You should spend about 20 minutes on Questions 1-13, which are based on Reading Passage 1 below.
The history of the world’s most luxurious fabric, from ancient China to the present day.
Silk is a fine, smooth material produced from the cocoons – soft protective shells – that are made by mulberry silkworms (insect larvae). According to legend, it was Lei Tzu, wife of the Yellow Emperor, ruler of China around 3000 BC, who discovered silkworms. One version of the story tells how, during a walk in her husband’s gardens, she noticed silkworms damaging several mulberry trees. She collected a number of cocoons and sat down to rest. As she was sipping tea, one of the cocoons she had collected accidentally fell into the hot tea and began to unravel into a fine thread. Lei Tzu found she could wind this thread around her fingers. She then persuaded her husband to let her rear silkworms on a grove of mulberry trees. She also developed a special reel to draw fibers from the cocoon into a single thread strong enough to be woven into fabric. While the exact truth of this story is uncertain, it is known that silk cultivation has existed in China for several millennia.
Initially, silkworm farming was solely the responsibility of women, who handled the growing, harvesting, and weaving. Silk quickly became a symbol of status, and at first, only royalty could wear clothes made of silk. Gradually, these restrictions were relaxed until, by the Qing Dynasty (1644–1911 AD), even peasants were allowed to wear silk. During the Han Dynasty (206 BC–220 AD), silk became so valuable that it was also used as a unit of currency. Government officials were paid their salaries in silk, and farmers paid their taxes in grain and silk. The emperor also used silk as diplomatic gifts. Silk was used for various purposes, including fishing lines, bowstrings, musical instruments, and even paper. The earliest known use of silk paper was found in the tomb of a noble who died around 168 AD.
The demand for this exotic fabric eventually created the lucrative trade route now known as the Silk Road. Silk was sent westward while gold, silver, and wool were brought to the East. The route was named the Silk Road after its most precious commodity, which was valued more than gold. Stretching over 6,000 kilometers from Eastern China to the Mediterranean Sea, the route followed the Great Wall of China, climbed the Pamir mountain range, crossed modern-day Afghanistan, and passed through the Middle East with a major trading hub in Damascus. From there, goods were shipped across the Mediterranean Sea. Few merchants traveled the entire route; goods were mostly handled by a series of middlemen.
With mulberry silkworms native to China, the country was the world’s sole producer of silk for many centuries. The secret of silk-making eventually reached the rest of the world through the Byzantine Empire, which ruled over the Mediterranean region of southern Europe, North Africa, and the Middle East from 330–1453 AD. According to legend, monks working for the Byzantine emperor Justinian smuggled silkworm eggs to Constantinople (modern-day Istanbul, Turkey) in 550 AD, hidden inside hollow bamboo walking canes. The Byzantines were as secretive as the Chinese, and for many centuries the weaving and trading of silk fabric remained a strict imperial monopoly. In the seventh century, however, the Arabs conquered Persia and captured its magnificent silks.
As the Arabs spread across Africa, Sicily, and Spain, they also spread silk production. By the tenth century, Andalusia in southern Spain had become Europe’s main silk-producing center. By the thirteenth century, Italy had taken over as Europe’s leading silk producer and exporter. Venetian merchants traded silk extensively and encouraged silk growers to settle in Italy. Even today, silk produced in the Como province of northern Italy enjoys an esteemed reputation.
The nineteenth century and the rise of industrialization saw the decline of Europe’s silk industry. Cheaper Japanese silk, which benefited from the opening of the Suez Canal, was one major factor. In the twentieth century, new man-made fibers like nylon replaced silk in products such as stockings and parachutes. The two world wars, which interrupted the supply of raw materials from Japan, further stifled Europe’s silk industry. After World War II, Japan restored its silk production, improving both quality and output. Japan remained the world’s largest producer and exporter of raw silk until the 1970s. In recent decades, however, China has gradually regained its position as the world’s biggest producer and exporter of raw silk and silk yarn. Today, around 125,000 metric tons of silk are produced worldwide, with nearly two-thirds of that production taking place in China.
You should spend about 20 minutes on Questions 14-26, which are based on Reading Passage 2 below.
Animal migration, however it is defined, is far more than just the movement of animals. It can loosely be described as travel that takes place at regular intervals – often in an annual cycle – involving many members of a species and rewarded only after a long journey. It suggests inherited instinct. Biologist Hugh Dingle has identified five characteristics that apply, in varying degrees and combinations, to all migrations. These are: prolonged movements that take animals outside familiar habitats; movements that tend to be linear rather than zigzagging; special behaviours concerning preparation (such as overfeeding) and arrival; special allocations of energy; and, lastly, an intense focus on the greater mission, which keeps migrating animals undistracted by temptations and undeterred by challenges that would turn other animals aside.
For instance, an arctic tern, on its 20,000 km flight from the extreme south of South America to the Arctic Circle, will ignore the offer of a nice smelly herring from a bird-watcher’s boat. While local gulls would eagerly dive for such handouts, the tern flies on. Why? The arctic tern resists distraction because it is driven at that moment by an instinctive sense of something we humans find admirable: a larger purpose. In other words, it is determined to reach its destination. The bird senses that it can eat, rest, and mate later. Right now, its undivided intent is arrival.
Reaching a gravelly coastline in the Arctic, where other arctic terns have gathered, serves its larger evolutionary purpose: finding a place, time, and set of conditions in which it can successfully hatch and rear offspring.
Migration is a complex phenomenon, and biologists define it differently depending on the animals they study. Joel Berger, of the University of Montana, who works on the American pronghorn and other large terrestrial mammals, prefers a simple, practical definition for his research: "movements from a seasonal home area to another home area and back again." Generally, this back-and-forth movement is driven by the need to seek resources that aren’t available year-round in a single area.
However, daily vertical movements by zooplankton in the ocean – upward by night to seek food, downward by day to avoid predators – can also be considered migration. So can the movement of aphids, when they deplete the young leaves on one food plant and their offspring then fly onward to a different host plant, with no aphid ever returning to its starting point.
Dingle, an evolutionary biologist who studies insects, has a more intricate definition that includes the five features distinguishing migration from other movements. His definition accounts for the fact that, for instance, aphids become sensitive to blue light (from the sky) when it’s time for their big journey and to yellow light (reflected from tender young leaves) when it’s time to land. Birds prepare for migration by fattening themselves through heavy feeding. The value of Dingle’s definition, he argues, is that it highlights what the phenomenon of wildebeest migration shares with that of aphids, guiding researchers towards understanding how evolution has shaped these behaviours.
Human activities, however, are having a detrimental impact on animal migration. The pronghorn, a species resembling an antelope though unrelated, is the fastest land mammal in the New World. One population spends its summer in the mountainous Grand Teton National Park in the western USA, following a narrow route from the mountains across a river and onto the plains, where they endure the frozen months feeding mainly on sagebrush cleared of snow. These pronghorn are notable for their rigid migration route, which constricts at three critical bottlenecks. If they can’t pass through these during their spring migration, they can’t reach their summer grazing grounds. If they can’t pass through again in autumn to escape onto the windblown plains, they are likely to die trying to survive the deep snow. Dependent on distance vision and speed to stay safe from predators, pronghorn traverse high, open land where they can see and run. At one bottleneck, forested hills rise to form a V, leaving only a 150-metre-wide corridor filled with private homes. Increasing development threatens to block this passageway entirely.
Conservation scientists, along with some biologists and land managers within the USA’s National Park Service and other agencies, are now focusing on preserving migratory behaviours, not just species and habitats. A National Forest has recognized the pronghorn’s migratory path, much of which passes across its land, as a protected corridor. However, neither the Forest Service nor the Park Service can control what happens on private land at a bottleneck. With some other migrating species, the challenge is even more complex, involving longer distances, multiple jurisdictions, more borders, and greater dangers along the way. Wisdom and determination will be required to ensure that migrating species can continue their journeying a while longer.
You should spend about 20 minutes on Questions 27-40, which are based on Reading Passage 3 below.
A
Occasionally, in some difficult musical compositions, there are beautiful but simple parts that even a beginner can play. Mathematics is similar. Some discoveries in advanced mathematics do not require specialized knowledge, such as algebra, geometry, or trigonometry. Instead, they may involve basic arithmetic, like "the sum of two odd numbers is even," and common sense. Each of the eight chapters in this book demonstrates this phenomenon, making it accessible for anyone to understand every step of the reasoning.
B
One of my goals in writing this book is to provide readers who have not had the opportunity to engage with real mathematics a chance to appreciate the mathematical way of thinking. I aim to reveal not only some fascinating discoveries but also, more importantly, the reasoning behind them. This book differs from most general public mathematics books, which often present the lives of mathematicians, describe important applications, or focus on mathematical procedures assuming some algebraic proficiency.
C
I hope this book will help bridge the notorious gap between the humanities and the sciences, or, more specifically, the intuitive right brain and the analytical left brain. As the chapters will illustrate, mathematics is not confined to analytical and numerical aspects; intuition plays a significant role. This alleged gap can be narrowed or completely overcome because each of us uses only a fraction of our brain's full capacity. To demonstrate our potential, I mention various individuals: a structural engineer who is also an artist, an electrical engineer who is an opera singer, an opera singer who has published mathematical research, and a mathematician who writes short stories.
D
Other scientists have written books explaining their fields to non-scientists but have had to omit the mathematical foundations of their theories. Consequently, readers remain spectators rather than participants, as mathematics is often essential for describing the details of scientific theories, whether about the expanding universe, subatomic particles, or chromosomes. While broad scientific theories can be sketched intuitively, their detailed descriptions often resemble mathematics texts.
E
Nonetheless, non-mathematical readers can gain a substantial understanding of mathematical reasoning. This book provides details that illustrate the mathematical style of thinking, which involves sustained, step-by-step analysis, experiments, and insights. Readers will likely turn the pages more slowly than they would with a novel or newspaper. Having a pencil and paper handy to check claims and conduct experiments may be helpful.
F
As I wrote, I considered two types of readers: those who enjoyed mathematics until a negative experience, often around fifth grade, led them away, and mathematics enthusiasts who will find much that is new throughout the book. This book also serves readers looking to sharpen their analytical skills. Many careers, such as law and medicine, require precise analysis. Each chapter offers practice in following a sustained and closely argued line of thought. Testimonials show how mathematics can develop such skills:
G
A physician wrote: “The discipline of analytical thought processes in mathematics prepared me extremely well for medical school. In medicine, one must thoroughly analyze a problem before finding a solution. The process is similar to doing mathematics.”
A lawyer noted: “Although I had no background in law, I performed well at one of the best law schools. I attribute much of my success to having learned through the study of mathematics, especially theorems, how to analyze complex principles. Lawyers who have studied mathematics can master legal principles more effectively than most others.”
I hope you will share my delight in seeing how simple, even naive, questions can lead to remarkable solutions and how theoretical discoveries can have unexpected applications.