2 . 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.

3 . “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:

5 . The Florida Aquarium (Meets animal welfare guidelines)

Open hours: 9:30 AM — 5:00 PM

The Florida Aquarium is an educational and fun-filled wonderland, home to thousands of animals and plants. Kids will especially enjoy wearing a wetsuit to walk among the underwater inhabitants and explore coral caves. It’s an immersive learning journey for the whole family. Ticket prices vary based on several factors including weather, day of week, holidays, local events and attendance patterns. Click here for more information.

Monterey Bay Aquarium (Meets animal welfare guidelines)

Open hours: 10:00 AM — 5:00 PM (Tuesday — Friday); 10:00 AM — 6:00 PM (Saturday — Sunday)

Located by the oceanfront, the Monterey Bay Aquarium offers a window into the rich marine life of the area with over 200 exhibits and 80,000 plants and animals on display. Here, you can see leopard sharks weave through kelp forests at one of the tallest aquarium exhibits in the world, sardines swimming past a 90-foot aquarium window, and cute sea otters frolicking.

Tickets are only available online so be sure to book before you go.

Admission: Adult (ages 18 — 69) $59.95; Youth $49.95 (ages 13 — 17); Child $44.95 (ages 5 — 12) Four and under free; Senior $49.95 (ages 70+).

Tennessee Aquarium (Meets animal welfare guidelines)

Open hours: 10:00 AM — 5:00 PM (Sunday — Friday); 9:00 AM — 5:00 PM (Saturday)

This aquarium has two buildings: River Journey, which showcases freshwater habitats from around the globe, and Ocean Journey, where travelers can view magnificent sea creatures. We recommend spending at least three hours at the aquarium as there are over 10,000 animals here. Weekends are the busiest, so consider visiting on a weekday for a quieter and more intimate experience. There’s timed entry to the aquarium, so plan ahead when booking your tickets.

Admission: Adult $39.95; Youth (Ages 5 — 17) $29.95

6 . Conflict in communities is usually about the task or the person. Of course, sometimes it’s hard to separate one from the other.

Task conflict happens when people have different ideas of what needs to be done. It points to potential differences in opinion about everything you can imagine that is essential for a group: mission, priorities of tasks, compensation mechanism (机制), decision-making mechanisms, etc. Task conflict is not a problem when people realize the source of the conflict is the task and not the people. Community members must resolve tension inclusively with everyone’s voice being heard and acknowledged. However, this does not mean that the solution must include everyone’s opinion. After the conversation, everyone should feel that they had a fair chance to express their opinion and that it was taken seriously by others and not brushed aside.

Conflict between people is tricky because it’s attacking a person’s essence and self-worth. Often this form of conflict, relationship conflict, happens when two conditions are met: First, people have different values or are holding different assumptions, and secondly, neither party can see beyond their own biases. With relationship conflict, the person is perceived to be the problem and is being attacked by others. Each party assumes that most people are on their side and that the other person is acting out of self-interest. This eventually leads to people disagreeing with each other, not for the task’s sake but to prove the other person is wrong.

Sometimes conflict originates in a task. People might prefer different tools or different approaches. If this initial controversy is ignored or not dealt with appropriately, the relatively easy task conflict turns into a more complex relationship conflict. When relationship conflict occurs, a lot of things are reactive rather than reflective. People stop thinking and act impulsively (冲动地).

All in all, remember that every culture has its own way of handling conflict. Some people consider it dishonest if an argument is not addressed openly, while in other cultures, such a discussion will not be acceptable. It comes down to “Don’t assume everyone thinks like you”.

7 . Concrete is one of the most widely used building materials today. It’s a composite material made from a mixture of broken stone or gravel, sand, Portland cement, and water, which can be spread or poured into molds and forms a mass resembling stone on hardening.

Around 3000 BC, the Egyptians used early concrete forms in their building.

One of concrete’s key ingredients is cement (水泥), which is thought to have been devised in Europe in 1300 BC. Later, cement would be combined with other materials to make a substance more similar to what we know as concrete today. The Romans, for example, are famed for their concrete; many structures built using it still stand today. But it could be older than that.

Middle eastern builders coated the outside of their clay fortresses with a thin, moist layer of burned limestone (石灰石), which chemically reacted with gasses in the air to form a hard, protective surface.

Around or before the third millennium BC, Nabataean traders or Bedouins built the first concrete-like structures in the southern Syria and northern Jordan regions. By 700 BC, the significance of lime was known, which led to the development of mortar supply kilns (窑厂) for the construction of rubble-wall houses, and concrete floors.

In 1824, Portland cement was invented by Joseph Aspdin of England. George Bartholomew laid down the first concrete-paved street in the US in 1893, which still exists.

By the end of the 19th century, steel-reinforced concrete was developed. In 1902, August Perret designed and built an apartment building in Paris using steel-reinforced concrete. This building had wide admiration and popularity for concrete and influenced the development of reinforced concrete.

In 1921, Eugene Freyssinet pioneered reinforced-concrete construction by building two airship hangars at Orly Airport in Paris.

9 . My son works at a local sheltered workshop for the disabled a couple of days a week. On those days I drive him there. We almost always arrive at the same time as Miss Stacey. She is a beautiful woman who has been my son s friend his whole life. Cerebral palsy (脑瘫) has limited her to a wheel chair. It has twisted (扭曲) her arms and legs and made it difficult for her to speak. Yet, each time I see her, her soul shines through. There is a light in her eyes that makes you smile. There is a happiness in her smile that warms your heart. There is a love that is shown out from her and touches everyone she meets. In spite of what cerebral palsy has done to her body, her spirit burns bright.

Stacey has been a light of love and joy in my life and in so many others. She has been my son’s friend through grade school, high school, their twenties, and now into their thirties. I can still remember the smiles on their faces when I would go to pick my boy up after school. In spite of the hard work caring for children with special needs all day, they still had such a sense of happiness just by being with them. I can see it too on the faces of those devoted people who work with Stacey today. It is as if they became better just by being with such a sweet soul.

It really breaks my heart when I think that there was a time when physically and mentally disabled children were limited to institutions because they were seen as worthless at some point. In truth, they are the greatest teachers of love we will ever have. What matters is how purely and unconditionally we love. What matters is the light we shine from within. I only hope to live as lovingly, kindly, and joyfully as she does one day.