Knuth 是非常著名的計算機科學家，有讀過 CS 應該都聽過這位大師，他最有名的貢獻是撰寫經典巨著《電腦程式設計藝術》，洋洋灑灑預計要出七大冊，目前還在撰寫中！ (我有時候在想：寫這麼厚，最後看完的能有幾人呢 ... XD)
一、關於講者
唐納德·爾文·克努斯 (Donald Ervin Knuth，漢名：高德納)：1938 年 1 月 10 日 ~
高德納出生於美國密爾沃基，是著名的電腦科學家，為 1974 年圖靈獎得主，史丹福大學計算機系榮譽退休教授。高德納教授為現代電腦科學的先驅人物，創造了演算法分析的領域，在數個理論計算機科學的分支做出基石般的貢獻。在電腦科學及數學領域發表了多部具廣泛影響的論文和著作。
高德納最為人知的事蹟是，他是經典巨著《電腦程式設計藝術》（The Art of Computer Programming）的作者。此書是計算機科學界最受高度敬重的參考書籍之一，被《美國科學家》雜志列為 20 世紀最重要的 12 本物理科學類專著之一，與愛因斯坦《相對論》、狄拉克《量子力學》、理查·費曼《量子電動力學》等經典比肩而立。
此外還是排版軟體 TEX 和字型設計系統 Metafont 的發明人。提出文學編程的概念，並創造了 WEB 與 CWEB 軟體，作為文學編程開發工具。
在 CS 大學課程中有很多地方可以看到高德納的事蹟：
- 資料結構中 B-Tree 多元樹結構。
- 演算法中 Knuth–Morris–Pratt 字串搜尋演算法。
- 編譯器中 LR(K) 類語法剖析器。
- 論文時，用 LaTex 寫數學式。
他也說了不少讓許多程式設計師心有戚戚焉的名言：
過早最佳化是萬惡的根源。
A person does not really understand something until after teaching it to a computer.
一個人在教會電腦之前，別說他真懂得什麼。
Computers are good at following instructions, but not at reading your mind.
電腦善於遵循指令，但不善於理解你的思維。
Beware of bugs in the above code; I have only proved it correct, not tried it.
小心上面程式中的 bug；我只證明這些程式是正確的，但沒有試過。
p.s. 上面這句可以相對於 E. W. Dijkstra 的名句 “In programming, nothing is cheaper than not introducing the bugs in the first place.” 來看；Knuth 的觀點在當前偏應用的程式設計師圈中較能接受，因為現實情境中大家總是在事後除錯，而較少以證明的方式保證程式的健壯性。
二、原文講稿及部分中文翻譯
1974 年 Donald E. Knuth 的圖靈獎演講 - 計算機編程：一門藝術
When Communications of the ACM began publication in 1959, the members of ACM'S Editorial Board made the following remark as they described the purposes of ACM'S periodicals [2]:
"If computer programming is to become an important part of computer research and development, a transition of programming from an art to a disciplined science must be effected."
Such a goal has been a continually recurring theme during the ensuing years; for example, we read in 1970 of the "first steps toward transforming the art of programming into a science" [26]. Meanwhile we have actually succeeded in making our discipline a science, and in a remarkably simple way: merely by deciding to call it "computer science."
早在1959年 「美國計算機學會通訊」（Communications of the ACM）刊行之初，通訊編委會就學會期刊發行之目的做出過如下說明：「如果計算機編程要想成為計算機研究和發展中的重要一環，就必須實現其從一門藝術到一門嚴肅科學的轉變」。這個目標一直是接下若干年來被不斷重申的主題；例如，我們在 1970 年曾讀到 「編程從藝術變為科學的首要幾步」。與此同時，我們確實已經成功地將我們的學科打造成一門科學，而且是以一種不費吹灰之力的方式：僅僅是決定把它叫做「計算機科學」。
Implicit in these remarks is the notion that there is something undesirable about an area of human activity that is classified as an "art"; it has to be a Science before it has any real stature. On the other hand, I have been working for more than 12 years on a series of books called "The Art of Computer Programming." People frequently ask me why I picked such a title; and in fact some people apparently don't believe that I really did so, since I've seen at least one bibliographic reference to some books called "The Act of Computer Programming."
在那些言論之中暗藏著一種觀念，就是認為有某種不太對勁的東西存在於那個被劃歸為「藝術」的人類活動領域中；它必須得是一門科學才能具有一點真正的地位。另一方面，十二多年以來，我一直在編寫一部叢書,名為「計算機編程的藝術」（The Art of Computer Programming）。人們經常問我為什麼選用了這麼一個書名；事實上，一些人顯然並不相信我的確取了這麼個書名，因為我見到過至少有一個參考文獻上列出了某些書, 名字叫做「計算機編程的行為」（The Act of Computer Programming）
In this talk I shall try to explain why I think "Art" is the appropriate word. I will discuss what it means for something to be an art, in contrast to being a science; I will try to examine whether arts are good things or bad things; and I will try to show that a proper viewpoint of the subject will help us all to improve the quality of what we are now doing.
在本次講演中，我將試圖解釋為什麼我認為「藝術」是個合適的字眼。我要討論某件東西若成為一門藝術，比照它成為一門科學，將會意味著什麼；而且我將闡述，一種對該學科恰當的看法將會幫助我們所有人提高當前從事的工作的質量。
One of the first times I was ever asked about the title of my books was in 1966, during the last previous ACM national meeting held in Southern California. This was before any of the books were published, and I recall having lunch with a friend at the convention hotel. He knew how conceited I was, already at that time, so he asked if I was going to call my books "An Introduction to Don Knuth." I replied that, on the contrary, I was naming the books after him. His name: Art Evans. (The Art of Computer Programming, in person.)
被問及書名的事最初是發生在1966年，是在上次南加州舉行的 ACM 全國大會期間。那時叢書一本也還沒出版，並且我記得是在和一個朋友在舉行會議的賓館共進午餐。他知道我是多麼自負，在那時候就就這樣了，所以他問我能不能給書起名叫「Don Knuth 導論」（An Introduction to Don Knuth）。我回答說，恰恰相反，我將用他的名字給書命名。他的名字叫: Art Evans.
From this story we can conclude that the word "art" has more than one meaning. In fact, one of the nicest things about the word is that it is used in many different senses, each of which is quite appropriate in connection with computer programming. While preparing this talk, I went to the library to find out what people have written about the word "art" through the years; and after spending several fascinating days in the stacks, I came to the conclusion that "art" must be one of the most interesting words in the English language.
從這個故事中，我們可以得出結論，「藝術」這個字不僅僅只有一個意思。事實上，這個詞最妙的地方在於，它能用在很多語境中，而每一個語義都能和計算機編程很恰當的聯系起來。在准備本次演講時，我去圖書館查找了歷年來人們對「藝術」這個詞都說道了些什麼；在書庫裡迷戀幾天後，我得出結論：「藝術」（Art）一定是英語語言中最有趣的詞之一。
The Arts of Old 藝術的古義
If we go back to Latin roots, we find ars, artis meaning "skill." It is perhaps significant that the corresponding Greek word was τεχνη, the root of both "technology" and "technique."
如果我們追查到拉丁詞根，我們發現 ars, artis 是表示「技能」的意思。或許重要的是，它所對應的希臘詞為（希臘文），是「科技」和「技術」兩個詞共同的詞根。
Nowadays when someone speaks of "art" you probably think first of "fine arts" such as painting and sculpture, but before the twentieth century the word was generally used in quite a different sense. Since this older meaning of "art" still survives in many idioms, especially when we are contrasting art with science, I would like to spend the next few minutes talking about art in its classical sense.
如今，當人們說起「art」，你可能最先想到的是「工藝美術」，比如繪畫和雕塑。但在 12 世紀以前，這個詞通常被用於相當不同的涵義。由於「art」的這種舊義在很多成語中仍具有生命力，特別是當我們把藝術和科學做對比的時候, 所以我想接下來化幾分鐘講一講藝術（Art）的經典涵義。
In medieval times, the first universities were established to teach the seven so-called "liberal arts," namely grammar, rhetoric, logic, arithmetic, geometry, music, and astronomy. Note that this is quite different from the curriculum of today's liberal arts colleges, and that at least three of the original seven liberal arts are important components of computer science. At that time, an "art" meant something devised by man's intellect, as opposed to activities derived from nature or instinct; "liberal" arts were liberated or free, in contrast to manual arts such as plowing (cf. [6]). During the middle ages the word "art" by itself usually meant logic [4], which usually meant the study of syllogisms.
在中世紀，最初的一批大學建成，講授所謂的七種「文科」（liberal arts），即語法，修辭，邏輯，算術，幾何，音樂和天文。注意這和今天的文科院校的課程設置大相徑庭. 最初的七門liberal arts中至少有三門是計算機科學的重要組成。在那個時期，「art」指人的智力構想出來的東西，它與源自於自然或出於本能的行為相對。「liberal」art 是指被解放的或自由的，與manual art，例如耕種相對。在中世紀，「art」一詞本身通常指邏輯學，而且通常指對三段論（演繹）的研究。
Science vs. Art 科學 vs 藝術
The word "science" seems to have been used for many years in about the same sense as "art"; for example, people spoke also of the seven liberal sciences, which were the same as the seven liberal arts [1]. Duns Scotus in the thirteenth century called logic "the Science of Sciences, and the Art of Arts" (cf. [12, p. 34f]). As civilization and learning developed, the words took on more and more independent meanings, "science" being used to stand for knowledge, and "art" for the application of knowledge. Thus, the science of astronomy was the basis for the art of navigation. The situation was almost exactly like the way in which we now distinguish between "science" and "engineering."
看起來，在相當長的歲月中,「科學」（Science）幾乎被用做和「藝術」（art）同義；例如，人們也有七種 liberal sciences 的說法，這與七種 liberal arts 說的是同一個意思。隨著文明和知識的發展，兩個詞的涵義越來越獨立，「科學」被用來代表知識，而「藝術」代表對知識的應用。因此，天文科學是航海藝術的基礎。這種情況和我們現在區分「科學」和「工程」幾乎是一模一樣。
Many authors wrote about the relationship between art and science in the nineteenth century, and I believe the best discussion was given by John Stuart Mill. He said the following things, among others, in 1843 [28]:
Several sciences are often necessary to form the groundwork of a single art. Such is the complication of human affairs, that to enable one thing to be done, it is often requisite to know the nature and properties of many things... Art in general consists of the truths of Science, arranged in the most convenient order for practice, instead of the order which is the most convenient for thought. Science groups and arranges its truths so as to enable us to take in at one view as much as possible of the general order of the universe. Art... brings together from parts of the field of science most remote from one another, the truths relating to the production of the different and heterogeneous conditions necessary to each effect which the exigencies of practical life require.
在 19 世紀, 有很多人著述藝術和科學的關系，我認為最好討論是 John Stuart Mill 提出的。他在 1843 年，說了包括在下面的一段話：
單單一門藝術通常需要幾門科學做基礎。這是由於人類活動的復雜性，以致於若想做成一件事，通常需要了解 很多事情的本質和特性…… 藝術一般包含著科學的真理，以最便於實踐，而不是以最便於思考的方式組織起來。科學歸類並組織其真理，以便讓我們對盡可能多的宇宙普遍秩序建立起統一的看法。藝術…把相互之間有天壤之別的科學領域融合起來，即，那些人類各種現實生活所密切需要的, 創造不同的、各向異性條件所相關的真理。
As I was looking up these things about the meanings of "art," I found that authors have been calling for a transition from art to science for at least two centuries. For example, the preface to a textbook on mineralogy, written in 1784, said the following [17]: "Previous to the year 1780, mineralogy, though tolerably understood by many as an Art, could scarce be deemed a Science."
當我考究「藝術」涵義的時候，我發現在至少兩個世紀中，著作者們一直在倡導藝術向科學轉變。例如，在一本寫於 1784 年的礦物學教科書的前言中，是這樣寫的：「在 1780 年之前，礦物學，雖然被很多人大度地理解為一門藝術，但若視之為科學，卻是驚世駭俗。」
According to most dictionaries "science" means knowledge that has been logically arranged and systematized in the form of general "laws." The advantage of science is that it saves us from the need to think things through in each individual case; we can turn our thoughts to higher-level concepts. As John Ruskin wrote in 1853 [32]: "The work of science is to substitute facts for appearances, and demonstrations for impressions."
依照大多數字典，「科學」指能邏輯地條理和系統化為普遍「定律」的知識。科學的優點是使我們不必通過個例來思考事情；我們能把思維轉向更高層次的概念。正如 John Ruskin 在 1853 年寫道：「科學的工作是用事實取代表象，用實證取代印象」。
It seems to me that if the authors I studied were writing today, they would agree with the following characterization: Science is knowledge which we understand so well that we can teach it to a computer; and if we don't fully understand something, it is an art to deal with it. Since the notion of an algorithm or a computer program provides us with an extremely useful test for the depth of our knowledge about any given subject, the process of going from an art to a science means that we learn how to automate something.
在我看來，如果我研究過的那些作者們今天仍在寫作的話，他們也許同意以下的劃分：科學是這樣一種知識，我們能如此透徹理解，以至於我們可以把它教授給一台計算機；如果我們不能完全理解某件事物，對付它將是一門藝術。因為一個算法概念或者一段計算機程序提供給我們一種極其有用的測試手段，可以用來檢測我們對某個特定知識掌握的深度，因此，從藝術走向科學的過程便意味著我們學會如何實現自動化。
Artificial intelligence has been making significant progress, yet there is a huge gap between what computers can do in the foreseeable future and what ordinary people can do. The mysterious insights that people have when speaking, listening, creating, and even when they are programming, are still beyond the reach of science; nearly everything we do is still an art.
人工智能已經取得了重要的進展，然而，在可預見的將來，計算機所能做的比起普通人所能做的還存在著巨大的差距。人們在聽，說，創造，甚至在編程時所具有的神奇的洞察力依然超越了科學之所能及；我們所做的幾乎每件事依然是一門藝術。
From this standpoint it is certainly desirable to make computer programming a science, and we have indeed come a long way in the 15 years since the publication ot the remarks I quoted at the beginning of this talk. Fifteen years ago computer programming was so badly understood that hardly anyone even thought about proving programs correct; we just fiddled with a program until we "knew" it worked. At that time we didn't even know how to express the concept that a program was correct, in any rigorous way. It is only in recent years that we have been learning about the processes of abstraction by which programs are written and understood; and this new knowledge about programming is currently producing great payoffs in practice, even though few programs are actually proved correct with complete rigor, since we are beginning to understand the principles of program structure. The point is that when we write programs today, we know that we could in principle construct formal proofs of their correctness if we really wanted to, now that we understand how such proofs are formulated. This scientific basis is resulting in programs that are significantly more reliable than those we wrote in former days when intuition was the only basis of correctness.
從這個觀點來看，讓計算機編程成為一種科學當然是很誘人的，而且，從我演講開始時所引用的那個觀點發表算起，我們在 15 年裡確實走過了很長的一段路。十五年前，人們對計算機編程的理解是如此貧乏，以致於沒有人甚至想過要證明程序的正確性；我們只是一味鼓搗一道程序直到我們「知道」它能運行了。那時，我們甚至不知道如何用一種嚴格的方式來表達一種概念, 說明一段程序是正確。只是在近年來，我們才開始學習編寫及理解程序時所運用的抽象過程；這種關於編程的新知識正在實踐中取得很大的成效，因為我們正在開始理解程序結構的原理，即便是在實際中，很少有程序能被完全嚴格地證明為正確的。問題的要點是，當我們今天編程時，我們知道在原則上，我們能構造出正規證明來證明程序的正確性，如果我們確實想這樣做的話。而且現在我們也理解這種證明是如何表述出來的。這種科學基礎正讓程序的可靠性顯著提高，比起過去我們寫程序時，正確性與否全要靠直覺。
The field of "automatic programming" is one of the major areas of artificial intelligence research today. Its proponents would love to be able to give a lecture entitled "Computer Programming as an Artifact" (meaning that programming has become merely a relic of bygone days), because their aim is to create machines that write programs better than we can, given only the problem specification. Personally I don't think such a goal will ever be completely attained, but I do think that their research is extremely important, because everything we learn about programming helps us to improve our own artistry. In this sense we should continually be striving to transform every art into a science: in the process, we advance the art.
「自動編程」 是當今人工智能研究的主要領域之一。它的支持者也許喜歡能做個題為「計算機編程: 一種手工藝」 的講座（Computer Programming as an Artifact）（意思是編程已成為昔日黃花），因為他們的目標是創造出僅僅給出說明書，就能編寫程序的機器，而且編寫的比我們更好。我個人的觀點，並不認為這種目標將能完全實現，但我的確認為他們的研究極其重要，因為我們從編程中學到的每一點都幫助我們提高自身的藝術修養。在這種意義上，我們應該繼續努力，把每一種藝術轉變成科學：在這個過程中，我們把藝術推向前進。
Science and Art
Our discussion indicates that computer programming is by now both a science and an art, and that the two aspects nicely complement each other. Apparently most authors who examine such a question come to this same conclusion, that their subject is both a science and an art, whatever their subject is (cf. [25]). I found a book about elementary photography, written in 1893, which stated that "the development of the photographic image is both an art and a science" [13]. In fact, when I first picked up a dictionary in order to study the words "art" and "science," I happened to glance at the editor's preface, which began by saying, "The making of a dictionary is both a science and an art." The editor of Funk & Wagnall's dictionary [27] observed that the painstaking accumulation and classification of data about words has a scientific character, while a well-chosen phrasing of definitions demands the ability to write with economy and precision: "The science without the art is likely to be ineffective; the art without the science is certain to be inaccurate."
When preparing this talk I looked through the card catalog at Stanford library to see how other people have been using the words "art" and "science" in the titles of their books. This turned out to be quite interesting.
For example, I found two books entitled The Art of Playing the Piano [5, 15], and others called The Science of Pianoforte Technique [10], The Science of Pianoforte Practice [30]. There is also a book called The Art of Piano Playing: A Scientific Approach [22].
Then I found a nice little book entitled The Gentle Art of Mathematics [31], which made me somewhat sad that I can't honestly describe computer programming as a "gentle art." I had known for several years about a book called The Art of Computation, published in San Francisco, 1879, by a man named C. Frusher Howard [14]. This was a book on practical business arithmetic that had sold over 400,000 copies in various editions by 1890. I was amused to read the preface, since it shows that Howard's philosophy and the intent of his title were quite different from mine; he wrote: "A knowledge of the Science of Number is of minor importance; skill in the Art of Reckoning is absolutely indispensible."
Several books mention both science and art in their titles, notably The Science of Being and Art of Living by Maharishi Mahesh Yogi [24]. There is also a book called The Art of Scientific Discovery [11], which analyzes how some of the great discoveries of science were made.
So much for the word "art" in its classical meaning. Actually when I chose the title of my books, I wasn't thinking primarily of art in this sense, I was thinking more of its current connotations. Probably the most interesting book which turned up in my search was a fairly recent work by Robert E. Mueller called The Science of Art [29]. Of all the books I've mentioned, Mueller's comes closest to expressing what I want to make the central theme of my talk today, in terms of real artistry as we now understand the term. He observes: "It was once thought that the imaginative outlook of the artist was death for the scientist. And the logic of science seemed to spell doom to all possible artistic flights of fancy." He goes on to explore the advantages which actually do result from a synthesis of science and art.
A scientific approach is generally characterized by the words logical, systematic, impersonal, calm, rational, while an artistic approach is characterized by the words aesthetic, creative, humanitarian, anxious, irrational. It seems to me that both of these apparently contradictory approaches have great value with respect to computer programming.
Emma Lehmer wrote in 1956 that she had found coding to be "an exacting science as well as an intriguing art" [23]. H.S.M. Coxeter remarked in 1957 that he sometimes felt "more like an artist than a scientist" [7]. This was at the time C.P. Snow was beginning to voice his alarm at the growing polarization between "two cultures" of educated people [34, 35]. He pointed out that we need to combine scientific and artistic values if we are to make real progress.
Works of Art
When I'm sitting in an audience listening to a long lecture, my attention usually starts to wane at about this point in the hour. So I wonder, are you getting a little tired of my harangue about "science" and "art"? I really hope that you'll be able to listen carefully to the rest of this, anyway, because now comes the part about which I feel most deeply.
When I speak about computer programming as an art, I am thinking primarily of it as an art form, in an aesthetic sense. The chief goal of my work as educator and author is to help people learn how to write beautiful programs. It is for this reason I was especially pleased to learn recently [32] that my books actually appear in the Fine Arts Library at Cornell University. (However, the three volumes apparently sit there neatly on the shelf, without being used, so I'm afraid the librarians may have made a mistake by interpreting my title literally.)
My feeling is that when we prepare a program, it can be like composing poetry or music; as Andrei Ershov has said [9], programming can give us both intellectual and emotional satisfaction, because it is a real achievement to master complexity and to establish a system of consistent rules.
Furthermore when we read other people's programs, we can recognize some of them as genuine works of art. I can still remember the great thrill it was for me to read the listing of Stan Poley's SOAP II assembly program in 1958; you probably think I'm crazy, and styles have certainly changed greatly since then, but at the time it meant a great deal to me to see how elegant a system program could be, especially by comparison with the heavy-handed coding found in other listings I had been studying at the same time. The possibility of writing beautiful programs, even in assembly language, is what got me hooked on programming in the first place.
Some programs are elegant, some are exquisite, some are sparkling. My claim is that it is possible to write grand programs, noble programs, truly magnificent ones!
Taste and Style
The idea of style in programming is now coming to the forefront at last, and I hope that most of you have seen the excellent little book on Elements of Programming Style by Kernighan and Plauger [16]. In this connection it is most important for us all to remember that there is no one "best" style; everybody has his own preferences, and it is a mistake to try to force people into an unnatural mold. We often hear the saying, "I don't know anything about art, but I know what I like." The important thing is that you really like the style you are using; it should be the best way you prefer to express yourself.
Edsger Dijkstra stressed this point in the preface to his Short Introduction to the Art of Programming [8]:
It is my purpose to transmit the importance of good taste and style in programming, [but] the specific elements of style presented serve only to illustrate what benefits can be derived from "style" in general. In this respect I feel akin to the teacher of composition at a conservatory: He does not teach his pupils how to compose a particular symphony, he must help his pupils to find their own style and must explain to them what is implied by this. (It has been this analogy that made me talk about "The Art of Programming.")
Now we must ask ourselves, What is good style, and what is bad style? We should not be too rigid about this in judging other people's work. The early nineteenth-century philosopher Jeremy Bentham put it this way [3, Bk. 3, Ch. 1]:
Judges of elegance and taste consider themselves as benefactors to the human race, whilst they are really only the interrupters of their pleasure... There is no taste which deserves the epithet good, unless it be the taste for such employments which, to the pleasure actually produced by them, conjoin some contingent or future utility: there is no taste which deserves to be characterized as bad, unless it be a taste for some occupation which has a mischievous tendency.
When we apply our own prejudices to "reform" someone else's taste, we may be unconsciously denying him some entirely legitimate pleasure. That's why I don't condemn a lot of things programmers do, even though I would never enjoy doing them myself. The important thing is that they are creating something they feel is beautiful.
In the passage I just quoted, Bentham does give us some advice about certain principles of aesthetics which are better than others, namely the "utility" of the result. We have some freedom in setting up our personal standards of beauty, but it is especially nice when the things we regard as beautiful are also regarded by other people as useful. I must confess that I really enjoy writing computer programs; and I especially enjoy writing programs which do the greatest good, in some sense.
There are many senses in which a program can be "good," of course. In the first place, it's especially good to have a program that works correctly. Secondly it is often good to have a program that won't be hard to change, when the time for adaptation arises. Both of these goals are achieved when the program is easily readable and understandable to a person who knows the appropriate language.
Another important way for a production program to be good is for it to interact gracefully with its users, especially when recovering from human errors in the input data. It's a real art to compose meaningful error messages or to design flexible input formats which are not error-prone.
Another important aspect of program quality is the efficiency with which the computer's resources are actually being used. I am sorry to say that many people nowadays are condemning program efficiency, telling us that it is in bad taste. The reason for this is that we are now experiencing a reaction from the time when efficiency was the only reputable criterion of goodness, and programmers in the past have tended to be so preoccupied with efficiency that they have produced needlessly complicated code; the result of this unnecessary complexity has been that net efficiency has gone down, due to difficulties of debugging and maintenance.
The real problem is that programmers have spent far too much time worrying about efficiency in the wrong places and at the wrong times; premature optimization is the root of all evil (or at least most of it) in programming.
We shouldn't be penny wise and pound foolish, nor should we always think of efficiency in terms of so many percent gained or lost in total running time or space. When we buy a car, many of us are almost oblivious to a difference of $50 or $100 in its price, while we might make a special trip to a particular store in order to buy a 50 cent item for only 25 cents. My point is that there is a time and place for efficiency; I have discussed its proper role in my paper on structured programming, which appears in the current issue of Computing Surveys [21].
Less Facilities: More Enjoyment
One rather curious thing I've noticed about aesthetic satisfaction is that our pleasure is significantly enhanced when we accomplish something with limited tools. For example, the program of which I personally am most pleased and proud is a compiler I once wrote for a primitive minicomputer which had only 4096 words of memory, 16 bits per word. It makes a person feel like a real virtuoso to achieve something under such severe restrictions.
A similar phenomenon occurs in many other contexts. For example, people often seem to fall in love with their Volkswagens but rarely with their Lincoln Continentals (which presumably run much better). When I learned programming, it was a popular pastime to do as much as possible with programs that fit on only a single punched card. I suppose it's this same phenomenon that makes APL enthusiasts relish their "one-liners." When we teach programming nowadays, it is a curious fact that we rarely capture the heart of a student for computer science until he has taken a course which allows "hands on" experience with a minicomputer. The use of our large-scale machines with their fancy operating systems and languages doesn't really seem to engender any love for programming, at least not at first.
It's not obvious how to apply this principle to increase programmers' enjoyment of their work. Surely programmers would groan if their manager suddenly announced that the new machine will have only half as much memory as the old. And I don't think anybody, even the most dedicated "programming artists," can be expected to welcome such a prospect, since nobody likes to lose facilities unnecessarily. Another example may help to clarify the situation: Film-makers strongly resisted the introduction of talking pictures in the 1920's because they were justly proud of the way they could convey words without sound. Similarly, a true programming artist might well resent the introduction of more powerful equipment; today's mass storage devices tend to spoil much of the beauty of our old tape sorting methods. But today's film makers don't want to go back to silent films, not because they're lazy but because they know it is quite possible to make beautiful movies using the improved technology. The form of their art has changed, but there is still plenty of room for artistry.
How did they develop their skill? The best film makers through the years usually seem to have learned their art in comparatively primitive circumstances, often in other countries with a limited movie industry. And in recent years the most important things we have been learning about programming seem to have originated with people who did not have access to very large computers. The moral of this story, it seems to me, is that we should make use of the idea of limited resources in our own education. We can all benefit by doing occasional "toy" programs, when artificial restrictions are set up, so that we are forced to push our abilities to the limit. We shouldn't live in the lap of luxury all the time, since that tends to make us lethargic. The art of tackling miniproblems with all our energy will sharpen our talents for the real problems, and the experience will help us to get more pleasure from our accomplishments on less restricted equipment.
In a similar vein, we shouldn't shy away from "art for art's sake"; we shouldn't feel guilty about programs that are just for fun. I once got a great kick out of writing a one-statement ALGOL program that invoked an innerproduct procedure in such an unusual way that it calculated the mth prime number, instead of an innerproduct [19]. Some years ago the students at Stanford were excited about finding the shortest FORTRAN program which prints itself out, in the sense that the program's output is identical to its own source text. The same problem was considered for many other languages. I don't think it was a waste of time for them to work on this; nor would Jeremy Bentham, whom I quoted earlier, deny the "utility" of such pastimes [3, Bk. 3, Ch. 1]. "On the contrary," he wrote, "there is nothing, the utility of which is more incontestable. To what shall the character of utility be ascribed, if not to that which is a source of pleasure?"
Providing Beautiful Tools
Another characteristic of modern art is its emphasis on creativity. It seems that many artists these days couldn't care less about creating beautiful things; only the novelty of an idea is important. I'm not recommending that computer programming should be like modern art in this sense, but it does lead me to an observation that I think is important. Sometimes we are assigned to a programming task which is almost hopelessly dull, giving us no outlet whatsoever for any creativity; and at such times a person might well come to me and say, "So programming is beautiful? It's all very well for you to declaim that I should take pleasure in creating elegant and charming programs, but how am I supposed to make this mess into a work of art?"
Well, it's true, not all programming tasks are going to be fun. Consider the "trapped housewife," who has to clean off the same table every day: there's not room for creativity or artistry in every situation. But even in such cases, there is a way to make a big improvement: it is still a pleasure to do routine jobs if we have beautiful things to work with. For example, a person will really enjoy wiping off the dining room table, day after day, if it is a beautifully designed table made from some fine quality hardwood.
Therefore I want to address my closing remarks to the system programmers and the machine designers who produce the systems that the rest of us must work with. Please, give us tools that are a pleasure to use, especially for our routine assignments, instead of providing something we have to fight with. Please, give us tools that encourage us to write better programs, by enhancing our pleasure when we do so.
It's very hard for me to convince college freshmen that programming is beautiful, when the first thing I have to tell them is how to punch "slash slash JoB equals so-and-so." Even job control languages can be designed so that they are a pleasure to use, instead of being strictly functional.
Computer hardware designers can make their machines much more pleasant to use, for example by providing floating-point arithmetic which satisfies simple mathematical laws. The facilities presently available on most machines make the job of rigorous error analysis hopelessly difficult, but properly designed operations would encourage numerical analysts to provide better subroutines which have certified accuracy (cf. [20, p. 204]).
Let's consider also what software designers can do. One of the best ways to keep up the spirits of a system user is to provide routines that he can interact with. We shouldn't make systems too automatic, so that the action always goes on behind the scenes; we ought to give the programmer-user a chance to direct his creativity into useful channels. One thing all programmers have in common is that they enjoy working with machines; so let's keep them in the loop. Some tasks are best done by machine, while others are best done by human insight; and a properly designed system will find the right balance. (I have been trying to avoid misdirected automation for many years, cf. [18].)
Program measurement tools make a good case in point. For years, programmers have been unaware of how the real costs of computing are distributed in their programs. Experience indicates that nearly everybody has the wrong idea about the real bottlenecks in his programs; it is no wonder that attempts at efficiency go awry so often, when a programmer is never given a breakdown of costs according to the lines of code he has written. His job is something like that of a newly married couple who try to plan a balanced budget without knowing how much the individual items like food, shelter, and clothing will cost. All that we have been giving programmers is an optimizing compiler, which mysteriously does something to the programs it translates but which never explains what it does. Fortunately we are now finally seeing the appearance of systems which give the user credit for some intelligence; they automatically provide instrumentation of programs and appropriate feedback about the real costs. These experimental systems have been a huge success, because they produce measurable improvements, and especially because they are fun to use, so I am confident that it is only a matter of time before the use of such systems is standard operating procedure. My paper in Computing Surveys [21] discusses this further, and presents some ideas for other ways in which an appropriate interactive routine can enhance the satisfaction of user programmers.
Language designers also have an obligation to provide languages that encourage good style, since we all know that style is strongly influenced by the language in which it is expressed. The present surge of interest in structured programming has revealed that none of our existing languages is really ideal for dealing with program and data structure, nor is it clear what an ideal language should be. Therefore I look forward to many careful experiments in language design during the next few years.
Summary
To summarize: We have seen that computer programming is an art, because it applies accumulated knowledge to the world, because it requires skill and ingenuity, and especially because it produces objects of beauty. A programmer who subconsciously views himself as an artist will enjoy what he does and will do it better. Therefore we can be glad that people who lecture at computer conferences speak about the state of the Art.
References
Donald E. Knuth 計算機編程的藝術
http://www.xys.org/forum/db/1/170/178.html
Donald E. Knuth, Programming As An Art, ACM Turing Award lecture, 1974.
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