001 计算思维-卡内基梅隆大学计算机系主任周以真（英汉对照版）

英文版CACM
Jeannette M. Wing (周以真)
(翻译：徐韵文，王飞跃, 校对：王飞跃）

Computational Thinking

It represents a universally applicable attitude and skill set everyone, not just computer scientists, would be eager to learn and use.

它代表着一种普遍的认识和一类普适的技能，每一个人，不仅仅是计算机科学家，都应热心于它的学习和运用。

Computational thinking builds on the power and limits of computing processes, whether they are executed by a human or by a machine. Computational methods and models give us the courage to solve problems and design systems that no one of us would be capable of tackling alone. Computational thinking confronts the riddle of machine intelligence: What can humans do better than computers? and What can computers do better than humans? Most fundamentally it addresses the question: What is computable? Today, we know only parts of the answers to such questions.

计算思维是建立在计算过程的能力和限制之上的，不管这些过程是由人还是由机器执行的。计算方法和模型给了我们勇气去处理那些原本无法由任何个人独自完成的问题求解和系统设计。计算思维直面机器智能的不解之谜：什么人类能比计算机做得更好？什么计算机能比人类做得更好？最基本的是它涉及这样的问题：什么是可计算的？今天，我们对这些问题的答案仍是一知半解。

Computational thinking is a fundamental skill for everyone, not just for computer scientists. To reading, writing, and arithmetic, we should add computational thinking to every child’s analytical ability. Just as the printing press facilitated the spread of the three Rs, what is appropriately incestuous about this vision is that computing and computers facilitate the spread of computational thinking.

计算思维是每个人的基本技能，不仅仅属于计算机科学家。在阅读、写作和算术（英文简称3R）之外，我们应当将计算思维加到每个孩子的解析能力之中。正如印刷出版促进了3R的传播，计算和计算机也以类似的正反馈促进了计算思维的传播。

Computational thinking involves solving problems, designing systems, and understanding human behavior, by drawing on the concepts fundamental to computer science. Computational thinking includes a range of mental tools that reflect the breadth of the field of computer science.

计算思维涉及运用计算机科学的基础概念去求解问题、设计系统和理解人类的行为。计算思维涵盖了反映计算机科学之广泛性的一系列思维活动。

Having to solve a particular problem, we might ask: How difficult is it to solve? and What’s the best way to solve it? Computer science rests on solid theoretical underpinnings to answer such questions precisely. Stating the difficulty of a problem accounts for the underlying power of the machine—the computing device that will run the solution. We must consider the machine’s instruction set, its resource constraints, and its operating environment.

当求解一个特定的问题时，我们会问：解决这个问题有多困难？怎样才是最佳的解决之道? 计算机科学根据坚实的理论基础来准确地回答这些问题。表明问题的困难程度是为了考量机器——就是用来运行其解的计算工具之基本能力。我们必须考虑机器的指令系统、它的资源约束和它的操作环境。

In solving a problem efficiently, we might further ask whether an approximate solution is good enough, whether we can use randomization to our advantage, and whether false positives or false negatives are allowed. Computational thinking is reformulating a seemingly difficult problem into one we know how to solve, perhaps by reduction, embedding, transformation, or simulation.

为了有效地求解一个问题，我们可能要进一步问：一个近似解是否就足够了，是否可以利用一下随机化，以及是否允许误正或误负。计算思维就是把一个看来困难的问题重新阐述成一个我们知道怎样解的问题，如通过约简、嵌入、转化和仿真的方法。

Computational thinking is thinking recursively. It is parallel processing. It is interpreting code as data and data as code. It is type checking as the generalization of dimensional analysis. It is recognizing both the virtues and the dangers of aliasing, or giving someone or something more than one name. It is recognizing both the cost and power of indirect addressing and procedure call. It is judging a program not just for correctness and efficiency but for aesthetics, and a system’s design for simplicity and elegance.

计算思维是一种递归思维。它是并行处理。它是把代码译成数据又把数据译成代码。它是由推广量纲分析进行的类型检查。对于别名或赋予人与物多个名字的做法，它既知道其益处又了解其害处。对于间接寻址和程序调用的做法，它既知道其威力又了解其代价。它评价一个程序时，不仅仅根据其准确性和效率，还有美学的考量，而对于系统的设计，还考虑简洁和优雅。

Computational thinking is using abstraction and decomposition when attacking a large complex task or designing a large complex system. It is separation of concerns. It is choosing an appropriate representation for a problem or modeling the relevant aspects of a problem to make it tractable. It is using invariants to describe a system’s behavior succinctly and declaratively. It is having the confidence we can safely use, modify, and influence a large complex system without understanding its every detail. It is modularizing something in anticipation of multiple users or prefetching and caching in anticipation of future use.

计算思维采用了抽象和分解来迎战浩大复杂的任务或者设计巨大复杂的系统。它是关注的分离。它是选择合适的方式去陈述一个问题，或者是选择合适的方式对一个问题的相关方面建模使其易于处理。它是利用不变量简明扼要且表述性地刻画系统的行为。它是我们在不必理解每一个细节的情况下就能够安全地使用、调整和影响一个大型复杂系统的信心。它就是为预期的多个用户而进行的模块化，它就是为预期的未来应用而进行的预置和缓存。

Computational thinking is thinking in terms of prevention, protection, and recovery from worst-case scenarios through redundancy, damage containment, and error correction. It is calling gridlock deadlock and contracts interfaces. It is learning to avoid race conditions when synchronizing meetings with one another.

计算思维是通过冗余、堵错、纠错的方式，在最坏情况下进行预防、保护和恢复的一种思维。它称堵塞为死结，叫合同为界面。它就是学习在谐调同步相互会合时如何避免竞争的情形。

Computational thinking is using heuristic reasoning to discover a solution. It is planning, learning, and scheduling in the presence of uncertainty. It is search, search, and more search, resulting in a list of Web pages, a strategy for winning a game, or a counterexample. Computational thinking is using massive amounts of data to speed up computation. It is making trade-offs between time and space and between processing power and storage capacity.

计算思维是利用启发式推理来寻求解答。它就是在不确定情况下的规划、学习和调度。它就是搜索、搜索、再搜索，最后得到的是一系列的网页，一个赢得游戏的策略，或者一个反例。计算思维是利用海量的数据来加快计算。它就是在时间和空间之间，在处理能力和存储容量之间的权衡。

Consider these everyday examples: When your daughter goes to school in the morning, she puts in her backpack the things she needs for the day; that’s prefetching and caching. When your son loses his mittens, you suggest he retrace his steps; that’s backtracking. At what point do you stop renting skis and buy yourself a pair?; that’s online algorithms. Which line do you stand in at the supermarket?; that’s performance modeling for multi-server systems. Why does your telephone still work during a power outage?; that’s independence of failure and redundancy in design. How do Completely Automated Public Turing Test(s) to Tell Computers and Humans Apart, or CAPTCHAs, authenticate humans?; that’s exploiting the difficulty of solving hard AI problems to foil computing agents.

考虑这些日常中的事例：当你女儿早晨去学校时，她把当天需要的东西放进背包；这就是预置和缓存。当你儿子弄丢他的手套时，你建议他沿走过的路回寻；这就是回推。在什么时候你停止租用滑雪板而为自己买一对呢？这就是在线算法。在超市付账时你应当去排哪个队呢？这就是多服务器系统的性能模型。为什么停电时你的电话仍然可用？这就是失败的无关性和设计的冗余性。完全自动的大众图灵测试是如何区分计算机和人类（简称CAPTCHA）的，即CAPTCHAs是怎样鉴别人类的？这就是充分利用求解人工智能难题之艰难来挫败计算代理程序。

Computational thinking will have become ingrained in everyone’s lives when words like algorithm and precondition are part of everyone’s vocabulary; when nondeterminism and garbage collection take on the meanings used by computer scientists; and when trees are drawn upside down.

计算思维将渗入到我们每个人的生活之中，那时诸如算法和前提条件已成为每个人日常词汇的一部分，非确定论和垃圾收集已含有计算机学家所指的含义，而树已常常被倒过来画了。

Thinking like a computer scientist means more than being able to program a computer. It requires thinking at multiple levels of abstraction.

像计算机科学家一样思考意味着不仅仅能够计算机编程。 它需要在多个抽象层面上进行思考。

We have witnessed the influence of computational thinking on other disciplines. For example, machine learning has transformed statistics. Statistical learning is being used for problems on a scale, in terms of both data size and dimension, unimaginable only a few years ago. Statistics departments in all kinds of organizations are hiring computer scientists. Schools of computer science are embracing existing or starting up new statistics departments.

我们已见证了计算思维在其它学科中的影响。例如，机器学习已经改变了统计学。就数据尺度和维数而言，统计学习用于各类问题的规模仅在几年前还是不可想象的。各种组织的统计部门都聘请了计算机科学家。计算机学院系正在联姻已有或开设新的统计部门。

Computer scientists’ recent interest in biology is driven by their belief that biologists can benefit from computational thinking. Computer science’s contribution to biology goes beyond the ability to search through vast amounts of sequence data looking for patterns. The hope is that data structures and algorithms—our computational abstractions and methods—can represent the structure of proteins in ways that elucidate their function. Computational biology is changing the way biologists think. Similarly, computational game theory is changing the way economists think; nanocomputing, the way chemists think; and quantum computing, the way physicists think.

计算机学家们近来对生物科学的兴趣是由他们坚信生物学家能够从计算思维中获益的信念驱动的。计算机科学对于生物学的贡献决不限于其能够在海量时序数据中搜索寻找模式规律的本领。最终的希望是数据结构和算法——我们的计算抽象和方法——能够以阐释其功能的方式表示蛋白质的结构。计算生物学正在改变着生物学家的思考方式。类似地，计算博弈理论正改变着经济学家的思考方式，纳米计算改变着化学家的思考方式，量子计算改变着物理学家的思考方式。

This kind of thinking will be part of the skill set of not only other scientists but of everyone else. Ubiquitous computing is to today as computational thinking is to tomorrow. Ubiquitous computing was yesterday’s dream that became today’s reality; computational thinking is tomorrow’s reality.

这种思维将成为不仅仅是其他科学家，而且是其他每一个人的技能组合之部分。普在计算之于今天就是计算思维之于明天。普在计算是已变为今日之现实的昨日之梦，计算思维就是明日之现实。

WHAT IT IS, AND ISN’T

它是什么，又不是什么

Computer science is the study of computation— what can be computed and how to compute it. Computational thinking thus has the following characteristics:

计算机科学是计算的学问——什么是可计算的，怎样去计算。因此，计算思维具有以下特性：

Conceptualizing, not programming. Computer science is not computer programming. Thinking like a computer scientist means more than being able to program a computer. It requires thinking at multiple levels of abstraction;

概念化，不是程序化。计算机科学不是计算机编程。像计算机科学家那样去思维意味着远远不止能为计算机编程。它要求能够在抽象的多个层次上思维。

Fundamental, not rote skill. A fundamental skill is something every human being must know to function in modern society. Rote means a mechanical routine. Ironically, not until computer science solves the AI Grand Challenge of making computers think like humans will thinking be rote;

基础的，不是机械的技能。基础的技能是每一个人为了在现代社会中发挥职能所必须掌握的。生搬硬套之机械的技能意味着机械的重复。具有讽刺意味的是，只有当计算机科学解决了人工智能的宏伟挑战——使计算机像人类一样思考之后，思维才会变成机械的生搬硬套。

A way that humans, not computers, think. Computational thinking is a way humans solve problems; it is not trying to get humans to think like computers. Computers are dull and boring; humans are clever and imaginative. We humans make computers exciting. Equipped with computing devices, we use our cleverness to tackle problems we would not dare take on before the age of computing and build systems with functionality limited only by our imaginations;

人的，不是计算机的思维。计算思维是人类求解问题的一条途径，但决非试图使人类像计算机那样地思考。计算机枯燥且沉闷；人类聪颖且富有想象力。我们人类赋予计算机以激情。配置了计算设备，我们就能用自己的智慧去解决那些计算时代之前不敢尝试的问题，就能建造那些其功能仅仅受制于我们想象力的系统。

Complements and combines mathematical and engineering thinking. Computer science inherently draws on mathematical thinking, given that, like all sciences, its formal foundations rest on mathematics. Computer science inherently draws on engineering thinking, given that we build systems that interact with the real world. The constraints of the underlying computing device force computer scientists to think computationally, not just mathematically. Being free to build virtual worlds enables us to engineer systems beyond the physical world;

数学和工程思维的互补与融合。计算机科学在本质上源自数学思维，因为像所有的科学一样，它的形式化解析基础筑于数学之上。计算机科学又从本质上源自工程思维，因为我们建造的是能够与实际世界互动的系统。基本计算设备的限制迫使计算机学家必须计算性地思考，不能只是数学性地思考。构建虚拟世界的自由使我们能够超越物理世界去打造各种系统。

Ideas, not artifacts. It’s not just the software and hardware artifacts we produce that will be physically present everywhere and touch our lives all the time, it will be the computational concepts we use to approach and solve problems, manage our daily lives, and communicate and interact with other people; and

是思想，不是人造品。不只是我们生产的软件硬件人造品将以物理形式到处呈现并时时刻刻触及我们的生活，更重要的是还将有我们用以接近和求解问题、管理日常生活、与他人交流和互动之计算性的概念；而且，

For everyone, everywhere. Computational thinking will be a reality when it is so integral to human endeavors it disappears as an explicit philosophy.

面向所有的人，所有地方。当计算思维真正融入人类活动的整体以致不再是一种显式之哲学的时候，它就将成为现实。

Many people equate computer science with computer programming. Some parents see only a narrow range of job opportunities for their children who major in computer science. Many people think the fundamental research in computer science is done and that only the engineering remains. Computational thinking is a grand vision to guide computer science educators, researchers, and practitioners as we act to change society’s image of the field. We especially need to reach the pre-college audience, including teachers, parents, and students, sending them two main messages:

许多人将计算机科学等同于计算机编程。有些家长为他们主修计算机科学的孩子看到的只是一个狭窄的就业范围。许多人认为计算机科学的基础研究已经完成，剩下的只是工程部分而已。当我们行动起来去改变这一领域的社会形象时，计算思维就是一个引导着计算机教育家、研究者和实践者的宏大愿景。我们特别需要走进大学之前的听众，包括老师、父母、学生，向他们传送两个主要信息：

Intellectually challenging and engaging scientific problems remain to be understood and solved. The problem domain and solution domain are limited only by our own curiosity and creativity; and

智力上极有挑战性并且引人入胜的科学问题依旧亟待理解和解决。这些问题的范围和解决方案的范围之唯一局限就是我们自己的好奇心和创造力；同时

One can major in computer science and do anything. One can major in English or mathematics and go on to a multitude of different careers. Ditto computer science. One can major in computer science and go on to a career in medicine, law, business, politics, any type of science or engineering, and even the arts.

一个人可以主修计算机科学并且干什么都行。一个人可以主修英语或者数学，接着从事各种各样的职业。计算机科学也一样。一个人可以主修计算机科学，接着从事医学、法律、商业、政治，以及任何类型的科学和工程，甚至艺术工作。

Professors of computer science should teach a course called “Ways to Think Like a Computer Scientist” to college freshmen, making it available to non-majors, not just to computer science majors. We should expose pre-college students to computational methods and models. Rather than bemoan the decline of interest in computer science or the decline in funding for research in computer science, we should look to inspire the public’s interest in the intellectual adventure of the field. We’ll thus spread the joy, awe, and power of computer science, aiming to make computational thinking commonplace.

计算机科学的教授应当为大学新生开一门称为“怎么像计算机科学家一样思维”的课，面向非专业的，而不仅仅是计算机科学专业的学生。我们应当使大学之前的学生接触计算的方法和模型。我们应当设法激发公众对于计算机领域中的科学探索之兴趣，而不是悲叹对其兴趣的衰落或者哀泣其研究经费的下降。所以，我们应当传播计算机科学的快乐、崇高和力量，致力于计算思维的常识化。

本文引用地址：http://blog.sciencenet.cn/home.php?mod=space&uid=2374&do=blog&id=8104

相关文章:从计算思维到计算文化:http://blog.sciencenet.cn/home.php?mod=space&uid=2374&do=blog&id=8105

蒲定东补：

周以真在文中提及

Computational thinking is reformulating a seemingly difficult problem into one we know how to solve, perhaps by reduction, embedding, transformation, or simulation.

计算思维就是把一个看来困难的问题重新阐述成一个我们知道怎样解的问题，如通过约简、嵌入、转化和仿真的方法。

计算思维：解构、模式识别、模式归纳（抽象）、算法设计；
抽象思维：破解、离散、变换、拟合；
信息工程思维：数据化、建模、计算、仿真；
诗格：起、承、转、合；
修辞格：隐喻、反讽、转喻、提喻；
古希腊哲人爱比克泰德的哲思：物是，如其然；物已非，其惘然；物既非，不然其然；物复是，如其未然；
《周易》占卜：元、亨、利、贞；

本文发表于2007年第3卷第11期的中国计算机学会通讯。