想起遥远的1954年，一切都如梦似幻。那一年，我即将成为一名高中生，我的父亲订阅了一本叫《大众电子》的杂志，送给我作礼物。他之所以这样做，是因为他本身是一名科学家，而他的大儿子貌似在科学和数学上有点天赋，但这个孩子正在被可恶的科幻小说带坏。事实上，我的确有足够理由让他这样想。那时，我如饥似渴地看科幻小说，我会晚上十一点坐在厨房里，一边吃着巨型三文治，一边读着关于百万年后移居火星的小说。而我的父亲，当然希望我读的是代数或者物理的书籍。
Long ago,in a year so far in the past (1954) that my life then as a high school freshman now seems like a dream, my father gave me the gift of a subscription to a new magazine called Popular Electronics. He did this because he was a scientist, and his oldest son seemed to have talents in science and mathematics that were in danger of being subverted by the evil of science fiction. I had, in fact, given him plenty of reason for such concern. I devoured science fiction in those days, you see, often sitting in the kitchen at eleven at night eating a huge sandwich and reading a novel set on Mars a million years in the future. Dad, of course, would have preferred that I be reading a book on algebra or physics.
作为一个聪明人，我的父亲当然不会明令禁止我读科幻小说，而是通过一些技术类故事，比如每月《大众电子》里面“卡尔和杰瑞”的故事，间接地让我放弃科幻小说。卡尔和杰瑞是两名高中电子奇才，用今天的话说，就是极客或书呆子。他们每个月，都会经历一场刺激的冒险之旅，而每一次，他们都能凭借着专业知识化险为夷。他们是“哈迪男孩”和“汤姆斯威夫特”的结合体（两部均为美国少儿冒险小说）。父亲的计划，就是让我与卡尔和杰瑞一起，探索求真，而不是与罗伯特·海因莱因小说中那些神经质的时间旅行者厮混。
Being a clever man, he decided not to simply forbid the science fiction, but rather to outflank the science fiction stories by getting me to read technical stories, like the “Carl and Jerry” tales that appeared each month in Popular Electronics. Carl and Jerry were two high school electronics whiz kids, geeks or nerds, in today’s unattractive terms who managed each month to get involved in some exciting adventure in which their technical knowledge saved the day. They were a 1950s amalgamation of the Hardy Boys and Tom Swift. My father’s plan was to get me to identify with Carl and Jerry, instead of with Robert Heinlein’s neurotic time travelers.
当然，父亲的迂回策略真的奏效（尽管我从未真正放弃过科幻小说）。我不单对卡尔和杰瑞的故事着了迷，而且还被每期杂志的电子制作项目深深吸引。我从杂志中学会了如何读电子原理图。杂志编辑们使用了流行的分解图进行讲解，生动有趣。这些图对于曾玩过邮购电子工具套件的人来说一定不会陌生。我在家后面的车库里，建起了一个工作坊，制作了许多有趣的小电器。
Well, Dad’s devious plan worked (although I never completely gave up the science fiction), and I got hooked not only on Carl and Jerry but also on the electronic construction projects the magazine featured in each issue. I learned how to read electrical schematics from the magazine, whose editors used the same exploded-view, pictorial wiring diagrams that became so well known to all who ever built an electronic, mail-order kit. I constructed a home workshop in the garage behind the house, and a lot of amazing gadgets were built.
我最大的成就，是造出了一台“掌计器”（用于测量观众掌声音量），在一年学校的达人秀中，评委们就用上了这台仪器。这个仪器无非就是一个拾音器，一个音频功放，和一个连接到功放输出接口的500毫安计。但对我影响最大的，既不是这个仪器，也不是我在高中期间制造的其他仪器，而是一台根本不可能造出来的仪器。当时我根本没想到这一点。我的年少轻狂背后，是对理论的巨大无知。
My greatest success was an “applause meter” that was used by the judges at the high school talent show one year —— a loudspeaker pick-up, an audio amplifier, and a 500 microampere meter wired into the amplifier output was all it really was. But what really had the greatest impact on me wasn’t that gadget, or any of the others that I built during my high school years. It was one that, in a burst of youthful enthusiasm exceeded only by my enormous ignorance of theory, I didn’t realize is impossible to build.
1955年4月，《大众电子》如期来到我的邮箱，里面有这么一张神奇的照片——一盏台灯，发出的不是光锥，而是暗锥！我当时看傻了眼，惊叹道，科学是多么的神奇啊！（我敢说，在你所知的14岁少年里，除了情景喜剧里的那些，谁会说出这样的话）。根据该照片配文，其中的奥秘在于这盏台灯并不是连接到一个普通的电源，而是连接到一个产生“反极电”电源上。另一张照片中，一根电烙铁插到反极电源上。它的表面被冰覆盖着！还有一张照片，一块电热板上面是一个已被冻成冰块的托盘！这块电热板，因为接到了反极电源上，现在已变成了电冰板。我还记得，我目不转睛地看着这三张照片，产生了一阵阵晕眩。这实在太神奇了！
When the April 1955 issue of Popular Electronics arrived in the mail, one of the inside photographs displayed an incredible sight —— a desk lamp emitting not a cone of light, but, instead, a cone of darkness! My eyes bugged out when I saw that. What wondrous science was at work here, I gasped (metaphorically speaking, of course, because what fourteen-year-old kid do you know, other than in a TV sitcom, who actually talks like that?). The secret, according to the accompanying article, was that the lamp was not plugged into a normal power outlet, but rather into an outlet delivering contra-polar power.Another photograph showed a soldering iron plugged into the contra-polar power outlet -- it was covered with ice! And another displayed a frozen ice tray on a hot plate, except it was now a cold plate because it was plugged into contra-polar power. I looked at those three photographs, and I remember my pulse rate elevated and I felt a momentary spell of faintness. This was simply wonderful.
当然，这只是编辑们开的一个大玩笑，他们通过精湛的修图技巧，达到了这种效果。当我把这篇文章拿给我父亲看时，他暼了一眼后，转头看着我，觉得我既可怜又可笑，这是我后来才意识到的。我的父亲不是一名电气工程师，也不是一名物理学家，但他拥有一个化学博士学位，因此，对于苯环和分子键以外的技术知识，他也不至于一无所知。他马上就对反极电产生怀疑，因为这有可能违背了已知的七个基本物理定律。但是他并没有嘲笑我，而是简单地说，“孩子，看看日期吧”。之前，我根本没有留意到封面上的“四月”，也没有留意到下面一行字，“致四月的第一天”，这时我才恍然大悟。那种被完全愚弄的强烈尴尬，我依然记得清清楚楚。这个恶搞，其实在文末的脚注4，已暗示得十分明显。那是一段虚构的引用：“反极性能源委员会实务，第46卷，1324-1346页（编者著：来自一艘不明飞行物的文件重印件）”
Well, of course it was all just a huge editorial joke, aided by some nifty photographic retouching. When I showed the article to my father, he glanced at it and then looked at me with what I now know was a mixture of pity and amusement. Dad wasn’t an electrical engineer or a physicist, but with a Ph.D. in chemistry he wasn’t totally ignorant of technical matters that fell outside the realm of benzene rings and molecular bonds. He immediately suspected that “contra-polar power” probably violated perhaps seven different fundamental principles of physics. Rather than laughing at me, however, he simply said, “Son, look at the date on the cover.” I had not noticed the “April” before, or even the subtitle, “In keeping with the first day of April,” but I quickly understood the significance. I still remember my enormous embarrassment at having been so completely taken in. Even I could recognize the “spoofiness” of contra-polar power once I got to the end of the article and read its footnote 4. It listed a phony citation, as follows: “Transactions of the Contra-Polar Energy Commission, Vol. 45, pp. 1324 1346 (Ed. Note A reprint of a document found in a flying saucer).”
正如所有高水平恶搞，这个恶搞本身包含了很多浅显易懂的常识，同时又用一种荒谬的手法呈现出来。这里我给你们模仿一下文中的句调，比如这一句就很典型：“当普通台灯使用反极性能源，台灯不产生光，而是吸收光，原来台灯照亮的地方，会变黑暗。（编者著：不要与所谓的“黑光”混淆，黑光只是一种没有任何可视元素的光。对于人类的眼睛，“黑光”等价于没有光。而由反极性能源产生的光，可以称之为“负光”，因为它减去了现有的光）”。
Like any good spoof, it had lots of tantalizing truths in it, but presented in a slightly goofy way. To give you a sample of the tone of the article, here’s a typical passage: “When ‘contra-polar energy’ is applied to an ordinary table lamp, light is not produced, but taken away, and the area affected by the lamp becomes dark. (Editor’s Note:This phenomenon should not be confused with ‘black light,’ so-called, which actually is merely light without any visible elements. As far as the human eye is concerned, ‘black light’ is equivalent to zero light; the light produced by contra-polar energy might be designated ‘negative light,’ since it subtracts from light already present.)”
为了蒙骗读者相信反极性能源的奇妙“特性”，配文下一句就马上称，“原子能之所以未能在（电子）爱好者之中普及，是因为要明白反极性能源的产生原理，需要非常高深的数学知识”。几十年后重新看这话，真是可笑至极，但当我1955年第一次看到时，却是非常合理。事实上，单单代数足以把反极性能源还有这篇所谓的科普文驳斥得体无原肤。反极电的工作原理，就是利用负平方根（而不是正平方根），在计算带电感电容的电路谐振频率时会用到。我本身对负频率充满兴趣（电气工程师们已经通过使用虚数i使之具有实际意义），然而，编辑们还不满足，并耍了一些聪明小手段，提出“负电阻”概念。
To set readers up for an “explanation” of the astounding properties of contra-polar energy, the very next sentence makes the following assertion, hilarious now, as I read it decades later, but quite logical to me in 1955: “One of the reasons why atomic energy has not yet become popular among home experimenters is that an understanding of its production requires a knowledge of very advanced mathematics.” Just algebra, however, would strip bare contra-polar energy, or so claimed the article. Contra-polar power “worked” by simply using the negative square root (instead of the positive root) in calculating the resonant frequency in a circuit containing both inductance and capacitance. The idea of negative frequency was intriguing to my mind (and electrical engineers have actually made sense out of it when combined with i), but then the editors played a few more clever tricks and came up with negative resistance.
夜里蜷缩在被窝，能感受到电热毯的热量；早上起床，吃一片香脆吐司，能感受到吐司的温暖，人们都明白，当电流通过电阻（正电阻）时，电阻会产生热。“明显地”，当电流通过负电阻时，温度会下降。因此，就有了前面提及的被冰覆盖的电烙铁和结冰了的托盘照片（但台灯生成暗锥的逻辑，对我来说依然不成立）。现在，负电阻真的出现了。电气工程师们早已注意到在特定条件下操作电弧，就能产生负电阻。比如，在电子元件出现之前，人们已经懂得利用这种电弧去制造十分先进的无线广播发射机，能传播音乐或者演说，不像赫兹发射机和马可尼火花间隙发射机，只能传播电报代码开关信号。进入大学之后，我才发现如果不了解虚数i的话，是无法从深层理论上了解到无线广播工作原理的。
As everybody knows who likes to curl up in a warm bed at night under an electric blanket, or who likes a crunchy piece of toast in the morning, resistors (positive resistors) get hot when conducting an electric current. “Obviously,” then, a negative resistor should cool down when conducting a current hence the soldering iron and the ice cube tray photographs. (The logic, if you can call it that, behind the cone of darkness out of a desk lamp still eludes me, however.) Now, there really is such a thing as negative resistance, and it has long been known by electrical engineers to occur in the operation, under certain specific conditions, of electric arcs. Such arcs were used, for example, in the very early pre-electronic days of radio to build extremely powerful transmitters that were able to broadcast music and human speech, rather than just the on-off telegraph code signals that were all the Hertz and Marconi sparkgap transmitters could send. Later, in college, I would learn that the operation of radio is impossible to understand, at a deep theoretical level, without an understanding of i.
尽管四十多年过去了，我的词汇量也似乎增加了，但是我依然不能向你描述，上述这一切对年轻的我带来的震撼。它使我意识到，电子世界有着太多宏大且激动人心的内容，远远比我还在车库捣鼓小电器时所想的多。后来，我从高中数学课里学到，有一些二次方程的解是复数，我意识到（不像我那些满脸困惑的同学）它不仅仅是枯燥的智力游戏。我已经明白到，虚数i不仅对电气工程师来说非常重要，而且它可以用于构建真正了不起的设备。
All of this was more fascinating to my young mind than I can tell you, even forty years later, even with a somewhat increased vocabulary. It showed me that there were big, exciting ideas in the world of electronics, bigger than I had ever imagined while out in the garage tinkering with my gadgets. And later, when in my high school algebra classes I was introduced to complex numbers as the solutions to certain quadratic equations, I knew (unlike my mostly perplexed classmates) that they were not just part of a sterile intellectual game. I already knew that i was important to electrical engineers, and to their ability to construct truly amazing devices.
1958年的一个清晨，也就是我读到负极性能源的三年半后，我坐上一列火车，从洛杉矶联合车站出发，向北开往帕洛阿尔托，到斯坦福大学开始大学生活。多年来，卡尔和杰瑞每期都出现在《大众电子》里，故事也随着他们也从高中新生，一直讲到他们成为虚构的袙沃大学的电气工程学生。像他们一样，我也正式开始了我奉献终生的事业，电气工程师。一到斯坦福，阅读即占据了我所有时间，很快地，我就放下了《大众电子》，但这本杂志，正好出现合适的时间。父亲的计划进行得比他想象中还要好。某程度上，我的整个职业生涯，都是年轻时对虚数i着迷的结果，而这也正是我写这本书的原因。
Three and a half years after reading about contra-polar power, I was sitting in an early morning train out of Los Angeles’ Union Station, heading north to Palo Alto on my way to join the Stanford University freshman class of 1958. Over the years that Carl and Jerry appeared in Popular Electronics,the tales chronicled their progression from high school freshmen to electrical engineering students at the fictional “Parvoo University” and, like them, I was taking the first step on the career path I’ve trodden ever since, as an electrical engineer. Once at Stanford I had more than enough to fill my days with reading and so I quickly drifted away from Popular Electronics,but it had been there at just the right time for me; Dad’s plan had worked better than he could have possibly hoped. In a certain sense, then, my whole professional life has been the result of my youthful fascination with the mystery of i and that is why I have written this book.
1852年1月13日，爱尔兰数学家威廉 汉密尔顿在一封写给好友，英格兰数学家奥古斯都 摩根的信中提到：“我想，要么是你，要么是我，但我希望是你，必须在某个时刻，写一本关于虚数i的历史书”。五天之后，摩根回信道：“虚数的历史，就像印度教历史，要梳理起来十分困难”。事实上，他们俩都没有写这段历史。据我所知，没有一个人做过这件事。这也是我写这本书的另一个原因。我纯粹想了解更多。
In a letter (dated January 13, 1852) to his English friend Augustus De Morgan, the Irish mathematician William Rowan Hamilton wrote, “I see that either you or I but I hope it will be you must write, some time or other, a history of i .” Five days later De Morgan replied, “As to a history of i , it would be no small job to do it well from the Hindoos downwards.” Well, neither Hamilton or De Morgan ever wrote that history and, as far as I know, nobody else has either. And so that’s another reason why I wrote this book. I simply wanted to learn more.
我的一大遗憾，就是我的父亲未能看到这本书。如果他能看到，我希望他会因为半个世纪前投资订阅了一本杂志，而倍感欣喜。
My one great regret is that Dad isn’t here to read it. But if he were, I hope he would be pleased at the result of his investment in a magazine subscription nearly a half century ago.
