4 . In a remote mountainous region in Pakistan, a cable car carrying six children and two adults became stuck in mid-air. However, this terrifying incident resulted in a remarkable display of bravery and intelligence as ordinary bystanders stepped up to save lives.

The incident began like any other day when the small group started their typical daily journey to school and the local shops aboard the shaky three cables broke, causing it to be suspended in the air.

Immediately, multiple rescue efforts were set into motion. The rescue mission lasted for over 10 hours. Military helicopters and local experts attempted to rescue the stuck car. However, the complex terrain (地形) and the cable car’s unsafe position made progress slow. By nightfall, the helicopter team had only rescued one child from the car.

The local administration called upon two local brothers, Sahib and Nasir, for their expert skill in operating temporary cable cars in the region. With limited resources available, the Khan brothers thought up a clever idea to reach the stuck cable car. They constructed a small temporary car using a zip line, allowing them to move over the risky terrain and approach the hanging cable car.

Nasir remained on the ground, assisting with the pulley (滑轮) system. Sahib bravely boarded the temporary car and started a dangerous journey to ward the stuck children. Once he reached the hanging car, Sahib carefully tied a rope around the children in the car. Making several trips, he secured the children and carried them across one at a time. He successfully transported two children to safety in this fashion.

With Sahib’s courageous efforts paving the way, local rescuers took over, using the same method to bring the remaining three children and the two adults back to safety. This heroic rescue mission is a powerful reminder that when people work together with a common goal in mind, they can brainstorm, even in the face of challenges that seemingly can’t be tackled successfully.

6 . 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.

8 . “The mountains are calling and I must go” — the famous quote is from John Muir(1838-1914), who is described as “the wilderness poet” and “the citizen of the universe.” He once jokingly referred to himself as a “poet-geologist-botanist and ornithologist (鸟类学家)-naturalist etc. etc.!” He is known as the Father of American National Parks.

Famed documentary filmmaker Ken Burns recently said, “As we got to know him… he was among the highest individuals in America; I’m talking about the level of Abraham Lincoln, Martin Luther King Jr., and Thomas Jefferson— people who have had a transformational effect on who we are.”

So where is the quote from? Well, John Muir was a productive writer. Whether he was writing poetry or simply letters to his family, John Muir was always putting pen to paper. The quote is from within one of his many letters written to his sister:

9 . Smith brought his three-month-old son out for breakfast one day. He was playing with his son and tending to him while eating, and just doing his _________ thing.

But then he noticed a _________ staring at him. He was _________. “What is going on?” “They kept _________ at me,” he wrote in a post.

As it _________, the strangers were just happy to see a dad spending time with his son, and they felt inspired while watching the _________. Smith had no way of knowing that until he paid for his meal. He was given by the waiter a _________ from the couple, saying what a great father he was and that they would like to leave some _________ for his meal.

“Today your meal is on my wife and me,” it read. “_________ that baby as long as possible. The Masons.”

For Smith, it was a happy moment of reassurance (认可) and feeling __________. He was touched by the generosity and noted that he didn’t have a father figure growing up, so spending this time with his son is super __________ to him.

He wrote that he’ll share this __________ with his son when he’s older and that he wants to teach him kindness and about the __________ of giving back.

“I make sure I’m __________,” Smith wrapped. “I get blessed — I want to __________ someone else.”

Gwyneth Paltrow and Victoria Beckham are fans of the Tracy Anderson Method, which involves dance-based classes using body resistance and very light hand weights. Her online programme includes a new weekly workout, as well as access to existing classes, her digital magazine and meal planning guides. It’s at ￡69 per month, but you get a discount for annual membership.tracyanderson.com

The singer Ellie Goulding and the fashion designer Henry Holland are said to be fans of Roar’s daily live classes, which include the Overdrive—a high energy weights-based workout focusing on upper-body strengthening and cardiovascular fitness. Their founder, the three times Olympian speed skater Sarah Lindsay, has also trained the broadcaster Piers Morgan and the DJ Nick Grimshaw. There’s a 14-day free trial, then membership starts at โ12.50per month with live daily workouts and unlimited access to the library. roar-fitness.com

The Thor actor Chris Hemsworth and his personal trainer Luke Zocchi launched the Centr app in 2019. It features 20 and 40-minute session s of HIIT, Pilates, yoga, boxing and guided meditation, plus recipe ideas, a meal planner and stress and well being support. It’s offering a free seven-day trial, and starts from £7.83permonth. centr.com

The former professional footballer and celebrity trainer Bradley Simmonds launched his platform, Get It Done, in 2020. The app includes daily live streamed and on-demand classes featuring yoga, core fitness and strength. From ￡22 per month. Getitdone. fitness