2009.02.25

科學家根據(jù)自己的經(jīng)驗和認識憑直覺所做的判斷常常被外行貼上“武斷”或者“專斷”的標簽。很多自以為具有探索精神的人甚至認為這些沒有100%根據(jù)的憑直覺的判斷缺乏邏輯，甚至是有悖于科學的自由探索精神。

我記得十年或者十多年前讀到著名的理論物理學家Freeman Dyson在楊振寧先生的一個生日（大概是70歲）聚會上的講話，談到他自己在1953年與費米的一次會面中，如何接受了費米憑直覺所做的判斷，放棄了自己當時正在做的研究，并改變研究方向，而至今仍感到幸運的故事。他在那個講話中提到這個故事，是要說明楊振寧先生曾經(jīng)在芝加哥大學的工作和學習，雖然并不是費米的入室弟子，但費米對于楊先生的科學思想和判斷仍然有非常重要的影響。

Dyson的那篇講話我是在《英語世界》雜志上看到的。過去20年我只偶然翻閱過一次《英語世界》，就讀到這篇文章，應該算是鬼使神差，也說明《英語世界》是值得推薦的一個刊物，雖然我很少讀。我在網(wǎng)上沒有找到Dyson的這篇講話，不過卻發(fā)現(xiàn)2004年的《自然》（Nature）雜志上有Dyson專門回憶與費米會面的這一經(jīng)歷的一篇更為詳細的短文章《Turning points -A meeting with Enrico Fermi》。所以把它找來放在這里，供有興趣的朋友們參考。

Nature雜志《Turning points -A meeting with Enrico Fermi》原文鏈接：http://www./nature/journal/v427/n6972/full/427297a.html

Dyson的故事說的是他剛出道的時候自己的一個理論計算結(jié)果能夠很好地解釋費米的一個重要的實驗結(jié)果，于是興高采烈地去芝加哥找費米討論。可是費米看都沒有看他的東西，就告訴他說他的計算不可能有意義。雖然費米當時并不真正知道正確的理論是什么，但費米給Dyson提供了很值得參考的幾條理由。費米說做好的理論與計算有兩種方式：

"There are two ways of doing calculations in theoretical physics", he said. "One way, and this is the way I prefer, is to have a clear physical picture of the process that you are calculating. The other way is to have a precise and self-consistent mathematical formalism. You have neither."

得知Dyson的理論中有近似，并且用到4個參數(shù)，費米又說：

"I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk."

Dyson的文章中說得很清楚，雖然他自己的計算結(jié)果與實驗符合很好，他后來為了學生的學位問題也把計算結(jié)果總結(jié)出來發(fā)表了一篇《物理學評論》的論文，但他還是接受了費米的判斷，自己很快就轉(zhuǎn)行去做凝聚態(tài)物理的研究了。直到十幾年后Gell-Mann發(fā)現(xiàn)了夸克，人們才知道Dyson當年的理論計算是基于不正確的理論。但是，費米的一席話拯救了Dyson，使他和他的學生們免于在“一個黑巷子中停滯不前”（getting stuck in a blind alley）。Dyson在文章開篇大有“聽君一席話，勝讀十年書”的味道。

One of the big turning points in my life was a meeting with Enrico Fermi in the spring of 1953. In a few minutes, Fermi politely but ruthlessly demolished a programme of research that my students and I had been pursuing for several years. He probably saved us from several more years of fruitless wandering along a road that was leading nowhere. I am eternally grateful to him for destroying our illusions and telling us the bitter truth.

按照我們科學網(wǎng)上有些人的看法，Dyson完全可以反過來指責費米是“武斷的學霸”。因為費米自己沒有充足的理由，也不了解Dyson的研究的細節(jié)，就直接宣判Dyson的研究是錯誤的，還拿了一些不是100%正確的說法來給自己的武斷的“判斷”做依據(jù)。Dyson完全可以選擇堅持下去，以證明自己的理論計算是可靠的和正確的。可是，事實表明費米當年憑直覺所做的判斷是正確的。

科學判斷和任何日常生活中的判斷一樣，從來都不是基于100%可靠的證據(jù)。但是，科學判斷和任何日常生活中的判斷同樣都存在對錯的問題。沒有人會說大科學家或者著名學者的判斷和理解就一定會100%正確，可是如果根據(jù)這一點就去肯定和支持那些質(zhì)疑他們的判斷的“小人物”的意見，99%（或者十有八九）以上的情況會是適得其反的。

其實有經(jīng)驗的學者和科學家會常常用費米上面的所提到的標準來判斷新的理論和計算結(jié)果，以及新的實驗結(jié)果，以免將大量的精力甚至經(jīng)費耗費在不值得深究的問題上。這樣做也許偶爾會錯過或者推遲某些方面的科學發(fā)現(xiàn)，但是更重要的是可以避免更多錯誤和浪費的發(fā)生。

我在與學生討論問題時，常常會提到Dyson的這個故事。迄今為止，我們在研究中所做的判斷的確是鮮有錯誤。人生苦短，將有限的精力浪費在追求看起來很美但其實不值得的課題上，還不如像我一樣抽時間在科學網(wǎng)上寫一些博客文章更好。

我對科學網(wǎng)上張志東先生的《激辯猜想》中提到的三維ising模型精確解的判斷遵循的就是費米對Dyson講的原則。或許我是錯的，也未可知。

Dyson的故事，算是對吳寶俊小朋友的博文《忽不忽悠與是否改行無關！》的一個回答，以及對我自己前兩天的《被改行的博士后忽悠了》博文的一個補充。

吳寶俊《忽不忽悠與是否改行無關！》博文鏈接：http://www.sciencenet.cn/m/user_content.aspx?id=216961

我的《被改行的博士后忽悠了》博文鏈接：http://www.sciencenet.cn/m/user_content.aspx?id=216791

我以前寫過一篇有關Dyson的書《Scientist as Rebel》（《作為反叛者的科學家》）的博文。希望了解的朋友也可以去看一看。

《贊美民間科學家》博文鏈接：http://www./m/user_content.aspx?id=6945

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Essay
Nature 427, 297 (22 January 2004) | doi:10.1038/427297a

標題：
Turning points - A meeting with Enrico Fermi

作者：Freeman Dyson, Freeman Dyson is at the Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA.

副題：How one intuitive physicist rescued a team from fruitless research.

正文： One of the big turning points in my life was a meeting with Enrico Fermi in the spring of 1953. In a few minutes, Fermi politely but ruthlessly demolished a programme of research that my students and I had been pursuing for several years. He probably saved us from several more years of fruitless wandering along a road that was leading nowhere. I am eternally grateful to him for destroying our illusions and telling us the bitter truth.

Fermi was one of the great physicists of our time, outstanding both as a theorist and as an experimenter. He led the team that built the first nuclear reactor in Chicago in 1942. By 1953 he was head of the team that built the Chicago cyclotron, and was using it to explore the strong forces that hold nuclei together. He made the first accurate measurements of the scattering of mesons by protons, an experiment that gave the most direct evidence then available of the nature of the strong forces.

At that time I was a young professor of theoretical physics at Cornell University, responsible for directing the research of a small army of graduate students and postdocs. I had put them to work calculating meson–proton scattering, so that their theoretical calculations could be compared with Fermi's measurements. In 1948 and 1949 we had made similar calculations of atomic processes, using the theory of quantum electrodynamics, and found spectacular agreement between experiment and theory. Quantum electrodynamics is the theory of electrons and photons interacting through electromagnetic forces. Because the electromagnetic forces are weak, we could calculate the atomic processes precisely. By 1951, we had triumphantly finished the atomic calculations and were looking for fresh fields to conquer. We decided to use the same techniques of calculation to explore the strong nuclear forces. We began by calculating meson–proton scattering, using a theory of the strong forces known as pseudoscalar meson theory. By the spring of 1953, after heroic efforts, we had plotted theoretical graphs of meson–proton scattering. We joyfully observed that our calculated numbers agreed pretty well with Fermi's measured numbers. So I made an appointment to meet with Fermi and show him our results. Proudly, I rode the Greyhound bus from Ithaca to Chicago with a package of our theoretical graphs to show to Fermi.

When I arrived in Fermi's office, I handed the graphs to Fermi, but he hardly glanced at them. He invited me to sit down, and asked me in a friendly way about the health of my wife and our new-born baby son, now fifty years old. Then he delivered his verdict in a quiet, even voice. "There are two ways of doing calculations in theoretical physics", he said. "One way, and this is the way I prefer, is to have a clear physical picture of the process that you are calculating. The other way is to have a precise and self-consistent mathematical formalism. You have neither." I was slightly stunned, but ventured to ask him why he did not consider the pseudoscalar meson theory to be a self-consistent mathematical formalism. He replied, "Quantum electrodynamics is a good theory because the forces are weak, and when the formalism is ambiguous we have a clear physical picture to guide us. With the pseudoscalar meson theory there is no physical picture, and the forces are so strong that nothing converges. To reach your calculated results, you had to introduce arbitrary  cut-off procedures that are not based either on solid physics or on solid mathematics."

In desperation I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, "How many arbitrary parameters did you use for your calculations?" I thought for a moment about our cut-off procedures and said, "Four." He said, "I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk." With that, the conversation was over. I thanked Fermi for his time and trouble, and sadly took the next bus back to Ithaca to tell the bad news to the students. Because it was important for the students to have their names on a published paper, we did not abandon our calculations immediately. We finished them and wrote a long paper that was duly published in the Physical Review with all our names on it. Then we dispersed to find other lines of work. I escaped to Berkeley, California, to start a new career in condensed-matter physics.

Looking back after fifty years, we can clearly see that Fermi was right. The crucial discovery that made sense of the strong forces was the quark. Mesons and protons are little bags of quarks. Before Murray Gell-Mann discovered quarks, no theory of the strong forces could possibly have been adequate. Fermi knew nothing about quarks, and died before they were discovered. But somehow he knew that something essential was missing in the meson theories of the 1950s. His physical intuition told him that the pseudoscalar meson theory could not be right. And so it was Fermi's intuition, and not any discrepancy between theory and experiment, that saved me and my students from getting stuck in a blind alley.