Mathematics and painting

Abstract

Mathematics and painting are interrelated in many ways. At a technical level mathematics can be used to enhance our appreciation of paintings. This was recently demonstrated beautifully by Taylor, Micolich, and Jones in their analysis of Jackson Pollock's drip paintings, which led them to the conclusion that Pollock's paintings are in a way figurative pictures. Relations also exist at a more basic level. Painting and mathematics can share subject matter, as is illustrated here by a discussion of the mathematical concepts 'open' and 'closed', which are related to paintings by Pollock, Kandinsky, Turner, and van Gogh. It is suggested in conclusion that mathematics and painting are so closely related and have so many similarities that it is reasonable to consider them simply as two different but complementary ways of visualising aspects of the concrete or abstract reality in which we are embedded.     

男王后:从历史叙事到文学叙事

男王后的故事源于《陈书.韩子高传》,随着时代的变迁,韩子高从历史走进了文学,他的姓氏、身份及人生际遇亦随之改变,一个青年骁将在文人的想象中逐步蜕变为王世贞《艳异编》中的帝王男宠,最后又被王骥德定格为以色事君的男王后。男王后故事的演变不仅形象体现了历史叙事与文学叙事之间的巨大差别,更折射出晚明男风盛行的社会状况以及男尊女卑性别霸权在男人内部的戏拟与复制。     

Narrative Inquiry: Theory and Practice

This article offers an overview of the method of narrative inquiry and explores competing trends in the use of the approach. It not only examines the theories relating to the method but also offers practical guidance on using narrative inquiry, including an exploration of what might count as a narrative and ways of analysing narrative data. The final section of the article presents two different examples of how narrative inquiry has been used. The first example is the use of narrative inquiry as a reflective learning process for students in an undergraduate curriculum. The second example is a narrative inquiry into staff experiences of role change in problem-based learning. Suggestions are also made as to how narrative inquiry might be adapted for use in geography in higher education.     

叙事型构·文本界限·叙事界域:传统指涉性的发现

在诺苏彝族的本土口头传统中,史诗“勒俄”的源文本是极其丰富和多元的,同时也有着极其强固的文本性属观念与口头叙事法则。在田野研究的逐步推进中,我们意识到必须认真检视自己的研究对象到底是什么,其内部的叙事机制是什么?那么,我们需要回答的相关问题是:1)史诗“勒俄”的源文本形态及其叙事结构的民间记忆方式是什么?2)在有关“勒俄”的民间话语中为什么会出现“公勒俄”/“母勒俄”和“黑勒俄”/“白勒俄”两套语汇,其间的传统涵义是什么?3)书面化的史诗本事与口头演述的史诗叙事有怎样的内在关联与区别,民间叙事的传统规定性是什么?一…     

Mathematics,Music and Chess

Abstract

Mathematicians, musicians and chess players were singled out by the British Foreign Office during the Second World War for the exacting task of breaking the German Enigma code at Bletchley Park. One of these cryptographers, the present author, has remained intrigued with the common factors linking these three noble activities of the human intellect: he suggests symbols of power and a logical tine of thought. But an expert in one activity need not excel in the others, he concludes.     

History,Differential Inclusions,and Narrative

Recent advances in the theory of dynamical systems, set‐valued analysis, and viability theory offer new and interesting perspectives on the shaping of social and historical time. Specific aspects of these theories are presented in several different areas to show their concrete applications in history and historical demo‐economy, and a parallel is established with novelist Tanizaki’s fictional technique. In connection with this, McCloskey’s 1991 comparison of storytelling with deterministic chaos is discussed and a critique of other models concerned with unpredictability in human affairs provided. Finally, the shapings of social and historical time are described in terms of the viable strategies at the heart of evolutionary processes involving human agents interacting with a variety of constraints. Sachiko could foresee great difficulties if her sister were to marry him, but at least for the time being they would not have to worry about what people thought. If on the other hand she married Itakura, she would be held up to public ridicule. Okubata seen by himself was not a happy choice, but he was certainly better than Itakura, and he could be their weapon to turn away the latter. 1 Junichiro Tanizaki, The Makioka Sisters (New York: Alfred A. Knopf, 1976), part 2, chapter 26, 278.
     

论历史叙述中的理解与解释

在实际生活中，人们往往要解释自己或他人已经历史化了的行为，因此回避不了历史叙述，它成了人类社会实践中的必要组成部分。当人们在不同程度上作为一位历史叙述者，通过理解个体自身的历史或生存情境，阐发自己的存在与实践目的，即进行历史叙述时，他已经置身于一个历史叙述的循环之中。历史叙述循环从现象上分为两个阶段，其一是叙述前的准备阶段，即阅读与历史理解阶段；其二是叙述阶段，即叙述与历史解释阶段。     

The Narrative Uses of Evidence

When scientific evidence is used in policy controversies, it is always embedded in narrative stories. The Narrative Policy Framework (NPF) is an empirical framework used to study the role of narratives in public policy. While the NPF has considered the relationship between evidence and narratives from different angles, it has not used a consistent approach in examining how evidence is embedded in narratives. This article develops a categorization of narrative uses of evidence. A narrative use of evidence is defined by the different roles that evidence plays in the plot of a narrative depending on which narrative element is addressed by a given piece of evidence. To distinguish different narrative uses of evidence, the article examines how competing coalitions use the Program for International Student Assessment (PISA) study in Swiss direct‐democratic campaigns on school policy. Quantitative and qualitative content analyses of newspaper articles and governmental documents show how evidence may relate to all main narrative elements and may play different roles in the plot of a narrative. The findings demonstrate significant differences in the narrative uses of PISA between coalitions related to the story types and narrative strategies that each coalition uses. Finally, the implications for future NPF research are discussed.     

论历史叙述中的主观性与历史评价

自18世纪末开始,历史学尾随近代自然科学的观念,追求客观性,为的是使历史学的独立学科地位奠定在科学观念的坚实基础之上。百余年的追求与积淀,使许多历史学家的心中打上了深深的客观主义烙印,“如实直书”一度成为历史学家孜孜以求的目标。这种对历史的客观本质及其可能性缺乏深思熟虑的观点,直到20世纪——这个被称为相对主义泛滥的世纪,仍然挥之不去。即使是20世纪新史学的旗帜——年鉴学派,也无法避免19世纪客