A Nonlinear Method for Measuring the Effects of Environmental Variations

Ever wonder if it is possible to construct a numeric scale for environmental variables, like one does for the temperature? This paper is an attempt to construct one. There are two main parts: section “Statistical Analysis of Variations” presents a general statistical strategy for environmental factor selection. Section “Nonlinear Analytical Geometric Model of Variations” develops an analytical geometric representation of system variations in response to environmental changes. The model is used to quantify the effects of environmental interactions. The paper treats only one-dimensional case, however, the derivation of the case of multiple independent factors follows immediately. The general method developed in this paper may prove applicable to many different fields, such as extensions beyond classical physics, economics, and other sciences. Section “Conclusion” provides an illustration of applications, examples and implications of the results.     

中算数学机械化思想在和算中的发展——解伏题的机械化特征

和算解伏题是关于多元高次联立方程组求解问题，因其在世界数学史上首次导入了行列式算法而向为学术界所重视。文章从数学机械化这一视角对其提出新的认识，重新讨论和算解伏题的消元理论问题，认为和算解伏题是中算代数化几何与以元天术为核心的代数演算的机械化数学传统的后续发展，关孝和给出了多元高次方程组消元的一般性程序，从而构筑了和算后期计算几何发达的基础，比诸行列式理论，解伏题的数学机械化思想的价值更为重要。     

Joint Orthomax Rotation of the Core and Component Matrices Resulting from Three-mode Principal Components Analysis

The analysis of a three-way data set using three-mode principal components analysis yields component matrices for all three modes of the data, and a three-way array called the core, which relates the components for the different modes to each other. To exploit rotational freedom in the model, one may rotate the core array (over all three modes) to an optimally simple form, for instance by three-mode orthomax rotation. However, such a rotation of the core may inadvertently detract from the simplicity of the component matrices. One remedy is to rotate the core only over those modes in which no simple solution for the component matrices is desired or available, but this approach may in turn reduce the simplicity of the core to an unacceptable extent. In the present paper, a general approach is developed, in which a criterion is optimized that not only takes into account the simplicity of the core, but also, to any desired degree, the simplicity of the component matrices. This method (in contrast to methods for either core or component matrix rotation) can be used to find solutions in which the core and the component matrices are all reasonably simple.     

划界问题:康德与前期维特根斯坦

维特根斯坦哲学与康德哲学有某种深刻联系.他在前期所进行的"语言批判"更多地受到康德的"理性批判"的影响."语言批判"和"理性批判"的核心都是"划界问题".本文深入分析和比较了康德的"划界"和前期维特根斯坦的"划界"之异同,指出"事实领域"与"价值领域"的划分是二人共同的基本观点.     

Local and Global Properties of the World

The essence of the method of physics is inseparably connected with the problem of interplay between local and global properties of the universe. In the present paper we discuss this interplay as it is present in three major departments of contemporary physics: general relativity, quantum mechanics and some attempts at quantizing gravity (especially geometrodynamics and its recent successors in the form of various pregeometry conceptions). It turns out that all big interpretative issues involved in this problem point towards the necessity of changing from the standard space-time geometry to some radically new, most probably non-local, generalization. We argue that the recent noncommutative geometry offers attractive possibilities, and gives us a conceptual insight into its algebraic foundations. Noncommutative spaces are, in general, non-local, and their applications to physics, known at present, seem very promising. One would expect that beneath the Planck threshold there reigns a "noncommutative pregeometry", and only when crossing this threshold does the usual space-time geometry emerges.     

Belief Systems and the Modeling Relation

The paper presents the most general aspects of scientific modeling and shows that social systems naturally include different belief systems (i.e. different models). Belief systems differ in a variety of respects, most notably in the selection of suitable qualities to encode and the internal structure of the observables. The following results emerge from the analysis: (1) conflict is explained by showing that different models encode different qualities, which implies that they model different realities; (2) explicitly connecting models to the realities that they encode makes it possible to clarify the relations among models; (3) by understanding that social systems are complex one knows that there is no chance of developing a maximal model of the system; (4) the distinction among different levels of depth implicitly includes a strategy for inducing change; (5) identity-preserving models are among the most difficult to modify; (6) since models do not customarily generate internal signals of error, strategies with which to determine when models are out of synch with their situations are especially valuable; (7) changing the form of power from a zero sum game to a positive sum game helps transform the nature of conflicts.     

心的科学认识何以可能?——从功能主义看心身问题

二元论与物理主义都不能对心身问题给出合理的解答,图林机功能主义在解释心身关系中也存在诸多困难,但并不导致取消主义。心仍然可以成为科学认识的对象,只不过认识心的方法必然是目的论功能主义的,而且目的论方法表明功能主义并不能给心带来惟一的、排它性的知识。     

量子逻辑解释优于哥本哈根解释吗——围绕投影法则的争论

弗里德曼和普特南认为,哥本哈根解释只能特设性地引入投影法则来符合实验事实,然而由量子逻辑则可以推导出投影法则,因此量子逻辑解释比哥本哈根解释更加优越.这一论断提出后不久就遭到了许多学者的反驳.海尔曼认为由量子逻辑推导投影法则的过程也是特设性的,巴布则认为由哥本哈根解释也可以推导出投影法则.随后,斯戴尔斯提出了由哥本哈根...     

试论绫织物的由来和早期生产

织物品种中的绫,其含义和适用范围现在和古代是有差别的;根据绫和纨在历史上的出现时间和它们的纹理,推断绫是由纨发展而来,阐述了绫织物这个名称的由来、演变和确立;从汉代绫生产地区的扩大,断言其时聚居在一些大城市的民间织工多已掌握并能运用有关的织作工艺织制绫织物,汉代民间绫织物消费的启动,为三国时期绫织物的大发展奠定了基础;绫能成为众多织物中一个有代表性地位的品种,是基之于其自身织作风格和特点,它的出现和存在,使中国古代丝织工艺迈出先秦的藩篱而步入一个崭新的境界。     

傣族古歌谣中的稻作年代考

傣族是中国西南少数民族之一,也是最古老的稻作民族百越族的后裔,《古歌谣》是傣族先民留下的反映本民族生产和生活的历史资料。该文从中国稻作技术的发展和傣族历法的由来两个方面,考察了傣族古歌谣中的稻作年代问题,认为《古歌谣》中所反映的稻作可能是唐宋,特别是明代以后的情况,并在此基础上讨论了汉族和傣族稻作文化的关系。     

有关《九章算术》的一些讨论

文章分为５部分,第一部分指出“晋武库”并非“晋朝武库”而是“晋王武库”,从而对刘徽作注年代问题给出了一个关键性的新论点,极易肯定刘徽注完成于魏景元四年。第二部分针对今本《九章算术》中有争议的部分,指出少广术、负笼术、宛田术、环田术、密率术、五家共井术等,本身无误,以前人们由于种种原因而对其作了不同的误解,亟待澄清。第三部分对体积理论作了详细讨论,提出《九章算术》时代应该已经有了成熟的棋验法并用以求     

第二次数学危机的实质是方法论的变革

数学的主要研究对象是“数”和“形”，与“数”的研究领域所对应的方法主要是运算方法，与“形”的研究领域所对应的方法主要是逻辑证明的方法，两种方法的结果都是确定无疑的。微积分的出现产生了一种新的方法，即分析方法，分析方法是“算”和“证”的结合，是通过无穷趋近而确定某一结果。古代数学中就发现了这一方法，牛顿和莱布尼兹创立微积分实际上是将这一方法程序化和运算化，这导致了对分析方法的误解，从运算方法的原则去指责分析方法的程序过程，这就是第二次数学危机的实质。戴德金使分析算术化，通过对实数的分划奠定分析方法的基础，指明了通过无穷趋近确定某一常数的确切性和惟一性，开始为分析注入严密性。     

星占对中国古代战争的影响──以北魏后秦之柴壁战役为例

北魏道武帝天兴五年（公元４０２年），当北魏在柴壁打败后秦部队时，太史令晁崇上奏“月晕左角”的天象，并预言带角的动物将暴死。稍后，竞如晁崇所料，发生大疫，部队的数百头牛只，同日皆死于路旁。根据推算，当时绝无发生月晕左角的可能，再就事件中的人物加以分析，竞发现牛疫的发生似乎带有强烈的人为因素，而天象是被当做影响军事决策的工具。此事件突显中国古代天文与军事的密切关系，因此该文希望藉此个案，讨论中国古代星占对战争的影响。     

等差级数与插值法

《周髀算经》中求“衡径”和“晷长”的方法可以视为一次插值法的应用，《大衍历》中“先定日数，径求积度及分”的方法实与刘徽提出的等差级数求和公式一致。一般来说，一个（ｋ—１）阶等差级数的求和公式等价于一个ｋ阶等间距插值公式。在中国古代数学中，等差级数和插值法是两个相互关联的题材，宋元数学家在充分认识高阶等差级数的基础上方有可能得到一般的等间距插值公式。     

美国大学的跨学科战略实践及其经验启示

进入21世纪以来,美国大学广泛实施了跨学科战略与行动计划。本研究通过多重组合案例形式详细介绍了美国研究型大学的跨学科战略、组织政策、组织结构与特色实践,建议我国应制定国家层次与大学层次的跨学科教育与研究战略,加快大学跨学科学术组织建设,以推动高等教育体系的制度创新与组织变革。     

工程史上的水门事件——Hydrolevel案例的经典伦理分析

Hydrolevel事件,被称为美国工程史上的水门事件,是一个以小见大,全面检视美国工程伦理状况的好案例。本文详尽地还原了H事件的事实真相,纠正了一些对它的误解,并将其背后众多的伦理意义展示出来,结合中国的实际,探讨了对于工程实践的突出意义。     

葫芦考略

葫芦被我国古人当作瓜类的一种，是我国栽培历史最悠久的植物之一，在距今七八年千的我国新石器遗址中曾发现它的残果和种子遗存，文字记载也很早。它在我国古代有着极为广泛的用途，除果实和叶子供食用和作药物外，成熟的果实还被用来制作各生活用具、乐器等等，另外瓜瓤被用作喂猪，种子被用于榨油浇制蜡烛，在中华文明发展进程中起着非常重要的作用。可能出于对这种植物极端推崇的缘故，古人甚至认为人类也由它发源而来。从有关历史资料来看，葫芦应是一种起源于我国的栽培植物，原产地可能在华南或华西南。     

清末黄宗宪的《容圆七术》初探

清末数学家黄宗宪在<容圆七术>中,对中国传统数学的容圆问题从几个方面做了推广,特别是用西方数学的圆锥曲线、轨迹方法及逻辑推理等知识解决新的容圆问题,其中不乏颇具新意的创见和成果.我们由此也可看到我国清末东、西方数学交融时期的许多现象.