今日说法

今日说法

第129集

2.0 |2023年10月23日 |已完结
简介:

  《今日说法》诞生于1999年1月2日,是中国中央电视台(cctv)第一档全日播法制栏目,已经成为家喻户晓的品牌栏目。栏目秉持“点滴记录中国法治进程”的理念,以“重在普法,监督执法,促进立法、服务百姓”为宗旨,全力打造“中国人的法律午餐”。栏目收视排名长期稳居央视前列,影响力持续增强,《12.4年度法治人物颁奖盛典》、《小撒探会》等特别节目铸就高端品质,使栏目实现了更大的社会动员能力和普法功能。

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我在人艺学表演
267
8.0
已完结
我在人艺学表演
8.0
更新时间:2023年10月10日
主演:蓝天野,吕中,冯远征,濮存昕,宋丹丹,岳秀清,龚丽君,杨佳音,唐烨,李伟建,曹磊,张晔子,曾泳醍
简介:

  在全力建设全国文化中心的首都北京,人民艺术的殿堂——北京人民艺术剧院,在2022年6月12日,迎来建院70周年纪念。在这70年间,群星璀璨。老舍、曹禺、焦菊隐、舒绣文、于是之、蓝天野、濮存昕等一代代艺术家,共同铸就了北京人艺的辉煌。这70年间,大戏云集。《茶馆》、《雷雨》、《骆驼祥子》、《天下第一楼》、《窝头会馆》等一部部精品佳作,一起点亮了北京人艺的荣光。
  在这个具有纪念意义的历史节点,北京广播电视台、中国移动咪咕公司、新纪实(北京)传媒投资有限公司,联合北京人民艺术剧院,重磅推出大型纪录片《我在人艺学表演》。这是呼应全国文化中心建设,聚焦青年人才成长的国内首档表演艺术题材纪录片。全片共十集。
  节目于2022年6月10日晚8:00整,登陆北京广播电视台科教频道、咪咕视频。
  北京人民艺术剧院副院长冯远征说“艺术人才的培养、选拔和储备是人艺辉煌得以延续的重要途径。”人才是根基,根深,文化大树才能枝繁叶茂。作为中国话剧殿堂级剧院,面对老中青演员迭代更新的问题,2019年12月,北京人民艺术剧院在停办三十四年后再次招收学员开设“表演学员培训班”,希望用自己的方法培养一批跟人艺风格“合槽”的演员。
  由北京广播电视台科教频道中心、新纪实(北京)传媒投资有限公司组成的《我在人艺学表演》摄制组,历时一年全程跟踪记录了从千余名报考者中选拔出来的十五名学员在“表演学员培训班”学习成长的故事。
  在《我在人艺学表演》纪录片中,我们能看到蓝天野、吕中、濮存昕、冯远征、宋丹丹、岳秀清、龚丽君等顶级表演艺术家的言传身教,见证十五位学员在声台形表全方位训练中经历的挑战、挫折与演技的蜕变。从基本功到业务课、从课堂学习到舞台实践、从舞台到生活的多彩故事。这是一部明星荟萃的纪录片版的“演员的诞生”、一部中国戏剧表演艺术殿堂级的影像教科书,也是广大观众了解北京人艺独特演剧风格的另类视角。
  好的表演如何定义?评价标准不是热搜,不是流量,更不是控评话术。好的表演,是演员和观众心与心的碰撞!我在人艺学表演,学的不只是表演,更是做艺、做人的道理。真正的演技在这里诞生,表演大师已就位。

3680
2022
我在人艺学表演
主演:蓝天野,吕中,冯远征,濮存昕,宋丹丹,岳秀清,龚丽君,杨佳音,唐烨,李伟建,曹磊,张晔子,曾泳醍
费马大定理
500
1.0
HD
费马大定理
1.0
更新时间:2025年02月23日
主演:Andrew Wiles,Barry Mazur,Kenneth Ribet
简介:

  本片从证明了费玛最后定理的安德鲁‧怀尔斯 Andrew Wiles开始谈起,描述了 Fermat's Last Theorm 的历史始末,往前回溯来看,1994年正是我在念大学的时候,当时完全没有一位教授在课堂上提到这件事,也许他们认为,一位真正的研究者,自然而然地会被数学吸引,然而对一位不是天才的学生来说,他需要的是老师的指引,引导他走向更高深的专业认知,而指引的道路,就在科普的精神上。
  从费玛最后定理的历史中可以发现,有许多研究成果,都是研究人员燃烧热情,试图提出「有趣」的命题,然后再尝试用逻辑验证。
  费玛最后定理:xn+yn=zn 当 n>2 时,不存在整数解
  1. 1963年 安德鲁‧怀尔斯 Andrew Wiles被埃里克‧坦普尔‧贝尔 Eric Temple Bell 的一本书吸引,「最后问题 The Last Problem」,故事从这里开始。
  2. 毕达哥拉斯 Pythagoras 定理,任一个直角三角形,斜边的平方=另外两边的平方和
  x2+y2=z2
  毕达哥拉斯三元组:毕氏定理的整数解
  3. 费玛 Fermat 在研究丢番图 Diophantus 的「算数」第2卷的问题8时,在页边写下了註记
  「不可能将一个立方数写成两个立方数之和;或者将一个四次幂写成两个四次幂之和;或者,总的来说,不可能将一个高於2次幂,写成两个同样次幂的和。」
  「对这个命题我有一个十分美妙的证明,这里空白太小,写不下。」
  4. 1670年,费玛 Fermat的儿子出版了载有Fermat註记的「丢番图的算数」
  5. 在Fermat的其他註记中,隐含了对 n=4 的证明 => n=8, 12, 16, 20 ... 时无解
  莱昂哈德‧欧拉 Leonhard Euler 证明了 n=3 时无解 => n=6, 9, 12, 15 ... 时无解
  3是质数,现在只要证明费玛最后定理对於所有的质数都成立
  但 欧基里德 证明「存在无穷多个质数」
  6. 1776年 索菲‧热尔曼 针对 (2p+1)的质数,证明了 费玛最后定理 "大概" 无解
  7. 1825年 古斯塔夫‧勒瑞-狄利克雷 和 阿得利昂-玛利埃‧勒让德 延伸热尔曼的证明,证明了 n=5 无解
  8. 1839年 加布里尔‧拉梅 Gabriel Lame 证明了 n=7 无解
  9. 1847年 拉梅 与 奥古斯汀‧路易斯‧科西 Augusti Louis Cauchy 同时宣称已经证明了 费玛最后定理
  最后是刘维尔宣读了 恩斯特‧库默尔 Ernst Kummer 的信,说科西与拉梅的证明,都因为「虚数没有唯一因子分解性质」而失败
  库默尔证明了 费玛最后定理的完整证明 是当时数学方法不可能实现的
  10.1908年 保罗‧沃尔夫斯凯尔 Paul Wolfskehl 补救了库默尔的证明
  这表示 费玛最后定理的完整证明 尚未被解决
  沃尔夫斯凯尔提供了 10万马克 给提供证明的人,期限是到2007年9月13日止
  11.1900年8月8日 大卫‧希尔伯特,提出数学上23个未解决的问题且相信这是迫切需要解决的重要问题
  12.1931年 库特‧哥德尔 不可判定性定理
  第一不可判定性定理:如果公理集合论是相容的,那么存在既不能证明又不能否定的定理。
  => 完全性是不可能达到的
  第二不可判定性定理:不存在能证明公理系统是相容的构造性过程。
  => 相容性永远不可能证明
  13.1963年 保罗‧科恩 Paul Cohen 发展了可以检验给定问题是不是不可判定的方法(只适用少数情形)
  证明希尔伯特23个问题中,其中一个「连续统假设」问题是不可判定的,这对於费玛最后定理来说是一大打击
  14.1940年 阿伦‧图灵 Alan Turing 发明破译 Enigma编码 的反转机
  开始有人利用暴力解决方法,要对 费玛最后定理 的n值一个一个加以证明。
  15.1988年 内奥姆‧埃尔基斯 Naom Elkies 对於 Euler 提出的 x4+y4+z4=w4 不存在解这个推想,找到了一个反例
  26824404+153656394+1879604=206156734
  16.1975年 安德鲁‧怀尔斯 Andrew Wiles 师承 约翰‧科次,研究椭圆曲线
  研究椭圆曲线的目的是要算出他们的整数解,这跟费玛最后定理一样
  ex: y2=x3-2 只有一组整数解 52=33-2
  (费玛证明宇宙中指存在一个数26,他是夹在一个平方数与一个立方数中间)
  由於要直接找出椭圆曲线是很困难的,为了简化问题,数学家採用「时鐘运算」方法
  在五格时鐘运算中, 4+2=1
  椭圆方程式 x3-x2=y2+y
  所有可能的解为 (x, y)=(0, 0) (0, 4) (1, 0) (1, 4),然后可用 E5=4 来代表在五格时鐘运算中,有四个解
  对於椭圆曲线,可写出一个 E序列 E1=1, E2=4, .....
  17.1954年 至村五郎 与 谷山丰 研究具有非同寻常的对称性的 modular form 模型式
  模型式的要素可从1开始标号到无穷(M1, M2, M3, ...)
  每个模型式的 M序列 要素个数 可写成 M1=1 M2=3 .... 这样的范例
  1955年9月 提出模型式的 M序列 可以对应到椭圆曲线的 E序列,两个不同领域的理论突然被连接在一起
  安德列‧韦依 採纳这个想法,「谷山-志村猜想」
  18.朗兰兹提出「朗兰兹纲领」的计画,一个统一化猜想的理论,并开始寻找统一的环链
  19.1984年 格哈德‧弗赖 Gerhard Frey 提出
  (1) 假设费玛最后定理是错的,则 xn+yn=zn 有整数解,则可将方程式转换为y2=x3+(AN-BN)x2-ANBN 这样的椭圆方程式
  (2) 弗赖椭圆方程式太古怪了,以致於无法被模型式化
  (3) 谷山-志村猜想 断言每一个椭圆方程式都可以被模型式化
  (4) 谷山-志村猜想 是错误的
  反过来说
  (1) 如果 谷山-志村猜想 是对的,每一个椭圆方程式都可以被模型式化
  (2) 每一个椭圆方程式都可以被模型式化,则不存在弗赖椭圆方程式
  (3) 如果不存在弗赖椭圆方程式,那么xn+yn=zn 没有整数解
  (4) 费玛最后定理是对的
  20.1986年 肯‧贝里特 证明 弗赖椭圆方程式无法被模型式化
  如果有人能够证明谷山-志村猜想,就表示费玛最后定理也是正确的
  21.1986年 安德鲁‧怀尔斯 Andrew Wiles 开始一个小阴谋,他每隔6个月发表一篇小论文,然后自己独力尝试证明谷山-志村猜想,策略是利用归纳法,加上 埃瓦里斯特‧伽罗瓦 的群论,希望能将E序列以「自然次序」一一对应到M序列
  22.1988年 宫冈洋一 发表利用微分几何学证明谷山-志村猜想,但结果失败
  23.1989年 安德鲁‧怀尔斯 Andrew Wiles 已经将椭圆方程式拆解成无限多项,然后也证明了第一项必定是模型式的第一项,也尝试利用 依娃沙娃 Iwasawa 理论,但结果失败
  24.1992年 修改 科利瓦金-弗莱契 方法,对所有分类后的椭圆方程式都奏效
  25.1993年 寻求同事 尼克‧凯兹 Nick Katz 的协助,开始对验证证明
  26.1993年5月 「L-函数和算术」会议,安德鲁‧怀尔斯 Andrew Wiles 发表谷山-志村猜想的证明
  27.1993年9月 尼克‧凯兹 Nick Katz 发现一个重大缺陷
  安德鲁‧怀尔斯 Andrew Wiles 又开始隐居,尝试独力解决缺陷,他不希望在这时候公布证明,让其他人分享完成证明的甜美果实
  28.安德鲁‧怀尔斯 Andrew Wiles 在接近放弃的边缘,在彼得‧萨纳克的建议下,找到理查德‧泰勒的协助
  29.1994年9月19日 发现结合 依娃沙娃 Iwasawa 理论与 科利瓦金-弗莱契 方法就能够完全解决问题
  30.「谷山-志村猜想」被证明了,故得证「费玛最后定理」
  ii
  费马大定理
  300多年以前,法国数学家费马在一本书的空白处写下了一个定理:“设n是大于2的正整数,则不定方程xn+yn=zn没有非零整数解”。
  费马宣称他发现了这个定理的一个真正奇妙的证明,但因书上空白太小,他写不下他的证明。300多年过去了,不知有多少专业数学家和业余数学爱好者绞尽脑汁企图证明它,但不是无功而返就是进展甚微。这就是纯数学中最着名的定理—费马大定理。
  费马(1601年~1665年)是一位具有传奇色彩的数学家,他最初学习法律并以当律师谋生,后来成为议会议员,数学只不过是他的业余爱好,只能利用闲暇来研究。虽然年近30才认真注意数学,但费马对数论和微积分做出了第一流的贡献。他与笛卡儿几乎同时创立了解析几何,同时又是17世纪兴起的概率论的探索者之一。费马特别爱好数论,提出了许多定理,但费马只对其中一个定理给出了证明要点,其他定理除一个被证明是错的,一个未被证明外,其余的陆续被后来的数学家所证实。这唯一未被证明的定理就是上面所说的费马大定理,因为是最后一个未被证明对或错的定理,所以又称为费马最后定理。
  费马大定理虽然至今仍没有完全被证明,但已经有了很大进展,特别是最近几十年,进展更快。1976年瓦格斯塔夫证明了对小于105的素数费马大定理都成立。1983年一位年轻的德国数学家法尔廷斯证明了不定方程xn+yn=zn只能有有限多组解,他的突出贡献使他在1986年获得了数学界的最高奖之一费尔兹奖。1993年英国数学家威尔斯宣布证明了费马大定理,但随后发现了证明中的一个漏洞并作了修正。虽然威尔斯证明费马大定理还没有得到数学界的一致公认,但大多数数学家认为他证明的思路是正确的。毫无疑问,这使人们看到了希望。
  为了寻求费马大定理的解答,三个多世纪以来,一代又一代的数学家们前赴后继,却壮志未酬。1995年,美国普林斯顿大学的安德鲁·怀尔斯教授经过8年的孤军奋战,用13
  0页长的篇幅证明了费马大定理。怀尔斯成为整个数学界的英雄。
  费马大定理提出的问题非常简单,它是用一个每个中学生都熟悉的数学定理——毕达
  哥拉斯定理——来表达的。2000多年前诞生的毕达哥拉斯定理说:在一个直角三角形中,
  斜边的平方等于两直角边的平方之和。即X2+Y2=Z2。大约在公元1637年前后 ,当费马在
  研究毕达哥拉斯方程时,他写下一个方程,非常类似于毕达哥拉斯方程:Xn+Yn=Zn,当n
  大于2时,这个方程没有任何整数解。费马在《算术》这本书的靠近问题8的页边处记下这
  个结论的同时又写下一个附加的评注:“对此,我确信已发现一个美妙的证法,这里的空
  白太小,写不下。”这就是数学史上着名的费马大定理或称费马最后的定理。费马制造了
  一个数学史上最深奥的谜。
  大问题
  在物理学、化学或生物学中,还没有任何问题可以叙述得如此简单和清晰,却长久不
  解。E·T·贝尔(Eric Temple Bell)在他的《大问题》(The Last Problem)一书中写到,
  文明世界也许在费马大定理得以解决之前就已走到了尽头。证明费马大定理成为数论中最
  值得为之奋斗的事。
  安德鲁·怀尔斯1953年出生在英国剑桥,父亲是一位工程学教授。少年时代的怀尔斯
  已着迷于数学了。他在后来的回忆中写到:“在学校里我喜欢做题目,我把它们带回家,
  编写成我自己的新题目。不过我以前找到的最好的题目是在我们社区的图书馆里发现的。
  ”一天,小怀尔斯在弥尔顿街上的图书馆看见了一本书,这本书只有一个问题而没有解答
  ,怀尔斯被吸引住了。
  这就是E·T·贝尔写的《大问题》。它叙述了费马大定理的历史,这个定理让一个又
  一个的数学家望而生畏,在长达300多年的时间里没有人能解决它。怀尔斯30多年后回忆
  起被引向费马大定理时的感觉:“它看上去如此简单,但历史上所有的大数学家都未能解
  决它。这里正摆着我——一个10岁的孩子——能理解的问题,从那个时刻起,我知道我永
  远不会放弃它。我必须解决它。”
  怀尔斯1974年从牛津大学的Merton学院获得数学学士学位,之后进入剑桥大学Clare
  学院做博士。在研究生阶段,怀尔斯并没有从事费马大定理研究。他说:“研究费马可能
  带来的问题是:你花费了多年的时间而最终一事无成。我的导师约翰·科茨(John Coate
  s)正在研究椭圆曲线的Iwasawa理论,我开始跟随他工作。” 科茨说:“我记得一位同事
  告诉我,他有一个非常好的、刚完成数学学士荣誉学位第三部考试的学生,他催促我收其
  为学生。我非常荣幸有安德鲁这样的学生。即使从对研究生的要求来看,他也有很深刻的
  思想,非常清楚他将是一个做大事情的数学家。当然,任何研究生在那个阶段直接开始研
  究费马大定理是不可能的,即使对资历很深的数学家来说,它也太困难了。”科茨的责任
  是为怀尔斯找到某种至少能使他在今后三年里有兴趣去研究的问题。他说:“我认为研究
  生导师能为学生做的一切就是设法把他推向一个富有成果的方向。当然,不能保证它一定
  是一个富有成果的研究方向,但是也许年长的数学家在这个过程中能做的一件事是使用他
  的常识、他对好领域的直觉。然后,学生能在这个方向上有多大成绩就是他自己的事了。
  ”
  科茨决定怀尔斯应该研究数学中称为椭圆曲线的领域。这个决定成为怀尔斯职业生涯中的
  一个转折点,椭圆方程的研究是他实现梦想的工具。
  孤独的战士
  1980年怀尔斯在剑桥大学取得博士学位后来到了美国普林斯顿大学,并成为这所大学
  的教授。在科茨的指导下,怀尔斯或许比世界上其他人都更懂得椭圆方程,他已经成为一
  个着名的数论学家,但他清楚地意识到,即使以他广博的基础知识和数学修养,证明费马
  大定理的任务也是极为艰巨的。
  在怀尔斯的费马大定理的证明中,核心是证明“谷山-志村猜想”,该猜想在两个非
  常不同的数学领域间建立了一座新的桥梁。“那是1986年夏末的一个傍晚,我正在一个朋
  友家中啜饮冰茶。谈话间他随意告诉我,肯·里贝特已经证明了谷山-志村猜想与费马大
  定理间的联系。我感到极大的震动。我记得那个时刻,那个改变我生命历程的时刻,因为
  这意味着为了证明费马大定理,我必须做的一切就是证明谷山-志村猜想……我十分清楚
  我应该回家去研究谷山-志村猜想。”怀尔斯望见了一条实现他童年梦想的道路。
  20世纪初,有人问伟大的数学家大卫·希尔伯特为什么不去尝试证明费马大定理,他
  回答说:“在开始着手之前,我必须用3年的时间作深入的研究,而我没有那么多的时间
  浪费在一件可能会失败的事情上。”怀尔斯知道,为了找到证明,他必须全身心地投入到
  这个问题中,但是与希尔伯特不一样,他愿意冒这个风险。
  怀尔斯作了一个重大的决定:要完全独立和保密地进行研究。他说:“我意识到与费
  马大定理有关的任何事情都会引起太多人的兴趣。你确实不可能很多年都使自己精力集中
  ,除非你的专心不被他人分散,而这一点会因旁观者太多而做不到。”怀尔斯放弃了所有
  与证明费马大定理无直接关系的工作,任何时候只要可能他就回到家里工作,在家里的顶
  楼书房里他开始了通过谷山-志村猜想来证明费马大定理的战斗。
  这是一场长达7年的持久战,这期间只有他的妻子知道他在证明费马大定理。
  欢呼与等待
  经过7年的努力,怀尔斯完成了谷山-志村猜想的证明。作为一个结果,他也证明了
  费马大定理。现在是向世界公布的时候了。1993年6月底,有一个重要的会议要在剑桥大
  学的牛顿研究所举行。怀尔斯决定利用这个机会向一群杰出的听众宣布他的工作。他选择
  在牛顿研究所宣布的另外一个主要原因是剑桥是他的家乡,他曾经是那里的一名研究生。
  1993年6月23日,牛顿研究所举行了20世纪最重要的一次数学讲座。两百名数学家聆
  听了这一演讲,但他们之中只有四分之一的人完全懂得黑板上的希腊字母和代数式所表达
  的意思。其余的人来这里是为了见证他们所期待的一个真正具有意义的时刻。演讲者是安
  德鲁·怀尔斯。怀尔斯回忆起演讲最后时刻的情景:“虽然新闻界已经刮起有关演讲的风
  声,很幸运他们没有来听演讲。但是听众中有人拍摄了演讲结束时的镜头,研究所所长肯
  定事先就准备了一瓶香槟酒。当我宣读证明时,会场上保持着特别庄重的寂静,当我写完
  费马大定理的证明时,我说:‘我想我就在这里结束’,会场上爆发出一阵持久的鼓掌声
  。”
  《纽约时报》在头版以《终于欢呼“我发现了!”,久远的数学之谜获解》为题报道
  费马大定理被证明的消息。一夜之间,怀尔斯成为世界上最着名的数学家,也是唯一的数
  学家。《人物》杂志将怀尔斯与戴安娜王妃一起列为“本年度25位最具魅力者”。最有创
  意的赞美来自一家国际制衣大公司,他们邀请这位温文尔雅的天才作他们新系列男装的模
  特。
  当怀尔斯成为媒体报道的中心时,认真核对这个证明的工作也在进行。科学的程序要
  求任何数学家将完整的手稿送交一个有声望的刊物,然后这个刊物的编辑将它送交一组审
  稿人,审稿人的职责是进行逐行的审查证明。怀尔斯将手稿投到《数学发明》,整整一个
  夏天他焦急地等待审稿人的意见,并祈求能得到他们的祝福。可是,证明的一个缺陷被发
  现了。
  我的心灵归于平静
  由于怀尔斯的论文涉及到大量的数学方法,编辑巴里·梅休尔决定不像通常那样指定
  2-3个审稿人,而是6个审稿人。200页的证明被分成6章,每位审稿人负责其中一章。
  怀尔斯在此期间中断了他的工作,以处理审稿人在电子邮件中提出的问题,他自信这
  些问题不会给他造成很大的麻烦。尼克·凯兹负责审查第3章,1993年8月23日,他发现了
  证明中的一个小缺陷。数学的绝对主义要求怀尔斯无可怀疑地证明他的方法中的每一步都
  行得通。怀尔斯以为这又是一个小问题,补救的办法可能就在近旁,可是6个多月过去了
  ,错误仍未改正,怀尔斯面临绝境,他准备承认失败。他向同事彼得·萨克说明自己的情
  况,萨克向他暗示困难的一部分在于他缺少一个能够和他讨论问题并且可信赖的人。经过
  长时间的考虑后,怀尔斯决定邀请剑桥大学的讲师理查德·泰勒到普林斯顿和他一起工作
  。
  泰勒1994年1月份到普林斯顿,可是到了9月,依然没有结果,他们准备放弃了。泰勒
  鼓励他们再坚持一个月。怀尔斯决定在9月底作最后一次检查。9月19日,一个星期一的早
  晨,怀尔斯发现了问题的答案,他叙述了这一时刻:“突然间,不可思议地,我有了一个
  难以置信的发现。这是我的事业中最重要的时刻,我不会再有这样的经历……它的美是如
  此地难以形容;它又是如此简单和优美。20多分钟的时间我呆望它不敢相信。然后白天我
  到系里转了一圈,又回到桌子旁看看它是否还在——它还在那里。”
  这是少年时代的梦想和8年潜心努力的终极,怀尔斯终于向世界证明了他的才能。世
  界不再怀疑这一次的证明了。这两篇论文总共有130页,是历史上核查得最彻底的数学稿
  件,它们发表在1995年5月的《数学年刊》上。怀尔斯再一次出现在《纽约时报》的头版
  上,标题是《数学家称经典之谜已解决》。约翰·科茨说:“用数学的术语来说,这个最
  终的证明可与分裂原子或发现DNA的结构相比,对费马大定理的证明是人类智力活动的一
  曲凯歌,同时,不能忽视的事实是它一下子就使数学发生了革命性的变化。对我说来,安
  德鲁成果的美和魅力在于它是走向代数数论的巨大的一步。”
  声望和荣誉纷至沓来。1995年,怀尔斯获得瑞典皇家学会颁发的Schock数学奖,199
  6年,他获得沃尔夫奖,并当选为美国科学院外籍院士。
  怀尔斯说:“……再没有别的问题能像费马大定理一样对我有同样的意义。我拥有如
  此少有的特权,在我的成年时期实现我童年的梦想……那段特殊漫长的探索已经结束了,
  我的心已归于平静。”
  费马大定理只有在相对数学理论的建立之后,才会得到最满意的答案。相对数学理论没有完成之前,谈这个问题是无力地.因为人们对数量和自身的认识,还没有达到一定的高度.
  iii
  费马大定理与怀尔斯的因果律-美国公众广播网对怀尔斯的专访
  358年的难解之谜
  数学爱好者费马提出的这个问题非常简单,它用一个每个中学生都熟悉的数学定理——毕达哥拉斯定理来表达。2000多年前诞生的毕达哥拉斯定理说:在一个直角三角形中,斜边的平方等于两个直角边的平方之和。即X2+Y2=Z2。大约在公元1637年前后 ,当费马在研究毕达哥拉斯方程时,他在《算术》这本书靠近问题8的页边处写下了这段文字:“设n是大于2的正整数,则不定方程xn+yn=zn没有非整数解,对此,我确信已发现一个美妙的证法,但这里的空白太小,写不下。”费马习惯在页边写下猜想,费马大定理是其中困扰数学家们时间最长的,所以被称为Fermat’s Last Theorem(费马最后的定理)——公认为有史以来最着名的数学猜想。
  在畅销书作家西蒙·辛格(Simon Singh)的笔下,这段神秘留言引发的长达358年的猎逐充满了惊险、悬疑、绝望和狂喜。这段历史先后涉及到最多产的数学大师欧拉、最伟大的数学家高斯、由业余转为职业数学家的柯西、英年早逝的天才伽罗瓦、理论兼试验大师库默尔和被誉为“法国历史上知识最为高深的女性”的苏菲·姬尔曼……法国数学天才伽罗瓦的遗言、日本数学界的明日之星谷山丰的神秘自杀、德国数学爱好者保罗·沃尔夫斯凯尔最后一刻的舍死求生等等,都仿佛是冥冥间上帝导演的宏大戏剧中的一幕,为最后谜底的解开埋下伏笔。终于,普林斯顿的怀尔斯出现了。他找到谜底,把这出戏推向高潮并戛然而止,留下一段耐人回味的传奇。
  对怀尔斯而言,证明费马大定理不仅是破译一个难解之谜,更是去实现一个儿时的梦想。“我10岁时在图书馆找到一本数学书,告诉我有这么一个问题,300多年前就已经有人解决了它,但却没有人看到过它的证明,也无人确信是否有这个证明,从那以后,人们就不断地求证。这是一个10岁小孩就能明白的问题,然后历史上诸多伟大的数学家们却不能解答。于是从那时起,我就试过解决它,这个问题就是费马大定理。”
  怀尔斯于1970年先后在牛津大学和剑桥大学获得数学学士和数学博士学位。“我进入剑桥时,我真正把费马大定理搁在一边了。这不是因为我忘了它,而是我认识到我们所掌握的用来攻克它的全部技术已经反复使用了130年。而这些技术似乎没有触及问题根本。”因为担心耗费太多时间而一无所获,他“暂时放下了”对费马大定理的思索,开始研究椭圆曲线理论——这个看似与证明费马大定理不相关的理论后来却成为他实现梦想的工具。
  时间回溯至20世纪60年代,普林斯顿数学家朗兰兹提出了一个大胆的猜想:所有主要数学领域之间原本就存在着的统一的链接。如果这个猜想被证实,意味着在某个数学领域中无法解答的任何问题都有可能通过这种链接被转换成另一个领域中相应的问题——可以被一整套新方案解决的问题。而如果在另一个领域内仍然难以找到答案,那么可以把问题再转换到下一个数学领域中……直到它被解决为止。根据朗兰兹纲领,有一天,数学家们将能够解决曾经是最深奥最难对付的问题——“办法是领着这些问题周游数学王国的各个风景胜地”。这个纲领为饱受哥德尔不完备定理打击的费马大定理证明者们指明了救赎之路——根据不完备定理,费马大定理是不可证明的。
  怀尔斯后来正是依赖于这个纲领才得以证明费马大定理的:他的证明——不同于任何前人的尝试——是现代数学诸多分支(椭圆曲线论,模形式理论,伽罗华表示理论等等)综合发挥作用的结果。20世纪50年代由两位日本数学家(谷山丰和志村五郎)提出的谷山—志村猜想(Taniyama-Shimura conjecture)暗示:椭圆方程与模形式两个截然不同的数学岛屿间隐藏着一座沟通的桥梁。随后在1984年,德国数学家格哈德·费赖(Gerhard Frey)给出了如下猜想:假如谷山—志村猜想成立,则费马大定理为真。这个猜想紧接着在1986年被肯·里贝特(Ken Ribet)证明。从此,费马大定理不可摆脱地与谷山—志村猜想链接在一起:如果有人能证明谷山—志村猜想(即“每一个椭圆方程都可以模形式化”),那么就证明了费马大定理。
  “人类智力活动的一曲凯歌”
  怀尔斯诡秘的行踪让普林斯顿的着名数学家同事们困惑。彼得·萨奈克(Peter Sarnak)回忆说:“ 我常常奇怪怀尔斯在做些什么?……他总是静悄悄的,也许他已经‘黔驴技穷’了。”尼克·凯兹则感叹到:“一点暗示都没有!”对于这次惊天“大预谋”,肯·里比特(Ken Ribet)曾评价说:“这可能是我平生来见过的唯一例子,在如此长的时间里没有泄露任何有关工作的信息。这是空前的。
  1993年晚春,在经过反复的试错和绞尽脑汁的演算,怀尔斯终于完成了谷山—志村猜想的证明。作为一个结果,他也证明了费马大定理。彼得·萨奈克是最早得知此消息的人之一,“我目瞪口呆、异常激动、情绪失常……我记得当晚我失眠了”。
  同年6月,怀尔斯决定在剑桥大学的大型系列讲座上宣布这一证明。 “讲座气氛很热烈,有很多数学界重要人物到场,当大家终于明白已经离证明费马大定理一步之遥时,空气中充满了紧张。” 肯·里比特回忆说。巴里·马佐尔(Barry Mazur)永远也忘不了那一刻:“我之前从未看到过如此精彩的讲座,充满了美妙的、闻所未闻的新思想,还有戏剧性的铺垫,充满悬念,直到最后到达高潮。”当怀尔斯在讲座结尾宣布他证明了费马大定理时,他成了全世界媒体的焦点。《纽约时报》在头版以《终于欢呼“我发现了!”久远的数学之谜获解》(“At Last Shout of ‘Eureka!’ in Age-Old Math Mystery”)为题报道费马大定理被证明的消息。一夜之间,怀尔斯成为世界上唯一的数学家。《人物》杂志将怀尔斯与戴安娜王妃一起列为“本年度25位最具魅力者”。
  与此同时,认真核对这个证明的工作也在进行。遗憾的是,如同这之前的“费马大定理终结者”一样,他的证明是有缺陷的。怀尔斯现在不得不在巨大的压力之下修正错误,其间数度感到绝望。John Conway曾在美国公众广播网(PBS)的访谈中说: “当时我们其他人(怀尔斯的同事)的行为有点像‘苏联政体研究者’,都想知道他的想法和修正错误的进展,但没有人开口问他。所以,某人会说,‘我今天早上看到怀尔斯了。’‘他露出笑容了吗?’‘他倒是有微笑,但看起来并不高兴。’”
  撑到1994年9月时,怀尔斯准备放弃了。但他临时邀请的研究搭档泰勒鼓励他再坚持一个月。就在截止日到来之前两周, 9月19日 ,一个星期一的早晨,怀尔斯发现了问题的答案,他叙述了这一时刻:“突然间,不可思议地,我发现了它……它美得难以形容,简单而优雅。我对着它发了20多分钟呆。然后我到系里转了一圈,又回到桌子旁看看它是否还在那里——它确实还在那里。”
  怀尔斯的证明为他赢得了最慷慨的褒扬,其中最具代表性的是他在剑桥时的导师、着名数学家约翰·科茨的评价:“它(证明)是人类智力活动的一曲凯歌”。
  一场旷日持久的猎逐就此结束,从此费马大定理与安德鲁·怀尔斯的名字紧紧地被绑在了一起,提到一个就不得不提到另外一个。这是费马大定理与安德鲁·怀尔斯的因果律。
  历时八年的最终证明
  在怀尔斯不多的接受媒体采访中,美国公众广播网(PBS)NOVA节目对怀尔斯的专访相当精彩有趣,本文节选部分以飨读者。
  七年孤独
  NOVA:通常人们通过团队来获得工作上的支持,那么当你碰壁时是怎么解决问题的呢?
  怀尔斯:当我被卡住时我会沿着湖边散散步,散步的好处是使你会处于放松状态,同时你的潜意识却在继续工作。通常遇到困扰时你并不需要书桌,而且我随时把笔纸带上,一旦有好主意我会找个长椅坐下来打草稿……
  NOVA:这七年一定交织着自我怀疑与成功……你不可能绝对有把握证明。
  怀尔斯:我确实相信自己在正确的轨道上,但那并不意味着我一定能达到目标——也许仅仅因为解决难题的方法超出现有的数学,也许我需要的方法下个世纪也不会出现。所以即便我在正确的轨道上,我却可能生活在错误的世纪。
  NOVA:最终在1993年,你取得了突破。
  怀尔斯:对,那是个5月末的早上。Nada,我的太太,和孩子们出去了。我坐在书桌前思考最后的步骤,不经意间看到了一篇论文,上面的一行字引起了我的注意。它提到了一个19世纪的数学结构,我霎时意识到这就是我该用的。我不停地工作,忘记下楼午饭,到下午三四点时我确信已经证明了费马大定理,然后下楼。Nada很吃惊,以为我这时才回家,我告诉她,我解决了费马大定理。
  最后的修正
  NOVA:《纽约时报》在头版以《终于欢呼“我发现了!”,久远的数学之谜获解》,但他们并不知道这个证明中有个错误。
  怀尔斯:那是个存在于关键推导中的错误,但它如此微妙以至于我忽略了。它很抽象,我无法用简单的语言描述,就算是数学家也需要研习两三个月才能弄懂。
  NOVA:后来你邀请剑桥的数学家理查德·泰勒来协助工作,并在1994年修正了这个最后的错误。问题是,你的证明和费马的证明是同一个吗?
  怀尔斯:不可能。这个证明有150页长,用的是20世纪的方法,在费马时代还不存在。
  NOVA:那就是说费马的最初证明还在某个未被发现的角落?
  怀尔斯:我不相信他有证明。我觉得他说已经找到解答了是在哄自己。这个难题对业余爱好者如此特别在于它可能被17世纪的数学证明,尽管可能性极其微小。
  NOVA:所以也许还有数学家追寻这最初的证明。你该怎么办呢?
  怀尔斯:对我来说都一样,费马是我童年的热望。我会再试其他问题……证明了它我有一丝伤感,它已经和我们一起这么久了……人们对我说“你把我的问题夺走了”,我能带给他们其他的东西吗?我感觉到有责任。我希望通过解决这个问题带来的兴奋可以激励青年数学家们解决其他许许多多的难题。
  iv
  谷山-志村定理(Taniyama-Shimura theorem)建立了椭圆曲线(代数几何的对象)和模形式(某种数论中用到的周期性全纯函数)之间的重要联系。虽然名字是从谷山-志村猜想而来,定理的证明是由安德鲁·怀尔斯, Christophe Breuil, Brian Conrad, Fred Diamond,和Richard Taylor完成.
  若p是一个质数而E是一个Q(有理数域)上的一个椭圆曲线,我们可以简化定义E的方程模p;除了有限个p值,我们会得到有np个元素的有限域Fp上的一个椭圆曲线。然后考虑如下序列
  ap = np − p,
  这是椭圆曲线E的重要的不变量。从傅里叶变换,每个模形式也会产生一个数列。一个其序列和从模形式得到的序列相同的椭圆曲线叫做模的。 谷山-志村定说:
  "所有Q上的椭圆曲线是模的"。
  该定理在1955年9月由谷山丰提出猜想。到1957年为止,他和志村五郎一起改进了严格性。谷山于1958年自杀身亡。在1960年代,它和统一数学中的猜想Langlands纲领联系了起来,并是关键的组成部分。猜想由André Weil于1970年代重新提起并得到推广,Weil的名字有一段时间和它联系在一起。尽管有明显的用处,这个问题的深度在后来的发展之前并未被人们所感觉到。
  在1980年代当Gerhard Freay建议谷山-志村猜想(那时还是猜想)蕴含着费马最后定理的时候,它吸引到了不少注意力。他通过试图表明费尔马大定理的任何范例会导致一个非模的椭圆曲线来做到这一点。Ken Ribet后来证明了这一结果。在1995年,Andrew Wiles和Richard Taylor证明了谷山-志村定理的一个特殊情况(半稳定椭圆曲线的情况),这个特殊情况足以证明费尔马大定理。
  完整的证明最后于1999年由Breuil,Conrad,Diamond,和Taylor作出,他们在Wiles的基础上,一块一块的逐步证明剩下的情况直到全部完成。
  数论中类似于费尔马最后定理得几个定理可以从谷山-志村定理得到。例如:没有立方可以写成两个互质n次幂的和, n ≥ 3. (n = 3的情况已为欧拉所知)
  在1996年三月,Wiles和Robert Langlands分享了沃尔夫奖。虽然他们都没有完成给予他们这个成就的定理的完整形式,他们还是被认为对最终完成的证明有着决定性影响。

470
1996
费马大定理
主演:Andrew Wiles,Barry Mazur,Kenneth Ribet
直升机在行动
399
10.0
HD
直升机在行动
10.0
更新时间:2023年11月02日
主演:马丁·辛
简介:

  Agusta 109K2: Alpine Medivac Rescue
  Straight Up's exploration of vertical flight begins with a high-impact alpine rescue amid an avalanche. The dramatic opening sequence documents the dangerous work of the Rega mountain rescue team and the invaluable role of the Agusta A109K2 helicopter in saving lives and minimizing injuries.
  As the camera pans over beautiful vistas of the snow-covered Swiss Alps, it cuts to a cornice, as a chunk of snow breaks free, triggering an avalanche. The tranquil scene is shattered as the avalanche thunders down the mountain slopes. With terrifying speed, it heads straight for a mother and child trapped in their car, wheels spinning on the icy road.
  The mother calls for help on her cell phone, and a second call from a snowplow prompts radio dispatch. The Rega mountain rescue team already is airborne en route to the scene, the red cross painted on the helicopter's white underbelly signaling that medical help is on the way. The mother escapes, but her son is missing. Within minutes of the helicopter landing, the rescue team dig out the car, extract the trapped boy, apply first aid, and airlift him and his mother to safety.
  A significant mountain hazard, avalanches are responsible for many deaths each year. Time is of the essence in avalanche rescue work. A person has a 90 percent chance of survival if found within the first 15 minutes, but one's chances of survival diminish with each passing minute. Not only do helicopters provide quick access for rescue teams, they also provide a lifeline to medical care. Flying the injured to the nearest hospital as rapidly as possible is not the only type of rescue operation; often helicopters bring the hospital to the injured, who receive treatment at the scene.
  The powerful avalanche was shot in British Columbia's Selkirk Mountains under the supervision of the Canadian Avalanche Association. The CAA controls avalanche risk for the safety of heli-skiers. To capture the avalanche head-on, avalanche expert and filmmaker Steve Krochel and David Douglas developed a quarter-inch-thick steel container for the IMAX camera, which was equipped with a triggering device and a beeper so that the camera could be found once the avalanche had swept it down the mountain.
  The rescue was completed in Switzerland's Bernina Pass near the Italian border. Filming the Rega rescue helicopter air-to-air sequence turned into an international excursion as Douglas chased the sunlight over Italy in one direction and in Austria in another before setting down in Switzerland. In another dramatic shot, Douglas centered the red cross in the crosshairs of the camera lens as the craft descended. To facilitate this shot, Douglas dug a hole in the snow large enough to accommodate himself and the IMAX camera. Inside the hole, 3 feet below the helicopter, he filmed its takeoff.
  According to Douglas, "The helicopter is the instrument of rapid response to natural physical and social disasters around the world, alleviating human suffering on a major scale. For the individual caught beyond the limits of training or equipment, often the last chance for survival is the hope that a helicopter will get to them in time. "
  The Pitcairn PCA 2, "Miss Champion"
  For centuries humans dreamed of flight. The Chinese, in the 12th century, developed a toy helicopter made from a pair of slats mounted on a stick, but serious efforts had to wait until the early 20th century. Then, after the Wright brothers' historic flight at Kitty Hawk, we dreamed of flight unfettered by the limitations of runways and airports. Yet by the early 1930s we were still at the dawn of the practical rotorcraft, which promised to give form to humanity's vision.
  The ten year period between 1925 and 1935 was an exciting time in aviation history, but few aircraft so caught and held the public's attention, as the Autogiro. Nicknamed the "flying windmill," this strange-looking aircraft was first successfully flown in 1923 by the Spanish inventor, Juan de la Cierva, who had been working on the development of such a craft since 1919. The Autogiro fascinated the air-minded public because of its remarkable performance and high degree of safety, attracting such leaders of American aviation as Charles Lindbergh and Amelia Earhart.
  Juan de la Cierva sold the American manufacturing rights to Harold Pitcairn in 1928. Pitcairn's Autogiro boasted a more modern fuselage with better aerodynamic qualities. It also provided prospective buyers with a choice of either a 300- or 420-horsepower engine.
  In the film, Harold Pitcairn's son Stephen flies "Miss Champion," a 1931 model. This Autogiro, used for promotion by the Champion Spark Plug Company, is controlled like an airplane, but is lifted with blades. Although the original rotor blades have seen 1,600 hours of flight time, they are still airworthy. With a 330-horsepower Wright R 975-E engine, the Autogiro has a cruising speed of 98 mph and a top speed of 118 mph. "Miss Champion" led a National Air Tour and made the then-risky 300- mile-long flight from Miami to Havana, Cuba. (Until then, the longest over-water flight by an Autogiro had been 25 miles in length.) Later, "Miss Champion" flew nonstop over a distance of 500 miles to Chichen Itza in the Yucatan rainforest. "Miss Champion" was retired from active service in 1932 after setting a new altitude record for rotary-wing aircraft. Climbing to a height of 21,500 feet in 1932, the Autogiro surpassed the previous record set by Amelia Earhart. Today, the Autogiro is considered to be the evolutionary "missing link" from which the practical helicopter was born.
  Forty years later Stephen Pitcairn began the formidable task of collecting and restoring examples of his father's aircraft. He tracked down "Miss Champion" and in October of 1982 began the painstaking task of restoration, using the original Pitcairn factory drawings. In the spring of 1985 "Miss Champion" flew again.
  The Bell 47G: A Flying Lesson
  Since Pitcairn's Autogiro, improved control systems allow the airframe to rise directly from the ground with a powered rotor. Straight Up! puts you in the pilot's seat of a Bell 47G as the basic elements of helicopter operation are demonstrated. The Bell 47G's single-rotor configuration is by far the most common type used today. Your flying lesson begins.
  As a helicopter pilot, the pilot uses all four limbs to fly, all at the same time! With the left hand holding the collective pitch control lever, he pulls up ever so slightly, and we go straight up into a slow-motion hover. The spinning rotor blades act as small wings, but they spin so fast that they create one continuous disc of lift. When the blades change angle, or pitch collectively, the helicopter rises or falls. The pilot's right hand always holds the cyclic control, effectively tilting the whirling disc above. Point left, tilt left. Point right, tilt right. The camera then closes in on the tail rotor. Once again, the altering of the blades affects direction. The chopper spins in response to the pilot's depressing one of the two foot pedals. If he depresses the second pedal, the helicopter spins in the opposite direction.
  The Piasecki H-21B Tandem Rotor Aircraft, "The Flying Banana"
  The last flying H-21B helicopter in the world takes off, heads for the beach and cruises 100 feet above the Pacific surf off the coast of California. One of the earliest tandem helicopters, the H-21B represents the birth of the heavy lift helicopters and dates back to the early 1950s. Nicknamed "The Flying Banana" for its shape, the H-21B had more power and greater stability than previous helicopters. The tandem-rotor H-21B carries two sets of wooden blades situated nearly 50 feet apart but operated by one set of helicopter flight controls. The pilot must be ever vigilant, as this helicopter could rapidly invert should the pilot let go of the controls.
  The vintage H-21B used for the film was decommissioned from the U.S. Air Force in 1972 and was restored by the California-based Classic Rotors: The Rare and Vintage Rotocraft Museum. This nonprofit museum and restoration facility, dedicated to the preservation of unique, vintage and rare rotorcraft, spent more than 10,000 hours returning the H-21B to airworthiness. Every hour flown requires 100 hours of maintenance. Classic Rotors is the only museum of its kind to maintain eight helicopters in flying condition. When its new facility in San Diego has been completed, the museum will expand its exhibits from 15 to 30 vintage rotorcraft.
  One of the highlights of its collection is a famous relative of the H-21B. This is a V 44 (the commercial version of the H-21)-nicknamed "The Holy One"-and is the only one to land at the Vatican and be blessed by the pope. While on a 1959 demonstration tour in Europe, the helicopter and its crew had provided help to Italian communities following a devastating earthquake.
  Future Helicopter Designs
  One aspect of current research centers around the development of "quiet technology" that will allow helicopters to become better neighbors and to operate more stealthily in police and military operations.
  Quiet technology advances rely on a combination of technologies, which include improved rotor blade design and the user of rotor systems with four or more blades. Replacing the tail rotor with a Coanda-effect NOTAR (NoTailRotor) system goes a long way in reducing noise, as does shrouding the tail rotor in an arrangement know as a "fan-in-fin." Other advances focus on noise-dampening air inlets and improved engine nozzles.
  New helicopter designs are tested in the world's largest wind tunnel at the NASA Ames Flight Research Center located at Moffett Field in California. Ames was founded in 1939 as an aircraft research laboratory of the National Advisory Committee for Aeronautics, which became part of the National Aeronautics and Space Administration (NASA) in 1958. NASA has the leading role in aerospace operations systems, which include air traffic control, flight effects on humans, and rotorcraft technology. NASA Ames scientists and engineers study robotic helicopters, high-speed hybrids, and advances in quiet technology. The center also has major responsibilities for the creation of design and development tools and for wind tunnel testing.
  The NASA-Bell XV-15 Tilt-rotor
  In the film, an XV-15 converts over Dallas-Fort Worth Airport. The XV-15 is an experimental rotorcraft, the parent of a new family of aircraft called "tilt-rotors." The tilt-rotor combines the hovering ability of the helicopter with the speed of a fixed-wing aircraft. The XV-15 can take off and land like a helicopter. The audience will see the engines tilting forward as the tilt-rotor becomes a high-speed plane.
  The Bell-Boeing V-22 Osprey
  A V-22 Osprey unwraps, emerging like a prehistoric flying dinosaur. Built primarily for the U.S. Marines, Air Force, and Navy, the V-22 Osprey has wings that pivot and rotors that fold to facilitate its storage at sea. In less than 90 seconds, you will see the V-22 complete this process. Although still classified as a tilt-rotor, it is faster, with three times the range and more than ten times the payload of its predecessor. It shows the promise of long-distance travel, without airports.
  The Hawk 4 Gyroplane
  Rotorcraft evolution is also in the hands of the entrepreneur, and this independent spirit is most evident in the Hawk 4 Gyroplane. While some designs produce groundbreaking changes, this aircraft brought the economy and safety of the Autogiro into the space age. A rotor is used for slow-speed flight, but at high-speed cruising all the lift is provided by the wing while the rotor has no lift. The Gyroplane shows promise as a high-speed, low-disc-loading rotorcraft.
  The Boeing-Sikorsky RAH-66 Comanche
  The Comanche rips and dips across the screen, set against a sunset. This prototype helicopter has stealth technology. It's smart, agile, fast and invisible to radar. It's the first helicopter to provide real-time digital data to headquarters. Seeing in the dark, sensing the forces at play around us and acting on the evidence in real time, the Comanche is a complex flying machine with a human being at its heart. Everyday, in unexpected ways, it extends our powers and puts us to work with a revolutionary tool.
  The Comanche is the central element of the U.S. Army's future Objective Force. In addition to its complement of missiles and 20-mm cannon, the aircraft carries state-of-the-art sensors and avionics to provide battlefield commanders with so much accurate information about enemy movements. This knowledge will translate into more precise targeting, increasing the effectiveness of friendly forces beyond current capabilities.
  The U.S. Army has defined a requirement of more than 1,200 Comanches for the Objective Force. The RAH Comanche, the army's 21st-century combat helicopter is being developed by the U.S. Army and a team of leading aerospace companies headed by the Boeing Company and Sikorsky Aircraft Corporation, a unit of United Technologies Corporation.
  The Sikorsky UH-60 Black Hawk and AS 350 B2 AStar Enforce the Law
  Events swiftly unfold as the radar plane spots an "unidentified" Cessna dropping bundles of drugs off the coast of Miami at dawn. A signal alerts the Marine and Air Branch of U.S. Customs who speed out to intercept the smugglers. Just as the drugs are transferred from boat to van, The AStar helicopter bursts over the treetops, deploying a tactical team to arrest the driver. While the smuggler's Cigarette boat attempts to escape, a Black Hawk helicopter dips down to create a giant backwash. In a stunning display of impeccable teamwork, this action forces the fleeing boat to swerve to a halt as a Customs boat cuts it off and apprehends the criminals.
  On a typical day, the U.S. Customs Service examines 1.3 million passengers, 2,642 aircraft, 50,889 trucks/containers, 355,004 other vehicles, 588 vessels, 64,923 entries and undertakes the following enforcement actions: 64 arrests, 107 narcotic seizures, 223 other seizures, 9 currency seizures. These amount to 5,059 pounds of narcotics, $443,907 in currency, $228,803 in conveyances, $525,791 in merchandise and more than $15,800 in arms and ammunition.
  Filmed over a period of five days off the coast of Miami, the air, land, and sea drug bust was staged by the U.S. Customs Service, which relies heavily on helicopters during such operations.
  U.S. Customs pilot, Tom Stanton, participated in the shoot with his co-pilot Kimberly Kessel. Kessel is one of seven women U.S. Customs pilots and only one of two qualified to fly Black Hawks. Both pilots volunteered to work with the film crew. Says Kessel, a graduate of Embry-Riddle Aeronautical University, "They were phenomenal, ready to try anything."
  In addition to daytime flights, Stanton flies the riskier night missions. "Flying at night is dangerous as you lose all perception of what's up or down because both the sky and ocean are black, so they just kind of run in together. There's no horizon on those dark nights," says the veteran pilot.
  Typically he flies from 300 to 500 feet above the water at 120 to 150 knots. "Not many people fly that low, even in the daytime," says Stanton. "There's no autopilot, so it's hands on. Plus you're chasing someone. You have to be aware. It can get tense out there."
  Stanton describes an air chase: "Once there's a target, we launch a jet with radar. The jet pilot calls the helicopter out and we link up, flying in formation. We follow the bad guy wherever he goes. If he has extended-range fuel tanks, we leapfrog and send another helicopter out to take up the chase. (The Black Hawk carries five hours of fuel.) When he gets into his landing configuration, we call the local police or sheriff to help us out." The Black Hawk, which can carry up to 14 people, typically carries 4 or 5 armed personnel, "so we instantly have a force of police officers there to get the bad guys."
  "If it's a boat, we have Cigarette boats like the smugglers. We'll call our boat and have it intercept." Stanton flies the Black Hawk next to the boat, making it hard for the smugglers to navigate. "It intimidates them into giving up. Sometimes they do [but] sometimes we chase them for hours. Or we'll follow them into a marina and block them until our boats come. If they hit the beach, we'll call the state police or sheriff, and they set up a perimeter so the guy can't get out."
  Stanton, who flies missions as often as once or twice a week, has been flying for 26 years, 13 of those as an army helicopter pilot before he joined U.S. Customs in Miami where he is the "standardization instructor pilot." He makes sure that everybody flies the same way, so that when they team up, the pilots easily work in tandem. Pilots fly 8-hour shifts and the operation goes on 24 hours a day, 7 days a week in areas covering both the Canadian and Mexican land borders, the Atlantic and Pacific coastlines, and the Gulf of Mexico.
  The MD 500E Helicopter
  A MD 500 helicopter hovers directly above 500,000-volt power lines. As it inches closer, a lightning bolt suddenly zaps out from the hot line, arcing toward the wand extended by a lineman perched on an aluminum platform that juts out from the helicopter. The "hot-line-qualified" lineman clamps onto the power lines, and helicopter backs off, leaving him to "wire walk," crawling along parallel lines to inspect the PPL power line grid, 100 feet off the ground. To reboard the helicopter, the lineman must "bond off," reversing the procedure.
  "I don't give two hoots and a holler about flying inside a helicopter. Put me outside, that's where I want to be," says Daniel "Spider" Lockhart, AgRotors lineman. There's only three things I've been afraid of most of my life: One was electricity, one was heights and the other was women. And, I'm married too," he grins. "The safest lineman is one that is afraid of electricity. When we bond to the power lines energized at half-a-million volts, we have to bring ourselves to the same potential. That is why you see that arc jumping out to our wand as we make both the helicopter and the power line at the same potential, so that we can eliminate the flow of current," explains the veteran lineman.
  Spider wears a protective hot suit, 75 percent Nomex for fire retardation and 25 percent stainless steel thread. "The metal thread basically means I have a cage around me that can be energized at very high voltage levels. A half-million volts pass over my body, but I can work without interference from the electricity."
  He continues, "Watching that electricity jump out while you're energizing the helicopter is a thrill. Getting on the wire, walking the wire to do repairs is a thrill. The biggest thrill I get is from doing what I do is being able to do both together-the electrical part and the helicopter part of it, the speed at which we can do it and still be safe. There are so many things that the helicopter enables us to do as linemen, which is very rewarding."
  The teamwork of the skilled helicopter pilots and highly trained linemen ensure that the PPL Corp. provides a constant source of electricity to its 1.3 million customers in Pennsylvania (in addition to 4.4 million in Latin America and Europe). To maintain the integrity of the transmission system to residential and commercial establishments, and to ensure the safety of the operation, the team plans and rehearses every move while on the ground before takeoff. Even so, unanticipated gusts of wind and glare from the wires can affect the pilot's depth perception, requiring total concentration during his hours at the controls. As the helicopter is isolated from the ground, the pilot and lineman, clad in protective stainless steel suits, must bond onto the transmission lines to bring themselves to the same voltage potential of the line to work safely-paralleling what a bird does when it sits on a wire.
  Probably the most unusual place that the director rigged the camera was on the end of the platform on the MD 500, which is designed to carry the lineman as he bonds onto the half-million-volt power line. "We took away the lineman and put the camera in his place; the lineman rode behind the camera and used his wand to draw the arc of electricity right onto the camera lens. I don't think it's been done before. It blew all the electronics out of the camera a couple of times before we figured out how to do it," recalls Douglas.
  The Boeing 234 Helicopter: Helilogging with Limited Environmental Damage
  Floating above the forest in northern California, a 12-ton Boeing 234 helicopter selects its target with precision. Selective logging is a process where only a portion of the available timber is removed from a logging site. A single tree is lifted straight up from the forest floor, leaving the rest of the area environmentally intact. Removing such timber-very often trees that are already dead or diseased-allows the remaining trees to thrive on the additional resources of sunlight, water, and soil nutrients. Helilogging is environmentally friendly in other ways as well. First, since the logs are lifted from the ground, little soil erosion, typical of conventional logging methods, occurs. Second, in many cases the helicopter is able to use existing roads for landings, meaning no new roads need to be built into the area being logged.
  Columbia Helicopters cuts more logs each year than any other helicopter logging company. To prepare the timber for the helicopter, the specially trained logging crew cut it into carefully weighed sections. Columbia's flight crews are among the most experienced at long-line work in the world. With speed and precision, they are able to move heavy loads of logs at the end of lines up to 350-feet long. Once the line is lowered from the Boeing 234 helicopter, steel tongs clamp the log and the entire tree is removed without disturbing the balance of nature. "It's kinda like lookin' down 25 stories and picking up a telephone pole," comments the helicopter pilot, Dave Stroupe, who deposits the timber at a nearby transfer yard. "The unique thing about this helicopter is that, when we take off from the ground, we weigh approximately 22,000 pounds. And we're rigged for about 26,000 pounds when we get low on fuel. So the load actually weighs more than the helicopter. It's exciting and harrowing all at the same time."
  The Boeing 234s have a lift capacity of 28,000 lb, (12,727 kg), but most often carry loads between 23,000 lb, (10,454 kg) to 24,000 lb (10,909 kg) due to elevation and air temperature considerations. The company trains loggers to work with helicopters because load weight is such a dramatic part of what they do. Weight is determined, using a formula, which are a function of the volume and the type of wood. Different tree species have different weights per volume.
  When one of the pilots suggested using the log as a platform for the camera, Douglas realized another exciting camera angle. The possibility existed that the branches could scrape off the camera as the log was hauled up. Douglas prevented this by placing the camera inside a heavy steel avalanche box, which he anchored on the end of a big log. Once the log was grappled, the helicopter hauled the protected camera right through the branches, giving the audience a breathtaking view from the perspective of the log! The U.S. Marine Corps AV-8B Harrier, AH-1W Cobra, CH-53E Super Stallion and CH-46E Sea Knight on a Military Mission
  An AV-8B Harrier jet demonstrates its vertical landing ability followed by a force reconnaissance inservice exercise from an aircraft carrier, as Marines climb aboard the CH-53E. AH-1W Cobras and Harriers form an assault-support package, as the reconnaissance team sets out on a mission to obtain invaluable intelligence about the enemy.
  Inside the CH-53E, the machine-gunner is at the ready as a Cobra fires three rockets. The action heats up as the IMAX camera captures the Marines fast-roping through the "hell hole" and sliding down a rope dangling from the CH-53E, landing in enemy territory. The leader of the reconnaissance team says, "By the time you get to touch rope in a live situation, you and your men feel tighter than family. Your fates are tied like the strands of a rope."
  Two hours later the Marines have completed their mission and are ready to be evacuated. Now the enemy hunts them on the ground. Trees shake as the rescue CH-53E helicopter hovers overhead, lowering a rope to the squad, now up to their waists in water. One after the other, in a matter of seconds, the men clip themselves onto the rope. "Extraction, even more than insertion, is when you need speed. You've been awful quiet. Suddenly, you're awful loud," says Sgt. James Kenneke, the squad leader. He's first in and last out. Lifted up, like washing on a line, the squad dangles beneath the helicopter as it is escorted by Cobras, out over the Atlantic.
  "It's a relief to get out. But there's that moment of doubt. Everything slows down while you're exposed � holding your breath for that happy ending. And when you get it, you feel on top of the world. Of course, then we've got to commute home just like everybody else," smiles Kennecke.
  The Mi-26 and Mi-8 Deliver Humanitarian Aid
  Sometimes, something very precious must be delivered behind enemy lines-food. Sierra Leone is a nation that has suffered years of conflict. From the food depot to the hot spot, helicopters provide an air bridge. Hoisting food and medical supplies to distressed people behind rebel-held territories, they have the ability to hop over hot zones in desperate situations.
  The world's largest production helicopter-the Russian-made Mi-26-is the workhorse for the United Nations (UN) peacekeeping operation in war-torn Sierra Leone. The heaviest production helicopter in the world, this majestic eight-bladed craft-one of four chartered by the UN from Russia-can carry a maximum of 44,090 lb (20,040 kg) of internal payload or up to 70 troops. The Mi-26's top speed is 183 mph (295 kph) and it has a range of 304 miles (400 km).
  In this sequence, the Mi-26 is loaded with cargo to supply UN troops protecting an isolated community in the center of rebel-held territory. The world's largest food agency, the UN World Food Program (WFP), organized a massive air campaign targeting internally displaced persons that had congregated near a clinic for malnourished children. Once rebels from the Revolutionary United Front (RUF) had surrounded the area and blocked road access, the WFP was prevented from completing a bulk distribution. Instead, they loaded up their Mi-8 and flew to the Daru clinic where the most vulnerable women and children were located.
  "All children under five who are malnourished are given a special feeding program in Daru. And the under-five are always the first ones you target for any kind of extreme malnourished cases, because they die very quickly," says Aya Shneerson, program officer for the WFP. "Daru is a kind of an island, a safe island, surrounded by areas that are unsafe," she says, "and for that reason, it always served as a sort of magnet for the very vulnerable people coming out."
  Another big WFP operation, Food for Peace, gives food to child ex-combatants, in an effort to attract them to disarmament and demobilization camps.
  The heavily laden craft flew out of the capital city, Freetown, situated on the west coast of Africa between Guinea on the north and Liberia on the south. The WFP supervises a variety of feeding programs in the displacement camps, feeding 5,000 in an operation that targeted Bunbuna, Kabala and Daru in 2000.
  Throughout the world, helicopters have saved millions of human lives. There are 777 million people in developing countries, according to the WFP. In 2001 the WFP fed 77 million hungry people (10 percent of the hungry poor) in 82 countries.
  Diamonds, which should have brought prosperity to Sierra Leone, instead resulted in one of the modern world's most brutal insurgencies, dating back to 1991 when rebels launched a war to overthrow the government. In the ensuing years, continuous battles between the various factions-rebels, the army and the government-displaced tens of thousands of innocent civilians, resulting in hunger and famine. In 1998 UN observers documented reports of ongoing atrocities and human rights abuses. In 1999 negotiations began between the government and the rebels, and an agreement was signed in Lome to end hostilities and form a government of national unity. By 2000, the UN's expanded role resulted in the deployment of 17,500 military peacekeeping personnel to various parts of the country. Free elections in May 2002 have given hope and a fresh started in Sierra Leone.
  The AS 350 B2 and AS 350 B3 Used for Wildlife Relocation
  In South Africa, helicopters are helping to save the black rhino from extinction. Protected in a few remote preserves, their numbers are rising. However, should the rhinos feel overcrowded, they will fight to the death. To protect the species, some must be relocated to safe habitats, but this is easier said than done.
  A platform dangles from a helicopter overhead. Inside another helicopter, flying low over the South African veldt, a man with a rifle takes aim at a black rhinoceros, dodging through the bushes below. The pilot concentrates on flying 5 feet above and 10 to15 feet behind the rhino. Anticipating its every move, a wildlife veterinarian pulls the trigger of his gun loaded with a tranquilizer dart, scoring a direct hit that successfully penetrates the rhino's inch-thick skin.
  "When I am darting animals like the black rhino, there is this immense trust between myself and Piet, the pilot," says wildlife veterinarian, Dr. Douw Grobler, who specializes in immunizations and translocations. "I know exactly what he's going to do and where he's going to place me. I don't have to think. I can just concentrate on the animals. I just know he's gong to put me there in the right spot at the right time. It's almost that he senses what the animal's going to do. In that way, he can change the animal's mind with his helicopter."
  Grobler has measured a specific drug dosage, which can keep a rhino asleep for up to two hours. Once the rhino is darted, the ground crew lands as soon as possible to undertake a multitude of tasks. They monitor the beast's vital signs, take skin and blood samples to study its basic health and to detect any nutrients that are lacking. This ensures that the habitat is healthy for long-term propagation. They also conduct pregnancy testing. Each rhino's ear is notched so that it can be identified easily from the air and ground. The tip of the second horn is removed to provide material for genetic research, and a transmitter is fitted into the rhino's horn for tracking its whereabouts. Poachers present a constant danger to the rhinos' security. Should a poacher remove the horn for export, the transmitter would trigger an alarm.
  When two males inhabit the same territory, one must be relocated before they battle to the death. Placing a sling in position, the crew rolls the rhino aboard the platform, making sure it is fully asleep. With a lifting capability of 3,500 lb (1,590 kg), the AStar B 3 can relocate the 2,250-lb (1022-kg) rhino to an area of the sanctuary that is accessible only by helicopter.
  The extensive research on eleven black rhinos acquired during the four-day shoot was made possible only through SK Film's financial contribution. "My field of expertise lies in the capture and relocation of African wildlife. I am extremely grateful to Straight Up! for sponsoring this incredibly important research and relocation program at the game park. Without the film, this research would not have happened," says Grobler, who organized the capture, research and relocation project, with the film's production crew. "Every animal is just so valuable," he says, "and any information that can be collected on them is worth its weight in gold."
  The prehistoric ancestor of today's rhinos existed more than 50 million years ago. Among today's five rhino species, the black rhino, which has two horns, has suffered the most spectacular rate of decline. From a population of 65,000 in 1970 it had been hunted almost to extinction, declining to a population of 2,300 by 1992-93. Current statistics indicate that the African black rhino population has risen to 3,500 as a result of the protection of nature reserves, developed by conservancy groups, agencies and governments to facilitate breeding and relocation programs.
  This segment of Straight Up! was filmed in one such reserve in South Africa, where black rhinos had been reintroduced in 1986. The helicopter, an irreplaceable co

3120
2002
直升机在行动
主演:马丁·辛
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