突然，全世界最大的麻烦来了！

一

破万！

一个隐形炸弹，终于爆发了！

今天，非洲疾控中心发布数据：非洲新冠肺炎累计确诊病例破万，已达10075例，死亡487。

从2月14日发现第一例确诊病例开始，短短53天时间，疫情蔓延到非洲大陆52个国家，仅莱索托、科摩罗2国暂未报告确诊病例，其他国家都沦陷了。

在一些国家，新冠肺炎的确诊病例，已经出现了10倍级别的增长。

是的，你没看错，疾疫的第三波蔓延，开始了：

第一波，是东亚。

第二波，是美欧。

第三波，极有可能是非洲印度中东南美。

东亚和美欧，这些国家，经济社会发达，政府力量较强，所以这些国家无论如何爆发，最终都是有控制能力的。

在疫情中，最危险的其实是几乎没有声音的非洲，如果非洲失控，那将是真正的人间地狱，你很可能会看到真正的人道主义危机。

我们只能祈祷，局面不会朝着最糟糕的方向去。

二

有人也许会说，非洲，超过13亿人口，现在确诊也就才1万人出头，何必如此大惊小怪！

你有所不知，现在非洲确诊人口少，并不是因为非洲人免疫力强，或非洲温度高，而是因为：

1、流动小，延缓了病毒的传播。

这次疫情首先发展到经济好的地方，大部分非洲人收入不高，连温饱都难以解决，哪里还有钱跑到富裕地区去旅行？

既然少有人跨国旅行，所以病毒传进非洲的速度，自然就慢一些。

克莱因瓶是一个不可定向的二维紧流形，而球面或轮胎面是可 克莱因瓶 克莱因瓶 定向的二维紧流形。如果观Sophie Amundsen was on her way home from school. She had walked the first part of the way with Joanna. They had been discussing robots. Joanna thought the hum From time to time there would be a few letters from the bank for her father, but then he was not a normal father. Sophie's father was the captain of a big oil tanker, and was away for most of the year. During the few weeks at a time when he was at home, he would shuffle around the house making it nice and cozy for Sophie and her mother. But when he was at sea he could seem very distant. There was only one letter in the mailbox--and it was for Sophie. The white envelope read: "Sophie Amundsen, 3 Clover Close." That was all; it did not say whothe mirror and said, "You are me." As she got no answer to this, she turned the sentence around and said, "I am you." Sophie Amundsen was often dissatisfied with her appearance. She was frequently told that she had beautiful almond-shaped eyes, but that was probably just something people said because her nose was too small and her mouth was a bit too big. And her ears were much too close to her eyes. Worst of all was her straight hair, which it was impossible to do anything with. Sometimes her father would stroke her hair and call her "the girl with the flaxen hair," after a piece of music by Claude De world come from? it said. I don't know, Sophie thought. Surely nobody really knows. And yet--Sophie thought it was a fair question. For the first time in her life she felt it wasn't right to live in the world without at least inquiring where it came from. The mysterious letters had made Sophie's head spin. She decided to go and sit in the den. The den was Sophie's top secret hiding place. It was where she went when she was terribly angry, terribly miserable, or terribly happy. Today she was simply confused. * * * The red house was surrounded by a large garden with lots of flowerbeds, fruit bushes, fruit trees of different kinds, a spacious lawn with a glider and a little gazebo that Granddad had built for Granny when she lost their first child a few weeks after it was born. The child's name was Marie. On her gravestone w早知今日，何必当初？！如果早点鼓励戴口罩，也不至于今天疫情搞成这般田地！今天，美国终于改口了，正式表示：公共场合建议佩戴口罩！刚刚，美国疾控中心更新了对新冠病毒的个人防护指南，在指南里，增加了一项新的保护措施：美国民众不论健康或生病，出入公共场合均需配戴简单的布口罩或遮住面部，因为部分无症状感染者可能在不知不觉中将病毒传播给他人。紧跟着，特朗普也顺坡下驴了，他在新闻发布会上转达了美国疾控中心修改指南，正式建议：民众应在公共场所佩戴口罩。特朗普婆姨梅拉尼娅也通过社交媒体呼吁人们佩戴口罩，表示：“随着周末来临，请大家保持社交距离，认真佩戴口罩或遮盖面部。” 疾控中心、特朗普、梅拉尼娅，三连发！这真是180度大转变啊！别忘了，前几天，特朗普还在振振有词地说：我觉得不戴口罩也没关系，可以戴围巾，围巾懂吧？围巾会非常好！作为美国抗疫总指挥的是彭斯，以前更是公开说过，勤洗手、保持社交距离就行了，美国人没必要戴口罩！然而，豪言壮语没用啊，因为新冠病毒就是专门治各种不服的，最后口罩，还只能戴！现在，美国已累计确诊逾27万例，死亡病例7077例，与前一天相比，新增确诊病例35060例，连续第5天新增确诊数超2万，35个州和地区进入“重大灾难”状态！再这么扛下去，美国真要搞群体免疫了，而一旦全民感染，最终结局将是医疗系统彻底崩溃，死亡人数将在百万级别。感染了那么多，美国人终于要戴上口罩了，虽然有点迟了，但总是一件好事！唉，无知不是生存的障碍，傲慢才是。二 有些政客，变脸就是快！用不着你，就怒目相向，用得着你，就满脸堆笑！现在，美国终于反应过来，想要找口罩戴的时候，它突然发现，口罩产能集中在东亚特别是中国，本国口罩缺货，根本不够用！怎么办？老美第一本能反应，就是：抢！今天，德国一批20万只的FFP2口罩，在曼谷被美国“截胡”，直接转运美国，气得德国官员咒骂：这分明是“现代海盗行为”啊！20万只，抢了也不管用啊！怎么办？老美又使出第二招：截！现在，特朗普政府命令美国3M公司，不许再向加拿大和拉丁美洲出口防护口罩了，必须留在美国自己用。特朗普自己出面，炮轰3M：不准向加拿大和南美出口N95口罩！卧槽，还说是亲密盟友，这下把加拿大气坏了，特鲁多警告称，可能对特朗普这一决定采取报复性措施！3M公司也看不下去了，公然骂特朗普：反人道！抢+截，也不够用啊，毕竟，目前美国市场的口罩95%依赖海外供应，而中国是最大的口罩供应商。用不着你，叫你牛夫人，现在用得着你，美国政客一扭头，又开始叫你小甜甜了。看吧，美国大使馆，就突然又变脸了，开始感谢中国人的帮助了。驻华大使布兰斯塔德，特意在微博微信等各平台写了四段话。第一段说：我强调了现在就是向前看的时候，并对中国就出口需要的医疗用品到美国，对我国政府给予帮助，传达了我的感谢。嗯，现在要向前看了，我对中国帮助美国表达感谢。第二段说：美国大使馆已经辛勤工作，为美国和中国公司牵线，以满足美国对关键个人防护用品不断增加的即刻需求。我们正与中国政府官员紧密合作，加快来自中国的货物运输。还是同一个主题，我们要辛勤工作，我们要帮助运送中国货物，满足美国人的迫切需求。第三段、第四段继续重复：向前同行。看懂了没有，洋洋洒洒几百字，其实说得就是一个意思：第一医疗用品，第二医疗用品，第三，还是医疗用品！然后，美国食品和药品管理局（FDA）也表示，在确认满足相关要求的前提下，将允许美国医疗机构使用中国生产的KN95口罩。唉，要说情商高，我还真是佩服美国人！看吧，在25日七国集团外长会议上，美国国务卿蓬佩奥故意将新冠病毒称作“武汉病毒”，无底线开撕。前几天，美国政府还放大质量问题，拒绝批准进口中国KN95口罩，阻挠中国产品进入。现在一看，感染人数指数级增长，还有很多无症状感染者，不进口中国口罩等医疗用品，终归扛不住了！这下，美国政客的脸，马上阴转晴了，说感谢中国，感恩有你，感谢命运，向前同行！节操碎了一地有没有？当然，向前同行并没错，毕竟，不管美国政客如何，大家共同的敌人只有病毒，中国应该有这气度，有这胸怀。只不过美国啊美国，你的脸能不能不要变得这么快，否则真的很容易让人想起，那个农夫与蛇的故事！三 灾难是一面照妖镜，疫情之下，人性被一览无余，各个国家的面容，也被照了个彻底。还记得两个月前，很多国家都等着看中国的热闹。批判、侮辱的言论不绝于耳。可现在，疫情蔓延全球，中国却成为了全世界的诺亚方舟，而很多国家都通过疫情中中国的表现，重新审视起了中国，刷新了对中国的认知。现在，中国正在全力以赴，联手协助其他国家抗疫，打败新冠肺炎这个人类共同的敌人，并用自己的复工复产和努力勤奋，推动全球经济的繁荣。中国人正用自己的仁慈之心、用自己的责任担当、用自己的人道主义精神，举起全球互助大旗，提供力所能及的支援，为全球战疫注入不可替代的“正能量”！一ere the words: "Little Marie to us came, greeted us, and left again." Down in a corner of the garden behind all the raspberry bushes was a dense thicket where neither flowers nor berries would grow. Actually, it was an old hedge that had once marked the boundary to the woods, but because nobody had trimmed it for the last twenty years it had grown into a tangled and impenetrable mass. Granny used to say the hedge made it harder for the foxes to take the chickens during the war, when the chickens had free range of the garden. To everyone but Sophie, the old hedge was just as useless as the rabbit hutches at the other end of the garden. But that was only because they hadn't discovered Sophie's secret. Sophie had known about the little hole in the hedge for as long as she could remember. When she crawled through it she came into a large cavity between the bushes. It was like a little house. She knew nobody would find her there. Clutching the two envelopes in her hand, Sophie ran through the garden, crouched down on all fours, and wormed her way through the hedge. The den was almost high enough for her to stand upright, but today she sat down on a clump of gnarled roots. From there she could look out through tiny peepholes between the twigs and leaves. Although none of the holes was bigger than a small coin, she had a good view beginning. Oh, drat! She opened the two envelopes again. Who are you早知今日，何必当初？！如果早点鼓励戴口罩，也不至于今天疫情搞成这般田地！今天，美国终于改口了，正式表示：公共场合建议佩戴口罩！刚刚，美国疾控中心更新了对新冠病毒的个人防护指南，在指南里，增加了一项新的保护措施：美国民众不论健康或生病，出入公共场合均需配戴简单的布口罩或遮住面部，因为部分无症状感染者可能在不知不觉中将病毒传播给他人。紧跟着，特朗普也顺坡下驴了，他在新闻发布会上转达了美国疾控中心修改指南，正式建议：民众应在公共场所佩戴口罩。特朗普婆姨梅拉尼娅也通过社交媒体呼吁人们佩戴口罩，表示：“随着周末来临，请大家保持社交距离，认真佩戴口罩或遮盖面部。” 疾控中心、特朗普、梅拉尼娅，三连发！这真是180度大转变啊！别忘了，前几天，特朗普还在振振有词地说：我觉得不戴口罩也没关系，可以戴围巾，围巾懂吧？围巾会非常好！作为美国抗疫总指挥的是彭斯，以前更是公开说过，勤洗手、保持社交距离就行了，美国人没必要戴口罩！然而，豪言壮语没用啊，因为新冠病毒就是专门治各种不服的，最后口罩，还只能戴！现在，美国已累计确诊逾27万例，死亡病例7077例，与前一天相比，新增确诊病例35060例，连续第5天新增确诊数超2万，35个州和地区进入“重大灾难”状态！再这么扛下去，美国真要搞群体免疫了，而一旦全民感染，最终结局将是医疗系统彻底崩溃，死亡人数将在百万级别。感染了那么多，美国人终于要戴上口罩了，虽然有点迟了，但总是一件好事！唉，无知不是生存的障碍，傲慢才是。二 有些政客，变脸就是快！用不着你，就怒目相向，用得着你，就满脸堆笑！现在，美国终于反应过来，想要找口罩戴的时候，它突然发现，口罩产能集中在东亚特别是中国，本国口罩缺货，根本不够用！怎么办？老美第一本能反应，就是：抢！今天，德国一批20万只的FFP2口罩，在曼谷被美国“截胡”，直接转运美国，气得德国官员咒骂：这分明是“现代海盗行为”啊！20万只，抢了也不管用啊！怎么办？老美又使出第二招：截！现在，特朗普政府命令美国3M公司，不许再向加拿大和拉丁美洲出口防护口罩了，必须留在美国自己用。特朗普自己出面，炮轰3M：不准向加拿大和南美出口N95口罩！卧槽，还说是亲密盟友，这下把加拿大气坏了，特鲁多警告称，可能对特朗普这一决定采取报复性措施！3M公司也看不下去了，公然骂特朗普：反人道！抢+截，也不够用啊，毕竟，目前美国市场的口罩95%依赖海外供应，而中国是最大的口罩供应商。用不着你，叫你牛夫人，现在用得着你，美国政客一扭头，又开始叫你小甜甜了。看吧，美国大使馆，就突然又变脸了，开始感谢中国人的帮助了。驻华大使布兰斯塔德，特意在微博微信等各平台写了四段话。第一段说：我强调了现在就是向前看的时候，并对中国就出口需要的医疗用品到美国，对我国政府给予帮助，传达了我的感谢。嗯，现在要向前看了，我对中国帮助美国表达感谢。第二段说：美国大使馆已经辛勤工作，为美国和中国公司牵线，以满足美国对关键个人防护用品不断增加的即刻需求。我们正与中国政府官员紧密合作，加快来自中国的货物运输。还是同一个主题，我们要辛勤工作，我们要帮助运送中国货物，满足美国人的迫切需求。第三段、第四段继续重复：向前同行。看懂了没有，洋洋洒洒几百字，其实说得就是一个意思：第一医疗用品，第二医疗用品，第三，还是医疗用品！然后，美国食品和药品管理局（FDA）也表示，在确认满足相关要求的前提下，将允许美国医疗机构使用中国生产的KN95口罩。唉，要说情商高，我还真是佩服美国人！看吧，在25日七国集团外长会议上，美国国务卿蓬佩奥故意将新冠病毒称作“武汉病毒”，无底线开撕。前几天，美国政府还放大质量问题，拒绝批准进口中国KN95口罩，阻挠中国产品进入。现在一看，感染人数指数级增长，还有很多无症状感染者，不进口中国口罩等医疗用品，终归扛不住了！这下，美国政客的脸，马上阴转晴了，说感谢中国，感恩有你，感谢命运，向前同行！节操碎了一地有没有？当然，向前同行并没错，毕竟，不管美国政客如何，大家共同的敌人只有病毒，中国应该有这气度，有这胸怀。只不过美国啊美国，你的脸能不能不要变得这么快，否则真的很容易让人想起，那个农夫与蛇的故事！三 灾难是一面照妖镜，疫情之下，人性被一览无余，各个国家的面容，也被照了个彻底。还记得两个月前，很多国家都等着看中国的热闹。批判、侮辱的言论不绝于耳。可现在，疫情蔓延全球，中国却成为了全世界的诺亚方舟，而很多国家都通过疫情中中国的表现，重新审视起了中国，刷新了对中国的认知。现在，中国正在全力以赴，联手协助其他国家抗疫，打败新冠肺炎这个人类共同的敌人，并用自己的复工复产和努力勤奋，推动全球经济的繁荣。中国人正用自己的仁慈之心、用自己的责任担当、用自己的人道主义精神，举起全球互助大旗，提供力所能及的支援，为全球战疫注入不可替代的“正能量”！一? Where does the world come from? What annoying questions! And anyway where did the letters come from? That was just as mysterious, almost. Who had jolted Sophie out of her everyday existence and suddenly brought her face to face with the great riddles of the universe? For the third time Sophie went to the mailbox. The mailman had just delivered the day's mail. Sophie fished out a bulky pile of junk mail, periodicals, and a couple of letters for her mother. There was also a postcard of a tropical beach. She turned the card over. It had a Nor-wegian stamp on it and was postmarked "UN Battalion." Could it be from Dad? But wasn't he in a completely different place? It wasn't his handwriting either. Sophie felt her pulse quicken a little as she saw who the postcard was addressed to: "Hilde Moller Knag, c/o Sophie Amundsen, 3 Clover Close ..." The rest of the address was correct. The card read: Dear Hilde, Happy 15th birthday! As I'm sure you'll understand, I want to give you a present that will help you grow. Forgive me for sending the card c/o Sophie. It was the easiest way. Love from Dad. Sophie raced back to the house and into the kitchen. Her mind was in a turmoil. Who was this "Hilde," whose fifteenth birthday was just a month before her own? Sophie got out the telephone book. There were a lot of people called Moller, and quite a few called Knag. But there was nobody in the entire dire早知今日，何必当初？！如果早点鼓励戴口罩，也不至于今天疫情搞成这般田地！今天，美国终于改口了，正式表示：公共场合建议佩戴口罩！刚刚，美国疾控中心更新了对新冠病毒的个人防护指南，在指南里，增加了一项新的保护措施：美国民众不论健康或生病，出入公共场合均需配戴简单的布口罩或遮住面部，因为部分无症状感染者可能在不知不觉中将病毒传播给他人。紧跟着，特朗普也顺坡下驴了，他在新闻发布会上转达了美国疾控中心修改指南，正式建议：民众应在公共场所佩戴口罩。特朗普婆姨梅拉尼娅也通过社交媒体呼吁人们佩戴口罩，表示：“随着周末来临，请大家保持社交距离，认真佩戴口罩或遮盖面部。” 疾控中心、特朗普、梅拉尼娅，三连发！这真是180度大转变啊！别忘了，前几天，特朗普还在振振有词地说：我觉得不戴口罩也没关系，可以戴围巾，围巾懂吧？围巾会非常好！作为美国抗疫总指挥的是彭斯，以前更是公开说过，勤洗手、保持社交距离就行了，美国人没必要戴口罩！然而，豪言壮语没用啊，因为新冠病毒就是专门治各种不服的，最后口罩，还只能戴！现在，美国已累计确诊逾27万例，死亡病例7077例，与前一天相比，新增确诊病例35060例，连续第5天新增确诊数超2万，35个州和地区进入“重大灾难”状态！再这么扛下去，美国真要搞群体免疫了，而一旦全民感染，最终结局将是医疗系统彻底崩溃，死亡人数将在百万级别。感染了那么多，美国人终于要戴上口罩了，虽然有点迟了，但总是一件好事！唉，无知不是生存的障碍，傲慢才是。二 有些政客，变脸就是快！用不着你，就怒目相向，用得着你，就满脸堆笑！现在，美国终于反应过来，想要找口罩戴的时候，它突然发现，口罩产能集中在东亚特别是中国，本国口罩缺货，根本不够用！怎么办？老美第一本能反应，就是：抢！今天，德国一批20万只的FFP2口罩，在曼谷被美国“截胡”，直接转运美国，气得德国官员咒骂：这分明是“现代海盗行为”啊！20万只，抢了也不管用啊！怎么办？老美又使出第二招：截！现在，特朗普政府命令美国3M公司，不许再向加拿大和拉丁美洲出口防护口罩了，必须留在美国自己用。特朗普自己出面，炮轰3M：不准向加拿大和南美出口N95口罩！卧槽，还说是亲密盟友，这下把加拿大气坏了，特鲁多警告称，可能对特朗普这一决定采取报复性措施！3M公司也看不下去了，公然骂特朗普：反人道！抢+截，也不够用啊，毕竟，目前美国市场的口罩95%依赖海外供应，而中国是最大的口罩供应商。用不着你，叫你牛夫人，现在用得着你，美国政客一扭头，又开始叫你小甜甜了。看吧，美国大使馆败新冠肺炎这个人类共同的敌人，并用自己的复工复产和努力勤奋，推动全球经济的繁荣。中国人正用自己的仁慈之心、用自己的责任担当、用自己的人道主义精神，举起全球互助大旗，提供力所能及的支援，为全球战疫注入不可替代的“正能量”！一ctory called Moller Knag. She examined the mysterious card again. It certainly seemed genuine enough; it had a stamp and a postmark. Why would a father send a birthday card to Sophie's address when it was quite obviously intended to go somewhere else? What kind of father would cheat his own daughter of a birthday card by purposely sending it astray? How could it be "the easiest way"? And above all, how was she supposed to trace this Hilde person? So now Sophie had another problem to worry about. She tried to get her thoughts in order: This afternoon, in the space of two short hours, she had been presented with three problems. The first problem was who had put the two white envelopes in her mailbox. The second was the difficult questions these letters contained. The third problem was who Hilde Moller Knag could be, and why Sophie had been sent her birthday card. She was sure that the three problems were interconnected in some way. They had to be, because until today she had lived a perfectly ordinary life.察克莱因瓶，有一点似乎令人困惑－－克莱因瓶的瓶颈和瓶身是相交的，换句话说，瓶颈上的某些点和瓶壁上的某些点占据了三维空间中的同一个位置。我们可以把克莱因瓶放在四维空间中理解：克莱因瓶是一个在四维空间中才可能真正表现出来的曲面。如果我们一定要把它表现在我们生活的三维空间中，我们只好将就点，把它表现得似乎是自己和自己相交一样。克莱因瓶的瓶颈是广泛地应用到了建筑，艺术，工业生产中。三维空间里的克莱因瓶 拓扑学的定义编辑 克莱因瓶定义为正方形区域 [0,1]×[0,1] 模掉等价关系(0,y)~(1,y), 0≤y≤1 和 (x,0)~(1-x,1), 0≤x≤1。类似于 Mobius Band, 克莱因瓶不可定向。但 Mobius 带可嵌入   ，而克莱因瓶只能嵌入四维（或更高维）空间。莫比乌斯带编辑 把一条纸带的一段扭180°，再和另一端粘起来就得到一条莫比乌斯带的模型。这也是一个只有莫比乌斯带、一个面的曲面，但是和球面、轮胎面和克莱因瓶不同的是，它有边（注意，它只有一条边）。如果我们把两条莫比烈爆炸。一般认为质量小于9倍太阳质量左右的恒星，在经历引力坍缩的过程后是无法形成超新星的。[75]  在大质量恒星演化到晚期，内部不能产生新的能量，巨大的引力将整个星体迅速向中心坍缩，将中心物质都压成中子状态，形成中子星，而外层下坍的物质遇到这坚硬的“中子核”反弹引起爆炸。这就成为超新星爆发，质量更大时，中心更可形成黑洞。[76]  在超新星爆发的过程中所释放的能量，需要我们的太阳燃烧900亿年才能与之相当。[77]  超新星研究有着关乎人类自身命运的深层意义。如果一颗超新星爆发的位置非常接近地球，目前国际天文学界普遍认为此距离在100光年以内，它就能够对地球的生物圈产生明显的影响，这样的超新星被称为近地超新星。有研究认为，在地球历史上的奥陶纪大灭绝，就是一颗近地超新星引起的，这次灭绝导致当时地球近60%的海洋生物消失。[78]

克莱因瓶是一个不可定向的二维紧流形，

但正如流行病学家安娜·罗加说的那样，虽然目前非洲病例较少，那是因为病毒传播需要时间，但是当前数字说明，一旦病毒开始传播，疫情就会像西班牙和意大利那样迅速蔓延。

2、检测少，导致确诊数据严重失真。

整个非洲有12亿人口，但54个国家和地区有43个的人均GDP尚不足5000美元，有40%的人生活在极端贫困以下，他们对生活的基本需求还停留在温饱阶段，哪里还有钱去核酸检测？

而从目前少量检测得出的数据看，非洲疫情不容乐观。

据西非国家布基纳法索报道，到3月23日，该国防疫部门接到疑似病例申报电话42000多个，但因为能力有限，只进行了数百例核酸测试，确诊数却高达99例，其中就有5个政府部长。

著名热带病和传染病专家特拉奥雷提出：非洲新冠病毒感染者的数量“被大大低估了”，因为一些国家并未对疑似患者进行检测。

一旦揭开盖子，非洲真实数据的肯定要比现在，严峻得多。

麻烦，确实大了！

三

病毒的传播逻辑，是指数级增长。

如果不予干预，它将在很短时间内，迅速蔓延。

从这个角度说，非洲已经突破了一万人的传播临界点，下一步疫情的发展，真是让人忧心忡忡。

1、人口密度大：非洲人口分布极不均匀，大部分人口居住在沿海少数几个地区，极易大规模、密集型传播！

非洲约有13.4亿人，人口密度每平方千米45人，由于历史和地形等原因，非洲的人口分布极不均匀。

像撒哈拉、卡拉哈里和纳米布三大沙漠区，人口密度在每平方千米0.5人以下。而尼罗河谷地、西北部地中海沿岸等地，面积仅占非洲的1%，却承载了非洲超过30%的人口。

比如，埃及开罗，人口密度为每平方英里2.44万人。

而非洲人口第一大国尼日利亚，其位于几内亚湾的拉各斯州，每平方英里有4.7万人，比上海（3.5万人左右）还拥挤。

大量人口挤在少数地带，让这些人很容易互相传染，病毒迅速播散！

2、自然环境差：非洲贫民窟林立，人们生活在充满垃圾和污水的环境中，获得清洁水、手套和口罩的机会有限，极易病毒传播。

非洲有很多贫民窟。

举个例子，非洲有一个贫民窟，叫基贝拉，这是个在地图上都找不到的贫民区。

这里的面积大约只有2.5平方公里，却蜗居着近100万人。房子都是用生锈的铁皮简易搭成的，紧密地排在一起，每个10多平米的房屋里，可以住下七八个人。

房屋外面是坑坑洼洼的土路，污水横流，蝇虫乱飞，臭气熏天。

这里没有自来水，没有排污管道，人均收入每天不到7元人民币，很多人一天只能吃上一顿饭。

在非洲，像这样的贫民区还有很多。 

在这样的地方，如果遭遇疫情，你如何要求他们戴口罩、勤洗手、居家隔离？他们可能一天不出门，就一天没饭吃。

更麻烦的是，在整个非洲大陆，水都是稀缺资源，更何况在这些人口密集的贫民窟里。

而预防新冠病毒，又需要勤洗手。人口稠密，没有自来水洗手，成为病毒传播的巨大隐患。 

贫民窟里，蚊蝇横飞、臭水横流的景象并不少见。许多发达国家，还喜欢把本国产生的垃圾，运到非洲。

在这样充满垃圾和污水的环境中，人们又很难获得清洁水、手套和口罩，极易病毒传播。

卫生条件恶劣，让非洲从来都是瘟疫肆虐之地，新冠疫情大概率也不会意外！

3、政府能力低：非洲不少国家多年战乱动荡，治安形势恶劣，政府缺乏对基层的控制力！

对付新冠肺炎，现在最有效的方法是隔离，把病毒控制在医院或隔离观察区，不会再传播。

但是，隔离对政府基层控制力要求极高，必须像中国这样，村支书在大喇叭里吆喝、社区工作人员在小区门口一站，就能让民众居家不出，才能办得到。

这种基层动员控制力，对于非洲这些国家恐怖袭击频繁、内战时有发生的国家来说，是极难做到的。

克莱因瓶是一个不可定向的二维紧流形，而球面或轮胎面是可 克莱因瓶 克莱因瓶 定向的二维紧流形。如果观Sophie Amundsen was on her way home from school. She had walked the first part of the way with Joanna. They had been discussing robots. Joanna thought the hum From time to time there would be a few letters from the bank for her father, but then he was not a normal father. Sophie's father was the captain of a big oil tanker, and was away for most of the year. During the few weeks at a time when he was at home, he would shuffle around the house making it nice and cozy for Sophie and her mother. But when he was at sea he could seem very distant. There was only one letter in the mailbox--and it was for Sophie. The white envelope read: "Sophie Amundsen, 3 Clover Close." That was all; it did not say who it was from. There was no stamp on it either. As soon as Sophie had closed the gate behind her she opened the envelope. It contained only a slip of paper no bigger than the envelope. It read: Who are you? Nothing else, only the three words, written by hand, and followed by a large question mark. She looked at the envelope again. The letter was definitely for her. Who could have dropped it in the mailbox? Sophie let herslly wanted her to be called Lillemor. Sophie tried to imagine herself shaking hands and introducing herself as Lillemor Amundsen, but it seemed all wrong. It was someone else who kept introducing herself. She jumped up and went into the bathroom with the strange letter in her hand. She stood in front of the mirror and stared into her own eyes. "I am Sophie Amundsen," she said. The girl in the mirror did not react with as much as a twitch. Whatever Sophie did, she did exactly the same. Sophie tried to beat her reflection to it with a lightning movement but the other girl was just as fast. "Who are you?" Sophie asked. She received no response to this either, but felt a momentary confusion as to whether it was she or her reflection who had asked the question. Sophie pressed her index finger to the nose in the mirror and said, "You are me." As she got no answer to this, she turned the sentence around and said, "I am you." Sophie Amundsen was often dissatisfied with her appearance. She was frequently told that she had beautiful almond-shaped eyes, but that was probably just something people se of a magic wand. Wasn't it extraordinary to be in the world right now, wandering around in a wonderful adventure! Sherekan sprang lightly across the gravel and slid into a dense clump of red-currant bushes. A live cat, vibrant with energy from its white whiskers to the twitching tail at the end of its sleek body. It was here in the garden too, but hardly aware of it in the same way as Sophie. As Sophie started to think about being alive, she began to realize that she would not be alive forever. I am in the world now, she thought, but one day I shall be gone. Was there a life after death? This was another question the cat was blissfully unaware of. It was not long since Sophie's grandmother had died. For more than six months Sophie had missed her every 早知今日，何必当初？！如果早点鼓励戴口罩，也不至于今天疫情搞成这般田地！今天，美国终于改口了，正式表示：公共场合建议佩戴口罩！刚刚，美国疾控中心更新了对新冠病毒的个人防护指南，在指南里，增加了一项新的保护措施：美国民众不论健康或生病，出入公共场合均需配戴简单的布口罩或遮住面部，因为部分无症状感染者可能在不知不觉中将病毒传播给他人。紧跟着，特朗普也顺坡下驴了，他在新闻发布会上转达了美国疾控中心修改指南，正式建议：民众应在公共场所佩戴口罩。特朗普婆姨梅拉尼娅也通过社交媒体呼吁人们佩戴口罩，表示：“随着周末来临，请大家保持社交距离，认真佩戴口罩或遮盖面部。” 疾控中心、特朗普、梅拉尼娅，三连发！这真是180度大转变啊！别忘了，前几天，特朗普还在振振有词地说：我觉得不戴口罩也没关系，可以戴围巾，围巾懂吧？围巾会非常好！作为美国抗疫总指挥的是彭斯，以前更是公开说过，勤洗手、保持社交距离就行了，美国人没必要戴口罩！然而，豪言壮语没用啊，因为新冠病毒就是专门治各种不服的，最后口罩，还只能戴！现在，美国已累计确诊逾27万例，死亡病例7077例，与前一天相比，新增确诊病例35060例，连续第5天新增确诊数超2万，35个州和地区进入“重大灾难”状态！再这么扛下去，美国真要搞群体免疫了，而一旦全民感染，最终结局将是医疗系统彻底崩溃，死亡人数将在百万级别。感染了那么多，美国人终于要戴上口罩了，虽然有点迟了，但总是一件好事！唉，无知不是生存的障碍，傲慢才是。二 有些政客，变脸就是快！用不着你，就怒目相向，用得着你，就满脸堆笑！现在，美国终于反应过来，想要找口罩戴的时候，它突然发现，口罩产能集中在东亚特别是中国，本国口罩缺货，根本不够用！怎么办？老美第一本能反应，就是：抢！今天，德国一批20万只的FFP2口罩，在曼谷被美国“截胡”，直接转运美国，气得德国官员咒骂：这分明是“现代海盗行为”啊！20万只，抢了也不管用啊！怎么办？老美又使出第二招：截！现在，特朗普政府命令美国3M公司，不许再向加拿大和拉丁美洲出口防护口罩了，必须留在美国自己用。特朗普自己出面，炮轰3M：不准向加拿大和南美出口N95口罩！卧槽，还说是亲密盟友，这下把加拿大气坏了，特鲁多警告称，可能对特朗普这一决定采取报复性措施！3M公司也看不下去了，公然骂特朗普：反人道！抢+截，也不够用啊，毕竟，目前美国市场的口罩95%依赖海外供应，而中国是最大的口罩供应商。用不着你，叫你牛夫人，现在用得着你，美国政客一扭头，又开始叫你小甜甜了。看吧，美国大使馆，就突然又变脸了，开始感谢中国人的帮助了。驻华大使布兰斯塔德，特意在微博微信等各平台写了四段话。第一段说：我强调了现在就是向前看的时候，并对中国就出口需要的医疗用品到美国，对我国政府给予帮助，传达了我的感谢。嗯，现在要向前看了，我对中国帮助美国表达感谢。第二段说：美国大使馆已经辛勤工作，为美国和中国公司牵线，以满足美国对关键个人防护用品不断增加的即刻需求。我们正与中国政府官员紧密合作，加快来自中国的货物运输。还是同一个主题，我们要辛勤工作，我们要帮助运送中国货物，满足美国人的迫切需求。第三段、第四段继续重复：向前同行。看懂了没有，洋洋洒洒几百字，其实说得就是一个意思：第一医疗用品，第二医疗用品，第三，还是医疗用品！然后，美国食品和药品管理局（FDA）也表示，在确认满足相关要求的前提下，将允许美国医疗机构使用中国生产的KN95口罩。唉，要说情商高，我还真是佩服美国人！看吧，在25日七国集团外长会议上，美国国务卿蓬佩奥故意将新冠病毒称作“武汉病毒”，无底线开撕。前几天，美国政府还放大质量问题，拒绝批准进口中国KN95口罩，阻挠中国产品进入。现在一看，感染人数指数级增长，还有很多无症状感染者，不进口中国口罩等医疗用品，终归扛不住了！这下，美国政客的脸，马上阴转晴了，说感谢中国，感恩有你，感谢命运，向前同行！节操碎了一地有没有？当然，向前同行并没错，毕竟，不管美国政客如何，大家共同的敌人只有病毒，中国应该有这气度，有这胸怀。只不过美国啊美国，你的脸能不能不要变得这么快，否则真的很容易让人想起，那个农夫与蛇的故事！三 灾难是一面照妖镜，疫情之下，人性被一览无余，各个国家的面容，也被照了个彻底。还记得两个月前，很多国家都等着看中国的热闹。批判、侮辱的言论不绝于耳。可现在，疫情蔓延全球，中国却成为了全世界的诺亚方舟，而很多国家都通过疫情中中国的表现，重新审视起了中国，刷新了对中国的认知。现在，中国正在全力以赴，联手协助其他国家抗疫，打败新冠肺炎这个人类共同的敌人，并用自己的复工复产和努力勤奋，推动全球经济的繁荣。中国人正用自己的仁慈之心、用自己的责任担当、用自己的人道主义精神，举起全球互助大旗，提供力所能及的支援，为全球战疫注入不可替代的“正能量”！一single day. How unfair that life had to end! Sophie stood on the gravel path, thinking. She tried to think extra hard about being alive so as to forget that she would not be alive forever. But it was impossible. As soon as she concentrated on being alive now, the thought of dying also came into her mind. The same thing happened the other way around: only by conjuring up an intense feeling of one day being dead could she appreciate how terribly good it was to be alive. It was like two sides of a coin that she kept turning over and over. And the bigger and clearer one side of the coin became, the bigger and clearer the other side became too. You can't experience being alive without realizing that you have to die, she thought. But it's just as impossible to realize you have to die without thinking how incredibly amazing it is to be alive. Sophie remembered Granny saying something like that the day the doctor told her she was ill. "I never realized how rich life was until now," she said. How tragic that most people had to get ill before they understood what a gift it was to be alive. Or else they had to find a mysterious letter in the mailbox! Perhaps she should go and see if any more letters had arrived. Sophie hurried to the gate and looked inside the green mailbox. She was startled to find that it contained another white envelope, exactly like the first. But the mailbox had definitely been empty when she took the first envelope! This envelope had her name on it as well. She tore it open and fished out a note the same size as the first one. Where does the world come from? it said. I don't know, Sophie thought. Surely nobody really knows. And yet--Sophie thought it was a fair question. For the first time in her life she felt it wasn't right to live in the world without at least inquiring where it came from. The mysterious letters had made Sophie's head spin. She 早知今日，何必当初？！如果早点鼓励戴口罩，也不至于今天疫情搞成这般田地！今天，美国终于改口了，正式表示：公共场合建议佩戴口罩！刚刚，美国疾控中心更新了对新冠病毒的个人防护指南，在指南里，增加了一项新的保护措施：美国民众不论健康或生病，出入公共场合均需配戴简单的布口罩或遮住面部，因为部分无症状感染者可能在不知不觉中将病毒传播给他人。紧跟着，特朗普也顺坡下驴了，他在新闻发布会上转达了美国疾控中心修改指南，正式建议：民众应在公共场所佩戴口罩。特朗普婆姨梅拉尼娅也通过社交媒体呼吁人们佩戴口罩，表示：“随着周末来临，请大家保持社交距离，认真佩戴口罩或遮盖面部。” 疾控中心、特朗普、梅拉尼娅，三连发！这真是180度大转变啊！别忘了，前几天，特朗普还在振振有词地说：我觉得不戴口罩也没关系，可以戴围巾，围巾懂吧？围巾会非常好！作为美国抗疫总指挥的是彭斯，以前更是公开说过，勤洗手、保持社交距离就行了，美国人没必要戴口罩！然而，豪言壮语没用啊，因为新冠病毒就是专门治各种不服的，最后口罩，还只能戴！现在，美国已累计确诊逾27万例，死亡病例7077例，与前一天相比，新增确诊病例35060例，连续第5天新增确诊数超2万，35个州和地区进入“重大灾难”状态！再这么扛下去，美国真要搞群体免疫了，而一旦全民感染，最终结局将是医疗系统彻底崩溃，死亡人数将在百万级别。感染了那么多，美国人终于要戴上口罩了，虽然有点迟了，但总是一件好事！唉，无知不是生存的障碍，傲慢才是。二 有些政客，变脸就是快！用不着你，就怒目相向，用得着你，就满脸堆笑！现在，美国终于反应过来，想要找口罩戴的时候，它突然发现，口罩产能集中在东亚特别是中国，本国口罩缺货，根本不够用！怎么办？老美第一本能反应，就是：抢！今天，德国一批20万只的FFP2口罩，在曼谷被美国“截胡”，直接转运美国，气得德国官员咒骂：这分明是“现代海盗行为”啊！20万只，抢了也不管用啊！怎么办？老美又使出第二招：截！现在，特朗普政府命令美国3M公司，不许再向加拿大和拉丁美洲出口防护口罩了，必须留在美国自己用。特朗普自己出面，炮轰3M：不准向加拿大和南美出口N95口罩！卧槽，还说是亲密盟友，这下把加拿大气坏了，特鲁多警告称，可能对特朗普这一决定采取报复性措施！3M公司也看不下去了，公然骂特朗普：反人道！抢+截，也不够用啊，毕竟，目前美国市场的口罩95%依赖海外供应，而中国是最大的口罩供应商。用不着你，叫你牛夫人，现在用得着你，美国政客一扭头，又开始叫你小甜甜了。看吧，美国大使馆，就突然又变脸了，开始感谢中国人的帮助了。驻华大使布兰斯塔德，特意在微博微信等各平台写了四段话。第一段说：我强调了现在就是向前看的时候，并对中国就出口需要的医疗用品到美国，对我国政府给予帮助，传达了我的感谢。嗯，现在要向前看了，我对中国帮助美国表达感谢。第二段说：美国大使馆已经辛勤工作，为美国和中国公司牵线，以满足美国对关键个人防护用品不断增加的即刻需求。我们正与中国政府官员紧密合作，加快来自中国的货物运输。还是同一个主题，我们要辛勤工作，我们要帮助运送中国货物，满足美国人的迫切需求。第三段、第四段继续重复：向前同行。看懂了没有，洋洋洒洒几百字，其实说得就是一个意思：第一医疗用品，第二医疗用品，第三，还是医疗用品！然后，美国食品和药品管理局（FDA）也表示，在确认满足相关要求的前提下，将允许美国医疗机构使用中国生产的KN95口罩。唉，要说情商高，我还真是佩服美国人！看吧，在25日七国集团外长会议上，美国国务卿蓬佩奥故意将新冠病毒称作“武汉病毒”，无底线开撕。前几天，美国政府还放大质量问题，拒绝批准进口中国KN95口罩，阻挠中国产品进入。现在一看，感染人数指数级增长，还有很多无症状感染者，不进口中国口罩等医疗用品，终归扛不住了！这下，美国政客的脸，马上阴转晴了，说感谢中国，感恩有你，感谢命运，向前同行！节操碎了一地有没有？当然，向前同行并没错，毕竟，不管美国政客如何，大家共同的敌人只有病毒，中国应该有这气度，有这胸怀。只不过美国啊美国，你的脸能不能不要变得这么快，否则真的很容易让人想起，那个农夫与蛇的故事！三 灾难是一面照妖镜，疫情之下，人性被一览无余，各个国家的面容，也被照了个彻底。还记得两个月前，很多国家都等着看中国的热闹。批判、侮辱的言论不绝于耳。可现在，疫情蔓延全球，中国却成为了全世界的诺亚方舟，而很多国家都通过疫情中中国的表现，重新审视起了中国，刷新了对中国的认知。现在，中国正在全力以赴，联手协助其他国家抗疫，打败新冠肺炎这个人类共同的敌人，并用自己的复工复产和努力勤奋，推动全球经济的繁荣。中国人正用自己的仁慈之心、用自己的责任担当、用自己的人道主义精神，举起全球互助大旗，提供力所能及的支援，为全球战疫注入不可替代的“正能量”！一decided to go and sit in the den. The den was Sophie's top secret hiding place. It was where she went when she was terribly angry, terribly miserable, or terribly happy. Today she was simply confused. * * * The red house was surrounded by a large garden with lots of flowerbeds, fruit bushes, fruit trees of different kinds, a spacious lawn with a glider and a little gazebo that Granddad had built for Granny when she lost their first child a few weeks after it was born. The child's name was Marie. On her gravestone were the words: "Little Marie to us came, greeted us, and left again." Down in a corner of the garden behind all the raspberry bushes was a dense thicket where neither flowers nor berries would grow. Actually, it was an old hedge that had once marked the boundary to the woods, but because nobody had trimmed it for the last twenty years it had grown into a tangled and impenetrable mass. Granny used to say the hedge made it harder for the foxes to take the chickens during the war, when the chickens had free range of the garden. To everyone but Sophie, the old hedge was just as useless as the rabbit hutches at the other end of the garden. But that was only because they hadn't discovered Sophie's secret. Sophie had known about the little hole in the hedge for as long as she could remember. When she crawled through it she came into a large cavity between the bushes. It was like a little house. She knew nobody would find her there. Clutching the two envelopes in her hand, Sophie ran through the garden, crouched down on all fours, and wormed her way through the hedge. The den was almost high enough for her to stand upright, but today she sat down on a clump of gnarled roots. From there she could look out through tiny peepholes between the twigs and leaves. Although none of the holes was bigger than a small coin, she had a good view beginning. Oh, drat! She opened the two envelopes again. Who are you? Where does the world come from? What annoying questions! And anyway where did the letters come from? That was just as mysterious, almost. Who had jolted Sophie out of her everyday existence and suddenly brought her face to face with the great riddles of the universe? For the third time Sophie went to the mailbox. The mailman had just delivered the day's mail. Sophie fished out a bulky pile of junk mail, periodicals, and a couple of letters for her mother. There was also a postcard of a tropical beach. She turned the card over. It had a Nor-wegian stamp on it and was postmarked "UN Battalion." Could it be from Dad? But wasn't he in a completely different place? It wasn't his handwriting either. Sophie felt her pulse quicken a little as she saw who the postcard was addressed to: "Hilde Moe problems. The first problem was who had put the two white envelopes in her mailbox. The second was the difficult questions these letters contained. The third problem was who Hilde Moller Knag could be, and why Sophie had been sent her birthday card. She was sure that the three problems were interconnected in some way. They had to be, because until today she had lived a perfectly ordinary life.察克莱因瓶，有一点似乎令人困惑－－克莱因瓶的瓶颈和瓶身是相交的，换句话说，瓶颈上的某些点和瓶壁上的某些点占据了三维空间中的同一个位置。我们可以把克莱因瓶放在四维空间中理解：克莱因瓶是一个在四维空间中才可能真正表现出来的曲面。如果我们一定要把它表现在我们生活的三维空间中，我们只好将就点，把它表现得似乎是自己和自己相交一样。克莱因瓶的瓶颈是广泛地应用到了建筑，艺术，工业生产中。三维空间里的克莱因瓶 拓扑学的定义编辑 克莱因瓶定义为正方形区域 [0,1]×[0,1] 模掉等价关系(0,y)~(1,y), 0≤y≤1 和 (x,0)~(1-x,1), 0≤x≤1。类似于 Mobius Band, 克莱因瓶不可定向。但 Mobius 带可嵌入   ，而克莱因瓶只能嵌入四维（或更高维）空间。莫比乌斯带编辑 把一条纸带的一段扭180°，再和另一端粘起来就得到一条莫比乌斯带的模型。这也是一个只有莫比乌斯带、一个面的曲面，但是和球面、轮胎面和克莱因瓶不同的是，它有边（注意，它只有一条边）。如果我们把两条莫比烈爆炸。一般认为质量小于9倍太阳质量左右的恒星，在经历引力坍缩的过程后是无法形成超新星的。[75]  在大质量恒星演化到晚期，内部不能产生新的能量，巨大的引力将整个星体迅速向中心坍缩，将中心物质都压成中子状态，形成中子星，而外层下坍的物质遇到这坚硬的“中子核”反弹引起爆炸。这就成为超新星爆发，质量更大时，中心更可形成黑洞。[76]  在超新星爆发的过程中所释放的能量，需要我们的太阳燃烧900亿年才能与之相当。[77]  超新星研究有着关乎人类自身命运的深层意义。如果一颗超新星爆发的位置非常接近地球，目前国际天文学界普遍认为此距离在100光年以内，它就能够对地球的生物圈产生明显的影响，这样的超新星被称为近地超新星。有研究认为，在地球历史上的奥陶纪大灭绝，就是一颗近地超新星引起的，这次灭绝导致当时地球近60%的海洋生物消失。[78]

克莱因瓶是一个不可定向的二维紧流形，

2019年，非洲共发生3471次恐怖袭击，创下历史记录，非洲多年战乱动荡，政府没有基层控制力，就无法采取有效的隔离措施。

4、营养条件差：非洲有大量贫困人口，蝗灾的袭来，更是让民众食不果腹，抵抗力差，大量抵抗力差的人群成为病毒传播的温床！

美国布鲁金斯学会的报告指出，极端贫困日益成为非洲的一个现象。非洲人在全世界极端贫困人口中的占比大约为2/3。现在，非洲12亿人口中，有2.57亿人口处于饥饿状态。

今年发生的蝗虫灾难，已经摧毁了埃塞俄比亚和索马里共计70000公顷农田，更是让非洲承受更大的粮食压力，吃饭的需求都顾不上，次一等的病毒威胁，就只能先放放了！

糟糕的是，新冠肺炎的易感人群，是营养条件差、拥有基础疾病的老年人，而非洲大量人群因为长期饥饿，导致身体瘦弱、营养不良、抵抗力低下，还有2600万人感染艾滋病毒，在新冠肺炎面前更是缺乏抵抗力。

5、医疗资源少：非洲国家在医疗资源上的投入远远不及发达国家，一旦疫情爆发，非常容易发生医疗挤兑，爆发人道主义灾难！

非洲拥有全球17%的人口，承担了23%的疾病负担，但只有1%的医疗支出。

非洲平均每1000人只有1.8张床位，而韩国这个数字是12.3，德国是8。

医院少，医院硬件落后，每万人拥有医护人员数量极低，这决定了非洲一旦真的遇到大规模传染病，几乎没有抵抗手段。

以肯尼亚为例，肯尼亚医生资源极度匮乏，全国医患比例是1：7000，导致不少患者由于排队过长，而将小病拖成大病，造成不必要的死亡。

非洲大国乌干达拥有4400万人口，但最大的国立医院才有1500张病床，ICU全负荷工作，也只能收治60人。

甚至有人笑称，乌干达政府的部长数量多于重症监护病床。

被誉为非洲最稳定的国家加纳，有3000万人口，却连一家口罩生产商也没有。

一旦不能快速发现和控制病毒传播，非洲脆弱的卫生系统就会瞬间超载，被挤爆，并非危言耸听。

现在，联合国专家已经拉响警报：非洲距离暴发意大利和西班牙那样的“残酷疫情风暴”仅有两三周时间。而考虑到非洲脆弱的卫生系统，很可能很难抵挡新冠肺炎疫情的冲击！

写到这里，不仅为非洲、为全世界可怜的人民，一声叹息。。。

四

当贫困遇上新冠，非洲穷人的遭遇并不是孤例。

全球疫情蔓延，当我们把关注的目光投向美国、意大利等欧美国家时，或许应该同时去看看一些确诊人数看似不高的国家和地区，比如非洲，比如印度，比如中东。

如果说，欧美像一间茅草屋，已经引燃，那么，这些欠发达地区，就像是一个火药桶，随时可能爆炸。

克莱因瓶是一个不可定向的二维紧流形，而球面或轮胎面是可 克莱因瓶 克莱因瓶 定向的二维紧流形。如果观Sophie Amundsen was on her way home from school. She had walked the first part of the way with Joanna. They had been discussing robots. Joanna thought the hum From time to time there would be a few letters from the bank for her father, but then he was not a normal father. Sophie's father was the captain of a big oil tanker, and was away for most of the year. During the few weeks at a time when he was at home, he would shuffle around the house making it nice and cozy for Sophie and her mother. But when he was at sea he could seem very distant. There was only one letter in the mailbox--and it was for Sophie. The white envelope read: "Sophie Amundsen, 3 Clover Close." That was all; it did not say who it was from. There was no stamp on it either. As soon as Sophie had closed the gate behind her she opened the envelope. It contained only a slip of paper no bigger than the envelope. It read: Who are you? Nothing else, only the three words, written by hand, and followed by a large question mark. She looked at the envelope again. The letter was definitely for her. Who could have dropped it in the mailbox? Sophie let herslly wanted her to be called Lillemor. Sophie tried to imagine herself shaking hands and introducing herself as Lillemor Amundsen, but it seemed all wrong. It was someone else who kept introducing herself. She jumped up and went into the bathroom with the strange letter in her hand. She stood in front of the mirror and stared into her own eyes. "I am Sophie Amundsen," she said. The girl in the mirror did not react with as much as a twitch. Whatever Sophie did, she did exactly the same. Sophie tried to beat her reflection to it with a lightning movement but the other girl was just as fast. "Who are you?" Sophie asked. She received no response to this either, but felt a momentary confusion as to whether it was she or her reflection who had asked the question. Sophie pressed her index finger to the nose in the mirror and said, "You are me." As she got no answer to this, she turned the sentence around and said, "I am you." Sophie Amundsen was often dissatisfied with her appearance. She was frequently told that she had beautiful almond-shaped eyes, but that was probably just something people said because her nose was too small and her mouth was a bit too big. And her ears were much too close to her eyes. Worst of all was her straight hair, which it was impossible to do anything with. Sometimes her father would stroke her hair and call her "the girl with the flaxen hair," after a piece of music by Claude Debussy. It was all right for him, he was not condemned to living with this straight dark hair. Neither mousse nor styling gel had the slightest effect on Sophie's hair. Sometimes she thought she was so ugly that she wondered if sh. As Sophie started to think about being alive, she began to realize that she wouow rich life was until now," she said. How tragic that most people had to get ill before they understood what a gift it was to be alive. Or else they had to find a mysterious letter in the mailbox! Perhaps she should go and see if any more letters had arrived. Sophie hurried to the gate and looked inside the green mailbox. She was startled to find that it contained another white envelope, exactly like the first. But the mailbox had definitely been empty when she took the first envelope! This envelope had her name on it as well. She tore it open and fished out a note the same size as the first one. Where does the world come from? it said. I don't know, Sophie thought. Surely nobody really knows. And yet--Sophie thought it was a fair question. For the first time in her life she felt it wasn't right to live in the world without at least inquiring where it came from. The mysterious letters had made Sophie's head spin. She decided to go and sit in the den. The den was Sophie's top secret hiding place. It was where she went when she was terribly angry, terribly miserable, or terribly happy. Today she was simply confused. * * * The red house was surrounded by a large garden with lots of flowerbeds, fruit bushes, fruit trees of different kinds, a spacious lawn with a glider and a little gazebo that Granddad had built for Granny when she lost their first child a few weeks after it was born. The child's name was Marie. On her gravestone were the words: "Little Marie to us came, greeted us, and left again." Down in a corner of the garden behind all the raspberry bushes was a dense thicket where neither flowers nor berries would grow. Actually, it was an old hedge that had once marked the boundary to the woods, but because nobody had trimmed it for the last twenty years it had grown into a tangled and impenetrable mass. Granny used to say the hedge made it harder for the foxes to take the chickens during the war, when the chickens had free range of the garden. To everyone but Sophie, the old hedge was just as useless as the rabbit hutches at the other end of the garden. But that was only because they hadn't discovered Sophie's secret. Sophie had known about the little hole in the hedge for as long as she could remember. When she crawled through it she came into a large cavity between the bushes. It was like a little house. She knew nobody早知今日，何必当初？！如果早点鼓励戴口罩，也不至于今天疫情搞成这般田地！今天，美国终于改口了，正式表示：公共场合建议佩戴口罩！刚刚，美国疾控中心更新了对新冠病毒的个人防护指南，在指南里，增加了一项新的保护措施：美国民众不论健康或生病，出入公共场合均需配戴简单的布口罩或遮住面部，因为部分无症状感染者可能在不知不觉中将病毒传播给他人。紧跟着，特朗普也顺坡下驴了，他在新闻发布会上转达了美国疾控中心修改指南，正式建议：民众应在公共场所佩戴口罩。特朗普婆姨梅拉尼娅也通过社交媒体呼吁人们佩戴口罩，表示：“随着周末来临，请大家保持社交距离，认真佩戴口罩或遮盖面部。” 疾控中心、特朗普、梅拉尼娅，三连发！这真是180度大转变啊！别忘了，前几天，特朗普还在振振有词地说：我觉得不戴口罩也没关系，可以戴围巾，围巾懂吧？围巾会非常好！作为美国抗疫总指挥的是彭斯，以前更是公开说过，勤洗手、保持社交距离就行了，美国人没必要戴口罩！然而，豪言壮语没用啊，因为新冠病毒就是专门治各种不服的，最后口罩，还只能戴！现在，美国已累计确诊逾27万例，死亡病例7077例，与前一天相比，新增确诊病例35060例，连续第5天新增确诊数超2万，35个州和地区进入“重大灾难”状态！再这么扛下去，美国真要搞群体免疫了，而一旦全民感染，最终结局将是医疗系统彻底崩溃，死亡人数将在百万级别。感染了那么多，美国人终于要戴上口罩了，虽然有点迟了，但总是一件好事！唉，无知不是生存的障碍，傲慢才是。二 有些政客，变脸就是快！用不着你，就怒目相向，用得着你，就满脸堆笑！现在，美国终于反应过来，想要找口罩戴的时候，它突然发现，口罩产能集中在东亚特别是中国，本国口罩缺货，根本不够用！怎么办？老美第一本能反应，就是：抢！今天，德国一批20万只的FFP2口罩，在曼谷被美国“截胡”，直接转运美国，气得德国官员咒骂：这分明是“现代海盗行为”啊！20万只，抢了也不管用啊！怎么办？老美又使出第二招：截！现在，特朗普政府命令美国3M公司，不许再向加拿大和拉丁美洲出口防护口罩了，必须留在美国自己用。特朗普自己出面，炮轰3M：不准向加拿大和南美出口N95口罩！卧槽，还说是亲密盟友，这下把加拿大气坏了，特鲁多警告称，可能对特朗普这一决定采取报复性措施！3M公司也看不下去了，公然骂特朗普：反人道！抢+截，也不够用啊，毕竟，目前美国市场的口罩95%依赖海外供应，而中国是最大的口罩供应商。用不着你，叫你牛夫人，现在用得着你，美国政客一扭头，又开始叫你小甜甜了。看吧，美国大使馆，就突然又变脸了，开始感谢中国人的帮助了。驻华大使布兰斯塔德，特意在微博微信等各平台写了四段话。第一段说：我强调了现在就是向前看的时候，并对中国就出口需要的医疗用品到美国，对我国政府给予帮助，传达了我的感谢。嗯，现在要向前看了，我对中国帮助美国表达感谢。第二段说：美国大使馆已经辛勤工作，为美国和中国公司牵线，以满足美国对关键个人防护用品不断增加的即刻需求。我们正与中国政府官员紧密合作，加快来自中国的货物运输。还是同一个主题，我们要辛勤工作，我们要帮助运送中国货物，满足美国人的迫切需求。第三段、第四段继续重复：向前同行。看懂了没有，洋洋洒洒几百字，其实说得就是一个意思：第一医疗用品，第二医疗用品，第三，还是医疗用品！然后，美国食品和药品管理局（FDA）也表示，在确认满足相关要求的前提下，将允许美国医疗机构使用中国生产的KN95口罩。唉，要说情商高，我还真是佩服美国人！看吧，在25日七国集团外长会议上，美国国务卿蓬佩奥故意将新冠病毒称作“武汉病毒”，无底线开撕。前几天，美国政府还放大质量问题，拒绝批准进口中国KN95口罩，阻挠中国产品进入。现在一看，感染人数指数级增长，还有很多无症状感染者，不进口中国口罩等医疗用品，终归扛不住了！这下，美国政客的脸，马上阴转晴了，说感谢中国，感恩有你，感谢命运，向前同行！节操碎了一地有没有？当然，向前同行并没错，毕竟，不管美国政客如何，大家共同的敌人只有病毒，中国应该有这气度，有这胸怀。只不过美国啊美国，你的脸能不能不要变得这么快，否则真的很容易让人想起，那个农夫与蛇的故事！三 灾难是一面照妖镜，疫情之下，人性被一览无余，各个国家的面容，也被照了个彻底。还记得两个月前，很多国家都等着看中国的热闹。批判、侮辱的言论不绝于耳。可现在，疫情蔓延全球，中国却成为了全世界的诺亚方舟，而很多国家都通过疫情中中国的表现，重新审视起了中国，刷新了对中国的认知。现在，中国正在全力以赴，联手协助其他国家抗疫，打败新冠肺炎这个人类共同的敌人，并用自己的复工复产和努力勤奋，推动全球经济的繁荣。中国人正用自己的仁慈之心、用自己的责任担当、用自己的人道主义精神，举起全球互助大旗，提供力所能及的支援，为全球战疫注入不可替代的“正能量”！一 would find her there. Clutching the two envelopes in her hand, Sophie ran through the garden, crouched down on all fours, and wormed her way through the hedge. The den was almost high enough for her to stand upright, but today she sat down on a clump of gnarled roots. From there she could look out through tiny peepholes between the twigs and leaves. Although none of the holes was bigger than a small coin, she had a good view beginning. Oh, drat! She opened the two envelopes again. Who are you? Where does the world come from? What annoying questions! And anyway where did the letters come from? That was just as mysterious, almost. Who had jolted Sophie out of her everyday existence and suddenly brought her face to face with the great riddles of the universe? For the third time Sophie went to the mailbox. The mailman had just delivered the day's mail. Sophie fished out a bulky pile of junk mail, periodicals, and a couple of letters for her mother. There was also a postcard of a tropical beach. She turned the card over. It had a Nor-wegian stamp on it and was postmarked "UN Battalion." Could it be from Dad? But wasn't he in a completely different place? It wasn't his handwriting either. Sophie felt her pulse quicken a little as she saw who the postcard was addressed to: "Hilde Moller Knag, c/o Sophie Amundsen, 3 Clover Close ..." The rest of the address was correct. The card read: Dear Hilde, Happy 15th birthday! As I'm sure you'll understand, I want to give you a present that will help you grow. Forgive me for sending the card c/o Sophie. It was the easiest way. Love from Dad. Sophie raced back to the house and into the kitchen. Her mind was in a turmoil. Who was this "Hilde," whose fifteenth birthday was just a month before her own? Sophie got out the telephone bo早知今日，何必当初？！如果早点鼓励戴口罩，也不至于今天疫情搞成这般田地！今天，美国终于改口了，正式表示：公共场合建议佩戴口罩！刚刚，美国疾控中心更新了对新冠病毒的个人防护指南，在指南里，增加了一项新的保护措施：美国民众不论健康或生病，出入公共场合均需配戴简单的布口罩或遮住面部，因为部分无症状感染者可能在不知不觉中将病毒传播给他人。紧跟着，特朗普也顺坡下驴了，他在新闻发布会上转达了美国疾控中心修改指南，正式建议：民众应在公共场所佩戴口罩。特朗普婆姨梅拉尼娅也通过社交媒体呼吁人们佩戴口罩，表示：“随着周末来临，请大家保持社交距离，认真佩戴口罩或遮盖面部。” 疾控中心、特朗普、梅拉尼娅，三连发！这真是180度大转变啊！别忘了，前几天，特朗普还在振振有词地说：我觉得不戴口罩也没关系，可以戴围巾，围巾懂吧？围巾会非常好！作为美国抗疫总指挥的是彭斯，以前更是公开说过，勤洗手、保持社交距离就行了，美国人没必要戴口罩！然而，豪言壮语没用啊，因为新冠病毒就是专门治各种不服的，最后口罩，还只能戴！现在，美国已累计确诊逾27万例，死亡病例7077例，与前一天相比，新增确诊病例35060例，连续第5天新增确诊数超2万，35个州和地区进入“重大灾难”状态！再这么扛下去，美国真要搞群体免疫了，而一旦全民感染，最终结局将是医疗系统彻底崩溃，死亡人数将在百万级别。感染了那么多，美国人终于要戴上口罩了，虽然有点迟了，但总是一件好事！唉，无知不是生存的障碍，傲慢才是。二 有些政客，变脸就是快！用不着你，就怒目相向，用得着你，就满脸堆笑！现在，美国终于反应过来，想要找口罩戴的时候，它突然发现，口罩产能集中在东亚特别是中国，本国口罩缺货，根本不够用！怎么办？老美第一本能反应，就是：抢！今天，德国一批20万只的FFP2口罩，在曼谷被美国“截胡”，直接转运美国，气得德国官员咒骂：这分明是“现代海盗行为”啊！20万只，抢了也不管用啊！怎么办？老美又使出第二招：截！现在，特朗普政府命令美国3M公司，不许再向加拿大和拉丁美洲出口防护口罩了，必须留在美国自己用。特朗普自己出面，炮轰3M：不准向加拿大和南美出口N95口罩！卧槽，还说是亲密盟友，这下把加拿大气坏了，特鲁多警告称，可能对特朗普这一决定采取报复性措施！3M公司也看不下去了，公然骂特朗普：反人道！抢+截，也不够用啊，毕竟，目前美国市场的口罩95%依赖海外供应，而中国是最大的口罩供应商。用不着你，叫你牛夫人，现在用得着你，美国政客一扭头，又开始叫你小甜甜了。看吧，美国大使馆，就突然又变脸了，开始感谢中国人的帮助了。驻华大使布兰斯塔德，特意在微博微信等各平台写了四段话。第一段说：我强调了现在就是向前看的时候，并对中国就出口需要的医疗用品到美国，对我国政府给予帮助，传达了我的感谢。嗯，现在要向前看了，我对中国帮助美国表达感谢。第二段说：美国大使馆已经辛勤工作，为美国和中国公司牵线，以满足美国对关键个人防护用品不断增加的即刻需求。我们正与中国政府官员紧密合作，加快来自中国的货物运输。还是同一个主题，我们要辛勤工作，我们要帮助运送中国货物，满足美国人的迫切需求。第三段、第四段继续重复：向前同行。看懂了没有，洋洋洒洒几百字，其实说得就是一个意思：第一医疗用品，第二医疗用品，第三，还是医疗用品！然后，美国食品和药品管理局（FDA）也表示，在确认满足相关要求的前提下，将允许美国医疗机构使用中国生产的KN95口罩。唉，要说情商高，我还真是佩服美国人！看吧，在25日七国集团外长会议上，美国国务卿蓬佩奥故意将新冠病毒称作“武汉病毒”，无底线开撕。前几天，美国政府还放大质量问题，拒绝批准进口中国KN95口罩，阻挠中国产品进入。现在一看，感染人数指数级增长，还有很多无症状感染者，不进口中国口罩等医疗用品，终归扛不住了！这下，美国政客的脸，马上阴转晴了，说感谢中国，感恩有你，感谢命运，向前同行！节操碎了一地有没有？当然，向前同行并没错，毕竟，不管美国政客如何，大家共同的敌人只有病毒，中国应该有这气度，有这胸怀。只不过美国啊美国，你的脸能不能不要变得这么快，否则真的很容易让人想起，那个农夫与蛇的故事！三 灾难是一面照妖镜，疫情之下，人性被一览无余，各个国家的面容，也被照了个彻底。还记得两个月前，很多国家都等着看中国的热闹。批判、侮辱的言论不绝于耳。可现在，疫情蔓延全球，中国却成为了全世界的诺亚方舟，而很多国家都通过疫情中中国的表现，重新审视起了中国，刷新了对中国的认知。现在，中国正在全力以赴，联手协助其他国家抗疫，打败新冠肺炎这个人类共同的敌人，并用自己的复工复产和努力勤奋，推动全球经济的繁荣。中国人正用自己的仁慈之心、用自己的责任担当、用自己的人道主义精神，举起全球互助大旗，提供力所能及的支援，为全球战疫注入不可替代的“正能量”！一ok. There were a lot of people called Moller, and quite a few called Knag. But there was nobody in the entire directory called Moller Knag. She examined the mysterious card again. It certainly seemed genuine enough; it had a stamp and a postmark. Why would a father send a birthday card to Sophie's address when it was quite obviously intended to go somewhere else? What kind of father would cheat his own daughter of a birthday card by purposely sending it astray? How could it be "the easiest way"? And above all, how was she supposed to trace this Hilde person? So now Sophie had another problem to worry about. She tried to get her thoughts in order: This afternoon, in the space of two short hours, she had been presented with three problems. The first problem was who had put the two white envelopes in her mailbox. The second was the difficult questions these letters contained. The third problem was who Hilde Moller Knag could be, and why Sophie had been sent her birthday card. She was sure that the three problems were interconnected in some way. They had to be, because until today she had lived a perfectly ordinary life.察克莱因瓶，有一点似乎令人困惑－－克莱因瓶的瓶颈和瓶身是相交的，换句话说，瓶颈上的某些点和瓶壁上的某些点占据了三维空间中的同一个位置。我们可以把克莱因瓶放在四维空间中理解：克莱因瓶是一个在四维空间中才可能真正表现出来的曲面。如果我们一定要把它表现在我们生活的三维空间中，我们只好将就点，把它表现得似乎是自己和自己相交一样。克莱因瓶的瓶颈是广泛地应用到了建筑，艺术，工业生产中。三维空间里的克莱因瓶 拓扑学的定义编辑 克莱因瓶定义为正方形区域 [0,1]×[0,1] 模掉等价关系(0,y)~(1,y), 0≤y≤1 和 (x,0)~(1-x,1), 0≤x≤1。类似于 Mobius Band, 克莱因瓶不可定向。但 Mobius 带可嵌入   ，而克莱因瓶只能嵌入四维（或更高维）空间。莫比乌斯带编辑 把一条纸带的一段扭180°，再和另一端粘起来就得到一条莫比乌斯带的模型。这也是一个只有莫比乌斯带、一个面的曲面，但是和球面、轮胎面和克莱因瓶不同的是，它有边（注意，它只有一条边）。如果我们把两条莫比烈爆炸。一般认为质量小于9倍太阳质量左右的恒星，在经历引力坍缩的过程后是无法形成超新星的。[75]  在大质量恒星演化到晚期，内部不能产生新的能量，巨大的引力将整个星体迅速向中心坍缩，将中心物质都压成中子状态，形成中子星，而外层下坍的物质遇到这坚硬的“中子核”反弹引起爆炸。这就成为超新星爆发，质量更大时，中心更可形成黑洞。[76]  在超新星爆发的过程中所释放的能量，需要我们的太阳燃烧900亿年才能与之相当。[77]  超新星研究有着关乎人类自身命运的深层意义。如果一颗超新星爆发的位置非常接近地球，目前国际天文学界普遍认为此距离在100光年以内，它就能够对地球的生物圈产生明显的影响，这样的超新星被称为近地超新星。有研究认为，在地球历史上的奥陶纪大灭绝，就是一颗近地超新星引起的，这次灭绝导致当时地球近60%的海洋生物消失。[78]

克莱因瓶是一个不可定向的二维紧流形，

如果说韩国疫情6月之前难以结束，欧美疫情秋季都难以结束，那么非洲疫情一旦彻底爆发，就不是今年能不能结束的问题，而是深不见底了。恐怕，这个病毒就要永远留在人类社会中了。

看到这里，你也许就明白了，当今世界，的确是一个命运共同体，今天的我们同在一片着了火的森林里，一荣未必俱荣，一毁肯定俱毁。

这一切，就像张文宏医生日前接受采访时说的那样，全球疫情不取决于控制得最好的国家，而取决于控制得最差的国家。“只要世界上还有一个国家没有控制好”，这个病毒“就会向全世界蔓延”。

而当印度和非洲出现新冠疫情流行时，就可以确切地说新冠肺炎是一场人类灾难，全世界要团结，帮医疗资源不足的国家抗疫。

只有全球疫情得到缓解，中国才不需像现在这么严防死守，从这个角度说，帮助其他国家防控疫情，其实也是保护中国自己。

只有合作，互助，团结起来打败它，才是唯一的出路，否则谁也没法笑到最后。

看到这里，你也许就明白了，为什么我们要向100多个国家，提供力所能及的援助，为什我们正在联手世界各国，全力以赴研发疫苗！

早在3月22日，中国就向非洲运送了540万只口罩、108万套试剂盒、4万套防护服和6万个防护面罩，平均分配给54个非洲国家。

因为这背后，是一条条鲜活的生命，一个个可爱的孩子，一个个可能破碎的家庭！

恻隐之心，人皆有之，就像马云在微博里说的那样：“善良是真正的自信。设身处地，急人所困是真正的强大。”

“今天的世界，充满着各种观点，各种看法，各种杂音，所有的声音我们都可以有不同意见，但是无论国别信仰，任何人不应该对无助民众求生求救的呼声冷嘲热讽、坐看笑话。”

看到这里，你也许就明白了，那些阴阳怪气地说“中国在利用抗疫援助对外施加影响力”的西方政客，有多么可恨！

就像华春莹在新闻发布会上批评的那样：

“我很想问问这些阴阳怪气说风凉话的人，他们到底为抗击疫情做了什么？难道他们真的希望中国此时无动于衷吗？见死不救吗？”

是啊，现在全球疫情到了如此地步，这些政客关心的不是怎么防控疫情，而是琢磨怎么甩锅，怎么抹黑中国；关心的不是世人的疾苦，而是醉心于对中国的指责！

污名化中国，向中国泼脏水，这些美国政客难道不怕真相大白之后，被钉上历史的耻辱柱吗？

走自己的路，让别人说去吧，西方政客low，西方政客自乱阵脚，我们不能被他们带到沟里去！

克莱因瓶是一个不可定向的二维紧流形，而球面或轮胎面是可 克莱因瓶 克莱因瓶 定向的二维紧流形。如果观Sophie Amundsen was on her way home from school. She had walked the first part of the way with Joanna. They had been discussing robots. Joanna thought the hum From time to time there would be a few letters from the bank for her father, but then he was not a normal father. Sophie's father was the captain of a big oil tanker, and was away for most of the year. During the few weeks at a time when he was at home, he would shuffle around the house making it nice and cozy for Sophie and her mother. But when he was at sea he could seem very distant. There was only one letter in the mailbox--and it was for Sophie. The white envelope read: "Sophie Amundsen, 3 Clover Close." That was all; it did not say who it was from. There was no stamp on it either. As soon as Sophie had closed the gate behind her she opened the envelope. It contained only a slip of paper no bigger than the envelope. It read: Who are you? Nothing else, only the three words, written by hand, and followed by a large question mark. She looked at the envelope again. The letter was definitely for her. Who could have dropped it in the mailbox? Sophie let herslly wanted her to be called Lillemor. Sophie tried to imagine herself shaking hands and introducing herself as Lillemor Amundsen, but it seemed all wrong. It was someone else who kept introducing herself. She jumped up and went into the bathroom with the strange letter in her hand. She stood in front of the mirror and stared into her own eyes. "I am Sophie Amundsen," she said. The girl in the mirror did not react with as much as a twitch. Whatever Sophie did, she did exactly the same. Sophie tried to beat her reflection to it with a lightning movement but the other girl was just as fast. "Who are you?" Sophie asked. She received no response to this either, but felt a momentary confusion as to whether it was she or her reflection who had asked the question. Sophie pressed her index finger to the nose in the mirror and said, "You are me." As she got no answer to this, she turned the sentence around and said, "I am you." Sophie Amundsen was often dissatisfied with her appearance. She was frequently told that she had beautiful almond-shaped eyes, but that was probably just something people said because her nose was too small and her mouth was a bit too big. And her ears were much too close to her eyes. Worst of all was her straight hair, which it was impossible to do anything with. Sometimes her father would stroke her hair and call her "the girl with the flaxen hair," after a piece of music by Claude Debussy. It was all right for him, he was not condemned to living with this straight dark hair. Neither mousse nor styling gel had the slightest effect on Sophie's hair. Sometimes she thought she was so ugly that she wondered if she was malformed at birth. Her mother always went on about her difficult labor. But was that really what determined how you looked? Wasn't it odd that she didn't know who she was? And wasn't it unreasonable that she hadn't been allowed to have any say in what she would look like? Her looks had just been dumped on her. She could choose her own friends, but she certainly hadn't chosen herself. She had not even chosen to be a human being. What was a human being? Sophie looked up at the girl in the mirror again. "I think I'll go upstairs and do my biology homework," she said, almost apologetically. Once she was out in the hall, she thought, No, I'd rather go out in the garden. "Kitty, kitty, kitty!" Sophie chased the cat out onto the doorstep and closed the front door behind her. As she stood outside on the gravel path with the mysterious letter in her hand, the strangest feeling came over her. She felt like a doll that had suddenly been brought to life by the wave of a magic wand. Wasn't it extraordinary to be in the world right now, wandering around in a wonderful adventure! Sherekan sprang lightly across the gravel and slid into a dense clump of red-currant bushes. A live cat, vibrant with energy from its white whiskers to the twitching tail at the end of its sleek body. It was here in the garden too, but hardly aware of it in the same way as Sophie. As Sophie started to think about being alive, she began to realize that she would not be alive forever. I am in the world now, she thought, but one day I shall be gone. Was there a life after death? This was another question the cat was blissfully unaware of. It was not long since Sophie's grandmother had died. For more than six months Sophie had missed her every single day. How unfair that life had to end! Sophie stood on the gravel path, thinking. She tried to think extra hard about being alive so as to forget that she would not be alive forever. But it was impossible. As soon as she concentrated on being alive now, the thought of dying also came into her mind. The same thing happened the other way around: only by conjuring up an intense feeling of one day being dead could she appreciate how terribly good it was to be alive. It was like two sides of a coin that she kept turning over and over. And the bigger and clearer one side of the coin became, the bigger and clearer the other side became too. You can't experience being alive without realizing that you have to die, she thought. But it's just as impossible to realize you have to die without thinking how incredibly amazing it is to be alive. Sophie remembered Granny saying something like that the day the doctor told her she was ill. "I never realized how rich life was until now," she said. How tragic that most people had to get ill before they understood what a gift it was to be alive. Or else they had to find a mysterious letter in the mailbox! Perhaps she should go and see if any more letters had arrived. Sophie hurried to the gate and looked inside the green mailbox. She was startled to find that it contained another white envelope, exactly like the first. But the mailbox had definitely been empty when she took the first envelope! This envelope had her name on it as well. She tore it open and fished out a note the same size as the first one. Where does the world come from? it said. I don't know, Sophie thought. Surely nobody really knows. And yet--Sophie thought it was a fair question. For the first time in her life she felt it wasn't right to live in the world without at least inquiring where it came from. The mysterious letters had made Sophie's head spin. She decided to go and sit in the den. The den was Sophie's top secret hiding place. It was where she went when she was terribly angry, terribly miserable, or terribly happy. Today she was simply confused. * * * The red house was surrounded by a large garden with lots of flowerbeds, fruit bushes, fruit trees of different kinds, a spacious lawn with a glider and a little gazebo that Granddad had built for Granny when she lost their first child a few weeks after it was born. The child's name was Marie. On her gravestone were the words: "Little Marie to us came, greeted us, and left again." Down in a corner of the garden behind all the raspberry bushes was a dense thicket where neither flowers nor berries would grow. Actually, it was an old hedge that had once marked the boundary to the woods, but because nobody had trimmed it for the last twenty years it had grown into a tangled and impenetrable mass. Granny used to say the hedge made it harder for the foxes to take the chickens during the war, when the chickens had free range of the garden. To everyone but Sophie, the old hedge was just as useless as the rabbit hutches at the other end of the garden. But that was only because they hadn't discover早知今日，何必当初？！如果早点鼓励戴口罩，也不至于今天疫情搞成这般田地！今天，美国终于改口了，正式表示：公共场合建议佩戴口罩！刚刚，美国疾控中心更新了对新冠病毒的个人防护指南，在指南里，增加了一项新的保护措施：美国民众不论健康或生病，出入公共场合均需配戴简单的布口罩或遮住面部，因为部分无症状感染者可能在不知不觉中将病毒传播给他人。紧跟着，特朗普也顺坡下驴了，他在新闻发布会上转达了美国疾控中心修改指南，正式建议：民众应在公共场所佩戴口罩。特朗普婆姨梅拉尼娅也通过社交媒体呼吁人们佩戴口罩，表示：“随着周末来临，请大家保持社交距离，认真佩戴口罩或遮盖面部。” 疾控中心、特朗普、梅拉尼娅，三连发！这真是180度大转变啊！别忘了，前几天，特朗普还在振振有词地说：我觉得不戴口罩也没关系，可以戴围巾，围巾懂吧？围巾会非常好！作为美国抗疫总指挥的是彭斯，以前更是公开说过，勤洗手、保持社交距离就行了，美国人没必要戴口罩！然而，豪言壮语没用啊，因为新冠病毒就是专门治各种不服的，最后口罩，还只能戴！现在，美国已累计确诊逾27万例，死亡病例7077例，与前一天相比，新增确诊病例35060例，连续第5天新增确诊数超2万，35个州和地区进入“重大灾难”状态！再这么扛下去，美国真要搞群体免疫了，而一旦全民感染，最终结局将是医疗系统彻底崩溃，死亡人数将在百万级别。感染了那么多，美国人终于要戴上口罩了，虽然有点迟了，但总是一件好事！唉，无知不是生存的障碍，傲慢才是。二 有些政客，变脸就是快！用不着你，就怒目相向，用得着你，就满脸堆笑！现在，美国终于反应过来，想要找口罩戴的时候，它突然发现，口罩产能集中在东亚特别是中国，本国口罩缺货，根本不够用！怎么办？老美第一本能反应，就是：抢！今天，德国一批20万只的FFP2口罩，在曼谷被美国“截胡”，直接转运美国，气得德国官员咒骂：这分明是“现代海盗行为”啊！20万只，抢了也不管用啊！怎么办？老美又使出第二招：截！现在，特朗普政府命令美国3M公司，不许再向加拿大和拉丁美洲出口防护口罩了，必须留在美国自己用。特朗普自己出面，炮轰3M：不准向加拿大和南美出口N95口罩！卧槽，还说是亲密盟友，这下把加拿大气坏了，特鲁多警告称，可能对特朗普这一决定采取报复性措施！3M公司也看不下去了，公然骂特朗普：反人道！抢+截，也不够用啊，毕竟，目前美国市场的口罩95%依赖海外供应，而中国是最大的口罩供应商。用不着你，叫你牛夫人，现在用得着你，美国政客一扭头，又开始叫你小甜甜了。看吧，美国大使馆，就突然又变脸了，开始感谢中国人的帮助了。驻华大使布兰斯塔德，特意在微博微信等各平台写了四段话。第一段说：我强调了现在就是向前看的时候，并对中国就出口需要的医疗用品到美国，对我国政府给予帮助，传达了我的感谢。嗯，现在要向前看了，我对中国帮助美国表达感谢。第二段说：美国大使馆已经辛勤工作，为美国和中国公司牵线，以满足美国对关键个人防护用品不断增加的即刻需求。我们正与中国政府官员紧密合作，加快来自中国的货物运输。还是同一个主题，我们要辛勤工作，我们要帮助运送中国货物，满足美国人的迫切需求。第三段、第四段继续重复：向前同行。看懂了没有，洋洋洒洒几百字，其实说得就是一个意思：第一医疗用品，第二医疗用品，第三，还是医疗用品！然后，美国食品和药品管理局（FDA）也表示，在确认满足相关要求的前提下，将允许美国医疗机构使用中国生产的KN95口罩。唉，要说情商高，我还真是佩服美国人！看吧，在25日七国集团外长会议上，美国国务卿蓬佩奥故意将新冠病毒称作“武汉病毒”，无底线开撕。前几天，美国政府还放大质量问题，拒绝批准进口中国KN95口罩，阻挠中国产品进入。现在一看，感染人数指数级增长，还有很多无症状感染者，不进口中国口罩等医疗用品，终归扛不住了！这下，美国政客的脸，马上阴转晴了，说感谢中国，感恩有你，感谢命运，向前同行！节操碎了一地有没有？当然，向前同行并没错，毕竟，不管美国政客如何，大家共同的敌人只有病毒，中国应该有这气度，有这胸怀。只不过美国啊美国，你的脸能不能不要变得这么快，否则真的很容易让人想起，那个农夫与蛇的故事！三 灾难是一面照妖镜，疫情之下，人性被一览无余，各个国家的面容，也被照了个彻底。还记得两个月前，很多国家都等着看中国的热闹。批判、侮辱的言论不绝于耳。可现在，疫情蔓延全球，中国却成为了全世界的诺亚方舟，而很多国家都通过疫情中中国的表现，重新审视起了中国，刷新了对中国的认知。现在，中国正在全力以赴，联手协助其他国家抗疫，打败新冠肺炎这个人类共同的敌人，并用自己的复工复产和努力勤奋，推动全球经济的繁荣。中国人正用自己的仁慈之心、用自己的责任担当、用自己的人道主义精神，举起全球互助大旗，提供力所能及的支援，为全球战疫注入不可替代的“正能量”！一ed Sophie's secret. Sophie had known about the little hole in the hedge for as long as she could remember. When she crawled through it she came into a large cavity between the bushes. It was like a little house. She knew nobody would find her there. Clutching the two envelopes in her hand, Sophie ran through the garden, crouched down on all fours, and wormed her way through the hedge. The den was almost high enough for her to stand upright, but today she sat down on a clump of gnarled roots. From there she could look out through tiny peepholes between the twigs and leaves. Although none of the holes was bigger than a small coin, she had a good view beginning. Oh, drat! She opened the two envelopes again. Who are you? Where does the world come from? What annoying questions! And anyway where did the letters come from? That was just as mysterious, almost. Who had jolted Sophie out of her everyday existence and suddenly brought her face to face with the great riddles of the universe? For the third time Sophie went to the mailbox. The mailman had just delivered the day's mail. Sophie fished out a bulky pile of junk mail, periodicals, and a couple of letters for her mother. There was also a postcard of a tropical beach. She turned the card over. It had a Nor-wegian stamp on it and was postmarked "UN Battalion." Could it be from Dad? But wasn't he in a completely different place? It wasn't his handwriting either. Sophie felt her pulse quicken a little as she saw who the postcard was addressed to: "Hilde Moller Knag, c/o Sophie Amundsen, 3 Clover Close ..." The rest of the address was correct. The card read: Dear Hilde, Happy 15th birthday! As I'm sure you'll understand, I want to give you a present that will help you grow. Forgive me for sending the card c/o Sophie. It was the easiest way. Love from Dad. Sophie raced back to the house and into the kitchen. Her mind was in a turmoil. Who was this "Hilde," whose fifteenth birthday was just a month before her own? Sophie got out the telephone book. There were a lot of people called Moller, and quite a few called Knag. But there was nobody in the entire directory called Moller Knag. She examined the mysterious card again. It certainly seemed genuine enough; it had a stamp and a postmark. Why would a father send a birthday card to Sophie's address when it was quite obviously intended to go somewhere else? What kind of father would cheat his own daughter of a birthday card by purposely sending it astray? How could it be "the easiest way"? And above all, how was she supposed to trace this Hilde person? So now Sophie had another problem to worry about. She tried to get her thoughts in order: This afternoon, in the space of two short hours, she had been presented with three problems. The first problem was who had put the two white envelopes in her mailbox. The second was the difficult questions these letters contained. The third problem was who Hilde Moller Knag could be, and why Sophie had been sent her birthday card. She was sure that the three problems were interconnected in some way. They had to be, because until today she had lived a perfectly ordinary life.察克莱因瓶，有一点似乎令人困惑－－克莱因瓶的瓶颈和瓶身是相交的，换句话说，瓶颈上的某些点和瓶壁上的某些点占据了三维空间中的同一个位置。我们可以把克莱因瓶放在四维空间中理解：克莱因瓶是一个在四维空间中才可能真正表现出来的曲面。如果我们一定要把它表现在我们生活的三维空间中，我们只好将就点，把它表现得似乎是自己和自己相交一样。克莱因瓶的瓶颈是广泛地应用到了建筑，艺术，工业生产中。三维空间里的克莱因瓶 拓扑学的定义编辑 克莱因瓶定义为正方形区域 [0,1]×[0,1] 模掉等价关系(0,y)~(1,y), 0≤y≤1 和 (x,0)~(1-x,1), 0≤x≤1。类似于 Mobius Band, 克莱因瓶不可定向。但 Mobius 带可嵌入   ，而克莱因瓶只能嵌入四维（或更高维）空间。莫比乌斯带编辑 把一条纸带的一段扭180°，再和另一端粘起来就得到一条莫比乌斯带的模型。这也是一个只有莫比乌斯带、一个面的曲面，但是和球面、轮胎面和克莱因瓶不同的是，它有边（注意，它只有一条边）。如果我们把两条莫比烈爆炸。一般认为质量小于9倍太阳质量左右的恒星，在经历引力坍缩的过程后是无法形成超新星的。[75]  在大质量恒星演化到晚期，内部不能产生新的能量，巨大的引力将整个星体迅速向中心坍缩，将中心物质都压成中子状态，形成中子星，而外层下坍的物质遇到这坚硬的“中子核”反弹引起爆炸。这就成为超新星爆发，质量更大时，中心更可形成黑洞。[76]  在超新星爆发的过程中所释放的能量，需要我们的太阳燃烧900亿年才能与之相当。[77]  超新星研究有着关乎人类自身命运的深层意义。如果一颗超新星爆发的位置非常接近地球，目前国际天文学界普遍认为此距离在100光年以内，它就能够对地球的生物圈产生明显的影响，这样的超新星被称为近地超新星。有研究认为，在地球历史上的奥陶纪大灭绝，就是一颗近地超新星引起的，这次灭绝导致当时地球近60%的海洋生物消失。[78]

克莱因瓶是一个不可定向的二维紧流形，

在全球这个紧要关头，我们要用中国人的仁慈之心、用中国人的责任担当、用中国人的人道主义精神，举起全球互助大旗，力所能及提供支援，为全球战疫注入不可替代的“正能量”！

非常时期，才是体现一个真正大国之大的时刻！

此时此刻，行胜于言！！

中国加油！

世界加油！

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