求教心切。以下内容,词不达意。敬请指教!敬请批评! 同伦(Homotopy):统一场的一个下流解! 孙冰老师:您把俺吓尿了! 真傻昨天的博文《反思麦克斯韦经典电磁理论宣言》贴出之后,真的达到了“求教”目的! 孙冰老师 http://blog.sciencenet.cn/home.php?mod=spaceuid=3388899 2018-8-30 08:04 写到: 今天俺看到时,顿时惊呆了!三观尽毁!! 什么是物理学家要的“统一”? 什么是“统一”? wiki 百科里给出的圆锥曲线的一般形式: 矩阵形式: 可是,常见二次曲线的标准形式为: 困惑: 什么是“统一”? 此外,还有胡新平老师 2016 年的统一《一、二次曲线的轨迹统一及性质》。 同伦(Homotopy):统一场的一个下流解! https://en.wikipedia.org/wiki/Homotopy 百度百科对“函数的同伦”的解释: 苏联《数学百科全书》扩展版( wiki 版)里说: https://www.encyclopediaofmath.org/index.php/Homotopy A formalization of the intuitive idea of deformability of one mapping into another. More exactly, two mappings f and g are called homotopic (denoted by f ~ g ) ifthere exists a family of continuous mappings …… 把电磁理论作为一端,把引力理论作为另一端,用一个同伦( Homotopy )之后,引力-电磁居然被这样下流地统一了! 二次曲线,或多或少就是被这样“下流”地写出了一般的形式!! 统一:小心毁三观! 奥卡姆剃刀(简约法则, Occam's razor,Ockham's razor,Ocham's razor,law of parsimony ),到底该怎么理解? 简洁与美,美与真, ……,诸多观念,到底该怎么理解? 像二元二次曲线的一般形式一样,统一引力和电磁,算是统一吗?什么是我们想要的统一? 【用“泄露”的电磁相互作用,来表示“引力相互作用”:类似气体分子的瞬时偶极( instantaneous dipole )。】是真傻几年前给出的“物理”统一。 【或许在别的拟合函数形式下,引力-电磁的统一会变得容易?】是真傻 2018-01-15 之前给出的“数学”统一。 最后,真诚地感谢并祝福《科学网》!祝《科学网》越办越好! 《科学网》,就是我们的“奥林匹亚科学院( Akademie Olympia,Olympia Academy )”! 比 Conrad Habicht,Maurice Solovine 和 Albert Einstein 更好的奥林匹亚科学院! 相关链接: 圆锥曲线,百度百科 https://baike.baidu.com/item/%E5%9C%86%E9%94%A5%E6%9B%B2%E7%BA%BF Conic section, From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Conic_section 同伦,百度百科 https://baike.baidu.com/item/%E5%90%8C%E4%BC%A6 Homotopy. Encyclopedia of Mathematics https://www.encyclopediaofmath.org/index.php/Homotopy Homotopy, mathematics, Britannica.com https://www.britannica.com/science/homotopy Homotopy, From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Homotopy Homotopy, from Wolfram MathWorld http://mathworld.wolfram.com/Homotopy.html 胡新平. 一、二次曲线的轨迹统一及性质 . 数学通报, 2016, 55(12): 47-51, 54. 奥卡姆剃刀原理,百度百科 https://baike.baidu.com/item/%E5%A5%A5%E5%8D%A1%E5%A7%86%E5%89%83%E5%88%80%E5%8E%9F%E7%90%86 Occam's razor, From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Occam%27s_razor Occam's razor, philosophy, Britannica.com https://www.britannica.com/topic/Occams-razor 2018-08-29, 反思麦克斯韦经典电磁理论宣言 http://blog.sciencenet.cn/blog-107667-1131694.html 2018-01-15(2012-04-12), SI 基本单位中安培定义的两种可能缺陷----中科院科学智慧火花 http://idea.cas.cn/viewdoc.action?docid=4681 Olympia Academy, From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Olympia_Academy 感谢您的指教! 感谢您指正以上任何错误! 感谢您提供更多的相关资料!
客观存在的物质世界是统一的! 为了研究方便,有了“科学”。 当我们过于注重“分科”的时候,我们会离真理越来越远。 逻辑系统,是有明显局限性的。 演绎:结论蕴含在前提里; 归纳:完全性很难做到; 类比:只是部分的相似性。 实验高于逻辑:实践是检验真理的唯一标准。 例如,Mathematics The science of quantitative relations and spatial forms in the real world. Being inseparably connected with the needs of technology and natural science, the accumulation of quantitative relations and spatial forms studied in mathematics is continuously expanding; so this general definition of mathematics becomes ever richer in content. Mathematics. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Mathematicsoldid=23895 阿诺德: 俄罗斯人对知识、科学和数学的态度一直保持着俄语“ Intelligentsiya 的古老传统。这个词是其他语言中没有的,因为没有其他国家有一个类似的由学者、医生、艺术家、教师等组成的阶层,他们永远把为社会作贡献为先,个人名利在后。 俄罗斯数学传统的另一特点是倾向于全面地把数学看成一个充满活力的有机体。西方学界有可能一个人只是数学上某一方面的专家,而对相邻分支一无所知。一个学者涉猎较广在西方学界被看成一大缺点,而恰恰在俄罗斯一个学者研究领域太窄被看成同样程度的不足。 张永祥 ,2014-06-27,顶级科学大 师丝语: 俄罗 斯玩不玩CNS? 精选 http://blog.sciencenet.cn/blog-1076418-806951.html 感谢您的批评指正!
迈向力学与控制统一的数学与计算框架 Toward a Unified Mathematical and Computational Framework for Control and Mechanics Fei-Yue Wang The Key Laboratory of Complex Systems and Intelligence Science Chinese Academy of Sciences, Beijing, China Abstract This is a brief review on the recent book: Duality System in Applied Mechanics and Optimal Control , by Wan-Xie Zhong, published by Kluwer Academic Publishers , 2004. The book represents a significant effort to re-establish the historic and deep tie between control and mechanics by striving to connect and integrate concepts, methods, and algorithms in mechanics and control so that a unified framework can be established for both analytical and computational purposes. Clearly, it has demonstrated that the duality system method can be used as a mathematical and systematic foundation to deal with many important concepts and problems in both mechanics and control. This book is not only very useful for research and applications, but also extremely helpful for multidisciplinary curriculum development when students from one field are trying to learning and applying concepts and methods from the other field. Introduction Control and Mechanics have a deep and historical relationship ever since the birth of classical and modern control theory. Many great mathematicians had pioneered in both areas over the last two centuries. In early 1920s, von Karman, a giant in both applied mathematics and mechanics, had made a significant contribution in bring in rigorous mathematics into engineering and opened the era of engineering science that still impacts our engineering education and research today. In my opinion, the very idea of engineering science is responsible at least partly for the birth of modern control theory, and it is not a coincident that exact 50 years ago it was von Karman’s protege, H.S. Tsien (or X. S. Qian), the father of China’s Space Program, especially its Rocketry, also a giant in mechanics and late in both control and systems engineering, wrote the first milestone book in modern control engineering and application, Engineering Cyberneti cs (McGraw-Hill Book Company, Inc., 1954), when Tsian was a professor at California Institute of Technology. One can see the obvious trace of mechanics and applied mathematics in Tsien’s control book. However, for many years, it seems that this historic and deep tie between mechanics and control, at least from the aspect of structural mechanics, has been overlooked and almost lost today. For many of us today, control is more of an EE-orientated than a ME disciplinary. For the benefit of both areas, especially with the new development of modern computational methods and tools, we must re-establish a close and strong tie between control and mechanics. Duality System in Applied Mechanics and Optimal Control represents one of successful and valuable attempts along this direction by a leading expert in both applied mechanics and control theory. The book strives to connect and integrate concepts, methods, and algorithms in mechanics and control so that a unified framework can be established for both analytical and computational purposes. The state space approach has been used as the mathematical basis for building the analogy and one to one correspondence between mechanics and control, especially structural mechanics and optimal control. From the aspect of mechanics, this enables us to reformulate basic equations for elasticity theory using Hamiltonian dual variables and transfer the corresponding mathematics from the traditional Euclidean geometric into symplectic geometric one. As a result, the symplectic eigen-function expansion approach can be used to solve analytically many problems in elasticity that are hard or impossible to solve using the traditional solution methodology by the try-and-error technique, called semi-inverse method. Likewise, from the aspect of control, the analogy leads to new understanding and insight of key control problems in terms of well-studied classical problems in mechanics, especially vibration problems in structural mechanics, so that many effective algorithms and computational methods in mechanics can be applied to solve the corresponding control problems. Clearly, the book has demonstrated that the duality system method can be used as a mathematical and systematic foundation to deal with many important concepts and problems in both mechanics and control. It must be pointed out that this is not only very useful for research and applications, but also extremely helpful for multidisciplinary curriculum development. Review The book is organized into 6 chapters, starting with a brief historical, mathematical, and somewhat philosophical introduction to developments in mechanics and control and the precise integration method, a key computational method in structural mechanics developed by the author and his research group. Roughly speaking, the first 4 chapters constitute the mathematical and mechanics foundation for the entire book, Chapter 5 focuses on the application of state space method in elasticity, specifically elastic systems with single continuous coordinates or one-dimensional systems, while Chapter 6 concentrates on the utilization of computational methods and algorithms for solving control problems, especially the use of the precise integration method for predication, filtering, smoothing, optimal control and robust control. Chapter 1 presents the concepts and methods involving analytical dynamics, Lagrangian and Hamiltonian systems, Legendre transformation, dual variables, canonical transformation, symplectic systems, Poisson bracket, action, the Hamilton-Jacobi equation and separation of variables. The theme of this chapter is that the importance of Hamiltonian formulation goes well beyond analytical dynamics: it also provides a foundation for dealing with key problems in optimal control, robust control, elasticity, vibration, wave propagation, multi-body dynamics, and so on. One of the important objectives here is to establish a unified methodology under the sympletic frame for various disciplines based on the use of duality variables and reformulation of governing equations of dynamic systems into Hamiltonian forms. Chapter 2 summaries key topics and problems in the structural vibration theory, especially the symplectic eigen-problem for gyrosocopic systems and the corresponding algorithms. Issues related to the eigen-value count are also addressed. Chapters 3 and 4 provide the preliminaries for probability, stochastic processes, and random vibration of structures. Most of the materials in those two chapters are standard but the introduction and discussion of Lin's Pseudo Excitation Method (PEM) for solving linear response problems are quite new and interesting. Compared with the traditional approach, the PEM has significantly improved the computational efficiency and enables us to solve more practical and complicated problems in non-stationary random vibrations of real-world structural systems. Chapter 5 deals with elastic systems with single continuous coordinate or one-dimensional elastic systems. The key idea in this chapter is the establishment of the analogy between structural mechanics and optimal control by considering the single spatial coordinate as "time" coordinate and then transferring the original higher order spatial differential equations into a set of first-order "state space" equations. In this way, the traditional semi-analytical method and wave propagation problems in elasticity can now be solved analytically and systematically using the duality system theory. However, the original initial value problems for analytical dynamics become the two point boundary value problems for structural mechanics, which can be easily solved numerically with the precise integration algorithm Detailed discussions and procedures for solving matrix Riccati differential equations with precise integration as well as eigenvector based solutions of Riccati and Hamilton equations are illustrated. Finally, Chapter 6 addresses issues of applying methods in mechanics for linear optimal control systems and corresponding computational problems. Actually, many methods used in this chapter have been discussed in the previous chapter since the same analogy between control and mechanics is still valid and applied here. For example, the precise integration algorithms are extensively used for solving various matrix differential equations in smoothing, filtering, and predicating operations, as well as in LQG optimal control and H ∞ robust control, with specific consideration for combing on-line light iterative calculation with off-line intensive one-time computation so that the real-time computational work can be reduced to minimum. Clearly, the use of internal mixed energy concept is essential for applying methods in mechanics to control problems. The physical interpretation of the solution of Riccati equation, i.e., the solution matrix corresponds to the end flexibility matrix, offers useful information for its precise integration and analytical solution based on state eigen-vectors, as well as the observation that the eigen-solution based analytical method should be combined with the precise integration to solve Riccati differential equation and the filter equation. More interesting, it is pointed out that critical sub-optimal parameters in H ∞ robust control and filtering correspond to the extended Rayleigh quotients, thus many effective variational and numerical methods in structural mechanics, such as the W-W algorithm can be applied for robust control problems. Concluding Remarks This book only represents part of Professor Zhong’s effort to bring control and mechanics together under a unified mathematical and computational framework, as one can see from his recent papers and two previous Chinese books: Symplectic Elasticity (co-authored with Weian Yao, Higher Education Press , 2002) and Computational Structural Mechanics and Optimal Control ( Dalian University of Technology Press , 1993). Overall, this book is a very successful initial effort but more works are needed towards a completed and unified framework. In addition, there are still many open research topics involved, especially for problems in distributed parameter systems in both control and mechanics. As for the improvement of this book, I hope in its new version the English will be checked more carefully since sometimes one can see obvious traces of direct translation of Chinese into English. More than 20 years ago, I was fortunate to have the opportunity to be Professor Zhong’s teaching assistant for his summer seminar course on Computational Structural Mechanics in Hangzhou, China. Today as a senior scientist in China, Prof. Zhong is still extremely active and engaged himself in exploring new topics and disciplinary. I must say that I deeply admire and respect his academic spirit, tireless effort, and endless energy in pursuing new knowledge and conducting solid research works. 此文发表于《自动化学报》, Vol. 32, No.2, pp.318-320
迈向力学与控制统一的数学与计算框架 Toward a Unified Mathematical and Computational Framework for Control and Mechanics Fei-Yue Wang The Key Laboratory of Complex Systems and Intelligence Science Chinese Academy of Sciences, Beijing, China Abstract This is a brief review on the recent book: Duality System in Applied Mechanics and Optimal Control , by Wan-Xie Zhong, published by Kluwer Academic Publishers , 2004. The book represents a significant effort to re-establish the historic and deep tie between control and mechanics by striving to connect and integrate concepts, methods, and algorithms in mechanics and control so that a unified framework can be established for both analytical and computational purposes. Clearly, it has demonstrated that the duality system method can be used as a mathematical and systematic foundation to deal with many important concepts and problems in both mechanics and control. This book is not only very useful for research and applications, but also extremely helpful for multidisciplinary curriculum development when students from one field are trying to learning and applying concepts and methods from the other field. Introduction Control and Mechanics have a deep and historical relationship ever since the birth of classical and modern control theory. Many great mathematicians had pioneered in both areas over the last two centuries. In early 1920s, von Karman, a giant in both applied mathematics and mechanics, had made a significant contribution in bring in rigorous mathematics into engineering and opened the era of engineering science that still impacts our engineering education and research today. In my opinion, the very idea of engineering science is responsible at least partly for the birth of modern control theory, and it is not a coincident that exact 50 years ago it was von Karman’s protege, H.S. Tsien (or X. S. Qian), the father of China’s Space Program, especially its Rocketry, also a giant in mechanics and late in both control and systems engineering, wrote the first milestone book in modern control engineering and application, Engineering Cyberneti cs (McGraw-Hill Book Company, Inc., 1954), when Tsian was a professor at California Institute of Technology. One can see the obvious trace of mechanics and applied mathematics in Tsien’s control book. However, for many years, it seems that this historic and deep tie between mechanics and control, at least from the aspect of structural mechanics, has been overlooked and almost lost today. For many of us today, control is more of an EE-orientated than a ME disciplinary. For the benefit of both areas, especially with the new development of modern computational methods and tools, we must re-establish a close and strong tie between control and mechanics. Duality System in Applied Mechanics and Optimal Control represents one of successful and valuable attempts along this direction by a leading expert in both applied mechanics and control theory. The book strives to connect and integrate concepts, methods, and algorithms in mechanics and control so that a unified framework can be established for both analytical and computational purposes. The state space approach has been used as the mathematical basis for building the analogy and one to one correspondence between mechanics and control, especially structural mechanics and optimal control. From the aspect of mechanics, this enables us to reformulate basic equations for elasticity theory using Hamiltonian dual variables and transfer the corresponding mathematics from the traditional Euclidean geometric into symplectic geometric one. As a result, the symplectic eigen-function expansion approach can be used to solve analytically many problems in elasticity that are hard or impossible to solve using the traditional solution methodology by the try-and-error technique, called semi-inverse method. Likewise, from the aspect of control, the analogy leads to new understanding and insight of key control problems in terms of well-studied classical problems in mechanics, especially vibration problems in structural mechanics, so that many effective algorithms and computational methods in mechanics can be applied to solve the corresponding control problems. Clearly, the book has demonstrated that the duality system method can be used as a mathematical and systematic foundation to deal with many important concepts and problems in both mechanics and control. It must be pointed out that this is not only very useful for research and applications, but also extremely helpful for multidisciplinary curriculum development. Review The book is organized into 6 chapters, starting with a brief historical, mathematical, and somewhat philosophical introduction to developments in mechanics and control and the precise integration method, a key computational method in structural mechanics developed by the author and his research group. Roughly speaking, the first 4 chapters constitute the mathematical and mechanics foundation for the entire book, Chapter 5 focuses on the application of state space method in elasticity, specifically elastic systems with single continuous coordinates or one-dimensional systems, while Chapter 6 concentrates on the utilization of computational methods and algorithms for solving control problems, especially the use of the precise integration method for predication, filtering, smoothing, optimal control and robust control. Chapter 1 presents the concepts and methods involving analytical dynamics, Lagrangian and Hamiltonian systems, Legendre transformation, dual variables, canonical transformation, symplectic systems, Poisson bracket, action, the Hamilton-Jacobi equation and separation of variables. The theme of this chapter is that the importance of Hamiltonian formulation goes well beyond analytical dynamics: it also provides a foundation for dealing with key problems in optimal control, robust control, elasticity, vibration, wave propagation, multi-body dynamics, and so on. One of the important objectives here is to establish a unified methodology under the sympletic frame for various disciplines based on the use of duality variables and reformulation of governing equations of dynamic systems into Hamiltonian forms. Chapter 2 summaries key topics and problems in the structural vibration theory, especially the symplectic eigen-problem for gyrosocopic systems and the corresponding algorithms. Issues related to the eigen-value count are also addressed. Chapters 3 and 4 provide the preliminaries for probability, stochastic processes, and random vibration of structures. Most of the materials in those two chapters are standard but the introduction and discussion of Lin's Pseudo Excitation Method (PEM) for solving linear response problems are quite new and interesting. Compared with the traditional approach, the PEM has significantly improved the computational efficiency and enables us to solve more practical and complicated problems in non-stationary random vibrations of real-world structural systems. Chapter 5 deals with elastic systems with single continuous coordinate or one-dimensional elastic systems. The key idea in this chapter is the establishment of the analogy between structural mechanics and optimal control by considering the single spatial coordinate as "time" coordinate and then transferring the original higher order spatial differential equations into a set of first-order "state space" equations. In this way, the traditional semi-analytical method and wave propagation problems in elasticity can now be solved analytically and systematically using the duality system theory. However, the original initial value problems for analytical dynamics become the two point boundary value problems for structural mechanics, which can be easily solved numerically with the precise integration algorithm Detailed discussions and procedures for solving matrix Riccati differential equations with precise integration as well as eigenvector based solutions of Riccati and Hamilton equations are illustrated. Finally, Chapter 6 addresses issues of applying methods in mechanics for linear optimal control systems and corresponding computational problems. Actually, many methods used in this chapter have been discussed in the previous chapter since the same analogy between control and mechanics is still valid and applied here. For example, the precise integration algorithms are extensively used for solving various matrix differential equations in smoothing, filtering, and predicating operations, as well as in LQG optimal control and H ∞ robust control, with specific consideration for combing on-line light iterative calculation with off-line intensive one-time computation so that the real-time computational work can be reduced to minimum. Clearly, the use of internal mixed energy concept is essential for applying methods in mechanics to control problems. The physical interpretation of the solution of Riccati equation, i.e., the solution matrix corresponds to the end flexibility matrix, offers useful information for its precise integration and analytical solution based on state eigen-vectors, as well as the observation that the eigen-solution based analytical method should be combined with the precise integration to solve Riccati differential equation and the filter equation. More interesting, it is pointed out that critical sub-optimal parameters in H ∞ robust control and filtering correspond to the extended Rayleigh quotients, thus many effective variational and numerical methods in structural mechanics, such as the W-W algorithm can be applied for robust control problems. Concluding Remarks This book only represents part of Professor Zhong’s effort to bring control and mechanics together under a unified mathematical and computational framework, as one can see from his recent papers and two previous Chinese books: Symplectic Elasticity (co-authored with Weian Yao, Higher Education Press , 2002) and Computational Structural Mechanics and Optimal Control ( Dalian University of Technology Press , 1993). Overall, this book is a very successful initial effort but more works are needed towards a completed and unified framework. In addition, there are still many open research topics involved, especially for problems in distributed parameter systems in both control and mechanics. As for the improvement of this book, I hope in its new version the English will be checked more carefully since sometimes one can see obvious traces of direct translation of Chinese into English. More than 20 years ago, I was fortunate to have the opportunity to be Professor Zhong’s teaching assistant for his summer seminar course on Computational Structural Mechanics in Hangzhou, China. Today as a senior scientist in China, Prof. Zhong is still extremely active and engaged himself in exploring new topics and disciplinary. I must say that I deeply admire and respect his academic spirit, tireless effort, and endless energy in pursuing new knowledge and conducting solid research works. 此文发表于《自动化学报》, Vol. 32, No.2, pp.318-320
REPORT A Toward a Universal Understanding of the Scaling Laws in Human and Animal Mobility This paper attempts to present a universal understanding of the laws of human and animal mobility. In this attempt, the paper more or less fails. I am not convinced that it is an adequate universal explanation. However, I found the paper quite fascinating for a number of reasons, and highly recommend publication in EPL, provided some changes are made (see below). The use of the Shannon entropy to study random searches, for example, is very interesting. The main results are also very interesting. 文章地址 http://arxiv.org/PS_cache/arxiv/pdf/1008/1008.4394v3.pdf
老外在nature发文想用系统科学方法统一中医和西医,我国医学工作者们有危机感了么? 由于自己研究方向和系统科学多少有点关系,留意了一下nature最新一期的文章,文章观点虽是PERSPECTIVE,但却让人不敢大意。想起很久以前看过季羡林老先生的《留德十年》,里面讲了这样一件事,说是中国人到国外学习中文和古汉语。发人深省。希望类似的事情不要再发生了。 Perspective: All systems go Jan van der Greef Journal name:NatureVolume:480,Page:S87Date published:(22 December 2011)DOI:doi:10.1038/480S87aPublished online 21 December 2011
作者:辛思为 http://xys5.dxiong.com/xys/ebooks/others/science/misc/kexue39.txt 新语丝(XYS20111020) 上Blackhole 的“科学是什么?不是什么?”说了很多,但是我觉得还是没有把握科学的实质精神。我这里尝试把科学的精神实质说得简单些。 一,科学跟信仰 其实,科学也可以看作某种信仰,即“科学信仰”。有句话说You can do very little with faith, but you can do nothing without faith,“信仰不是万能的,没有信仰是万万不能的”。科学家至少要对科学方法有信仰,信仰复杂事物、现象可以通过简单事物、现象的引申、组合加以解释。科学家至少要信仰科学的基本原理“自洽性”和“实证性”,科学家要信仰世界是统一的,各种事物、现象之间存在相关性(因此才能从简单事物、现象去解释复杂事物、现象)。 二,科学的常识性 科学的本质认为世界是一致的,因此可以从简单的、已知事物、现象的去解释、推测复杂的未知的事物、现象。其起点是简单、已知的东西,这就是常识。 爱因斯坦说过,“整个科学不过是日常思维的提升”(The whole of science is nothing more than a refinement of everyday thing)。所谓“日常”思维,就是“常识性”的思维。这也意味着科学体系可以从常识中推导出来。竺可桢也认为,“科学并不神秘,不过是有组织的常识而已” (《竺可桢全集》第一卷:244)。 科学理论是个有组织的、从简单现象推导出复杂现象的推导体系。推导体系必须有初始起点,这就是“公理”或者“公设”(基本假设)。 我们以欧几里德的五条几何公理为例,看看公理的特点: 1)由任意一点到任意一点可作直线。 2)一条有限直线可以继续延长。 3)以任意点为中心及任意的距离可以画圆。 4)凡直角都相等。 5)从直线外一点,只能作一条平行直线。 构成这些公理命题的概念“点”和“直线”也都是最简单的。“点”是没有面积和体积的,当然是最简单的空间概念。“直线”就是方向保持不变的线条,比起不断改变方向的曲线当然是更简单的。 这些公理都简单、平凡得形同废话。然而整个欧氏几何学的宏伟理论大厦就是以这些公理为起点,加上形式逻辑的推理而构成的。 另外五条欧氏一般公理也是如此简单: 1)若 a=c 且 b=c,则 a = b(等量代换公理)。 2)若 a=b 且 c=d,则 a+c = b+d(等量加法公理)。 3)若 a=b 且 c=d,则 a-c = b-d(等量减法公理)。 4)完全叠合的两个图形是全等的(移形叠合公理)。 5)全量大于分量,即 a+ba(全量大于分量公理)。 其中前面三条一般公理,实际上也是代数学的基础。 美国诗人米雷(E.S.V. Millay, 1892~1950)用诗的语言赞叹说,“只有欧氏见过赤裸之美” (Euclid alone has looked at beauty bare.)。我们换个角度说,只有欧氏看到了“赤裸裸的最简单的事实的伟大力量”。 当然,“数学是否科学”这一问题没有统一看法。但就数学具有内部自洽性这点,符合科学的定义。数学一旦得到应用,就要受到事实的实证,这也符合科学的定义。因此有人甚至认为“数学是科学的科学”。如果如此,“数学是科学的科学”,数学的理论架构是所有科学的基础和模式。数学公理的特征也是其他科学中公理的应有特征。 让我们看看数学之外,其他一些根据常识建立起理论的例子。 达尔文生物演化理论建立在“遗传”、“变异”和“自然选择”这三个常识性现象之上。生物体的上下代之间总有相似处,这就是“遗传”,是谁都知道的常识。但上下代生物体又不能完全一样,总有差异,这就是“变异”,也是谁都知道的常识。 至于“自然选择”,即不利于生存的变异个体容易被淘汰,这也是常识。但一般人对此只看到结果明显的例子,如残伤的后代不容易生存。而达尔文看到了微小的变异差别,经过时间长河的积累、放大,结果也会很明显。或者说明显的适应变化现象是通过微小的变化积累而成。例如1000个适应能力稍微差一些的人,跟另外1000个适应能力稍微强些的人比较,其适应结果粗看并不明显。比方说其中可能只有1%的人在总体上表现出不适应生存的结果。大部分人会看到99%而说这种差别对生存没有影响,而达尔文就能看到这1%经过时间的放大,会产生巨大的后果。这种超乎常人的“见微知著”洞察力,正是达尔文的伟大之处。有人在赞扬达尔文这种洞察力时说,“渺小的心灵只关注异常现象,而伟大的心灵却关注平凡之事”(Little minds are interested in the extraordinary, great minds the commonplace)。其实,这种洞察力不仅是“见微知著”,同 时也是“见著知微”,看到明显的甚至极端的变异现象的效果而联系到不明显的细微的变异的效果。在极大和极小之间看到了“一致性”。 其实,生物育种中的“人工选择”跟“自然选择”,原理是一样的。世界各民族都有丰富的育种经验;可见,人种选择是很常识的方法。达尔文不过把人工选择延伸到物种的自然演化中而已。 作为常识的科学基本要素的普遍存在,不妨用庄子对“道”的一段论述来比喻(如果把“道”理解为基本原理、公理)。 东郭子问于庄子曰:“所谓道,恶乎在?”庄子曰:“无所不在。”东郭子曰:“期而后可。”庄子曰:“在蝼蚁。”曰:“何其下邪?”曰:“在稊稗。”曰:“何其愈下邪?”曰:“在瓦甓。”曰:“何其愈甚邪?”曰:“在屎溺。”《庄子?知北游》。 这段文字表明了:“道”(根本法则)的无所不在。例如生物学家在以屎为生的屎壳郎中,同样也能发现自然淘汰、适者生存的物种演化原理。 三,中国文化之缺乏科学精神 为何在中国科学精神要扎根是如此之难?因为我们的传统文化中没有科学精神。表现之一是战国时期的百家争鸣虽然成就辉煌,但就是缺少古希腊文明中的逻辑学和几何学这么两家。这说明中国文化中缺少严格逻辑思维,特别是演绎思维的传统。百家争鸣,主要靠比兴、比喻等类推方法。 其次,以儒家为代表的传统思想是重“善”(仁义)重“价值观”而轻“真”的伦理学。一事当前,不问真假是非,先分“敌、我”和“(我)善、(敌)恶”,古代就有“夷夏之辨”的“非我族类其心必异”的指导思想。西学东渐后,我们把本义为“真相”的truth 误译成具有价值色彩强烈的“真理”。误译的结果导致“真理”一词的在现代汉语中的使用率大大超过“真相”,助长了一种凡事价值判断挂帅而轻视乃至藐视事实真相的政治文化氛围。价值判断先于真相辨的一个结果是,判断敌我先于判断是非,极端的例子就是“文化大革命”中流行的“凡是敌人拥护的,我们就要反对”。这就是只问“实用价值”(是否对自己有好处,还不同于“伦理价值”)而不问是非,这实际上就是定敌我先于定是非,是正常逻辑的颠倒,必然导致思想的极大混乱和社会的极大动乱。而其实,“真相”往往比“真理”更重要,因为弄清真相是获得真理(正确认识)的前提。 如今某些人的强调“中国特色”,拒绝普世价值,还是对“夷夏之辨”思路的继承,因为那些价值观不是我们自己创造的。又如国际上已经有成功办大学,成功培育人才的许多经验,现成地放在那里,我们就是不肯虚心学习,美其名曰“摸索自己的路”。象“学术自由是科学发展的根本前提”,早已经是现代社会的常识了,我们在培养人才方面就是不愿意承认这一点。 近来看到白岩松一篇文章说要“捍卫常识,建设理性,追求信仰”,觉得这个提法很好。现代中国的现实是,连捍卫常识都要付出巨大的,甚至是生命的代价,因此强调常识,捍卫常识,是在中国提倡科学精神的首要任务。
相对大气纠正的目的是为了使得两幅影像的DN值具有可比性;变化检测的目的在于检测出两幅影像之间发生变化的像素。乍一看,相对大气纠正应该先于变化检测,因为两幅影像没有可比性的话,就没法通过比较发现变化的像素。对于全自动的相对大气纠正和变化检测程序而言,实际上两者是互相纠缠的。 全自动的相对大气纠正要求能够自动找到影像中没有发生变化的像素‘pseudo-invariant features’(PIFs),而这就要求能有全自动的变化检测技术把发生变化的像素剔除;而全自动的变化检测技术却要求首先影像之间的像素的DN值是在统一的大气条件下。看了大量文献,一个算法能够同时做到相对大气纠正和变化检测是大势所趋,比如A. A. Nielsen和M. J. Canty的IR-MAD算法(A Method for Unsupervised Change Detection and Automatic Radiometric Normalization in Multispectral Data,2010)。以下是在我的另一种算法(暂时叫IN-AT),(没有IR-MAD源代码,没有与之比较过),胜在简单、快速。 两幅影像重叠区域变化检测: 经过相对大气纠正后的拼接: