a new print head. Cartridges also hold chips that report ink levels, and some hold only a few millilitres of ink. Millilitre for millilitre, the liquid is one of the more expensive fluids a household buys.
Industry uses the same physics on a different scale. Wide presses print fabric for clothing, replacing screen printing for short runs. Ceramic tiles are decorated with pigmented inks that are fired in the kiln along with the glaze. Electronics firms print conductive silver inks to lay down circuit tracks and antennas. In every case the appeal is the same: a digital file can be printed without a plate or a screen, so that small batches become economic.
The most unexpected application is biological. A modified head can deposit living cells suspended in nutrient liquid, building tissue layer by layer in a process known as bioprinting. Researchers have printed skin, cartilage and simple blood vessels. The difficulties are considerable: the forces inside a nozzle can damage cells, the liquid must set without harming them, and printed tissue needs vessels fine enough to carry oxygen. No printed organ is yet in routine use, but the desk printer and the cell printer share a modest ambition: to place a very small amount of liquid, very accurately, in the right place.
You should spend about 20 minutes on Questions 27–40, which are based on Reading Passage 3 below.
Can an Algorithm Be Fair?
A review of the growing argument over automated decisions
Every day, decisions that were once made by people are made instead by software. A bank decides whether to grant a loan, a hospital allocates extra care to patients it thinks are deteriorating, a court uses a questionnaire to estimate whether a defendant will reoffend. The attraction is obvious: a program can process far more cases than any official, applies the same rule to everyone and never has a bad afternoon. The fear is equally obvious. If the data used to build such a program reflect past injustice, the program may reproduce it while wrapping it in the language of mathematics. My argument is that the choice we face is not between biased people and neutral machines, but between two kinds of fallible judgement.
The best-known case concerns a tool called COMPAS, used in several American states to help courts decide who should be released on bail. A defendant answers a questionnaire, and the software produces a score estimating the likelihood of reoffending. In 2016 the investigative news organisation ProPublica obtained the records of more than 7,000 people assessed in Broward County, Florida, and compared the scores with what actually happened over the following two years. It concluded that black defendants who did not reoffend were considerably more likely than white defendants to have been labelled high risk, while white defendants who did reoffend were more likely to have been labelled low risk.
The company that made the tool, then called Northpointe, replied that the analysis was misleading. Its score, it pointed out, was calibrated: among defendants who received the same rating, the proportion who went on to reoffend was much the same whatever their race. The tool was also about as accurate for one group as for the other. Both sides, in other words, were describing the same arithmetic and drawing opposite conclusions from it. This was not a public-relations failure. It was a sign of something deeper.
Within a year, researchers had shown that the dispute could not be settled by collecting better data. Several papers, including one by the statistician Alexandra Chouldechova, demonstrated that when the underlying rates of reoffending differ between two groups, no predictor can simultaneously be well calibrated within each group and have equal rates of false positives and false negatives. Since the base rates were not equal, the tool could not possibly have satisfied both definitions of fairness at once, whatever it was fed. The problem was not a defect in the software. It was arithmetic.
This result is uncomfortable because it means that the decision about which definition to adopt cannot be made by engineers. It is a moral and political choice about which errors we are willing to tolerate. If the aim is to reduce the number of people wrongly detained, then equal false-positive rates matter most. If the aim is to identify accurately those who present a genuine danger, calibration matters most. A formula cannot tell us which of these aims a society should prefer, and pretending otherwise simply hides the judgement inside the machine.
Bias can also enter long before any calculation begins, through the choice of what to predict. A model of reoffending is usually trained on arrest records, but an arrest is not the same as an offence: it reflects where police patrol and whom they stop. A model trained on arrests therefore learns about policing as well as about crime. Something similar happened at Amazon, which in 2018 abandoned an experimental system for screening job applications. Trained on a decade of mostly male applicants, it had learned to favour CVs containing words associated with men and to penalise those containing the word 'women's'. Nobody had programmed that preference.
Removing protected characteristics from the data does not solve the problem, because other variables carry the same information. A postcode, a school or a pattern of online behaviour may all act as proxies for ethnicity or income. Nor is the difficulty confined to obvious cases of discrimination. A widely cited 2018 study by Joy Buolamwini and Timnit Gebru tested three commercial systems for analysing faces and found that their error rates were far higher for darker-skinned women than for lighter-skinned men — in one case roughly 35 per cent against under 1 per cent. The training data had simply contained fewer such faces.
Where does this leave the courts? In 2016 a case in Wisconsin reached the state's supreme court after a man was sentenced partly on the basis of a COMPAS score. The court allowed the practice but held that the judge should be told about the tool's limitations. The ruling points towards a sensible principle: a score may inform a decision but must not make it. That requires a human being with the authority to depart from the recommendation. Studies of automation bias show that people defer to a machine's output even when it conflicts with their own judgement.
What, then, should be done? The answer is not to abandon algorithmic decisions, which in many settings are more consistent and more accurate than the officials they replace, but to treat them as institutions that must be audited. Error rates should be published separately for the groups a system affects, and an appeals route should exist for individuals. Fairness must also be re-examined after deployment, because populations change and the models themselves are periodically retrained. An algorithm is not unfair because it is a machine. It is unfair when it conceals a choice that should have been made openly; the task is to find out where the judgement has gone.
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