2/27/2005 01:17:00 am|W|P|CHERUB|W|P|《自然哲学之数学原理》是牛顿一生中最重要的科学著作,书中构建了科学有史以来第一个完整的、科学的宇宙论和科学理论体系,并试图用统一的力学原因解释从地面物体到天体的所有运动和现象,它所造成的影响极其深远。 1986年,这部划时代巨著出版整整三百周年,英国皇家学会专门举办了隆重的纪念大会。在这次大会上,著名的流体力学权威詹姆士.莱特希尔爵士发表了令人震惊的道歉宣言。他说:“今天,我们深深意识到,我们 的前辈对牛顿力学惊人成就的崇拜,促使他们认为世界具有可预见性,的确,我们在1960年以前大都倾向于相信这个说法,但现在我们知道这是错误的。我们曾经误导了公众,向他们宣传说满足牛顿运动定律的系统是决定论的,可在1960年后这已被证明不是真的,为此,我们愿意向公众表示道歉。”这种看似出乎意料的举动,却是发展着的科学的一种正常的表现,实际上是科学对自身发展的一种反思。 当科学从牛顿时代走来,辉煌的成功使得它得意忘形,认为自己终将具有预测一切的能力:万事万物都已经由物理定律规定了下来,一个细节都不能 更改。过去、现在和未来都像已经写好的剧本,宇宙的发展只能严格地按照这个剧本进行,不允许加以任何的发挥。这就是牛顿力学的可预见性假设,是决定论的或者说是确定论的牛顿力学送给我们的礼物。18世纪,法国著名科学家拉普拉斯曾以此为依据豪迈地宣告:如果已知宇宙中每一粒子的位置和速度,我就能够预测整个宇宙的未来。 这一美好的图景在20世纪变得黯淡了许多,先是遭遇量子论的严重挑战,随后又被兴起的混沌学彻底击碎。 1963年,美国气象学家洛仑兹建立了一个描述大气对流状况的数学模型,叫洛仑兹动力学方程。这是一个简单确定性方程。说它简单,因为它只有三个变量用来分别代表大气中的风速、温度和气压;说它是确定性的,因为它不含有任何随机项,初始值也可以给定。但就是由这个方程所描述的只有三个变量的简单确定性系统里,却让我们出乎意料地见到了混沌,见识了混沌非比寻常的特性。 洛仑兹动力学方程描绘出的运动轨迹,具有一种奇特的形状,象一只展开了双翼的蝴蝶,在中国科技馆里有这个运动轨迹的动态展示。在这个奇妙精巧的蝴 蝶上,确定性和随机性被有机地结合在一起:一方面,运动的轨迹必然落在“蝴蝶”上,绝不会远离它们而去,这是确定性的表现,表明系统未来的所有运动都被限制在一个明确的范围之内。另一方面,运动轨迹变化缠绕的规则却是随机性的,任何时候你都无法准确判定运动的轨迹将落在“蝴蝶”的哪一侧翅膀上的哪一点上。也就是说,这个系统运动大的范围是确定的,可预测的;但是运动的细节是随机的,不可预测的。 可以用想象来体验这种感受:你,正在天安门广场上等一辆公共汽车。这辆车正在绕着北京城不停地行驶。你知道它肯定会来,而且将重 复地经过广场,但你却不知道究竟该到哪一个地方去等它,因为它每次在广场上停靠的地点都是不确定的。奇怪之处并不是这种不可预测性本身,而在于你知道驾车的司机是个极为严谨的人,他在一丝不苟地按照一个极为确定的指令——洛仑兹动力方程驾驶他的汽车。换句话说,最让人奇怪的地方是,不可预测性这种本来应该是随机性系统才会具有的特性,却堂而皇之地出现在确定性系统中了。 混沌学的研究指出,具有这种奇怪特性的系统就是混沌系统,只有混沌系统才会在仅有区区几个变量(三个以上)的简单确定性系统中出现随机性,而且,这种随机 性是确定性系统内在的随机性。 确定性系统内在的随机性具有两方面的含义,一是说它出现在一个没有受到任何外力作用的简单确定性系统中。二是说它与普通的随机性相比有根本的不同。对于普通的随机性来说,当认识深入,所能收集到的信息量增大时,它的随机性就有可能降低,甚至完全消失。而对于内在的随机性,你就是搜集再多的信息,也不能使这种随机性降低或者消失。因此,它是所在系统的一种根本的、内在的、无法根除的性质。 以往,当我们面对一个因素众多的系统时,能够为无法把握它找到借口:“对它的了解还有待深入”,但同时也充满希望:“早晚有一天会彻底认识它,从而预测它的整个行为。” 确定性系统内在随机性的发现却将我们的希望变成了奢望,它实际上告诉我们,哪怕只有区区三个变量,只要有非线性作用其中,你就不要指望对系统运动的细节了如指掌,更不要奢望预测它精细的未来。 定神想想,你我一定都有过这样的体验:当你最不想为人们所关注时,却阴差阳错地成为事件的焦点;当你尽心尽力、小心翼翼做一件事时,却在最后一刻功败垂成;… …;总之,“如果坏事有可能发生,不管这种可能性多么小,它总会发生,并造成最大的损失。”这就是大名鼎鼎的墨菲定律。自1949年在玩笑中诞生之后,墨菲定律的不时应验总让人们感到困惑,是什么造成了这种不确定性?现在,混沌学给我们解了惑,它告诉我们这是复杂系统的内在随机性造成的。正是内在随机性导致的不可预测性使人无法准确地操纵和控制局面。 以2004年末发生的印度洋大地震为例,依照板块构造理论,在板块的边缘出现断裂而引发地震是极为正常的,苏门答腊岛正位于板块的边缘,因此发生地震本身并不令人吃惊,然而 ,在这个时间,在这个岛上,发生这样大烈度的地震,却无法从板块构造理论中推测出来。这实在令人沮丧! 不过,内在随机性的存在虽然导致一些“坏”的不确定性的出现,但同时也打开了另一扇门:你可能与千载难逢的好机会迎头碰上。(当然,遇上机会并不一定就能成功,还要看你能不能发觉和把握机会,可这并非我们现在要说的话题。)最明显的表现是在艺术家身上,当画家、诗人、作家和作曲家处身于混沌之中时,创造力最为活跃。混沌中的内在随机性蕴含着创造性。 内在的随机性并不会让我们陷入不可知论,因为混沌仍是有规律的;却把我们从盲目乐观的可预见性幻想中唤醒。这种来自牛顿力学的幻想已经使人类沉醉了三百年,并将世界简化到失真的地步,而现在世界将在一定程度上恢复其原有的复杂性。|W|P|110946706495255022|W|P|内在的不确定性|W|P|2/18/2005 12:56:00 am|W|P|CHERUB|W|P|It's been tested thoroughly. Successful! the following codes are in CPZDoc.cpp #include "ChildFrm.h" //... // new document CMultiDocTemplate* pMultiDocTemplate = (CMultiDocTemplate*) GetDocTemplate(); CPZDoc* pNewDoc = (CPZDoc*) pMultiDocTemplate->CreateNewDocument(); // modify new document content here // new view connected to this new document and display the view CChildFrame* pNewChildFrame = (CChildFrame*) pMultiDocTemplate->CreateNewFrame(pNewDoc, NULL); pMultiDocTemplate->InitialUpdateFrame(pNewChildFrame, pNewDoc, TRUE);|W|P|110868834054951994|W|P|Open a New Document and a New View|W|P|2/15/2005 02:57:00 am|W|P|CHERUB|W|P|expense: from 18.09.04 - 13.02.05 有账单的开销: 145.74 + 525.93 = 671.67 Pounds 有票据的交通开销: 108.35 + 25 = 133.35 Pounds + National Express online order 30.25 = 163.60 Pounds In total: 835.27 Pounds Rent: 200 * 6 + 60 = 1260 Pounds Phone: 12.5 *2 + 30 = 55 Pounds 轻易可查开销: 835.27 + 1260 + 55 = 2150.27 Easy Jet flight ticket : 106.62 So, 可查开销till now: 2256.89 Pounds (exclude flight ticket 350) Statement shows that: From family : 24390 Recent balance is : 22461.95 Total expense: 1928.05 income: 161.19(Javelin) + 42.24(University) + 50 (Tuition Fee rebound) + 154(Takeaway) = 407.43 Pounds Cash in hand : 209 Pounds Total balance: 22461.95(Bank) + 209(Cash) = 22670.95|W|P|110843629768577368|W|P|Life Expense|W|P|3/16/2005 07:25:00 pm|W|P|Blogger Angelina|W|P|Only 2000 pounds for half a year? I can't believe it!11/22/2005 05:32:00 am|W|P|Blogger job opportunitya|W|P|Powerful blog. The site was incredible and will be
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