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数学物理学

数学物理学

翻新的挂毯

01 Apr 2010

大自然的图案:三部分挂毯–形状,流动,分支
Philip 球
2009牛津大学出版社
每磅£14.99(320pp / 272pp / 272pp)

诱人的模板

蜂箱,蝴蝶和贝壳的标记,树枝,雪花和云层:自然世界充满了图案。这些模式中的许多模式似乎无关,但是它们之间相似之处的暗示表明,我们应该能够将其起源追溯到一些共同的来源。

在某些情况下,图案的来源可能是纯粹的物理过程,可以在实验室中在受控条件下进行复制并以简洁的数学术语进行分析。但是对于生物和社会系统中形成的结构,模式生成机制更难确定。自然选择(或其在社会或经济系统中的类似物)可能有很多诡计,可以创建任意形式的模式。但是,如果自然选择偏向于特定类型的复杂结构,那么可能会有一些一般性的规律在起作用,我们可以通过应用类似于为物理系统开发的技术来辨别。当前许多跨学科研究集中在观察到的选定模式可以理解为在相对简单的物理过程中产生的程度。

性质’s Patterns Philip 球 describes how scientists have approached the pattern-formation problem 和 explains a number of their successes. 在 a series of case studies he illustrates how physical 和 chemical processes can account for certain observed patterns in geological 和 biological systems. The examples he selects come from a wide range of fields, including condensed-matter physics, physical chemistry, fluid dynamics, biophysics, physiology, geology 和 even social-network theory. The result –虽然并不总是容易阅读–是简单物理原理产生的令人惊讶的复杂结构的迷人窗口。

性质’s Patterns 呈现为三部曲,分别有独立的 形状,流量分行 each concentrating on a different aspect of pattern formation. Taken together, the three books constitute a substantially revised 和 expanded edition of 球’s earlier book 自制挂毯。在序言中 形状, part one of the trilogy, 球 states that the new format does the subject more justice, but does not say how. I agree that organizing the material into three broad categories was a good move. However, there would have been a distinct advantage to collecting all three in a single volume: the communities working on these problems overlap substantially, 和 the results are more satisfying when viewed as a coherent body of work.

As a science journalist, 球’方法是发展历史故事情节,将每个科学解释锚定到特定研究人员。他的著作激发了人们对科学正确的信心,并且他努力展示现代解释是如何被先前的工作所激发,促成的以及有时是可以预期的。这样做确实具有教学目的:在许多情况下,较早的工作更容易掌握,因此可以为您解决当前的问题。因此,对于那些希望大致了解科学在解释模式和产生什么样的问题方面所拥有的知识的人–谁还不准备解决任何数学问题– the stories that 球 presents may be just the right vehicle.

For me, however, the effect was a bit overwhelming. Each book reads more like a history of ideas than a set of scientific results, 和 I found it hard to keep the relevant science in mind while following long tangents of primarily historical interest. To get the full benefit, readers must be prepared to pause frequently to refresh their memory about how the current discussion fits into the developing storyline. 球 suggests that readers also take time to perform some experiments of their own. I heartily agree, 和 I particularly recommend making the soap-film structures. There is no substitute for watching the real process by which patterns form, seeing them in 3D, 和 viewing how robust or fragile they are – all of which help clarify the science that 球 is trying to explain.

While experts may find a few points where they would have chosen to emphasize different features or draw finer distinctions between systems 球 takes to be analogous, he has on the whole done an excellent job of including relevant caveats 和 avoiding false conceptual impressions. He does miss some important opportunities, however. It struck me as odd, for example, that 形状 没有提及固体中原子或液晶中分子的顺序,也没有提及晶体的多面形状。在这三种情况下,物理学都是众所周知的,并且它们中的任何一个都可以提供基本概念的清晰说明,例如对称破坏和远距离有序。包括它们在内也将加强这样的信息,即在传统物理学的背景下开发的概念方法为更广阔的领域做出了巨大贡献。我的建议是将80页上的气泡和蜂箱中的一半切掉,以便为晶体留出空间。

球’s choices of which researchers to highlight are reasonable, though not comprehensive. The fact is that the broad scientific themes have been pieced together by many researchers rather than investigated definitively by one person, so 球’s story-based approach demands that he pick from among many alternatives. He has done a good job of balancing theory 和 experiment, covering work done around the world 和 representing the relevant scientific disciplines. The net effect, however, can be a bit disorienting to someone familiar with the science. The actual development of ideas about patterns involved multiple storylines playing out in parallel, 和 it would be interesting to know how 球 settled on the results he chose to highlight. Given his attention to many of the historical aspects of the science, a brief discussion of his own methodology would have made a nice addition, perhaps as an expanded preface.

A deeper problem is that it is hard to articulate a clear take-home message after reading one of the books. Following 球’一种思想思路需要极大的专注力,因为人们不仅要牢牢掌握科学线索,还必须牢牢掌握众多个人的名字和贡献。最后,这使得专家或新手都很难找到重要的科学主题。缓解此问题的一种方法可能是阅读结尾的结尾 分行 (该系列’ final book) before starting out. There, 球 provides a useful guide to the overarching scientific threads that tie the topics together –竞争,对称破坏,非平衡过程,耗散,不稳定性,相关性和缺陷。

过去,我曾经 自制挂毯 as one of several textbooks for a first-year undergraduate course on self-organization 和 the emergence of complex structure. 在 a seminar course for 15 students with varying backgrounds in mathematics 和 a teacher there to guide them, 球’早先的书效果很好,我很高兴看到他在书中添加了相当多的材料 性质’s Patterns 将其充实并更新。

I would like to think that there are a number of readers who would find the trilogy an exciting 和 rewarding project to tackle on their own, even outside a classroom setting. This is not the type of work, however, that will be devoured by teenagers who later cite it as their motivation to pursue a career in science. Such books are often inspirational precisely because they are not really comprehensible. 球’《三部曲》是为希望扩大自己的科学视野并学习了解他们在日常生活中遇到的结构的新方法的精明读者而写的。

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