克劳德·香农Claude Shannon

克劳德·香农的父亲也叫香农 Elwood 香农，母亲是Mabel Catherine Wolf。香农毕业于密歇根大学，1936年获得数学与电气工程学位。尽管他在数学方面并不出众，随后他前往麻省理工学院，于1940年获得电气工程硕士学位和数学博士学位。香农撰写了硕士论文A Symbolic Analysis of Relay and Switching Circuits，内容是利用乔治·布尔的代数来分析和优化继电器开关电路。他的博士论文研究的是群体遗传学。

在麻省理工学院，他还从事微分分析仪的工作，这是Vannevar Bush开发的一种早期机械计算机，用于求常微分方程的数值解。香农于1941年发表了Mathematical theory of the differential analyzer。在论文的引言中，他写道：-

最重要的结果[大多以带证明的定理形式给出]涉及一个或多个变量的函数可以被生成的条件，以及常微分方程可以被求解的条件。对函数的近似（无法精确生成的函数）、齿轮比的近似和自动速度控制给予了一些关注。

香农于1941年加入新泽西州的AT&T贝尔电话公司，担任研究数学家，并一直留在贝尔实验室直到1972年。Johnson在[5]中写道，香农：-

……以白天独处、晚上骑着独轮车在走廊里穿行而闻名。

贝尔实验室的同事D Slepian写道：

我们许多人带午饭来上班，玩数学黑板游戏，但香农很少来。他大多关着门工作。但如果你进去，他会非常耐心地帮助你。他能瞬间抓住问题。他确实是个天才。他是我认识的唯一一个我会用这个词来形容的人。

香农与弗瑞兹·约翰 Riordan合作，于1942年发表了一篇关于两端串联-并联网络数量的论文。这篇论文扩展了珀西·亚历山大·麦克马洪所获得的结果，后者于1892年在Electrician上发表了他的早期贡献。

香农在Bell System Technical Journal（1948年）上发表了A Mathematical Theory of Communication。这篇论文创立了信息论这一学科，他提出了一个通信系统的线性示意图模型。这是一个新想法。当时通信被认为需要将电磁波沿导线发送。通过沿导线发送一串1和0来传输图片、文字、声音等的想法——今天当我们从苏格兰圣安德鲁斯的服务器获取信息并在世界任何地方查看时，这似乎显而易见——在当时是根本性的新思想。

香农考虑了一个信息源，它生成由有限个符号组成的词。这些词通过一个信道传输，每个符号在信道中花费有限时间。该问题涉及统计学，假设如果$x_{n}$是信息源产生的第$n$个符号，则$x_{n}$过程是一个平稳随机过程。他给出了一种分析信号中误差项序列以找出其固有种类的方法，并将它们与控制系统的设计种类相匹配。在A Mathematical Theory of Communication中，首次引入了“比特”一词，香农表明向信号中添加额外比特可以纠正传输错误。Slepian在[2]的引言中写道：

本世纪可能没有哪一部著作比C E 香农的文章《通信的数学理论》更深刻地改变了人类对通信的理解，该文首次发表于1948年。香农论文中的思想很快被世界各地的通信工程师和数学家所采纳。它们被详细阐述、扩展，并用新的相关思想加以补充。这门学科蓬勃发展，成为科学史册中一个圆满而激动人心的篇章。

1949年3月27日，香农与Mary Elizabeth Moore结婚。他们有三个儿子和一个女儿；Robert、James、Andrew Moore和Margarita。他继续他的工作，展示布尔代数如何用于综合和简化继电器开关电路。他还证明了关于图的边着色结果，使得没有两条同色的边在一个顶点相遇。另一篇重要论文发表于1949年，是Communication theory of secrecy systems。

1952年，香农设计了一个实验，演示电话继电器的能力。1956年，他曾在麻省理工学院担任通信科学与数学访问教授，随后从1957年起被任命为该学院的教员，但仍保留贝尔电话公司的顾问职位。1958年，他成为唐纳科学讲席教授[1]：-

1958年他回到麻省理工学院后，继续骑着独轮车威胁走廊里的行人，有时还耍杂技增加危险。没有人能确定这些活动是某种新突破的一部分，还是他只是觉得好玩。例如，他研究过一种机动弹簧单高跷，他声称这将意味着他可以放弃同事们非常害怕的独轮车……

曾在麻省理工学院工作的同事R G Gallager写道：-

香农是看出二进制位是所有通信中的基本元素的人。那确实是他的发现，整个通信革命由此兴起。

他后来的工作关注人工智能中的一些想法。他设计了国际象棋程序和一个能解决迷宫问题的电子老鼠。国际象棋程序出现在1950年发表的论文Programming a computer for playing chess中。这一提议导致了1956年洛斯阿拉莫斯MANIAC计算机下的第一盘棋。这一年，香农发表了一篇论文，表明仅用两个状态就可以构造一台通用艾伦·图灵机。

晚年，他觉得这场他起了主要推动作用的通信革命走得太远了。他写道：-

信息论的重要性也许已经膨胀到超出其实际成就。

Marvin Minsky 对香农的描述如下：-

无论出现什么，他都兴致勃勃地投入其中，并用某种令人惊讶的资源来攻克它，这可能是某种新的技术概念，也可能是锤子和锯子加上一些木屑。对他来说，问题看起来越难，找到新东西的机会就越大。

他还将自己的发明天才应用于其他领域[1]：-

……他曾发明过一种双人版的独轮车，而且很可能确实没有人愿意和他一起骑。后来的一项发明——偏心轮毂的独轮车——会让人们跑到走廊里看他骑，像鸭子一样上下颠动。

香农因其工作获得了许多荣誉。一长串奖项中包括1940年的阿尔弗雷德·诺贝尔美国工程师学会奖、1966年的国家科学奖章、1985年的音频工程学会金奖和1985年的京都奖。2000年，他被古列尔莫·马可尼国际奖学金基金会授予马可尼终身成就奖。这是该组织——以其年度奖学金奖而闻名——第一次颁发这一特定奖项。

他患上了阿尔茨海默病，最后几年是在马萨诸塞州的一家疗养院度过的。

Claude E Shannon's father was also named Claude Elwood Shannon and his mother was Mabel Catherine Wolf. Shannon was a graduate of the University of Michigan, being awarded a degree in mathematics and electrical engineering in 1936. Although he had not been outstanding in mathematics, he then went to the Massachusetts Institute of Technology where he obtained a Master's Degree in electrical engineering and his Ph.D. in mathematics in 1940. Shannon wrote a Master's thesis A Symbolic Analysis of Relay and Switching Circuits on the use of Boole's algebra to analyse and optimise relay switching circuits. His doctoral thesis was on population genetics.

At the Massachusetts Institute of Technology he also worked on the differential analyser, an early type of mechanical computer developed by Vannevar Bush for obtaining numerical solutions to ordinary differential equations. Shannon published Mathematical theory of the differential analyzer in 1941. In the introduction to the paper he writes:-

The most important results [mostly given in the form of theorems with proofs] deal with conditions under which functions of one or more variables can be generated, and conditions under which ordinary differential equations can be solved. Some attention is given to approximation of functions (which cannot be generated exactly), approximation of gear ratios and automatic speed control.

Shannon joined AT&T Bell Telephones in New Jersey in 1941 as a research mathematician and remained at the Bell Laboratories until 1972. Johnson writes in [5] that Shannon:-

... became known for keeping to himself by day and riding his unicycle down the halls at night.

D Slepian, a colleague at the Bell Laboratories wrote:-

Many of us brought our lunches to work and played mathematical blackboard games but Claude rarely came. He worked with his door closed, mostly. But if you went in, he would be very patient and help you along. He could grasp a problem in zero time. He really was quite a genius. He's the only person I know whom I'd apply that word to.

Working with John Riordan, Shannon published a paper in 1942 on the number of two-terminal series-parallel networks. This paper extended results obtained by MacMahon who had published his early contribution in the Electrician in 1892.

Shannon published A Mathematical Theory of Communication in the Bell System Technical Journal (1948). This paper founded the subject of information theory and he proposed a linear schematic model of a communications system. This was a new idea. Communication was then thought of as requiring electromagnetic waves to be sent down a wire. The idea that one could transmit pictures, words, sounds etc. by sending a stream of 1s and 0s down a wire, something which today seems so obvious as we take this information from a server in St Andrews, Scotland, and view it anywhere in the world, was fundamentally new.

Shannon considered a source of information which generates words composed of a finite number of symbols. These are transmitted through a channel, with each symbol spending a finite time in the channel. The problem involved statistics with the assumption that if $x_{n}$ is the $n$th symbol produced by the source the $x_{n}$ process is a stationary stochastic process. He gave a method of analysing a sequence of error terms in a signal to find their inherent variety, matching them to the designed variety of the control system. In A Mathematical Theory of Communication , which introduced the word "bit" for the first time, Shannon showed that adding extra bits to a signal allowed transmission errors to be corrected. Slepian, in the introduction to [2], writes:-

Probably no single work in this century has more profoundly altered man's understanding of communication than C E Shannon's article, "A mathematical theory of communication", first published in 1948. The ideas in Shannon's paper were soon picked up by communication engineers and mathematicians around the world. They were elaborated upon, extended, and complemented with new related ideas. The subject thrived and grew to become a well-rounded and exciting chapter in the annals of science.

On 27 March 1949 Shannon married Mary Elizabeth Moore. They had three sons and one daughter; Robert, James, Andrew Moore, and Margarita. He continued his work showing how Boolean algebra could be used to synthesise and simplify relay switching circuits. He also proved results on colouring the edges of a graph so that no two edges of the same colour meet at a vertex. Another important paper, published in 1949, was Communication theory of secrecy systems.

In 1952 Shannon devised an experiment illustrating the capabilities of telephone relays. He had held a position as a visiting professor of communication sciences and mathematics at the Massachusetts Institute of Technology in 1956, then from 1957 he was appointed to the Faculty there, but remained a consultant with Bell Telephones. In 1958 he became Donner Professor of Science [1]:-

When he returned to MIT in 1958, he continued to threaten corridor-walkers on his unicycle, sometimes augmenting the hazard by juggling. No one was ever sure whether these activities were part of some new breakthrough or whether he just found them amusing. He worked, for example, on a motorised pogo-stick, which he claimed would mean he could abandon the unicycle so feared by his colleagues ...

R G Gallager, a colleague who worked at the Massachusetts Institute of Technology, wrote:-

Shannon was the person who saw that the binary digit was the fundamental element in all of communication. That was really his discovery, and from it the whole communications revolution has sprung.

His later work looked at ideas in artificial intelligence. He devised chess playing programs and an electronic mouse which could solve maze problems. The chess playing program appeared in the paper Programming a computer for playing chess published in 1950. This proposal led to the first game played by the Los Alamos MANIAC computer in 1956. This was the year that Shannon published a paper showing that a universal Turing machine may be constructed with only two states.

Latterly he felt that the communications revolution, which he had played a major role in starting, was going too far. He wrote:-

Information theory has perhaps ballooned to an importance beyond its actual accomplishments.

Marvin Minsky described Shannon as follows:-

Whatever came up, he engaged it with joy, and he attacked it with some surprising resource which might be some new kind of technical concept or a hammer and saw with some scraps of wood. For him, the harder a problem might seem, the better the chance to find something new.

He also applied his inventing genius to other areas [1]:-

... he once invented a two-seater version of his unicycle, and it is probably true that no one was anxious to share it with him. A later invention, the unicycle with an off-centre hub, would bring people out into the corridors to watch him as he rode it, bobbing up and down like a duck.

Shannon received many honours for his work. Among a long list of awards were the Alfred Nobel American Institute of American Engineers Award in 1940, the National Medal of Science in 1966, the Audio Engineering Society Gold Medal in 1985, and the Kyoto Prize in 1985. He was awarded the Marconi Lifetime Achievement Award by the Guglielmo Marconi International Fellowship Foundation in 2000. It was the first time that organization, known for its annual Fellowship Prize, gave this particular award.

He was afflicted by Alzheimer's disease, and he spent his last few years in a Massachusetts nursing home.