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概念史的“分段连续”看法

在科学理论发展的旅程中,概念的严格定义往往是成熟期的产物。过早聚焦于此,可能忽视了概念早期的丰富演进。然而,深究其前清晰时期的历史,意味着要在众多相互矛盾的观点中寻找和辨别,这一过程没有明确的界限,取决于个人对观点荒谬程度的容忍以及时间、精力和兴趣的投入。

比如,最近我正在看的一本书——M. Jammer (1957), Concepts of Force, Harvard University Press,里面就说到:

A serious difficulty in the study of the development of a scientific concept lies in the necessarily inherent vagueness of its definition. This complication arises from the fact that the concept in question finds its strict specification only through its exact definition in science. This definition, however, historically viewed, is a rather late and advanced stage in its development. To limit the discussion to the concept thus defined means to ignore a major part of its life history.

该书的一段书评所说:

The story is a long and complicated one, demanding great skill on the part of the writer in the choice of the relevant elements in an enormous body of more or less obscure material. He has to search for the origin of the idea in the groping attempts of our ancestors to give an explanation for motion in general, based on the analogy with human exertion and activity represented in such terms as effort, force, power, work. He must then proceed to note how these ideas were refined by abstract thinkers, given quantitative status, and made useful for the solution of practical problems…

R. Lindsay (1957), Science, 126 (3278):848

我想,要是我也面临这样的复杂任务,该怎么办呢?我认为,面对这一复杂任务,寻找不同观点间的共性成为一种有效策略。这包括识别这些观点的共同接受之处,或它们共同探索问题的方向。通过从关键资料中识别这些共性,再以此为标准筛选其他资料,可以有效避免在信息海洋中迷失方向。需要注意的是,这种“共性”往往只在特定的时间段内明显,随着时代的发展,共同关注的焦点也可能发生变化。因此,这种方法可以用“分段连续”的方式来描述,其任务就像是“用分段连续的函数去拟合散点数据”一样。

作为以太论者的雷诺

雷诺(Osborne Reynolds)是一个以太论者。

我在很多年前,在豆瓣小站写了一篇《剪切增稠和以太》,讲了雷诺构想了了剪胀性流体(dilatant fluid)的物理本质之后,认为这是以太的假想性质可能基于的物理机制。但是很快就有了Michelson-Morley实验,否定了以太的存在。事实上在光速不变实验之后,雷诺仍然写了一本书,用很坚深的数学去构建以太流体的理论。这些都可以在Wikipedia上查到。

事实上,雷诺作为以太论者的迹相,就在他最为著名的工作——提出雷诺数的论文中,就已经体现。他在文中直接明确“不存在绝对时空”,并由此陈述出了一个特别深刻的见解:

As there is no such thing as absolute space or absolute time recognized in mechanical philosophy, to suppose that the character of motion of fluids in any way depended on absolute size or absolute velocity, would be to suppose such motion without the pale of the laws of motion. If then fluids in their motions are subject to these laws, what appears to be the dependance of the character of the motion on the absolute size of the tube and on the absolute velocity of the immersed body, must in reality be a dependance on the size of the tube as compared with the size of some other object, and on the velocity of the body as compared with some other velocity.

O. Reynolds (1883) Phil. Trans. R. Soc. A 174:935

以太作为一个后来被替代掉的范式或研究纲领,却驱使它曾经的“常规科学家”,以“修建保护带”为初衷,催生出后来仍具有强大生命力的物理观念。

John W. Lamperti

教科书的前言总是有各种宝藏。我备课时找随机过程的书。这一本——

John Lamperti (1977), Stochastic Processes: A Survey of the Mathematical Theory, Springer-Verlag

的前言有大量文字讨论了“科学的双刃剑”问题。这也许跟这本书出版的1970年代的时代有关;当时美国越战引发大规模反战浪潮。但是在一本随机过程的课本中用一大半的前言篇幅来讨论这个问题,多少反映了作者本人的特点。因此我去搜索了这一个作者,不想却打开了一个新世界的大门。他确实是无论是在学术生涯之内还是之外都积极就政治话题发声。例如他发表过关于死刑是否对谋杀有震慑力的统计学研究工作。他除了两本统计学教科书之外,还写了三本社会和政策话题的书。我从他的个人页同中了解到了另一本普利策奖的奥本海默传记、美国对中美洲国家政治的积极干涉和由此犯下的罪行、以及2012年以来美国选举法的一些倒退性变化等许多话题。他是“科学家是否要关心政治”这个问题的最佳注脚:如果科学家要关心政治,那他应只有一种倾向那就是左的倾向;只有一种立场,那就是世界和平的立场。