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，把它表现得似乎和冰块组成的太阳系中的一类小天体，绕日运动。[64] 科学家使用探测器对彗星的化学遗留物进行分析，发现其主要成份A solemn stillness pervaded the once happy home on the hill, a stillness broken only by the sighing of the wind through the poplar trees. The stately, noble form of the queen of the household, who held sway over so many hearts, lay sleeping beneath the daisies in the cemetery not far distant. She had never been well after the shock occasioned by the sudden death of her eldest son. One by one the young people went forth to homes of their own. Abbie, having awakened at last to a realization of the truth of her father\\\\\\\\\'s prediction regarding Thomas Brigham, had long since married that wealthy lumberman. In his loneliness and sorrow came a call to the Chief to higher and harder work in his country\\\\\\\\\'s service. The County of York, in which Hull was situated, had a sufficiently large population to entitle it to representation in the Legislative Assembly, and, as the representation of the Province had been increased to eighty-four members, the electors of the county were called upon to choose their representative. Elections in those days were not so much a question of political opinion with the electors as personal preference and local considerations, so the Chief was elected by acclamation, and took his seat in the House as an independent member, the name of the constituency being changed to that of Ottawa County. The members, who in those days had not the prospect of a large indemnity to nail them to their seats, frequently deserted the Legislative Hall long before the session was over, notwithstanding which the White Chief was ever in his place, and voted intelligently on the burning questions of the day. While attending session at Quebec, he sat down to breakfast on one occasion with the son of his old friend, Louis Joseph Papineau, who was Speaker of the House at the time, and who happened to be staying at the same hotel. "I hear that a town is springing up like a mushroom on the opposite side of the river from Hull," said Mr. Papineau; "and that property on that side of the river has greatly enhanced in value."为氨、甲烷、硫化氢、氰化氢和甲醛。科学家得出结论称，彗星的气味闻起来像是臭鸡蛋、马尿、酒精和苦杏仁的气味综合。[65-66] “67P/楚留莫夫-格拉希门克”彗星 “67P/楚留莫夫-格拉希门克”彗星 [67] 在太阳系的周围还包裹着一个庞大的“奥尔特云”。星云内分布着不计其数的冰块、雪团和碎石。其中的某些会受太阳引力影响飞入内太阳系，这就是彗星。这些冰块、雪团和碎石演化路线的终点。在红巨星阶段的末期，恒星的中心会因为温度、压力不足或者核聚变达到铁阶段而停止产生能以外像恒星一样表现为一个光点的天体，但实际上它的光度和质量又和星系一样，我们叫它类星体，现在已发现了数千个这种天体。[74] 超新星，是恒星演化过程中的一个阶段。超新星爆发是某些恒星在演化接近末期时经历的一种剧烈爆炸。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，而球面是可 克瓶 克莱因瓶 定向的二维紧流形。如果观察克莱因瓶，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。克莱因瓶的瓶颈是穿过了第四维空间再和瓶底圈连起来的，并不穿过瓶壁。用扭结来打比方，如果把它看作平面上的曲线的话，那么它似乎自身相交，再一看似乎又断成了三截。但其实很容易明白，这个图形其实是三维空间中的曲线。它并不和自己相交，Abbie, who was the very reverse of her sister in appearance and disposition, still remained in the convent, the seclusion of which had not transformed her into a religious recluse—rather the reverse. Her association with gay daughters of wealthy Seigneurs and others had the effect of deepening her love of adventure and romance. Sally Smith continued to be her most intimate friend, and any holidays, which in those days were few and far between, were spent at the Citadel. One evening a young officer called, and during the absence of her mother from the room Sally said, her eyes dancing with mischief: "Let me introduce you to my friend, Miss Wabisca Onodis, Lieutenant Randall. Miss Onodis," she continued, "is the daughter of an Algonquin Chief, and is a boarder at the convent." "Aw, indeed," said the officer, "I should never have dreamed that your friend was an Indian girl. Have you had much difficulty in acquiring a knowledge of English?" asked the lieutenant. "Not at all," replied Abbie, "I understand everything that is said, but find difficulty at times in choosing words best fitted to give expression to my deepest emotions." "Aw, I quite understand. They say that the Indian nature is much more intense than that of other civilized nations. What is exceedingly difficult even for an Englishman must be much more so for one of your temperament. No language, I believe, either written nor spoken, can convey any adequate idea of the emotion of love, for instance. Is that your experience, Miss Onodis?" Just then Mrs. Smith entered, and the conversation turned to that perennial subject—the weather. The friendship thus formed soon ripened into more than a mere friendship. Frequent messages passed between the convent and the Citadel, messages in cypher, for Therese, an Indian girl, had furnished Abbie with a list of Algonquin words and phrases expressive of deep sentiment, which were quite unintelligible to the nuns, and as the officer was furnished with a similar vocabulary, messages were frequently carried by Sally between the two. This went on for some time until the nuns found a scrap of paper on the floor containing the following mysterious words: Nitam shaquoi yanque kitchioni chishim Kin mishiwaiasky nin Othai icha quisco. Ka qui nick kitayam. Wabisca Onodis. After matins the Mother Superior addressed about two hundred young women in the Assembly Hall in the following words: "Young ladies, a very mysterious letter has been found. It is evidently in the Indian language. It is probably intended for one of our Indian young ladies. Did anyone present lose a letter?" No one spoke. "O\\\\\\\\\'Jawa," said the superior, addressing a young Indian girl, "will you come forward and see if this letter is written in one of the Iroquois or one of Algonquin dialects?" O\\\\\\\\\'Jawa promptly came up the aisle, and scanning the paper, said: "It is Algonquin, Mother." "To whom is it addressed?" "To no one, Mother," she replied. "By whom is it signed?" "By a White Chief, Mother." "Please translate it," said the Mother Superior. O\\\\\\\\\'Jawa read slowly and deliberately: "First—last—and best, Thou art all the world to me. My heart burns. "Always yours, "WHITE CHIEF." "This letter," continued the Mother Superior, "evidently belongs to one of the Algonquin girls, who probably has been receiving secret missives of a similar nature from some white man. As you are aware, young ladies, this offence is punishable with expulsion. Deceit is the mother of all vices. The sisters cannot assume the responsibility of the care of any young lady who would deliberately deceive them in this way; therefore I am under the painful necessity of investigating this matter more fully. Therese, come forward. Your guilty face indicates that you were the recipient of this letter. Were you?" "I was not, Mother." "Then it was sent to you and the bearer dropped it before you saw it. Is not that the case?" "I do not know, Mother." "Have you ever received any communications of this nature before?" "I have not, Mother." "Do you know any White Chief?" "I do not, Mother." "Do you know for whom this missive was intended?" Therese hesitated. The question was repeated. "I do, Mother," she said. "Do you know by whom it was written?" Taking the letter in her hand she said, slowly: "I do, Mother." "Then, Therese, I must demand the names of both the sender and the intended recipient." "Who wrote that letter?" "I shall not tell," she said, slowly and with great determination. "I shall give you five minutes to answer my question, Therese, and if you stubbornly persist in concealing these facts from me I shall declare you expelled." There was silence in the hall—not a soul stirred. Therese stood calmly awaiting her doom, when suddenly there was a shuffling at the back of the hall and Abbie came forward and addressed the Superior: "I wrote that letter. It was intended for a young officer at the Citadel. If you are going to expel anyone, expel me." The Mother Superior hesitated. She looked at Abbie, then at Therese, and said, solemnly: "Tell us about it," said the officer. "You tell about it, father," said Bearie. "It is a long story," replied the Chief, "but I shall try to tell it as briefly as possible. The priest said that the French colonists had suffered much from the cruelty of the Iroquois tribes, who had decided to destroy the whole French colony. A Mohegan Indian told the French that eight hundred Indian warriors were encamped near Montreal, and would soon be joined by four hundred more from the Uttawas, and that they had planned to take Quebec, kill the Governor, burn up the town, massacre the inhabitants; after which they would proceed to do the same with Three Rivers and Montreal. "A young officer named Daulac, who was in command of the garrison at Montreal, proposed to entrap them on their way down the Ottawa and fight them. Sixteen young fellows from Montreal volunteered to go with him. They did not know much about canoeing, for they were a whole week in attempting to pass the swift current at St. Anne, at the head of the Island of Montreal. In the meantime they were overtaken by forty Hurons and several Christian Algonquins. When they saw the rushing, foaming waters of the Sault they decided to go no farther, for they knew that the Iroquois were sure to pass there. He pointed out a spot just below the rapids, where the woods slope gently down to the shore, where an old Algonquin palisade fort stood. \\\\\\\\\'It was,\\\\\\\\\' he said, \\\\\\\\\'a mere enclosure of trunks of trees planted in a circle.\\\\\\\\\' In a few days they saw two Iroquois canoes coming down the Sault. Daulac and his men hid behind the bushes and, as they landed, shot all but one, who escaped and fled through the forest to the main body. "\\\\\\\\\'Suddenly,\\\\\\\\\' said the priest, \\\\\\\\\'a fleet of canoes filled with Iroquois came bounding down the rapids. Soon as they landed they smashed the bark canoes of the French, and, kindling the bark, ran up to set fire to the palisade. Three times they attempted to storm the little fort, but were driven back by the deadly fire of the small garrison. Their rage was unbounded. They sent word to five hundred of their tribe, who were camped at the mouth of the Richelieu, to come to their aid. This so frightened the Hurons that they deserted and betrayed the smallness of their force to the enemy, who advanced with yells, firing as they came on. But again they had to fall back, owing to the deadly fire of the French. The latter held out for three days, and the Iroquois were on the verge of giving up the siege when they resolved to make one last attempt. They made large, heavy shields, four or five feet high, by lashing together three split logs fastened together with cross bars. Under cover of these they advanced, reached the palisade, and, crouching below the range of shot, hewed furiously with their axes until they cut their way through. Daulac filled a large musketoon with powder, and after plugging up the muzzle attached a fuse, and tried to throw it over the palisade, but it fell back among the French and exploded, killing and wounding several and blinding others.而是连续不断的一条曲线。在平面上一条曲线自然做不到这样，但是如果有第三维的话，它就可以穿过第三维来避开和自己相交。只是因为我们要把它画在二维平面上时，只好将就一点，把它画成相交或者断裂了的样子。克莱因瓶也一样，我们可以把它理解成处于四维空间中的曲面。在我们这个三维空间中，即使是最高明的能工巧匠，也不得不把它做成自身层意义。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光年以内的哲学、科学和文艺。这就是震撼欧洲的文艺复兴运动。文艺复兴首先发生于意大利，很快就扩大到波兰及欧洲其他国家。与此同时，商业的活跃也促进了对外贸易的发展。在“黄金”这个符咒的驱使下，许多欧洲冒险者远航非洲、印度及整个远东地区。远洋航行需要丰富的天文和地理知识，从实际中积累起来的观测资料，使人们感到当时流行的“地静天动”的宇宙学说值得怀疑，这就要求人们进一步去探索宇宙的秘密，从而推进了天文学和地理学的发展。1492年，意大利著名的航海家哥伦布发现新大陆，麦哲伦和他的同伴绕地球一周，证明地球是圆形的，使人们开始真正认识地球。[4] 对他国的影响 在教会严密控制下的中世纪，也发生过轰轰烈烈的宗教革命。因为天主教的很多教义不符合圣经的教诲，而加入了太多教皇的个人意志以及各类神学家的自身成果，所以很多信徒开始质疑天主教的教义和组织，发起回归圣经的行动来。捷克的爱国主义者、布拉格大学校长扬·胡斯（1369～1415年）在君士坦丁堡的宗教会议上公开谴责德意志封建主与天主教会对捷克的压迫和剥削。他虽然被反动教会处以火刑，但他的革命活动在社会上引起了强烈的反应。捷克农民在