1 . Ariel Procaccia has thought a lot about how to cut a cake over the last 15 years. As the father of three children, he knows how hard it is to divide a birthday cake to everyone’s satisfaction. But it’s also because Procaccia’s work focuses on exploring the mathematical rules for dividing stuff up fairly. One way to do that is to think abstractly about dessert.

For decades, researchers have been asking the seemingly simple question of how to cut a cake fairly. The answer reaches far beyond birthday parties. A mathematical problem at its heart, cake cutting connects strict reasoning to real-world issues of fairness, and so attracts not only mathematicians, but also social scientists, economists and more. “It’s a very elegant model in which you can distill what fairness really is, and reason about it,” Procaccia says.

The simplest approach is called the “divider-chooser” method, where one person cuts the cake into two equal pieces in his view, and the other person picks first. Each receives a piece that they feel is as valuable as the other’s. But when personal preferences are taken into account, even the easiest rule becomes complicated. Suppose Alice and Bob are to divide a cake, and Alice knows Bob prefers chocolate, she may knowingly divide the cake unequally so the smaller piece contains more chocolate. Then Bob will choose according to his preference, and Alice will get the larger piece. Both of them are satisfied with what they get, but the meaning of fairness changes in this situation.

The cake is a symbol for any divisible good. When cake-cutting principles are employed to settle disagreements, they are potentially helping the world find solutions. Procaccia has used fair division algorithms (算法) to model food distribution. Social scientist Haris Aziz is exploring situations ranging from how to divide up daily tasks to how to best schedule doctors’ shifts in hospitals.

Even after decades of investigation, cake cutting isn’t like a simple jigsaw puzzle (拼图) with a well-defined solution. Instead, over time, it has evolved into a kind of mathematical sandbox, a constructive playground that brings together abstract proofs and easy applications. The more researchers explore it, the more there is to explore.

2 . Those who had the pleasure of watching Benny Goodman at work saw a rather ordinary-looking man in rimless glasses and a conservative business suit; but they also saw a human being who could play the clarinet(单簧管) like no one before or since. This made Benny Goodman a unique individual.

Other Americans who have stood out from the flock include Joe DiMaggio, Beverly Sill, Ernest Hemingway and Jonas Salk. They, like Benny Goodman, were recognized and honored for no other reason than excellence.

It is doing something better than other people that makes us unique. Yet a surprising number of people still see individuality as a surface thing. They wear garish clothes, dye their hair strange colors and decorate their skin with tattoos to make some kind of social statement. But an ordinary guy who has dyed his hair purple or orange is nothing more than the same person with a funny-looking head.

The whole purpose of individuality is excellence. Those who invent, who improvise(即兴发挥), who know more about a subject than other people do, and who take something that doesn’t work and make it work––these people are the very soul of capitalism.

Charles Kettering didn’t like the idea of cranking a car to make it start, so he invented the electric starter. Henry Ford figured out the assembly-line technique and made it possible to mass-produce automobiles, and Elisha Otis, inventor of the elevator, indirectly created the city sky-line. These people understood that individualism means working at the top of one’s capacity.

The ones with the purple hair and the funky jewelry are just along for the ride, trying to be “different” and not knowing how to go about it.

The student who earns straight A’s on his report card has grasped the idea and has found the real meaning of individuality. So has the youngster who has designed his own spaceship, who gives piano recitals, who paints pictures of the world around him.

Benny Goodman understood it too. This is why he was at his best, blowing his clarinet, in a blue suit and black shoes.

3 . Pricing is managers’ biggest marketing headache. It’s where they feel the most pressure to perform and the least certain that they are doing a good job. All successful pricing efforts share two qualities: The policy combines well with the company’s overall marketing strategy, and the process is well-organized as a whole.

A company’s pricing policy sends a message to the market—it gives customers an important sense of a company’s philosophy. Consider Saturn Corporation (a wholly owned company of General Motors). Saturn wants to let consumers know that it is friendly and easy to do business with. Part of this concept is conveyed through initiatives such as inviting customers to the factory to see where the cars are made and sponsoring evenings at the dealership that combine a social event with training on car maintenance. But Saturn’s pricing policy sends a strong message as well. Can a friendly, trusting relationship be established with customers if a salesperson uses all the negotiating tricks in the book to try to separate them from that last $100? Of course not. Saturn has a “no hassle, no haggle” policy which removes the possibility of conflicts between dealer and potential customer. Customers have an easier time buying a car knowing that the next person in the door won’t negotiate a better deal.

Of course, there are typically many participants in the pricing process: Accounting provides cost estimates; marketing communicates the pricing strategy; sales provides specific customer input; production sets supply boundaries; and finance establishes the requirements for the entire company’s financial health. Input from diverse sources is necessary. However, problems arise when the philosophy of wide participation is carried over to the price-setting process without strong coordinating mechanisms (协调机制). For example, if the marketing department sets list prices, the salespeople negotiate discounts in the field, the legal department adjusts prices if necessary to prevent breaking the laws or contractual agreements, and the people filling orders negotiate price adjustments for delays in shipment, everybody’s best intentions usually end up bringing about less than the best results. In fact, the company may actually lose money on some orders.

4 . Obese people experience discrimination (歧视) in many parts of their lives, and the workplace is no exception. Studies have long shown that obese workers, defined as those with a body-mass index (BMI) of 30 or more, earn significantly less than their slimmer co-workers.

Yet the costs of weight discrimination may be even greater than previously thought. “The overwhelming evidence,” wrote the Institute for employment Studies, “is that it is only women living with obesity who experience the obesity wage penalty (薪资损失).” They were expressing a view that is widely aired in academic papers. To test it, The Economist has analyzed data concerning 23,000 workers from the American Time Use Survey, conducted by the Bureau of Labour Statistics. Our number-processing suggests that, in fact, being obese hurts the earnings of both women and men.

The data we analyzed cover men and women aged between 25 and 54 and in full-time employment. At a general level, it is true that men’s BMIs are unrelated to their wages. But that changes for men with university degrees. For them, obesity is associated with a wage penalty of nearly 8%, even after accounting for the separate effects of age, race, graduate education and marital status.

The conclusion — that well-educated workers in particular are penalized for their weight — holds for both sexes. Moreover, the higher your level of education, the greater the penalty. We found that obese men with a Bachelor’s degree (学士学位) earn 5% less than their thinner colleagues, while those with a Master’s degree earn 14% less. Obese women, it is true, still have it worse: for them, the equivalent figures are 12% and 19%, respectively (分别地).

Your line of work makes a difference, too. When we dealt with the numbers for individual occupations and industries, we found the greatest differences in high-skilled jobs. Obese workers in health care, for example, make 11% less than their slimmer colleagues; those in management roles make roughly 9% less, on average. In sectors such as construction and agriculture, meanwhile, obesity is actually associated with higher wages.

These results suggest that the total costs of wage discrimination borne by overweight workers in America are greater than expected. Now, it’s time for our governments to take it seriously.

7 . Plant-based products have been breaking into the foodie mainstream in the United States, after years in which vegan (素食的) burgers and milk alternatives knocked on the market’s door. That is partly because more companies are targeting people who seek to reduce the amount of meat they eat, rather than forswear it altogether.

Now, as fish alternatives begin to attract investment and land at restaurants in the United States and beyond, people who track the fishless fish sector say that it could achieve significant growth.

One reason, they say, is that consumers in rich countries are becoming more aware of the seafood industry’s environmental problems, including overfishing and the health risks of some seafood. Another is that today’s plant-based companies do a better job of approaching fish flavor than earlier ones did—an important consideration for non-vegetarians (非素食者).

“There are a number of people already looking at alternative hamburgers,” said Joshua Katz, an analyst at the consulting firm McKinsey who has studied the alt-protein (替代蛋白) industry. “You might actually say, ‘I should work on something else.’ And seafood is still a massive market with convincing reasons to work on.” People who reduce their consumption of animal proteins for environmental reasons often stop eating red meat, which requires enormous amounts of land and water to farm.

But alt-fish advocates say that seafood also comes with environmental problems. Unsustainable fishing practices have destroyed fisheries (鱼汤) in recent decades, a problem both for biodiversity and the millions of people who depend on the sea for income and food.

“It’s simply a smarter way to make seafood,” says Mirte Gosker, the acting managing director of the Good Food Institute Asia-Pacific, a nonprofit advocacy group that promotes alternative proteins. “Full stop.”

So far plant-based seafood products in the United States account for only 0.1 percent of the country’s seafood sales, less than 1.4 percent of the U.S. meat market occupied by plant-based meat alternatives. But alt-seafood enterprises worldwide received at least $83 million from investors in 2020, compared with $1 million three years earlier. As of this June, 83 companies were producing alt-seafood products around the world, a nearly threefold rise since 2017. All but 18 of those 83 companies focus on plant-based products. A dozen others are developing lab-grown seafood, which is not yet commercially available in any country.

8 . Country music has been long led by an age of “bro-country” — country music made by straight white men, best characterized by songs about drinking, trucks and blue jeans. Yet, at its core, country music is a type that is truly all about subversion. Country, essentially, takes the legend of the cowboy and turns it into an act, one that breaks away from tradition. In this new “bro-country” movement, subversion is completely lost, which is why someone like Orville Peck, with the first two chapters of his latest album “Bronco”,is so important for this age of country music.

The Toronto-based singer-songwriter Orville Peck announced “Bronco” on Feb. 7. In the trailer (预告片), the album was revealed to be released in three separate chapters weeks apart from each other.

The two chapters that have been released stay true to the musical stylings of country but often draw subtle influences from the closely related types of folk and rock, which may not be surprising given Peck’s time as a drummer in a punk band. As to the content, the first chapter of “Bronco” presents a more upbeat, somewhat positive feeling with its selection of songs like “C’mon Baby Cry”, “Outta Time”,“Dayton Sand”, and “Any Turn”, which in particular truly feels like the perfect jig (吉格舞曲) to square dance to. The second chapter of “Bronco”, with a focus on the fragile emotions that often lies at the core of the country type, explores darker topics, being largely made up of emotional songs that dive into topics like abusive relationships, loneliness, deep longing, and depression. While sharply different from one another, the two chapters fit amazingly well together. The songs draw on multiple contemporary inspirations, and in doing so stand out against what has become expected of country.

With the third and final chapter of “Bronco” coming on the road, we have reasons to believe that Peck will manage to meet and exceed public expectations and successfully made an album that may shake any who feel no appetite for the type of country music.