撰文 |?Frank?Wilczek

翻譯 |?胡風(fēng)、梁丁當(dāng)

中文版

構(gòu)建復(fù)雜模型往往會(huì)帶來新的突破，哪怕模型最終是有缺陷的。
著名物理學(xué)家理查德 · 費(fèi)曼（Richard Feynman）的黑板上，一個(gè)個(gè)數(shù)學(xué)式子和電報(bào)似的任務(wù)清單寫了又擦，擦了又寫。唯有一句話始終保留在黑板的左上角 ：“如果我不能創(chuàng)造，我就沒有真正理解?！敝钡?988年費(fèi)曼去世，這句話仍留在他的黑板上。我不知道這句話到底對費(fèi)曼意味著什么。但我猜，它某種程度上是一種自我告誡 ：“構(gòu)建模型！”
這句箴言深植于科學(xué)實(shí)踐。但在科學(xué)發(fā)展史上，這種研究方式可謂毀譽(yù)參半。著名的托勒密的“天球”和詹姆斯·克拉克 · 麥克斯韋（James Clerk Maxwell）的“機(jī)械以太”就是兩個(gè)典型的例子。
托勒密的著作《至大論》完成于公元150年，一直到16世紀(jì)它依然是天文學(xué)的最高數(shù)學(xué)理論。著作的核心是一個(gè)精心構(gòu)建的模型，用來模擬肉眼觀測到的恒星、太陽、月亮以及水星、金星、火星、木星和土星等行星在天空中的運(yùn)動(dòng)。這些天體嵌在一個(gè)個(gè)大小不一、旋轉(zhuǎn)速度不同的輪子上。其中一些輪子繞著另一個(gè)更大的輪子旋轉(zhuǎn)，后者又再繞著另一個(gè)輪子旋轉(zhuǎn)，形成所謂的本輪。在托勒密的數(shù)據(jù)驅(qū)動(dòng)體系中，地球被賦予特殊的地位，固定在模型的中心。
尼古拉斯 · 哥白尼（Miko?aj Kopernik）的研究基于托勒密體系，卻最終在根本上撼動(dòng)了托勒密體系。他注意到在托勒密本輪的大小和旋轉(zhuǎn)之間存在著一種系統(tǒng)性的聯(lián)系。在托勒密體系中，這些聯(lián)系不過是某種神秘的巧合。但哥白尼發(fā)現(xiàn)，如果在模型中允許地球以兩種方式運(yùn)動(dòng) ：每天繞軸轉(zhuǎn)動(dòng)，每年繞太陽運(yùn)行，則這種聯(lián)系就會(huì)自動(dòng)滿足。哥白尼的創(chuàng)新最終導(dǎo)致了對天體運(yùn)動(dòng)截然不同的解釋 ；在牛頓的經(jīng)典體系中，沒有虛構(gòu)的本輪，只有真實(shí)物體和描述它們的普適定律。它不再只是模型，而是赤裸裸的現(xiàn)實(shí)。
19世紀(jì)時(shí)，麥克斯韋為了嘗試?yán)斫怆姶努F(xiàn)象，設(shè)想了一個(gè)與眾不同的機(jī)械模型。他想象空間中堆滿了看不見的滾擺和齒輪，它們忠實(shí)地傳遞著電磁的力和能量。通過計(jì)算，麥克斯韋驚訝地發(fā)現(xiàn)這些假想機(jī)械中的擾動(dòng)居然以光速進(jìn)行傳播。他大膽地推斷光是一種電磁擾動(dòng)。后來，麥克斯韋拋棄了他的滾擺齒輪模型，提煉出了一組關(guān)于可觀測的電場和磁場的普適定律。這就是我們今天使用的所謂麥克斯韋方程組。又一次，當(dāng)真相如光芒噴薄而出，那些雜亂無章的模型也隨之煙消云散。
傳統(tǒng)的科學(xué)著作和論文往往對成熟的結(jié)果津津樂道，而忽視產(chǎn)生結(jié)果的曲折而充滿錯(cuò)誤的過程。所謂的科學(xué)“輝格派”對虛構(gòu)的托勒密“本輪”模型和麥克斯韋“機(jī)械以太”模型嗤之以鼻。然而，如果沒有托勒密精密的數(shù)學(xué)建模，哥白尼的革新和牛頓的發(fā)現(xiàn)也就無從談起。
同樣地，麥克斯韋的建模給他提供了一個(gè)“腳手架 ”：在最后被拆除前，它讓麥克斯韋有了一個(gè)可以搭建理論的工作平臺(tái)。在現(xiàn)代科學(xué)中，我們通過剪裁已有的材料與設(shè)計(jì)人工超材料來實(shí)現(xiàn)電磁場調(diào)控，這與麥克斯韋的思想一脈相承。
在一線工作的科學(xué)家喜歡宣傳“獨(dú)立于模型”的結(jié)果，而略過導(dǎo)致這些結(jié)果的混亂的創(chuàng)造性思維過程。這為讀者節(jié)省了時(shí)間，也讓科學(xué)家看起來很聰明。但當(dāng)結(jié)果真的很重要的時(shí)候，了解這些結(jié)果誕生的過程不僅有趣也富有啟發(fā)意義。詹姆斯·沃森（James Watson）在他的回憶錄《雙螺旋》（The Double Helix）中坦露了他發(fā)現(xiàn)DNA結(jié)構(gòu)的曲折經(jīng)歷，讓我們?nèi)绔@至寶。
我收到過的一個(gè)最好的幸運(yùn)餅，其中有一句類似費(fèi)曼格言的簽語 ：“實(shí)踐出真知?！边@是一個(gè)睿智的建議，無論科學(xué)還是生活，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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