Maths and Music

    An excellent way to kill a conversation is to say you are a mathematician. Tell others you are also a musician, however, and they will be hooked. Although there are obvious similarities between mathematical and musical activity, there is no direct evidence for the kind of magical connection many people seem to believe in.

    I'm partly referring here to the "Mozart effect", where children who have been played Mozart compositions are supposedly more intelligent, including at maths, than other children. It is not hard to see why such a theory would be popular: we would all like to become better at maths without putting in any effort. But the conclusions of the experiment that expressed the belief in the Mozart effect were much more modest. If you want your brain to work better, you clearly have to put in hard work. As for learning to play the piano, it also takes effort.

    Surely a connection is quite reasonable. Both maths and music deal with abstract structures, so if you become good at one, then it is likely that you become good at something more general that helps you with the other. If this is correct, it would show a connection between mathematical and musical ability. It would be more like the connection between abilities at football and tennis. To become better at one, you need to improve your fitness and coordination (协调). That makes you better at sport and probably helps with the other.

    Abstract structures don't exist only in maths and music. If you learn a language then you need to understand its abstract structures like grammar. Yet we don't hear people asking about a connection between mathematical and linguistic (语言的) ability. Maybe this is because grammar feels mathematical, so it wouldn't be surprising that mathematicians were better at learning grammar. Music, however, is strongly tied up with feelings and can be enjoyed even by people who know little about it. As such, it seems different from maths, so there wouldn't be any connection between the two.

    Let's see how we solve problems of the "A is to B as C is to D" kind. These appear in intelligence tests but they are also central to both music and maths. Consider the opening of Mozart's Eine Kleine Nachtmusik (小夜曲). The second phrase is a clear answer to the first. The listener thinks: "The first phrase goes upward and uses the notes of a G major chord (和弦); what would be the corresponding phrase that goes downward and uses the notes of a D7?" Music is full of puzzles like this. If you are good at them, expectations will constantly be set up in your mind. The best moments surprise you by being unexpected, but we need the expectations in the first place.

    The weather outside might be freezing at home, but that doesn't mean you have to spend the winter shivering. Instead, grab your bathing suit and sunscreen and head to these sunny spots that offer the best warm-weather getaways for every interest.

    The best city beaches: San Juan, Puerto Rico

    Being able to relax on a warm sandy beach in the middle of the winter is obviously a dream getaway, but not everyone wants their sand and surf to be hidden in a remote comer of an island. Instead, head to the sizzling（炎热的）city nightlife of San Juan, where the streets of chic Condado back right into the palm trees and lapping waves of the Atlantic beaches. Top chefs, stylish hotels, bars ， clubs, and shops are all just steps away from the tropical beaches. And since Puerto Rico is a United States Commonwealth, it's one of the easiest islands in the Caribbean to visit since you won't need a passport, have to change money, or even worry about your cell phone working. Puerto Rico is also one of the best tropical vacations you can take without leaving the United States.

    The best swimming holes: Riviera Maya, Mexico

    What's better than diving into the salty sea? Submerging in the crystal clear and salt-free waters of the naturally occurring limestone cenotes of the Riviera Maya and Yucatan Peninsula. Spend a sunny day exploring these natural cave pools filled cool filtered water that springs from the ground below and the lush palm forests that surround them. Then head back to the perfectly located Fairmont Mayakoba for comfortable rooms and modem Mexican cuisine.

    The best girlfriend getaways: New Orleans

    New Orleans vibrant nightlife and live-music scenes make the “Big Easy” a great girl's trip winter getaway (check out the Girl's Trip movie if you don't believe us). And even if your crew isn't one to seek out the boozy Bourbon Street crawl, there's plenty of amazing food to be discovered in the French Quarter, plenty of shopping and strolling in the Garden District, and warm weather cruises along the bayou, too. Check out these other great weekend getaways for girls trips.

    The best aquatic movie star-spotting: Clearwater, Florida

    If you want to meet a real movie star while also soaking up the sun, head to the Gulf shores of Clearwater, Florida. Here you can meet the stars of Dolphin Tale and Dolphin Tale 2, Winter and Hope, who are in residence full-time at the Clearwater Marine Aquarium. The amazing dolphins will probably make you want to hit the waves yourself, which won't be a problem since the beautiful white sand beaches here boast 361 days of sunshine per year. Next, don't miss these destinations that are even better in the winter.

    Fashions have a lot of rules. Most of them, however, are just wrong. But there's one rule that goes beyond tradition and into the field of scientific study of the brain: Black clothes are slimming. It all comes down to how your visual system processes the light. The below holes in each square are the same in size, yet the white hole looks bigger than the black hole.

    In the 1500s, Galileo Galilei noticed that some of the planets looked larger when viewed with the naked eye than they did when viewed through a telescope, making the white light of Venus appear eight to ten times larger than Jupiter in the night sky. He knew something strange must be going on with his vision to cause this illusion, but he wasn't sure what it was. Luckily, scientists never stopped wondering, and in 2014, they figured it out.

    Our visual system operates via two main channels: "on" neurons (神经元) that are sensitive to light things and "off" neurons that are sensitive to dark things. When it came to the dark "off" neurons, the researchers found that they responded predictably to dark shapes on a light background the greater the contrast between the two, the more active these neurons were. But the light on" neurons behaved unpredictably. Even with the same amount of contrast, light objects on a dark background caused a greater response in these neurons.

    This phenomenon makes some sense, evolutionarily speaking. In the dark of night, you'd want to be able to take in every bit of light you can get, so a visual system that enlarges light objects on a dark background could be very useful. However, it's not that hard to see dark objects in the light of day. It has some effects in the colors of your clothes and in the appearance of the planets—the brighter appearance of Venus in the night sky makes it look bigger than the darker Jupiter.

    It was already dark when an old man came to a small town. He found an inn and wanted to stay there for the night. After he had gone to his room, the owner said to his wife, "Look at his bag, dear. I'm sure there are lots of valuable things in it. I want to steal it when he is asleep."

    "No, no," said the woman. "He must look for his bag tomorrow morning. Then he'll take you before the judge." They thought and at last the woman had an idea. "We have forgetful grass," said the woman, "Why not put some into his food? If he has the food, he will forget to take his bag away." "How clever you are!" said the owner, "Don't forget it when you prepare supper for him."

    The old man had the food with the forgetful grass and went to bed. The next morning, when the owner got up, he found the door was open and the old man had left with his bag. He woke his wife up and said angrily, "What a fool! Your forgetful grass isn't useful at all."

    "No, no," said the woman. "I don't think so. He must forget something."

    "Oh, I've remembered!" The owner cried out suddenly, "He forgot…"

    In 1972, a social worker named Sanjit Bunker Roy founded Barefoot College in Tilonia, Rajasthan. Today the college trains women from villages for six months to build and maintain solar panels and other instruments. Barefoot College also offers education to the younger generation both during the day and at its solar bridge schools that meet by lamplight at night.

    The philosophy of Barefoot College is largely inspired by the principles of Gandhi, starting with equality beyond caste (种姓), gender or religion. As a matter of fact, women are prioritized (优先考虑) as an underserved population that is essential to bringing villages together. Another central principle of the college is self-reliance, teaching students to support and think for themselves.

    After the college's female students have completed their half-year of training, they return to their villages where they wait for solar panel parts to arrive from the college. Once they have all the pieces they need, they construct the panels and begin collecting solar energy. For each village, the college also provides solar lamps. Villagers can, in addition, order parts for other solar-powered devices, such as water heaters and cooking stoves. Once assembled, they and the lamps are powered by the solar panels.

    The effect on the villages is huge. Before the solar panels and lamps arrived  villagers had only candles to light their homes. This prevented adults from doing serious work at night, and it made studying difficult for children as well. As for physicians, they had difficulty treating patients and performing operations at night because they had to rely on flashlights.

    Now there is power for not only the electrical appliances that the college provides but also devices like televisions, radios and computers. For the first time, the villagers can even connect to the world through the Internet.

    There's so much to see and do in the coolest little capital. Here's our list of the top 5 must dos when you visit Wellington.