弗兰克·维尔切克是麻省理工学院物理学教授、量子色动力学的奠基人之一。因发现了量子色动力学的渐近自由现象，他在2004年获得了诺贝尔物理学奖。

撰文 | Frank Wilczek

翻译 | 胡风、梁丁当

中文版

构建复杂模型往往会带来新的突破，哪怕模型最终是有缺陷的。

著名物理学家理查德 · 费曼（Richard Feynman）的黑板上，一个个数学式子和电报似的任务清单写了又擦，擦了又写。唯有一句话始终保留在黑板的左上角 ：“如果我不能创造，我就没有真正理解。”直到1988年费曼去世，这句话仍留在他的黑板上。我不知道这句话到底对费曼意味着什么。但我猜，它某种程度上是一种自我告诫 ：“构建模型！”

这句箴言深植于科学实践。但在科学发展史上，这种研究方式可谓毁誉参半。著名的托勒密的“天球”和詹姆斯·克拉克 · 麦克斯韦（James Clerk Maxwell）的“机械以太”就是两个典型的例子。

托勒密的著作《至大论》完成于公元150年，一直到16世纪它依然是天文学的最高数学理论。著作的核心是一个精心构建的模型，用来模拟肉眼观测到的恒星、太阳、月亮以及水星、金星、火星、木星和土星等行星在天空中的运动。这些天体嵌在一个个大小不一、旋转速度不同的轮子上。其中一些轮子绕着另一个更大的轮子旋转，后者又再绕着另一个轮子旋转，形成所谓的本轮。在托勒密的数据驱动体系中，地球被赋予特殊的地位，固定在模型的中心。

尼古拉斯 · 哥白尼（Mikołaj Kopernik）的研究基于托勒密体系，却最终在根本上撼动了托勒密体系。他注意到在托勒密本轮的大小和旋转之间存在着一种系统性的联系。在托勒密体系中，这些联系不过是某种神秘的巧合。但哥白尼发现，如果在模型中允许地球以两种方式运动 ：每天绕轴转动，每年绕太阳运行，则这种联系就会自动满足。哥白尼的创新最终导致了对天体运动截然不同的解释 ；在牛顿的经典体系中，没有虚构的本轮，只有真实物体和描述它们的普适定律。它不再只是模型，而是赤裸裸的现实。

19世纪时，麦克斯韦为了尝试理解电磁现象，设想了一个与众不同的机械模型。他想象空间中堆满了看不见的滚摆和齿轮，它们忠实地传递着电磁的力和能量。通过计算，麦克斯韦惊讶地发现这些假想机械中的扰动居然以光速进行传播。他大胆地推断光是一种电磁扰动。后来，麦克斯韦抛弃了他的滚摆齿轮模型，提炼出了一组关于可观测的电场和磁场的普适定律。这就是我们今天使用的所谓麦克斯韦方程组。又一次，当真相如光芒喷薄而出，那些杂乱无章的模型也随之烟消云散。

传统的科学著作和论文往往对成熟的结果津津乐道，而忽视产生结果的曲折而充满错误的过程。所谓的科学“辉格派”对虚构的托勒密“本轮”模型和麦克斯韦“机械以太”模型嗤之以鼻。然而，如果没有托勒密精密的数学建模，哥白尼的革新和牛顿的发现也就无从谈起。

同样地，麦克斯韦的建模给他提供了一个“脚手架 ”：在最后被拆除前，它让麦克斯韦有了一个可以搭建理论的工作平台。在现代科学中，我们通过剪裁已有的材料与设计人工超材料来实现电磁场调控，这与麦克斯韦的思想一脉相承。

在一线工作的科学家喜欢宣传“独立于模型”的结果，而略过导致这些结果的混乱的创造性思维过程。这为读者节省了时间，也让科学家看起来很聪明。但当结果真的很重要的时候，了解这些结果诞生的过程不仅有趣也富有启发意义。詹姆斯·沃森（James Watson）在他的回忆录《双螺旋》（The Double Helix）中坦露了他发现DNA结构的曲折经历，让我们如获至宝。

我收到过的一个最好的幸运饼，其中有一句类似费曼格言的签语 ：“实践出真知。”这是一个睿智的建议，无论科学还是生活，都是如此。

英文版

The work of constructing elaborate systems often leads to breakthroughs—even when the systems themselves turn out to be flawed.

The blackboard of the famed physicist Richard Feynman mostly featured an everchanging mix of math and telegraphic to-do lists. But in the upper left-hand corner a boxed sentence lingered for years: “What I cannot create I do not understand.” It was still there when he died, in 1988. I don’t know exactly what that sentence meant to Feynman, but I suspect it was partly a self-reminding exhortation:“Make models!”

That advice has deep roots in scientific practice. It’s got a mixed reputation, though. Two famous historical examples, featuring Ptolemy’s “celestial spheres” and James Clerk Maxwell’s “mechanical ether,” show why.

Ptolemy’s treatise “Almagest” (Arabic for “The Greatest”) was the state of the art in mathematical astronomy from its genesis around the year 150 into the 16th century. Its centerpiece was an elaborate model that reproduced the observed motion of objects seen in the sky by the naked eye—stars, the sun, the moon, and the planets Mercury, Venus, Mars, Jupiter and Saturn. They were carried along by celestial spheres of different sizes, rotating at different rates. Some of the spheres had to roll onto other spheres, which rolled onto still others, making so-called epicycles. In Ptolemy’s data-driven system, Earth was taken to be a fixed vantage point at the center.

Nicolaus Copernicus (1473-1543), whose work ultimately undermined Ptolemy’s system, originally built upon it. He noticed systematic relationships among the sizes and rotations of Ptolemy’s spheres. Within Ptolemy’s system those relationships were mysterious coincidences, but Copernicus found that they followed automatically if one’s model allowed Earth to move in two ways: daily around an axis and yearly around the Sun. Copernicus’s reforms ultimately led to a radically different account of celestial motion; in Newton’s classical system there are no imaginary celestial spheres, but only physical bodies and universal laws. It is no mere model, but reality laid bare.

In the 19th century James Clerk Maxwell, striving to understand electricity and magnetism, imagined a different mechanical model. Maxwell’s space-filling mishmash of invisible wheels and gears faithfully transmitted the energies and forces of electrcity and magnetism. Amazingly, Maxwell discovered (by calculation) that disturbances within his machine spread at the observed speed of light. He boldly deduced that light is an electromagnetic disturbance. Later Maxwell dispensed with his wheels and gears, to distill a set of universal laws that only involve things we can observe, namely electric and magnetic fields. These are the so-called Maxwell equations that we use today. Here again, revealed reality blew away kludgy models.

Traditional science texts tend to celebrate mature results, while deprecating the meandering, often erratic processes that led to them. That so-called “Whiggish” tradition of science disdains the clutter of Ptolemy’s “epicycles” and Maxwell’s “mechanical ether.”Yet without Ptolemy’s mathematically precise modeling, Copernicus’s reforms and Newton’s revelations would have been unthinkable—literally.

Likewise, Maxwell’s modeling gave him a scaffolding he could build on (and later jettison). Its spirit lives on in the modern science of crafting known materials—and designing “meta-materials” —to sculpt the behavior of electromagnetic fields.

Practicing scientists like to advertise “modelindependent” results and suppress the messy creative thought processes that led to them. This saves time for readers, and makes the scientists look clever. But when results are truly important, it’s entertaining and instructive to find out how people got to them. James Watson’s memoir “The Double Helix” aired his dirty linen around discovering the structure of DNA and gifted us a gem.

My best-ever fortune cookie contained a variant of Feynman’s maxim: “The work will teach you how to do it.” It is wise advice, in science as in life.

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