克萊因瓶是一個不可定向的二維緊流形，而球面或輪胎面是可 克萊因瓶 克萊因瓶 定向的二維緊流形。如果觀察克萊因瓶，有一點似乎令人困惑－－克萊因瓶的瓶頸和瓶身是相交的，換句話近代科學興起的先驅者、是捍衛科學真理並為此獻身的殉道士。有另一種說法認為，近代以來關於羅馬梵蒂岡的地心說和哥白尼的日心說的鬥爭是被嚴重誇大的。布魯諾1600年遭受火刑的原因，並非因知行星圍繞太陽作圓周運動。然而，人們是否能接受哥白尼提出的新的宇宙模式呢？全世界的人——尤其是權力極大的天主教會是否相信太陽是宇宙中心這一說法呢？由於害怕教會的懲罰，哥白尼在世時不敢公開他的發現。1543年，這一發現才公諸天下。即使在那個時候，哥白尼的發現還不斷受到教會高無上的真理，凡是違背聖經的學說，Eighteen months passed. The Chief was in Quebec with Hannah and Abbie awaiting the arrival of Rug, who had been sent by his father to the Mother Land to dispose of two cargoes of timber. It was an unusually cold evening in June. Snow had been falling all day. The neighboring hills were covered with large feathery crystals, which, however, soon melted as the sun appeared for a moment before sinking behind the gray walls of the Castle St. Louis. Just as the evening gun was fired, news had reached the union Hotel that a vessel had been sighted near the Island of Orleans. It was ascertained that it was the Dorris, in command of Captain French, and that Rug was on board. They were soon speeding down Mountain Street in a caleche to the docks, where they secured passage in a small row-boat which was going out to the vessel. The genial captain invited them to take tea with him, and said that Rug was below supervising and arranging with the Customs Officer about the baggage of his numerous protégés, and would be on deck shortly. Hannah burst into a paroxysm of tears when she caught sight of her long-lost lover, who had been compelled to leave only a few weeks after their marriage. He looked twenty years older, and appeared careworn, haggard and ill. As they were seated round the table he gave an account of his travels. "When I received your letter," he said, addressing his father, "I chartered two vessels and persuaded Archie and Jonathan Campbell to go with me for a pleasure trip. We were nearly three months tossing about at the mercy of wind and wave when a hurricane swept the deck of the vessel, carrying with it the main-mast and sails. Water began to pour in at an alarming rate, and after a desperate struggle at the pumps the captain ordered all hands on deck. We felt that we had to prepare for the worst. The sailors had abandoned the pumps from exhaustion, and Jonathan and I took their places and worked until we, too, were exhausted, and as others took our places we retired to the stern, where we found Archie in a sheltered nook, seated upon a coil of rope, playing his violin, apparently oblivious of our perilous condition. "For two days the work at the pumps was a matter of life and death, and when at last the wind subsided we drifted about helplessly until a passing vessel saw our signals of distress and towed us from the Bay of Biscay to Bristol, where the necessary repairs were made to enable us to proceed to Liverpool. We soon disposed of the timber at good profit, and Jonathan, Archie and I took the stage-coach for London, where we had the honor of being presented at Court to gay Prince Geordie, who is acting as Regent, owing to his father's mental derangement. I wish you could have seen the Carleton House," he said, turning to Hannah. "He built it at a cost of ￡250,000 sterling, and had to sell his stud of race-horses and discharge most of his servants to meet the demands of the creditors, for he had led such a wild, dissipated life that the King and Parliament refused for a long time to help him out of his difficulties. "We visited many places of interest in London and 保護自然， 珠峰之殤 中國的一道「禁令」， 讓美聯社、衛報、每日郵報爭相報導。外網轟動一時， 國內卻沉默無聲：珠穆朗瑪峰封山清理， 每年只允許300人於春季攀登。任何單位和個人， 不得進入絨布寺以上核心區域旅遊。珠峰封山本是常事， 為何全世界都爭相報導？每個中國人都驕傲， 我們的西藏有頂好的風光：山鷹當空盤旋， 天是純粹的藍， 雪山是聖潔的白。但是諸多偽文青， 看了《岡仁波齊》， 就激動不已急著去朝聖。讀了倉央嘉措， 就要來一場說走就走的旅行。結果在這片心靈淨土， 留下了一地保險套！——別誤會，那是套在鞋上， 防止雨雪水滲進鞋裡的。諸多假驢友， 為了去聖地打卡， 在318國道川藏線上 拍下自己豎起大拇指吃泡麵的樣子， 相機一關，就把泡麵盒 扔到了路邊草地上！更有國內外無數登山愛好者， 帶著熊熊的徵服欲前來。無論成功或失敗， 都會在雪山上留下， 帳篷、氧氣管、塑膠袋等一山的垃圾！連犛牛都在垃圾堆裡覓食。可是該為珠峰環境破壞買單的， 明明是人類。每年的4月到6月， 10萬人蜂擁至珠峰大本營觀光。幾百支登山隊伍爬在珠峰上。這裡的環境無法建造廁所， 每個人都像原始人一樣隨地排洩。每年人潮退去後， 會留下整整12噸屎。1953年， 第一個人類徵服了珠峰。之後的56年裡， 4000位攀登者齊心協力， 留下了45000公斤垃圾， 和200多具屍體。「去了珠峰才知道，這裡的路標是屍體」 你不知道這句話有多悲傷。珠峰路標，名為「綠靴子」的屍體 這些垃圾，珠峰脆弱的生態自然無法分解。只能由當地的村民，一步一步爬上山，一筐一筐背下來，倒進坑道後慢慢脫水。分解它們需要長達數年的時間。搬運不了的垃圾， 只能就地焚燒。原本氧氣就稀薄， 高原的空氣也被汙染。珠峰的垃圾、糞便和屍體， 早已汙染了山腳下的水源。 藏民老人不得不背著背簍， 一路彎腰撿垃圾， 步履蹣跚，嚴寒缺氧。但是不撿， 水就髒了，空氣就渾濁了。除了豁出性命保護自己的家園， 他們別無他法。不止是高原。亞洲水源大量依賴冰川溶解， 喜馬拉雅就是「亞洲水塔」。一旦珠峰被汙染， 不安全水源會波及到的人， 足足有十億！雪崩時， 沒有一片雪花是無辜的。造孽時， 他們本以為事不關己。2018年， 尼泊爾製作了一部， 9.0分的紀錄片：《珠峰清道夫》。畫面無比粗糙， 卻看哭了億萬人。它記錄了一次清理珠峰的志願活動， 20位志願者， 每個人， 都做好了死的準備。珠峰海拔8000米以上的地帶， 被稱作「死亡地帶」。沒有當地的夏爾巴人當嚮導， 很少有人能活著下山。這次的志願者裡， 有11位夏爾巴村民。但是要完成一個月清理9萬斤垃圾 外帶一具屍體的任務， 小隊不得不爭分奪秒。越趕時間，缺氧頭痛就越重。普通人登頂珠峰一次， 就要炫耀一輩子。這支志願隊伍， 為了讓身體適應山頂的氣候， 要反覆登頂、下山數次。每登一次山， 都要掉10斤體重。為了避開高溫導致的融冰， 在零下40度的凌晨2點， 志願者們正式開始撿垃圾。一想到營地外的一地屍體， 他們也嚇得邁不開腿， 卻還是硬著頭皮去完成自己的使命。冒著大風雪， 把自己掛在一根繩子上緩慢挪動。你能想像， 人在65度的斜坡上吃飯睡覺嗎？一旦滑倒，必死無疑。他們卻要這樣生存29天：我不管是誰扔的垃圾， 讓村子喝上乾淨的水， 是我們的責任。 外界一直流傳著這樣的風涼話：夏爾巴人登山很厲害，能輕易把垃圾運下來，就算亂丟他們也會清理…… 其實，夏爾巴人的每一次登山，都是搭上性命的賭博。他們中很多人沒有手指腳趾，那是凍傷截肢了。憑什麼你有征服自然的私心，買單的卻是無辜村民的性命？他們一遍遍呼喊著：珠峰是我們的女神，我們的母親，能不能，別再汙染她…… 但是，雄心勃勃的登山者們聽不見。離頂峰只有咫尺之遙時，許多登山者不得不犧牲人性來換取生存。在這裡，氧氣瓶被偷是常事。在呼吸艱難、隨時會失去意識的高海拔地帶，人們能堅持住呼吸就已不易。更別說顧著環保。在珠峰面前，人們的素質高下立現。有些地方，人類就不該去！你可以挑戰生命的極限， 可以衝刺人生的新巔峰。但是你也必須知道， 那些你在極限情況下無力帶走的垃圾， 會成為珠峰，和珠峰腳下村民的噩夢。你是得到了朋友圈的一百個贊， 卻不知替你負重前行的人， 付出了怎樣的代價。那些在藏地亂扔垃圾的人， 請別自作多情了！憑什麼你一手汙染了藏地， 還讓藏地淨化你的心靈？西藏根本沒在等你， 你若不去，才是西藏的福氣。曾經的聖地， 部分地區成了垃圾場。如果不得不去，也請你牢記：除了照片，什麼都別拿；除了時間，什麼都別偷；除了腳印，什麼都別留。亂扔垃圾的人， 你就算登頂一萬次， 也改變不了自己的平庸。保護雪山的人， 你們basket of eggs, which he disposed of at a shilling per dozen, and so we continued on until the domes and towers of Quebec came in sight and I began to realize the inexpressible joy of being at home once more."* * Diary of Rev. Robert Bell and letters of R. Wright. Rug was a young man of great executive ability, a young man whose word could be relied upon with absolute certainty, a young man who proved himself the very soul of honor in all his business transactions.都被斥為「異端邪說」，凡是反對神權統治的人，都被處以火刑。新興的資產階級為自己的生存和發展，掀起了一場反對封建制度和教會迷信思想的鬥爭，出現了人文主義的思潮。他們使用的戰鬥武器，就是未被神學染汙的古希臘的哲學、科學和文藝。這就是震撼歐洲的文藝復興運動。文藝復興首先發生於義大利，很快就擴大到波蘭及歐洲其他國家。與此同時，商業的活躍也促進了對外貿易的發展。在「黃金」這個符咒的驅使下，許多歐洲冒險者遠航非洲、印度及整個遠東地區。遠洋航行需要豐富的天文和地理知識，從實際中積累起來的觀測資料，使人們感到當時流行的「地靜天動」的宇宙 CHAPTER IV. AN INDIAN SUITOR. 1803. Machecawa and his friend O'Jawescawa became frequent visitors at the Wigwam. They would come in the morning, uninvited, and sit silently all day long before the open fire and observe all that was going on. The spinning-wheel and hand-loom were objects of unceasing interest to them, and though it proved a great distraction to the children in their studies, and to the girls in the performance of their domestic duties, to have them there, they were always treated not only with respect but with consideration and kindness. One morning Machecawa stood gazing intently into the fire. His face wore an expression of perplexity. At length he turned to the White Chief, who was explaining a mathematical problem to one of his boys, and said: "Big Injun, he want to speak his thoughts from books. He want to know white man's Manitou." "May I teach him, father? Just for an hour every day?" said Chrissy, a tall, fair, thoughtful girl of seventeen, who was known throughout the settlement as the "Saint," for she had been led to take a serious view of life by a Quaker friend in the old school at Woburn. "It would be such a pleasure for me to lead him to a knowledge of the truth." The father readily granted the request, and it was arranged that he should receive instruction from Chrissy every morning while the younger boys were having their lessons. Never had teacher a more apt, humble, or willing pupil. Never had pupil a more considerate, patient, kind-hearted instructor. Over and over again did she repeat words and sentences until at last the Indian found, to his unspeakable joy, that he was beginning to acquire the words pretty freely. The morning hour with Machecawa proved of such interest that it was not an uncommon thing to see the White Chief and all the children listening intently to Chrissy and the Indian as they compared their respective creeds. One morning, after she had been giving an account of the creation and the deluge, she said, "Now, tell me what you think of these things. Do the Indians ever think of how the world was made? Did they ever hear of a flood?" Machecawa replied in broken English, the interpretation of which is as follows: The Indian believes that the great Manabozo is king of all other animal kings. The West Wind is his father, and his mother is grand-daughter of the Moon. Sometimes he is a wolf; sometimes a hare; sometimes he is a wicked spirit. Manabozo was hunting with his brother, a wolf, who fell through the ice in a lake and was eaten by snakes. Manabozo was very cross and changed himself into the stump of a tree and surprised the king of the serpents and killed him. The snakes were all Manitous, and they made the water flood the world. Manabozo climbed a tree which grew and grew as the flood came up and was saved from the wicked spirits. Manabozo looked over the waters and he saw a loon, and he cried to the loon for help to save the world. The loon went under the water to look for mud to build the world again, but he could not find the bottom. Then a muskrat tried, but he came up on his back nearly dead. Manabozo looked in his paws and found a little mud, and he took the mud and the dead body of the loon and with it created the world anew again. "And do you believe that?" said the White Chief. "Our tribe she believe like that," replied the Indian. "What is that thing tied round your neck, Machecawa?" said Bearie, the second son, a short, well knit, sturdy-looking youth of eighteen, whose every expression reflected a bright, happy, generous di 一個真正有閱歷的人，經歷足夠多的人，發現身邊可以責怪的人越來越少，因為懂得，人人都有他的難處。一個朋友最近剛從從老家重新殺回廣州。前段時間他媽媽病了，動了一次大手術。他回了一趟家，又回來了。回到廣州後，他整個人都變了，變得和顏悅色，溫柔平和。以前，他總非常鄙視那些從北上廣背著包回家去的人。按照他的標準，那都是沒能力在這座城市生存下去所以被拋棄的人，都是弱者、失敗者。不管是出於什麼原因，離開自己奮鬥的地方，就是撤退，而撤退就是宣告自己無能。他的價值觀也很硬，認為世界非黑即白，用成功和失敗作為衡量人生的唯一價值尺度，認為成功者就應該站在領獎臺上，萬眾矚目，接受鮮花掌聲；認為失敗者就應該躲到角落裡，暗自啜泣，接受自己和他人的責罵。他這次重回廣州，話風完全不一樣，不再那麼充滿雞血，開始包容，對手下的人也沒那麼苛刻，不再要求他們一味地加班，甚至勸告他們多花些時間在家人和朋友身上。 而對於那些準備從北上廣撤退回家當公務員的朋友，他也不像以前，跳起來指著人家鼻子罵你個慫貨，這麼容易就認輸了。他很真誠地跟別人說：「想清楚了吧，想清楚了就決定，每個人都有每個人的難處，畢竟只有你自己知道，什麼才是最重要的。」 他說：「我現在越來越能理解我身邊的人，理解他們的處境和選擇。」 這一切改變源自一年前，他得到消息說母親病了，而且非常嚴重，需要儘快手術。他匆匆請假回家陪著媽媽，他原本以為只要請幾天假陪媽度過手術這段時間就可以回廣州工作了，但是手術術後恢復周期實在太長，而且他看到他媽媽躺在病床上，實在不忍心一個人跑回廣州去談所謂的奮鬥和成功。於是他心一橫，辭職了，空檔了將近一年，專門陪著他媽媽做手術、住院、出院，陪著在家嘮嗑，出去旅遊。在這一年裡，他還遇到了很多之前在北上廣打拼的朋友，了解他們在老家的生活，也知道了他們為什麼最終選擇了回家。他想明白了很多事情。他說：「以前我媽媽沒病的時候，我不懂那些回家照顧父母的人，我覺得他們是找藉口，是失敗，如果有錢，幹嘛不找個保姆照顧呢？現在發現，父母真的是需要自己去照顧。」 「而且我最近也在思考，父母、家庭、事業，究竟什麼才是最重要的，不同的人選擇不同，會有不同的人生，而這些選擇，其實都應該是沒有失敗的。人，其實只有經歷以後，才會懂得。」 人生的確即是如此，只有真正經歷過很多事情之後，我們才會站在更高的維度去看待這個世界，而不是很單純地用自己私人的視角去苛責別人，去評判世界。同樣的情況，也常常發生在我們對父母的理解上。最近，看到一位母親寫的文章，她說：「以前媽媽總是讓我做這做那，讓我注意這個注意那個，那個時候我總是很不耐煩，覺得她囉嗦，總是責怪她。現在自己當了媽，才知道她當時的處境、想法。就像我媽經常說的，孩子，等你當了媽你就知道了。」 是的，年輕時，我們總是覺得與父母隔閡甚重。覺得他們思想陳舊，觀念老套，跟不上新的時代，難以與他們溝通。甚至，我們還會覺得他們反倒成了成長路上的攔路虎。那個時候，不太懂得家這個概念，只想著自己，想著未來，想著長大。後來，自己求學工作，結婚生子，把當年父母經歷的那些階段和事情都重新經歷了一遍，這才慢慢長大，有所感悟。當你成家了以後，你就會發現，需要考慮的事情，考慮的問題很多，家庭收入、家人健康、孩子成長、孩子教育等等，你就會開始懂得當初父母的那些話，做的那些事。也許你現在正在喋喋不休責怪你的父母；也許你現在正在責怪身邊的朋友同事，責怪他們為什麼不能堅持，為什麼放棄，為什麼做出這樣的選擇，等等。但是等你經歷了一些事情之後，你終究會明白他們。你也會懂得，生活，其實沒有一個簡單的標準，任何用成敗來評判他人的人，都很簡單粗暴，也非常幼稚。一個真正成熟的人，一個真正有所經歷的人，會發現身邊可以責怪的人越來越少，因為他越來越明白，人人都有他的難處，所以越來越能理解別人。sposition. "She am my Manitou," replied the Indian. "What is a Manitou? Every Indian you meet with seems to differ on the subject." "Some tam she am wan ting, some tam she am anodder." "That is evading the question," said Chrissy. "What kind of a Manitou have you got inside of that little bag which is tied round your neck?" persisted Bearie. "Will you let me see it?" "No! No!! No!!!" he said excitedly. "My Manitou she am not be pleese." "Come, now, old man," he said. "Tell us all about it." "What is it?" "How did you get it?" "What is it for?" "Waal," he said, reluctantly, "When I am a boy, me, just become a man, my fadder, he say, 'Machecawa, tam you got a manitou.' My face he paint black, black. He say, heem, 'you no eat no teeng seex days.' By em by I am dream some teeng, me, dat some teeng she am my manitou. She help me kill beeg bear; she mak dem Iroquois dogs run like one wild moose. My fadder she am pleese; she make my manitou on my arm—see!" he said, rolling up his sleeve. On his shoulder was the rude outline of a fish, which had been tatooed with sharp bones and with the juice of berries rubbed in. "But what is in the little bag?" asked Bearie. "Will you let me see it?" After a good deal of reluctance he gave in at last, and two curious boys untied the precious parcel, while the others, equally curious, looked over his shoulders at a few old broken fish bones which were all the little bag contained. "Well, old man," said Bearie, slowly replacing the sacred relics, "we put our faith in something better than that. The white man trusts the Great Spirit in heaven to care for him and to take him to heaven when he dies." "Any bear in hebben?" asked the Indian. "No," said Bearie, "only good people." "Dat hebben she am no good for big Injun," said Machecawa, sadly. "De happy hunting ground she am full of moose, buffalo, bear, beaver. She am far, far away at de end of land, where de sun she sleep—two, tree moons away. One beeg dog she am cross, an' she bark at dead Injun, but he go on, an' on, an' on, an' den he am glad." It began to dawn upon the vigilant mother at length that it was not so much the wonders of civilization nor the desire to "speak his thoughts from books" that led Machecawa day after day to the Wigwam, as an ever-increasing interest in her fun-loving daughter, Abbie, who was a year younger than Chrissy, and who seemed unconscious of the fact that the eyes of the red chief were ever upon her.學說值得懷疑，這就要求人們進一步去探索宇宙的秘密，從而推進了天文學和地理學的發展。1492年，義大利著名的航海家哥倫布發現新大陸，麥哲倫和他的同伴繞地球一周，證明地球是圓形的，使人們開始真正認識地球。[4] 對他國的影響 在教會嚴密控制下的中世紀，也發生過轟轟烈烈的宗教革命。因為天主教的很多教義不符合聖經的教誨，而加入了太多教皇的個人意志以及各類神學家的自身成果，所以很多信徒開始質疑天主教的教義和組織，發起回歸聖經的行動來。捷克的愛國主義者、布拉格大學校長揚·胡斯（1369～1415年）在君士坦丁堡的宗教會議上公開譴責德意志封建主與天主教會對捷克的壓迫和剝削。他雖然被反動教會處以火刑，但他的革命活動在社會上引起了強烈的反應。捷克農民在胡斯黨人的旗幟下舉行起義，這次運動也波及波蘭。1517年，在德國，馬丁·路德（1483～1546年）反對教會販賣贖罪符，與羅馬教皇公開決裂。1521年，路德又在沃爾姆國會上揭露羅馬教廷的罪惡，並提出建立基督教新教的主張。新教的教義得到許多國家的支持，波蘭也深受影響。